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Evaluation of the Biaxial Mechanical Properties of the Mitral Valve

1. Limit Switches Firewire IEEE 1394 Card Digital Camera High Speed Digital Camera High Speed Imaging PC Frame Grabber Frame Grabber Frame Grabber tems in red are only included in the High Speed Systems 161 7 2 Setup Orientation Motor B Load Cell 2 f Motor C Load Cell 1 162 7 3 Motor Wiring Diagram Motor Green Driver Yellow Ground Red Aa Parallel Black A Cable White B4 Green B Connect Orange amp Brown motor cables to each other Connect Blue and Yellow motor cables to each other 7 4 Load Cell Wiring Diagram AC DC Converter Load 1 DAQ Pin 66 Load 2 DAQ Pin 34 Blue AC DC Converter ees White Load 1 DAQ Pin 33 Load 2 DAQ Pin 68 a Inline Amplifier a 8 Parallel Cable Pins to ICM AMP Pin 1 5V Pin 2 5V Pin 14 PWM Pin 15 SIGN Pin 16 5V Pin 17 AMPEN See Galil Application Note 1425 for ICM AMP Terminal numbers 2 Black 3 Green White Load Cell p EE 163 7 5 Software Overview Use this diagram asa map of the LabView Wiring Diagram Main Program Loop Image Setup Reference Files Load Cell Calibratio
2. Figure 4 The organization of tropocollagen molecules to for collagen fibrils Reproduced from Fung Y C Biomechanics Mechanical Properties of Living Tissues 2nd ed 1993 New York Springer Verlag 568 To date over 30 distinct types of collagen have been identified Valve leaflets are composed mainly of type I collagen with some type III collagen Collagen is strongest in tension and primarily serves as a load bearing mechanism Collagen fibers are typically crimped in their stress free configuration 7 Due to this arrangement in some cases collagen fibers may not develop their full load bearing capacity until they are sufficiently distended Strand b Strand a Figure 5 Schematic showing the hydrogen bonding between strands that is responsible for collagen s strength A and the tri helical structure that the three collagen strands take when they assemble into a collagen fiber B Reproduced from Voet Biochemistry 1995 10 1 3 2 2 Elastin Elastin fibers are composed of proline and glycine rich amino acid linkages that do not possess the stabilizing hydroxylated or glycosylated residues present in collagen Elastin fibers are known to be highly distensible when compared to collagen and therefore the mechanical contribution of elastin to load bearing is most noticeable when the collagen fibers are not fully recruited The highly branched structure of elastin typically contains many coiled f
3. FIA IIIA III TISAI ARIAT LISI 0060090000009 005100006000 00 000 Radial Circumferential 1 0 1 5 2 0 2 5 3 0 Time Hours Figure 50 Stretch versus time curves for a typical biaxial creep experiment Minimal relaxation was observed on either axis Note the anisotropic leaflet behavior exhibited by the relatively higher radial stretch required to maintain the 90 N m membrane tension 111 Circumferential Radial Creep 96 0 03 seconds 1 second 3 hours Figure 51 Creep percentages were not statistically different from zero for any time point on the circumferential or radial axes 112 4 0 DISCUSSION 4 1 RELEVANCE OF STUDY This work details the first known study of the effects of stretch rate on the biaxial mechanical properties of the MVAL and indeed for any valve leaflet tissue These studies are the first to report the application of high stretch rate studies under biaxial loading for any soft tissue Furthermore this is the first study known to the authors to report biaxial creep results for any soft tissue and is the first relaxation study to incorporate physiological loading times and a physiological biaxial loading condition These findings are of particular importance to the development of time dependent constitutive models for valve leaflet tissues because they demonstrate tissue properties at physiologic stretch levels and rates This characteriz
4. 117 Ara ERR 123 46 RELATIONSHIP OF STRESS RELAXATION AND CREEP 124 4 7 COMPARISONS TO SMALL ANGLE X RAY SCATTERING RESULTS 125 48 STUDY LIMITATIONS 129 4 9 CONCLUSION S E Ea OOA ivan Pate 130 4 10 RECOMMENDATIONS FOR FUTURE STUDY eere 131 5 0 THESIS SUMMARY eea tete eret te te tese t NOR Wadd te i ede ea dederas 133 viii APPENDIX IB Lis ode eae podria dua o dote eee e n do 136 APPENDIX Q uscite cud pii a easi eet auos v ats 166 BIBEIOGRA RELY fom 182 ix LIST OF TABLES Table 1 Specimen ed ace i erede n Sete E ee 78 Table 2 Stretch measurement dati eap rr EH RR RR oco Blu a 86 Table 3 Peak loads for the ten cycle test using a latex test 88 Table 4 Circumferential and radial membrane tensions STDEV for all creep tests after the loading phase abe e e etu eb toe tds as cue eus 105 LIST OF FIGURES Figure 1 A cross section of the heart looking down on the four heart valves from the atria Reproduced from Otto CM Valvular Heart Disease Elsevier Inc 2004 3 Figure 2 A photograph of the MV leaflets A anterior leaflet P posterior leaflet Reproduced from Otto CM Valvular
5. LV Simulator a Pump Pressure Transducer Data Acquisition System Figure 15 Left heart simulating flow loop used by Sacks et al to quantify the surface stretches of the MV anterior leaflet Reproduced from Sacks et al Surface stretches in the anterior leaflet of the functioning mitral valve 28 Closed e In Vitro v In Vivo Normalized major principal stretch 0 0 0 2 0 4 0 6 0 8 1 0 Normalized time Figure 16 Principle stretches observed in left heart simulating flow loop closed symbols and in vivo using sonomicrometry method open symbols Reproduced from Sacks MS et al In vivo dynamic deformation of the mitral valve leaflet Annals of Thoracic Surgery Submitted 2005 29 2 054 PERAN qut a eat dias B i E Closed j Oop E 2 P E R E utut In Vitro In Vivo E 0 0 0 2 0 4 0 6 0 8 1 0 Normalized time Figure 17 Principle stretch rates versus time for the MV anterior leaflet under normal physiologic conditions Reproduced from Sacks MS et al In vivo dynamic deformation of the mitral valve leaflet Annals of Thoracic Surgery Submitted 2005 30 1 8 MECHANICAL PROPERTIES OF MITRAL VALVE LEAFLETS May Newman and Yin measured the mechanical properties of the MV leaflets in response to a series of different biaxial lea
6. Load Cells Imaging Positioning Test Settings Run Test High Speed Test 74 1 Test Settings Tab Specimen Dimensions Xilength mm ioco 00 Thickness mm 0 58 4 2 Specimen Dimension Inputs MM 4 3 Cycle Settings E 4 4 Stretch Limits Stretch Limits Stretch Limit 1 3 0000__ Stretch Limit 2 2 3 0000 4 5 Load Units Load settings 4 6 Test Loads Load Control N 13 59 0000 Tension Control N m Axis 2 59 0000 Stress Control kPa 4 7 Stretch Estimate Inputs 7 4 8 Correction Gain Input 44 9 File Settings Display File Settings You will be prompted to enter these when you start a test Test Name I C Documents and Settings biax Desktop BIAX USERS Khash SCI_2 10 min_3 Reference File C Documents and Settingslbiax DesktoplBIAX USERS Khash SCI_2 after 10 146 3 5 Test Settings Stretch Control b Stretch Control 1 0 vi ioj xj Ele Edt Operate Tools Browse Window Hep _ 5 1 Test Settings Tab 5 2 Specimen Dimension Inputs 5 3 Cycle Settings 5 4 Stretch Ratio Settings Stretch 1 1 4 5 5 Load Settings Stretch Ratio Steth2 k1 ow 9 Load Settings A 5 6 Test Load Limits Use Load Limits For This Test Load Control N 5 7 Stretch Settings Tension Control N m Stress Control kPa gt 5 8 Correction Gain Input Use Stretch L
7. 15 Figure 8 A B 2D echocardiographic images of mitral valve regurgitation in diastole and systole respectively C Color flow Doppler image showing the eccentric jet of regurgitation Reproduced from Otto CM Valvular Heart Disease Elsevier Inc 2004 19 Figure 9 Typical Pressure Volume loops for the normal heart mitral regurgitation and aortic regurgitation Reproduced from Otto CM Valvular Heart Disease Elsevier Inc 2004 20 Figure 10 On X bileaflet pyrolytic carbon mechanical aortic valve MCRI Inc 21 Figure 11 Porcine aortic valve Edwards Lifesciences 22 xi Figure 12 A drawing looking down on the mitral orifice showing the circumferential and radial specimen axes Reproduced from Reproduced from May Newman and Yin Biaxial Mechanical Properties of the Mitral Valve leaflets American Journal of Physiology 1995 C 23 Figure 13 Drawing of balance of forces in mitral apparatus in the left panel In the right panel potential effect of papillary muscle displacement to restretch leaflet closure causing mitral regurgitation Reproduced from Liel Cohen N Guerrero JL Otsuji Y Design of a new surgical approach for ventricular remodeling Circulation 2000 101 2756 25 Figure 14 Motion of marker placed on free edge of anterior leaflet Reproduced from Tsakiris AG Gor
8. 5 2 aoeonentoooneetoces e se 2 1 o a a oo 20 se 4 o rd oO La o e od ge b o ad 14 4 Q 14 co aid o o NU ge ane Q e Ato oO gt 20 T 1 0 T 0 200 400 600 800 1000 1200 20 40 60 80 100 120 Time ms Time ms 1s 0 1s 100 100 Circumferential Circumferential b o Radial so Radial e Cs 80 4 80 4 o t g o s04 2 2 2 S o S o a a E d Pu 404 0 e Re e jo 204 ato M il Time ms 1200 Time ms 80 100 Figure 40 Typical a Load versus time and b stretch versus time curves for 1s and 0 1s loading periods The load versus time and stretch versus time curves were similar for the full range of cycle periods As displayed above the device was able to accurately control rise time for different cycle periods Note the different time scales between the 1s and 0 1s plots 94 3 2 2 Effects of Stretch Rate on Stress Stretch Response The shapes of the tension vs stretch loading curves for all loading protocols 15s 1s 0 5s 0 1s 0 05s were very similar for each specimen tested Figure 41 To better present the stretch rate effects mean AP for each cycle period were pooled for all specimens Figure 42 No significant differences were found between any of the loading time protocols in both the circumferential p
9. Section 3 High Speed Biaxial Testing Protocols 3 1 Stress Relaxation Notes 1 Load Control 2 0 issimply an expansion of Load Control 1 0 All quas static protocolscan be run using Load Control 2 0 The displacements used in the stress relaxation loading are based on the displa cements of the final quasi static loading cycle If anything is unusual with the final quasi static cycle it is not recommended to proceed with the stress rela xation test It is strongly recommended that all stressrela xation tests are preceded by a standard quasr static biaxial protocol to ensure that no abnormal characteristics are present in the test sample Cumently a bug in the software causes every second stressrelaxation experiment to stop prematurely Forthis reason it is recommended that you save all necessary calibration files and reference files and manually shut down and restart the program between sequential stress rela xation experiments or fix this bug Protocol 1 Input the desired quasi static test settings Referto Biax Manual for instructions Click the High Speed Test Tab 1 1 Enterthe desired loading time in seconds in the loading time input box 1 6 Enter the desired duration for the stress relaxation portion of the experiment in the test duration input 1 7 Click the High Speed Test toggle 1 5 such that the indicator light tums to bright green Clicking thistoggle will direct the biaxial testing
10. A similar argument with the role of F and u interchanged gives du z dr F t Tk t r dr 0 3 These laws are linear Scaling the load by a given factor causes the elongation to be scaled by the identical amount and vice versa The functions c t t and k t t are the creep and relaxation functions respectively The application of the Boltzmann principle of superposition allows the use of a limited amount of experimental data from both static and time dependent experiments to predict the mechanical response of a tissue to a wide number of loading conditions 1 9 5 Modelling viscoelastic behavior quasilinear viscoelasticity In order to adequately model the viscoelastic properties of soft tissues under finite deformations the non linear stress stretch characteristics of the tissue must be considered 37 For this reason Fung has developed a theory known as quasi linear viscoelasticity QLV in which the relaxation function 0 is dependent on time as in the linear viscoelasticity formulation as well as stretch level This theory is termed quasi linear because the relaxation function may be separated into a reduced relaxation function G t that is a function of time only and an elastic response o e that is a function of stretch only 41 K e t G t o e 4 In this formulation the generalized form of G t proposed by Fung is given by 1 S e dr G t Le 5 5
11. Protocol 1 Protocol 2 Lagrangian Membrane Stress N m Protocol 4 Protocol 6 08 Protocol 3 60 50 40 30 Protocol 7 60 50 40 30 20 Lagrangian Membrane Stress N m 04 06 08 1 0 00 02 Figure 21 a The seven loading protocols used to characterize the biaxial stress stretch response and b response to all loading protocols for an AV cusp open circles along with the structural model fit demonstrating an excellent fit 35 1 9 VISCOELASTIC BEHAVIOR The term viscoelastic implies that the mechanical properties of such a material are composed of both a time dependent or viscous and a time independent or elastic component Much of the pioneering work on the viscoelasticity of living tissues was done by Fung who summarized the time dependence of biological tissues When a body is suddenly stretched and then the stretch is maintained constant afterward the corresponding stresses induced in the body decrease with time this phenomenon is called stress relaxation If the body is suddenly stressed and then the stress is maintained constant afterward the body continues to deform this phenomenon is called creep If the body is subjected to a cyclic loading the stress stretch relationship in the loading process is usually somewhat different from that in the unloading process this phe
12. cn T E 93 Figure 40 Typical a Load versus time and b stretch versus time curves for Is and 0 15 loading periods The load versus time and stretch versus time curves were similar for the full range of cycle periods As displayed above the device was able to accurately control rise time for different cycle periods Note the different time scales between the 1s and 0 1s POLES MMC ND E 94 Figure 41 Typical tension stretch curves for each loading cycle period 15s 1s 0 5s 0 1s and 0 05s for the circumferential a and radial b specimen directions Curves generally showed no apparent stretch rate dependence Note the different stretch scales between the circumferential and radial plots 5s e vetta tetas ed oem Wee Un i ied 96 Figure 42 The circumferential and radial stretches of the leaflet at the 90 N m equitension state pi oeil e Mu AN DU ce NG soe Sa a gues uet veu ei eas age es 97 Figure 43 Loading and unloading membrane tension T vs stretch curves for 15 1 0 5 and 0 1 second loading and unloading of a single specimen sse 100 Figure 44 Membrane stretch energy versus membrane tension for a typical loading cycle Note the larger amount of energy storage in the tissue at lower tension levels due to the relatively higher tissue extensibility at low stretch Ievels ise dotes mentita Rai tendo us 101 Figure 45 Energy stored or dissipated within the leaflet specimens during loadi
13. of load cells Model 31 Honeywell Sensotec Columbus OH via the analog digital converter The specification for hysteresis in each load cell was 0 5 data acquisition and image analysis was accomplished using custom software routines see Device Algorithms written using the LabView virtual instrumentation package Version 6 1 National Instruments Austin TX 2 1 3 Device software 2 1 3 1 Marker identification All images were recorded as 8 bit grayscale images This resolution provided 256 image intensity increments from black intensity 0 to white intensity 255 In order to facilitate the location of the graphite markers within the specimen images an intensity threshold was defined for each experiment which transformed the grayscale specimen images into black and white bitmaps Figure 30 This was convenient because the graphite markers were typically much darker than the leaflet surface 63 P Figure 30 A sample bitmap showing four markers black and the user defined marker subregions green This image thresholding technique did not always perform perfectly since occasionally the intensity levels of dark markings on the tissue surface or small shadows caused by leaflet surface textures were similar to those of the graphite markers To correct for this two additional algorithms were used to identify the markers First image subregions were defined for each marker Once defined detection of a given
14. through the MV occurs at the beginning of diastole This flow is driven primarily by passive forces supplemented with relaxation of the left ventricular myocardium and active movement of the mitral annulus 24 In order to properly regulate the left ventricular volume the mitral orifice must become enlarged beyond the size of the aortic valve Typically enlargement of the mitral orifice starts just before the end of systole and the orifice returns to its original smaller size at the end of diastole 2 During ventricular systole valve closure occurs when the two leaflets coapt to form an arc shaped closure line While the valve is closed both the anterior and posterior MV leaflets are generally shaped with a concave curvature to the left ventricle 29 After ventricular systole is completed the valve leaflets open starting from the center of the leaflets 30 and quickly reverse their curvature into a convex formation with respect to the left ventricle Subsequently the leaflets straighten and the edges of the valve separate The larger anterior leaflet then continues to open reaching a position more widely open than that of the posterior leaflet As systole becomes eminent the anterior leaflet then moves towards the closed configuration at a much faster rate than the posterior leaflet ensuring that the leaflets coapt properly and then return to the concave closed configuration Analysis of MV leaflet dynamics was performed by Tsakiris et al 31
15. 425E02 1 18E 01 7 87E 07 9 91E 01 1 31E 01 5 28E 00 6 87E 07 9 98E 01 8 2 25E 02 1 02 02 1 0 08 9 80E 01 9 92E 02 4 85E 00 9 30E 07 9 98E 01 Uniaxial Circumferentia _ T T 1 201Eo iosEo2 To0Es08 976EO1 2 aneo 102E02 1006 08 97EO1 1 T 3 1 Mean 3 79E 02 2 13E 00 6 76E 07 9 91E01 Mo SEM 144E02 212E 00 326E 07 6 31E03 M Uniaxial Radia __ _ 1L 135E92 803E 07 9 89E 01 3 8800 2 76 08 1 00E 00 LLL T LA88 92 426E 01 3 108408 9 89E 01 Lean _ T ES24E02 1 34E 00 222E 08 9 92E 01 SEM LL L238E 92 1 128 00 7 15E 07 3 66E 03 135 APPENDIX B BIAXIAL TESTING DEVICE USER S MANUAL 136 Biaxial Testing Manual Author s Jonathan Grashow Version 1 1 Orginal Release Date 3 17 05 Last Revision Date 3 24 05 137 Contents Section 1 Background material Section 2 xial Tester Description Section 3 Biaxial Testing Software Screens 3 1 Load Cell Calibration Screen 3 2 Image Setup Screen 3 3 Specimen Positioning Screen 3 4 Test Settings Screen Load Control 3 5 Test Settings Screen Stretch Control 3 6 Run Test Screen Section 4 Bia xial Testing Protocols 4 1 General Notes 4 2 Setting Up the Biaxial Testing Device 4 3 Pre
16. DEVICE PERFORMANCE eee 86 3 1 1 Stretch Measurement Accuracy id oe ceat uae ee 86 3 1 2 Load cell calibration quiate reden fada dua Rea e SRI RA EH Rt Ue Ren e SALA RUE 87 3 1 3 Ability to reach peak loads 87 3 1 4 Load cell momentum Senstttvity o acs sve tien eevee eae tied Dien 88 vil 3 1 5 System unde edet Ds aud 91 32 EFFECISOF STRETCH RATE abut Aube te ec ah 92 3 2 1 Device Conttol 4 5 ceni ive ipe Ute pide va o ipe ule 92 3 2 2 Effects of Stretch Rate on Stress Stretch 95 3 2 3 Effects of Stretch Rate on 2 98 3 3 STRESS RELAXATION AND CREEP reete 103 3 3 1 Device a 103 3 3 2 Biaxial Sttess RelaxatioDs uice due tesi aes us E ass eas us bei ta eds 105 3 3 3 aca cts ai n stb n att eeu 108 3 3 4 Reduced Relaxation Function Eis e ir ivre tem eee 109 3 3 5 mE 110 4 0 DISCUSSION utes oet b bei eeepc etc Saale d 113 4 RELBVANGE OF STUDY 113 42 MECHANICAL ANISOTROPD Y ue 114 4 3 STRETCH RATE EFFECT Soen Aurei de Oa d hae a das 115 44 STRESS REDARATION
17. M IM qs 63 2 1 334 Marker identification ere dear ego ere Aa es 63 vi 21 202 calculations eee toss nene get deal tt eed 65 21 25 29 Q asistatie controlen ey e m aulae voe EE RES 68 2 1 3 4 High stretch tate testing osse pde ge ideali tasto piedi E i abu 70 2 1 3 5 Stressrelaxati n testing Co rt facie ted tun Su od 70 241 36 Creep testing unco DE ea Bia tea raga alins Dat Qn asd UD aea 71 22 CHARACTERIZATION OF DEVICE 72 23 1 Stretch measurement uii oae noie ti detener exces teer pea T etuer Re d dete da 72 2 2 2 Loadcell calibration osos bs a rmn Un ME 73 2125 Ability to reach quasi static peak loads taceo tpa sei e bie beta ga T5 2 2 4 Load cell momentum 75 2 2 5 System FEAR AION es ani eel iab oto aee bes tr deese oru dde else quaii eet 76 23 BIAXIAL TESTING OF THE MV ANTERIOR LEAFLET eee 77 2 3 1 Specimen prep ratioN sss qaas eec nter a Ease pra 77 2 3 2 Quasi static biaxial TESTI ss ao eo ederent RA 80 2 3 3 High speed biaxial aai pae per dett 82 2 3 4 Kin matic Anal Vises cioe nee asi tibus eu Sd rA Obs ecu bed 84 2 3 5 Siatisticalmetheds a testes heu Venue rabie 85 340 URES GTS e ett eR eo hae ete ds meet at e tm ss 86 3 1 CHARACTERIZATION OF
18. Specimen Mounted in Biaxial Tester Preload of 0 5g 20 preconditioning cycles from 0 5g to 90 N m with 15s half cycle time Preconditioned tare reference Strain Rate Relaxation Strain Rate Creep Relaxation High speed Loading from 0 50 to 90 loading unloading cycles Loading from 0 5g to 90 N m with rise time of 0 1 with half cycle periods of 1 N m with rise time of 0 1 sec 0 5 0 1 0 05 and 1 sec sec Loading Unloading to 90 Displacements held Loading state constant for maintained at 90 N m 3 hours for 3 hours N m strain state determined in preconditioning cycles Figure 34 Biaxial stretch rate sensitivity creep stress relaxation and uniaxial stress relaxation protocols 81 Radial Specimen Axis Device Axis 2 Circumferential Specimen Axis Device Axis 1 Figure 35 Specimens were mounted in the biaxial testing device with the circumferential and radial specimen axes aligned with the device axes 2 3 3 High speed biaxial testing For the stretch rate sensitivity testing the carriage displacements required to stretch the specimen to the 90 N m equitension state in the preconditioning cycles were recorded and repeated for 5 additional high speed cycles in which the specimen was stretched and unstretched in loading and unloading cycle periods of 1 second 0 5 seconds 0 1 seconds 0 05 seconds and finally again in 1 second to assess test repeatability F
19. and the aorta while the pulmonary valve is located between the right ventricle and the pulmonary arteries Pulmonary veins Tricuspid valve E Mitral valve Pulmonary valve Figure 1 A cross section of the heart looking down on the four heart valves from the atria Reproduced from Otto CM Valvular Heart Disease Elsevier Inc 2004 1 2 MITRAL VALVE ANATOMY The mitral valve MV serves to prevent blood regurgitation into the left atrium during left ventricular contraction The complete valve apparatus consists of a saddle shaped annulus that adjoins the base of the left atrium to the two valve leaflets anterior and posterior which extend into the ventricle where they are connected to the papillary muscles via an intricate arrangement of chordae tendineae 1 5 The mitral annulus consists of both fibrous and muscular tissue The two major collagenous structures within the annulus are referred to as fibrous trigones Figure 3 Thin collagen bundles called the fila of Henle stretch circumferentially from each trigone into the mitral orifice The annular muscle predominant in the posterior region of the annulus is primarily oriented orthogonally to the annulus When the MV is opened by cutting one of the leaflets as in Figure 2 no distinct separation is observed between the two leaflets The anterior leaflet is generally somewhat larger and has a smooth appearance while the posterior leaflet tends to be smaller and has a
20. feature works best if you first manually Using the Free Movement buttons 3 2 stretch the specimen such that the loads displayed on the Loads graph 3 8 on the bottom of the Positioning tab 3 1 are close to the desired loads The autoloading feature is used during an actualtest in orderto ensure that the specimen retumsto the propertare loads between test cycles using the autoloading feature will give you an idea how thisfeature will perform during the actual test Selecting a tare load that istoo low typically below 0 59 oran allowable emorthat istoo small typically below 0 05g can cause errorsin the autoloading algorithm Protocol 1 2 Click on the Test Settings tab 4 1 5 1 at the top of the screen Enterthe specimen dimensions in the provided input boxes 4 2 or 5 2 Click on the Positioning tab atthe top of the screen 3 1 Select the desired units in the Preload Units selection box 3 5 Enter the Allowable Error X1 Preload and X2 Preload 3 6 If desired manually stretch the specimen until it is close to the desired tare loadsusing the Free Movement buttons 3 2 Click the Apply Load Button 3 7 The Program Status bar 3 9 at the bottom of the screen will display complete when the autoloading algorithm has finished 156 4 7 Running a Test Notes 1 During or before the test a live image can be toggled on oroff by clicking the Update Image button 6 3 at the top o
21. for only one stretch rate sensitivity stress relaxation or creep protocol 83 2 3 4 Kinematic analysis The leaflet stretches at the 90 N m equitension state AP and were used to quantify leaflet extensibility In the stretch rate sensitivity protocols leaflet hysteresis was evaluated by comparing the energy stored in the loading phase to the energy dissipated in the unloading phase for each loading rate Energy stored dissipated was calculated as the area beneath the T vs stretch curve Areas were calculated using a trapezoidal rule numerical integration For the stress relaxation protocols membrane tension data were normalized to the peak membrane tension observed for each leaflet For all specimens this peak membrane tension was reached immediately after the initial 0 1 second loading The relaxation percentage was calculated as R T TP for each axis Relaxation data was thinned to 20 data points evenly distributed through the duration of testing reduce processing time and then fit with a reduced relaxation function for long relaxation periods with a single phase relaxation distribution Where c was the magnitude of the relaxation distribution t was the short relaxation time constant and t2 was the long relaxation time constant Creep data was analyzed by comparing the circumferential and radial stretches at four time points immediately after the initial loading 4 95 300 milliseconds 47 1 second AP and 3
22. marker was only performed within the specified image subregion The main purpose of this technique was to eliminate the detection of erroneous marker like shapes that were sufficiently spatially separate from the markers themselves Because the marker positions within the image moved throughout the test once a marker was identified within a subregion the subregion was translated such that it was re centered on the marker By translating the subregions with the markers in this way markers always stayed within the defined subregion as long as they did not translate out of the image subregion in the time duration between individual frames approximately 0 1 seconds for the device control 64 camera and 0 002 seconds for the high speed digital camera To reduce the chances of this occurring the size of each individual marker subregion was increased to a level that accommodated the motions of the particular marker between frames After the marker subregions were defined a size threshold was applied to any markers that were identified within the subregions This was helpful due to the fact that discolorations on the surface of the leaflets were usually much larger than the graphite markers and had the added benefit of reducing the sensitivity of the marker tracking system to image noise which occasionally caused small image areas usually in the single pixel range to become dark Marker subregions and detected markers from the device control camera we
23. measurement results 73 Figure 32 A photograph of the calibration fixture mounted on the bath 74 2 2 3 Ability to reach quasi static peak loads The ability of the device of reach desired peak loading state was evaluated using a latex specimen For this experiment peak loads were set at 300g for both axes Peak specimen loads were measured for 10 quasi static cycles to assess the ability of the device to reach the desired peak loads 2 2 4 Load cell momentum sensitivity In order to assess the effects of rapid motion on the load cells carriage displacements similar to those predicted for testing were performed without any loads on the load cells This test measured the sensitivity of the load cells to rapid motions In this test one axis was totally unloaded while the other axis was sutured with a latex sample and was loaded to a stretch of 1 1 over 0 2 seconds 75 2 2 5 System relaxation In order to ensure that any stress relaxation observed in the leaflet testing was real and not simply a relaxation in the test system components a relaxation test was performed with the opposing sutures hooked to each other without any specimen By performing a test in this way the relaxation of the system was quantified and any relaxation greater than that observed in the system itself could be considered real Suture sets were loaded to a tension of 200g in 0 1 seconds and subsequent relaxation was measured for 3 hours 76 2 3
24. muscle on the left ventricular wall J Biomech 1997 30 10 p 1071 5 He S A A Fontaine E Schwammenthal A P Yoganathan and R A Levine Integrated mechanism for functional mitral regurgitation leaflet restriction versus coapting force in vitro studies Circulation 1997 96 6 p 1826 34 Perloff J K and W C Roberts The mitral apparatus functional anatomy of mitral regurgitation Circulation 1972 46 p 227 239 Tsakiris A G R Padiyar D A Gordon and I Lipton Left atrial size and geometry in the intact dog Am J Physiol 1977 232 2 p H167 72 Karlsson M O J R Glasson A F Bolger G T Daughters M Komeda L E Foppiano D C Miller and N B Ingels Jr Mitral valve opening in the ovine heart Am J Physiol 1998 274 2 Pt 2 p H552 63 Tsakiris A G D A Gordon Y Mathieu and L Irving Motion of both mitral valve leaflets a cineroentgenographic study in intact dogs J Appl Physiol 1975 39 3 p 359 66 Sacks M S Z He L Baijens S Wanant P Shah H Sugimoto and A P Yoganathan Surface strains in the anterior leaflet of the functioning mitral valve Annals of Biomedical Engineering 2002 30 10 p 1281 90 Iyengar A K S H Sugimoto D B Smith and M S Sacks Dynamic in vitro quantification of bioprosthetic heart valve leaflet motion using structured light projection Ann Biomed Eng 2001 29 11 p 963 73 May Newman K and F C Yin Biaxial mechanical behavior of exci
25. software to perform the stress rela xation test after completing the quasi static protocol Make sure to disable thistoggle by clicking the toggle again such that the indicator light is black before proceeding with any additional quasi static only experiments 175 Select the Test Settingstab and run a quasi static experiment as detailed in the Biax Manual Afterthe quasi static protocol is completed the software will wait forthe userto click the Trigger Test button 1 3 on the High Speed Test tab Before you triggerthe test checkthe final cycle of the quasi static protocol to ensure that nothing abnormal occured and that the carriage displacements resulted in a condition very close to the desired loads If you are using the high speed camera to track stretc hs during the initial loading phase ensure that the camera isready to receive the analog trigger signal from the biaxial testing software Pressthe Trigger Test button The specimen should be loaded in the userdefined duration and the stretches asloads should be plotted in real time on the screen 10 The test will continue forthe userspecified duration unless you select the Stop Test button 1 2 176 3 2 High Stretch Rate Testing Notes 1 Load Control 3 0 is simply an expansion of Load Control 1 0 All quasi static protocolscan be run using Load Control 3 0 The displacements used in the rapid loading and unloading cycles are based on the displac
26. the current study the details of the paradoxical stress relaxation behavior may be further explored 131 3 Creep experiments on the MV chordae tendineae o Current studies of the MV chordae tendineae include only dynamic loading and stress relaxation Since it may be more representative of the physiological condition creep experiments on the MV chordae tendineae may provide useful data 132 5 0 THESIS SUMMARY The list below summarizes the major findings of this study for the MVAL l Dynamic biaxial loading and unloading cycles revealed that the stress stretch relationship of the MVAL showed no dependence on stretch rate and indicated that the MVAL tissue may be functionally modeled as an anisotropic quasi elastic material Creep experiments revealed that creep in the MVAL at a physiological load state was functionally insignificant particularly when considered with respect to physiological creep duration of approximately 0 5 seconds Although the MVAL showed no creep stress relaxation experiments showed significant relaxation from the physiological loading state This result underscored the necessity of performing creep experiments on soft tissues since creep may be more representative of the physiological loading condition and cannot be satisfactorily described using stress relaxation data 133 APPENDIX A REDUCED RELAXATION FUNCTION FIT PARAMETERS 134 R 2 SSIs DEREN NEIN SNNT SES ERR 6
27. where S 1 is defined based on the stress response of the material to be modeled Experimental evidence has shown that the relaxation of soft tissues tends to decrease with time This behavior can be modeled simply using the following formulation S t A 6 for t lt t where c is the magnitude of relaxation t is the short time constant and v is the long time constant QLV has been used previously to model many soft tissues such as ligament 38 bladder 39 and valvular materials 40 to name just a few is analysis is very attractive because the QLV formulation is formed from continuous functions and the viscoelastic behavior may be described using only three physically meaningful mathematical parameters 42 1 9 6 Stretch rate sensitivity in soft tissues The hypothesis that the mechanical properties of the MV anterior leaflet may be sensitive to stretch rate necessitating the need to define the mechanical properties of the valve under physiologic stretch rates is based on several observations of the stretch rate sensitivity of the MV leaflet and other soft tissues throughout the biomechanical literature The dynamic viscoelasticity of the MVAL was investigated by Lim et al 41 who measured the bulge height of the MV leaflet in response to sinusoidal pressure gradients applied at frequencies varying from 0 5 to 5 0 Hz Their results suggested that the mechanical properties of the valve were dependent on stres
28. who measured the motions of both the anterior and posterior leaflets by tracking radiopaque markers sutured onto the valve leaflets and annulus using film angiograms and correlated the marker displacements with an electrocardiogram Of particular relevance is 24 their analysis of the anterior leaflet Figure 14 which showed the closing time of the leaflet to be approximately 63 milliseconds and the opening time to be approximately 42 seconds LV Closing force Mitral Valve Tethering Tethering Force Restrick Figure 13 Drawing of balance of forces in mitral apparatus in the left panel In the right panel potential effect of papillary muscle displacement to restretch leaflet closure causing mitral regurgitation Reproduced from Liel Cohen N Guerrero JL Otsuji Y Design of a new surgical approach for ventricular remodeling Circulation 2000 101 2756 25 DURATION OF OPENING TIME DIASTOLIC CLOSURE lee j ONSET OF CLOSURE 7 CLOSING TIME om el m 1 0 PARTIAL DIASTOUIC CLOSURE MAXIMUM OIASTOLIC 05 OPENING APP 0 500 1000 m sec i ECG AN P Q COMPLETE CLOSURE Figure 14 Motion of marker placed on free edge of anterior leaflet Reproduced from Tsakiris AG Gordon DA Mathieu Y et al Motion of both mitral valve leaflets a cineroentgenographic study in intact dogs J Appl Physiol 1975 39 359 26 1 7 1 Surface stretches of the anterior leaflet A re
29. 0 987 and radial p 0 996 directions In addition A9 and for all loading times were very similar to but generally were slightly greater than the peak stretches observed in left ventricle simulating flow loop 32 Moreover the ratio of the mean AXP J2 Peak 0 86 was very close in value 0 83 to the same ratio observed under simulated physiologic conditions These results suggest that the 90 N m peak tensions used in the present study were comparable to actual physiological stress levels 95 Circumferential 120 15s 1s 0 5s 0 1s 0 05s 100 4 80 4 di S EREK a 4 4 ru a 60 4 4 4 9 43 gua 40 4 20 VR I9 1 00 1 05 1 10 1 15 1 20 1 25 Stretch Radial 120 15s O 1s 1004 vw 05s v 0 15 0 055 80 4 Stretch Figure 41 Typical tension stretch curves for each loading cycle period 15s 1s 0 5s 0 1s and 0 05s for the circumferential a and radial b specimen directions Curves generally showed no apparent stretch rate dependence Note the different stretch scales between the circumferential and radial plots 96 15s 1s 0 5s 0 1s 0 05s Loading Time Figure 42 The circumferential and radial stretches of the leaflet at the 90 N m equitension state 97 32 3 Effects of Stretch Rate on Hysteresis Typical loading and unloading curves for a set of stretch
30. 06 Lee J M D R Boughner and D W Courtman The glutaraldehyde stabilized porcine aortic valve xenograft II Effect of fixation with or without pressure on the tensile viscoelastic properties of the leaflet material Journal of Biomedical Materials Research 1984 18 p 79 98 Rigby B J N Hirai J D Spikes and H Eyring The mechanical properties of rat tail tendon The Journal of General Physiology 1959 43 p 265 282 Lee J M and D R Boughner Mechanical properties of human pericardium Differences in viscoelastic response when compared with canine pericardium Circ Res 1985 57 3 p 475 81 186 63 64 65 66 Liao J L Yang J Grashow and M S Sacks Molecular orientation of collagen in intact planar connective tissues under biaxial stretch Acta Biomaterialia 2004 1 1 Cole W G D Chan A J Hickey and D E Wilcken Collagen composition of normal and myxomatous human mitral heart valves Biochem J 1984 219 2 p 451 60 Lis Y M C Burleigh D J Parker A H Child J Hogg and M J Davies Biochemical characterization of individual normal floppy and rheumatic human mitral valves Biochem J 1987 244 3 p 597 603 Merryman W D H Y S Huang F J Schoen and M S Sacks The effects of cellular contraction on aortic valve leaflet flexural stiffness Journal of Biomechanics In press 187
31. 1 1 2 1 3 1 4 Stretch Figure 43 Loading and unloading membrane tension T vs stretch curves for 15 1 0 5 and 0 1 second loading and unloading of a single specimen 100 Energy N m 0 20 40 60 80 100 T N m Figure 44 Membrane stretch energy versus membrane tension for a typical loading cycle Note the larger amount of energy storage in the tissue at lower tension levels due to the relatively higher tissue extensibility at low stretch levels 101 Membrane strain energy N m 15s 1s 0 5s Cycle Period Loading Unloading 0 1s Figure 45 Energy stored or dissipated within the leaflet specimens during loading and unloading phases with different cycle times 102 3 3 STRESS RELAXATION AND CREEP 3 3 1 Device control The stretching device was able to load the MVAL specimens to the 90 N m uniaxial or equibiaxial state smoothly with minimal vibrations over the initial 100 ms rise time Figure 46 Due to the rapid speeds required to load the tissue within the 100 ms rise time and the high level of stiffness in the MVAL at the 90 N m membrane tension level the stretching mechanism occasionally slightly overshot the 90 N m target Due to the rapid speeds required to load the tissue within the 100 ms rise time and the high level of stiffness in the MVAL at the 90 N m membrane tension level the stretching mechanism occasionally slightly overshot the 90 N m target Me
32. 8 1 9 3 40 1 9 4 Modeling viscoelastic behavior the Boltzmann superposition principle 40 1 9 5 Modelling viscoelastic behavior quasilinear viscoelasticity 41 1 9 6 Stretch rate sensitivity in soft 165066 ag need Rada 43 1 9 7 Creep and stress relaxation in soft tissues ssssssssseeeeeeneeneneen 44 1 10 MOTIVATION FOR THE CURRENT STUDY amp STUDY 5 46 ITO Specific Study Als eua E toin 48 20 METHODS ebat te Vot idet ae eta Lad a E EL 49 2 1 HIGH SPEED BIAXIAL TESTING DEVICE eee 49 2 1 1 Device specifications 2 c a sett sack e began cantar Nd MM ati See 49 2 1 1 1 Displacements and displacement rates essere 49 2311 2 Se NUES SA o RAE tec em EU I UE 50 2 1 1 3 Stretch amp load measurement 51 2 1 2 e en eae a ba oed pd vis axis d ed AL A cea 53 DADA Device OVeFvIQWi assieme nud iust iuventa i ael pads 33 2 1 2 2 Actuation components ordei et ce rr etie db ete ei Mie 56 2 1 2 3 Specimen attachments aote ren ebrei n e Peto pete ei ib uc re va 58 2 1 2 4 Specimen ioc ec eue Pee E o ued Falah arated sie nel eus 60 2 1 2 5 Stretch and load measurement UR Ren Te RARI RAE 60 2 1 3 SIE WAG sum ioris eu E EQ UA eS ae eS
33. AL over a one hour test duration The SAXS creep results show that the collagen D spacing does not change as would be expected since the specimen does not deform The SAXS stress relaxation results like our stress relaxation results are somewhat paradoxical These results showed relaxation behavior similar to that observed in our biaxial study but showed that the collagen D spacing diminished extensively during relaxation This suggests that the mechanism of stress relaxation may depend on a non collagenous component of the MVAL microstructure such as elastin or GAGs 125 BES 552 ex BB1 4 D periad 660 Figure 54 Membrane tension versus areal stretch for the same MVAL specimen Reproduced from Liao J 20 40 60 50 100 Lagrangian Membrane Stress N m Changes in collagen D spacing as a function of membrane tension left Unpublished Communication 126 Lagrangian Membrane Stress N m 120 100 8n 40 20 20 30 Areal Strain 92 40 B64 663 b 662 661 Areal Strain 96 660 659 0 a 40 60 1 20 30 40 50 B Time Minute Time Minute Figure 55 D spacing as a function of creep experiment duration left Areal stretch as a function of creep test duration for the same specimen right Reproduced from Liao J Unpublished Communication 127 1 1 Circumferential 1 0 o Radia
34. BIAXIAL TESTING OF THE MV ANTERIOR LEAFLET 2 3 1 Specimen preparation One set of eight designated for stretch rate sensitivity analysis a second set of eight designated for biaxial stress relaxation experiments a third set of six designated for uniaxial stress relaxation experiments and a fourth set of six designated for biaxial creep experiments fresh porcine anterior MV leaflets were obtained from a local slaughterhouse Table 1 Hearts were obtained immediately after slaughter whereupon the anterior leaflets were removed from each heart and were then stored in a phosphate buffered saline PBS solution and frozen for no longer than one week for later use Prior to testing each leaflet was thawed at 37 C and trimmed to provide a square specimen with sides parallel to the circumferential and radial axes of the leaflet Figure 33 Specimens were carefully cut out so that each specimen was centered circumferentially on the anterior leaflet and extended radially from just below the annulus to just above the first chordae tendineae attachment site Trimmed specimens had dimensions of 9 9 0 6 mm x 9 5 0 9 mm x 0 75 0 05 mm thickness measured in the center of the specimen specimen dimensions were measured by hand using calipers In order to attach the square specimen to the biaxial testing device four evenly spaced suture lines were hooked through each side of the specimen with stainless steel surgical staples for uniaxial experiments 2 edges
35. Communication eee 128 XV ACKNOWLEDGEMENTS Although I have worked at the Engineered Tissue Mechanics Laboratory ETML for five years sometimes I feel like it has only been a week and other times I feel like I can t remember what it was like to do anything else My time at ETML was spent with many great people whom I could not have survived without I would like to thank in no particular order Dan Hildebrand Thanh Lam Claire Gloeckner Wei Sun W David Merryman Hiroatsu Sugimoto Ajay Abad Khashayar Toosi John Stella and George Engelmayr for all of their help I would also like to thank my committee members Drs Debski Nagatomi and Sacks for all of their advice and help with my thesis Outside of the laboratory I also owe many thanks to my parents for the plethora of positive energy and pixie dust that have fueled my most important achievements Also I would like to thank to Kathryn Beardsley and Sol Dostilio for moral support and for convincing me that yes I would actually finish my thesis one day xvi 1 0 INTRODUCTION 1 1 ANATOMY AND PHYSIOLOGY OF THE HEART The heart propels blood through the circulation providing necessary nutrients and removing waste products from the many organ systems throughout the body The mammalian heart consists of four chambers the left and right atria and the left and right ventricles Figure 1 The walls of these chambers are composed of myocardium which contracts a
36. EVALUATION OF THE BIAXIAL MECHANICAL PROPERTIES OF THE MITRAL VALVE ANTERIOR LEAFLET UNDER PHYSIOLOGICAL LOADING CONDITIONS by Jonathan Sayer Grashow BS University of Pittsburgh 2002 Submitted to the Graduate Faculty of The School of Engineering in partial fulfillment of the requirements for the degree of Master of Science University of Pittsburgh 2005 UNIVERSITY OF PITTSBURGH SCHOOL OF ENGINEERING This thesis was presented by Jonathan Sayer Grashow It was defended on April 12 2005 and approved by Dr Richard Debski Assistant Professor Department of Bioengineering Assistant Professor Department of Orthopedic Surgery Dr Jiro Nagatomi Research Assistant Professor Department of Bioengineering Dr Michael Sacks William Kepler Whiteford Professor Department of Bioengineering Thesis Advisor EVALUATION OF THE BIAXIAL MECHANICAL PROPERTIES OF THE MITRAL VALVE ANTERIOR LEAFLET UNDER PHYSIOLOGICAL LOADING CONDITIONS Jonathan Sayer Grashow MS University of Pittsburgh 2005 It is a fundamental assumption that a repaired mitral valve MV or MV replacement should mimic the functionality of the native MV as closely as possible Thus improvements in valvular treatments are dependent on the establishment of a complete understanding of the mechanical properties of the native MV In this work the biaxial mechanical properties including the viscoelastic properties of the MV anterior leaflet MVA
37. Heart Disease Elsevier Inc 2004 5 Figure 3 Diagram from a pathological perspective with division of the septum illustrating the fibrous continuity between the mitral and aortic valves Reproduced from Anderson RH Wilcox BR The anatomy of the mitral valve in Wells FC Shapiro LM eds Mitral Valve Disease Oxford England Butterworth Heinemann 1996 6 Figure 4 The organization of tropocollagen molecules to for collagen fibrils Reproduced from Fung Y C Biomechanics Mechanical Properties of Living Tissues 2nd ed 1993 New Yorks Springer Verlag 308 uote tei tei e niacin deis ep tete tese Erde ae du Gre der aide dpa 8 Figure 5 Schematic showing the hydrogen bonding between strands that is responsible for collagen s strength A and the tri helical structure that the three collagen strands take when they assemble into a collagen fiber B Reproduced from Voet Biochemistry 1995 10 Figure 6 Picture illustrates the extensive branching characteristic of GAG molecules which account for their ability to attract and retain water molecules to enhance their molecular volume Reproduced from Alberts Molecular Biology of the Cell 1994 13 Figure 7 A map of the collagen fiber architecture of the MV anterior leaflet Colors from red highly aligned to blue randomly aligned represent the degree of collagen alignment
38. ITRAL VALVE HISTOLOGICAL STRUCTURE ceres 7 1 3 1 Tri layered leaflet 5 2 7 1 3 2 Passive components of the mitral s tere ceto re oe ette m pea NR 8 E321 Fossett tet a se arae etat bete E o 8 1 3 2 2 Elastin d nates 11 1 3 2 3 Glycosaminoglycans ode cele ta sul n e tank ce bete pn 11 1 3 3 Active components of the mitral 1 12 1 3 4 Small angle light scattering analysis of collagen architecture 14 L4 MITRAL VAEVE DISEASE itt teri eld deerat ub Ed dedita 16 1 4 1 Mitral valve stenosi Seni Uem bom ade ds e 16 1 4 2 Mitral valve regurgitation s esos epo vods tho men euet it oed DAE Mi rn qu pn diua 17 15 PROSTHETIC VALVE REPLACEMENTS eere teet ennt eset tn nein 21 16 VALVULAR COORDINATE 23 Lo UMITRAEVAEVEIDYNAMIGCS DO Qu M EE 24 1 7 1 Surface stretches of the anterior leaflet essere 27 1 8 MECHANICAL PROPERTIES OF MITRAL VALVE LEAFLETS 31 L9 VISCORLASTIC BEHAVIOR te ient tere a cle ee Ted PASE 36 1 9 1 Sifess telax quon testing iu aieo deceat condi dede nt edidi iat 37 1 9 2 Creep testini eder soe aeo Woe Md e nd a a e t v eda 3
39. L were explored A novel high speed biaxial testing device was developed to achieve stretch rates both below and beyond in vitro values reported for the MVAL Sacks et al ABME Vol 30 pp 1280 90 2002 Experiments were performed with this device to assess the effects of stretch rate from quasi static to physiologic on the stress stretch response in the native leaflet Additionally stress relaxation and creep tests were performed on the MVAL under physiologic biaxial loading conditions The results of these tests showed that the stress stretch responses of the MVAL during the loading phases were remarkably independent of stretch rate The results of the creep and relaxation experiments revealed that the leaflet exhibited significant relaxation but unlike traditional viscoelastic biological materials exhibited negligible creep These results suggested that the MVAL may be functionally modeled as an anisotropic quasi elastic material and highlighted the importance of performing creep experiments on soft iii tissues Additionally this study underscored the necessity of performing biaxial experiments in order to appropriately determine the mechanical properties of membranous tissues iv TABLE OF CONTENTS 1 0 INTRODUCTION ot tuse techn ist oret aa neis i Seed Face ee ted Oa alanis die 1 11 ANATOMY AND PHYSIOLOGY OF THE HEART eerte 1 12 VERE VAEVEANATOMY eost t epe bua eta meque ids cae eee sia eate 4 1 3 M
40. ak tension limit This was done as a safety measure to prevent specimen damage from over distension Once the carriages were stopped they were held for the duration of the loading time before returning to their original configuration In this case the carriage velocity correction was given by t measured E peak Ve Vo poet C peak 14 69 In this formulation is the time to reach the peak tension level in the loading cycle The effectiveness of these correction algorithms was obviously highly dependent on both the initial carriage velocity guesses and the correction factor Generally the 90 N m equitension level was reached in the proper loading duration 15 seconds in this experiment by the third loading unloading cycle In addition to correcting the initial carriage velocity guesses the correction algorithms allowed the carriage velocities to adapt as the specimen properties shifted due to preconditioning in the initial cycles 2 1 3 4 High stretch rate testing The high stretch rate testing was always performed after an initial set of 20 quasi static cycles Unlike the quasi static cycles corrections were not made between the high stretch rate cycles Instead the carriage velocities from the final quasi static cycle were simply scaled to accommodate the higher loading times For instance the carriage velocity on a given device axis for the first 1 second high speed cycle was calculated by multiplying the carr
41. an peak realized membrane tensions were 93 2 2 1 N m on the circumferential axis and 97 1 2 5 N m on the radial axis for uniaxial stress relaxation experiments and 102 2 2 8 N m on the circumferential axis and 103 4 3 4 N m on the radial axis for biaxial experiments Despite this overshoot the ratio of the peak circumferential and radial membrane tensions was always maintained near 1 0 99 0 01 in biaxial experiments For stress relaxation experiments the overshoot was not corrected however as stated in the methods section stress relaxation results were calculated and normalized for each specimen based on the peak membrane tension measured for the proper individual experiment In cases where overshoot occurred during creep experiments the membrane tension state was corrected within the first second of the test by the same device control algorithm that maintained the 90 N m equibiaxial tension state for the duration of the test The creep algorithm was able to 103 maintain the 90 N m membrane tensions very well over the entire duration of the creep tests Table 4 120 100 Circumferential 80 60 40 20 0 100 200 300 400 500 Time ms Figure 46 Typical membrane tension versus time curves for the first 500 ms of a biaxial stress relaxation experiment The biaxial stretching mechanism was able to load the specimens within the allotted 100 ms rise time with minimal vibrations and overshoot 104 Table 4 Cir
42. and strip biaxial filled symbols protocols Circles circumferential axis triangles radial axis Reproduced from May Newman and Yin Biaxial Mechanical Properties of the Mitral Valve leaflets American Journal of Physiology 1995 33 The nonlinear behavior measured in the quasi static biaxial testing was similar to the nonlinear pressure areal stretch relationship observed by Sacks et al in their left heart simulating flow loop Figure 20 In the May Newman study differences in the loading and unloading stress stretch curves were observed though no attempt was made to quantify this behavior In addition to the 10 displacements a select number of specimens were tested at higher stretch rates up to 40 per second for comparison The mechanical properties of these specimens were not found to be different from the specimens tested at the slower speeds Trans mitral pressure mmHg 1 0 12 14 1 6 1 8 Areal stretch Figure 20 Pressure areal stretch relationship of the MV anterior leaflet measured in left heart simulating flow loop Reproduced from Sacks et al Surface stretches in the anterior leaflet of the functioning mitral valve 34 This characteristic nonlinear stress stretch response has been observed for other valvular materials as well In their study on the biaxial mechanical properties of the aortic valve cusp Billiar and Sacks 35 reported similar nonlinearity anisotropy and mechanical coupling Figure 21
43. ation of the material properties of the native valve will provide an improved basis for the comparison and qualification of potential replacement materials and repair techniques and is a necessary step in the development of future computational models and material simulations 55 113 4 2 MECHANICAL ANISOTROPY The classic nonlinear stress stretch relationship exhibited by the MVAL leaflet observed in the present study was consistent with previous biaxial findings of May Newman and Yin 34 as well as the transvalvular pressure areal stretch relationship observed by Sacks et al 32 The three phase curve consisted of a roughly linear toe region in which the leaflet deformed extensively while developing minimal membrane tension followed by a highly nonlinear transition region in which leaflet stiffness increased rapidly before reaching a plateau and entering a second linear region Efforts have been made to explain this phenomena using collagen fiber recruitment theories 56 57 but the microstructural details remain to be elucidated for the MVAL In the present study for all leaflet specimens the circumferential axis exhibited lower stretch levels for a given tension level than did its radial counterpart This result supported the finding that the marker region used in this study consisted predominantly of circumferentially oriented collagen fibers 58 since collagen fibers primarily resist only axial loads This finding was also consiste
44. behavior of porcine aortic valve AV cusps 50 Vesely et al observed that the relaxation percentage and the rate of relaxation were dependent on stretch rate However in this case the relaxation of the AV decreased as the displacement rate in the initial loading phase increased Although the results of Provenzano and Vesely seem contradictory to our results these comparisons should be interpreted with caution since these studies reported the effects of stretch and stretch rate on a single specimen axis under uniaxial load Because our result describes differences between two axes of the same specimen the structural differences between specimen axes must also be considered 121 Previous Small Angle Light Scattering studies 32 have shown that the leaflet subsection used in our experiments consists predominantly of circumferentially oriented fibers This suggests that a larger portion of the 90 N m membrane tension was borne by collagen fibers in the circumferential direction than in the radial direction since collagen most effectively resists axial loads In their uniaxial stress relaxation study on the porcine MV chordae tendineae 40 Liao and Vesely linked decreases in relaxation rate and relaxation percentage to increased GAG content hypothesizing that interfibrillar GAG linkages decreased relaxation by resisting shearing between collagen fibers Using our result we may expand on this hypothesis to state that for the MVAL the increased
45. cation of any such model i e to optimize MV repair or replacement techniques would be used to predict behavior under physiological conditions 47 1 10 1 Specific study aims The goal of this work was to expand on previous studies by quantifying the biaxial viscoelastic properties of the MV anterior leaflet under physiological conditions Specific aims were 1 To develop a biaxial testing device capable of testing MV leaflet specimens under physiologic stretch and loading conditions at physiological stretch rates 2 To determine the stretch rate sensitivity of the MV anterior leaflet when loaded to physiologic stretch levels at stretch rates ranging from quasi static to physiological 3 To determine the stress relaxation and creep responses of the MV anterior leaflet at a physiologic stretch or loading state with physiologic initial rise times 48 2 0 METHODS 2 1 HIGH SPEED BIAXIAL TESTING DEVICE 2 1 1 Device specifications The following section describes the factors taken into account in the design of the high speed biaxial testing device These specifications were deemed to be those necessary to adequately represent the physiological properties of the MV leaflet 2 1 1 1 Displacements and displacement rates In order to adequately reproduce the stretch rates experienced by the MVAL in vivo the necessary displacements and displacement rates for the actuation components were determined based on the in vitro find
46. cations provided in the previous section 2 1 2 1 Device overview Figure 24 The high speed biaxial testing device mounted on a vibration isolation table 53 The high speed biaxial testing device Figures 24 25 consisted of four linear positioners each driven by a stepper motor The positioners were arranged around a central specimen bath with each specimen carriage arm reaching into the bath from a direction orthogonal to its axis of travel The positioners and bath were mounted on a custom designed support fixture that was built to be mounted on a vibration isolation tabletop This fixture raised the bath and positioners 6 above the tabletop so that the specimens could be imaged from below using a 45 mirror configuration Cameras were mounted separately on a single camera stand that allowed precise spatial adjustments on 3 axes In addition to holding the specimen and fluid the bath had inflow and outflow tubing connectors that allowed the bath fluid to be pumped into a heat exchanger so that fluid temperatures could be maintained at physiologic levels The device was controlled with a dual computer system Figure 26 with one computer designated for high speed imaging 54 m BERR ERR eee pmi Figure 25 Overhead schematic of the high speed biaxial testing device a stepper motors b screw driven linear actuators c load cells d specimen bath outlet e specimen bath inl
47. cent study by Sacks et al 32 measured the surface stretches of the anterior leaflet under physiologic conditions by tracking graphite markers glued onto the surface of the valve leaflet in a left heart simulating flow loop Figure 15 This study made use of two high speed digital cameras that were both focused on the leaflet but were oriented at thirty degrees to one another such that 3D spatial coordinates could be determined from the two camera images using a direct linear transform method 33 The results of this analysis confirmed that the anterior leaflet opened in approximately 70 milliseconds and closed in approximately 40 milliseconds and additionally confirmed that the leaflet deformation occurred faster during opening than they did in closure In this study the authors were able to quantify the surface stretches Figure 16 as well as the surface stretch rates of the anterior leaflet Figure 17 Additionally this study showed that after valve closure the leaflet stretch state remained constant while the valve was held closed for approximately 0 3 seconds during systole before finally returning to its original configuration as the valve opened The surface stretches observed by Sacks et al in vitro were confirmed in vivo in an unpublished study by Sacks et al in which sonomicrometry crystals were tracked on the MV leaflets of living sheep Figures 16 17 27 Resistance Atrial Compliance Reservoir High Speed Cameras
48. cumferential and radial membrane tensions STDEV for all creep tests after the initial loading phase Specimen Circumferential N m Radial N m 90 03 89 88 _ 6 8994 0131 8991 021 89 96 89 88 3 3 2 Biaxial Stress Relaxation Relaxation was observed on both the circumferential and radial axes Figure 47 The most drastic relaxation was observed within the first 15 minutes of testing but specimens continued to relax up to and beyond the 3 hour time point The change in membrane tension from immediately after initial loading at 100 ms to 3 hrs was statistically different for each specimen axis P 0 001 for both specimen axes Relaxation was always greater in the radial direction The ratio of circumferential to radial membrane tensions at 3 hours 1 10 0 02 was statistically different from the same ratio at 100 ms 0 99 0 01 P lt 0 001 and the relaxation percentage in the circumferential direction 24 67 0 93 was statistically different from the relaxation percentage in the radial direction 32 09 0 77 P lt 0 001 Figure 48 105 EIDO Circumferential Badia 0 0 0 5 1 0 1 5 2 0 2 5 3 0 Time hrs Figure 47 Membrane tension versus time curves for a typical stress relaxation experiment Membrane tension levels at 3 hours were statistically less than those immediately after loading 100 ms for both specimen axes 106 Circumferential 1 Radial Unia
49. d device axis showed no sensitivity to high speed motion Figure 36 Very little change was observed in the load data from the unloaded axis This was demonstrated by a linear function which was fit to the load data from the unloaded axis with a slope of 0 006 g s over the 0 2 second duration A plot of the residuals showed no clear pattern indicating that the unloaded axis was not affected by the high speed rapid acceleration or sudden deceleration of the carriage displacement 88 e Loaded Axis latex sample Unloaded Axis Load g 0 200 400 600 800 1000 Time ms Figure 36 Load versus time curves for the loaded axis closed symbols and unloaded axis open symbols showed that the load cell on the unloaded axis was not affected by rapid motions 89 e e 6e oo ep Mee te e ec e 9 98 e Residual g 0 200 400 600 800 1000 Time ms Figure 37 Residuals versus time for the unloaded axis showed no clear trend further indicating that the unloaded axis was not affected by rapid motions 90 3 1 5 System relaxation The suture only relaxation test Figure 38 showed that the level of relaxation in the system itself was minimal After the three hour test duration relaxation percentages were 1 2 percent on the first device axis and 1 6 percent on the second device axis 1 2 Normalized Tension 0 0 0 5 1 0 1 5 2 0 2 5 3 0 Time hrs F
50. d to maintain the constant stretch state can be assumed to be independent of fiber rotations It should be noted that currently many membranous tissues are subjected to uniaxial stress relaxation tests These tests while important in their own right are not true stress relaxation experiments since deformations are possible on the free specimen axis 37 E2 G t 3 i G t 2 G t t a b Figure 22 b The stress relaxation responses to three different stretch histories a Reproduced from Wineman AS Rajagopal KR Mechanical Response of Polymers Cambridge University Press 2000 1 9 2 Creep testing In a creep test Figure 23 a specimen is loaded to a desired load or stress level then the loading state is maintained for the duration of the test by adjusting the specimen stretch state In many instances the creep experiment provides more physiologically relevant data for bodily tissues than are provided by the stress relaxation test since in vivo most tissues are generally loaded with a certain force rather than stretched to a certain stretch state One disadvantage of the creep experiment is that unlike the stress relaxation case the fibers within a tissue specimen are free 38 to rotate and changes in the mechanical properties of the tissue cannot be isolated from the dynamic rearrangements of fibers within the material a b Figure 23 The creep responses b to three different stress h
51. de treated aortic valve cusp Part I Experimental results J Biomech Eng 2000 Feb 122 1 23 30 4 Wells SM Sacks MS Effects of fixation pressure on the biaxial mechanical behavior of porcine bioprosthetic heart valves with long term cyclic loading Biomaterials 2002 J un 23 11 2389 99 For Examples of High Speed Biaxial Experiments 1 NagatomiJ Gloeckner DC Chancellor MB DeGroat WC Sacks 5 Changesin the biaxial viscoelastic response of the urinary bladder following spinal cord injury Ann Biomed Eng 2004 Oct 32 10 1409 19 139 Section 2 Biaxial Tester Desc ription Figure 1 a Figure 1 Overhead schematic of the high speed biaxial testing device a stepper motors b screw driven linear actuators c load cells d specimen bath outlet e specimen bath inlet f heating element maintained bath temperature at 37 C g high speed digital camera high speed systems only h standard digital camera i beam splitter high speed systems only j sub specimen minor The actuation components of the biaxial testing device Fig 1 are four ball screw driven linear positioners 404XR Parker Hannafin Corp Irwin PA Each of these linear postioners is equipped with a 20mm lead capable of achieving a maximum camage velocity of 1 m s and maximum camage acceleration of 25 m s These four linear positioners are mounted in an opposing fashion such that one
52. don DA Mathieu Y et al Motion of both mitral valve leaflets a cineroentgenographic study in intact dogs J Appl Physiol 1975 39 359 26 Figure 15 Left heart simulating flow loop used by Sacks et al to quantify the surface stretches of the MV anterior leaflet Reproduced from Sacks et al Surface stretches in the anterior leaflet of the functioning mitral valve nennen ener 28 Figure 16 Principle stretches observed in left heart simulating flow loop closed symbols and in vivo using sonomicrometry method open symbols Reproduced from Sacks MS et al In vivo dynamic deformation of the mitral valve leaflet Annals of Thoracic Surgery Siren Bur 29 Figure 17 Principle stretch rates versus time for the MV anterior leaflet under normal physiologic conditions Reproduced from Sacks MS et al In vivo dynamic deformation of the mitral valve leaflet Annals of Thoracic Surgery Submitted 2005 30 Figure 18 Experimental setup for biaxial mechanical testing of the MV leaflet Reproduced from May Newman and Yin Biaxial Mechanical Properties of the Mitral Valve leaflets American Journal of Physiology 1995 tercie As rere beri ede ata ee 32 Figure 19 Membrane stress stretch relations from porcine anterior A and posterior B leaflets comparing equibiaxial open symbols and strip biaxial filled symbols protocols Circles circumferential axis tr
53. dynamic mechanical properties of the MVAL The combination of the stretch rate insensitivity of the stress level observed within the leaflet the lack of an appreciable level of tissue hysteresis at physiologic stretch rates and the lack of creep implies that the MVAL may be functionally modeled as a nonlinear quasi elastic anisotropic biological material The structural basis for this behavior is as yet unknown but is likely an important functional aspect of native MV tissues and warrants further study Also additional studies using small angle X ray scattering on MV leaflet collagen molecular structure under creep and relaxation as done for recently for pericardium 63 may help to provide a structural basis for the mechanical behavior observed in this study 130 4 10 RECOMMENDATIONS FOR FUTURE STUDY The results of this study have provided novel and important data on the MVAL but much remains to be studied before our understanding of mitral mechanics is complete Recommended future studies include 1 A duplication of the current study for the posterior mitral valve leaflet o This study would provide necessary data for the modeling of the posterior leaflet and would elucidate differences between the two leaflets 2 Stress relaxation study of the MV leaflet using a high resolution camera and magnifying lens o By studying the changes in the stretch state of all regions of the leaflet as opposed to only the central region used in
54. e mitral valve disease J Heart Valve Dis 2000 9 1 p 75 80 discussion 81 Perier P B Clausnizer and K Mistarz Carpentier sliding leaflet technique for repair of the mitral valve early results Annals of Thoracic Surgery 1994 57 p 383 386 Smedira N G R Selman D M Cosgrove P M McCarthy B W Lytle P C Taylor C Apperson Hansen R W Stewart and F D Loop Repair of anterior leaflet prolapse chordal transfer is superior to chordal shortening J Thorac Cardiovasc Surg 1996 112 2 p 287 91 discussion 291 2 David T E M Komeda C Pollick and R J Burns Mitral valve annuloplasty the effect of the type on left ventricular function Ann Thorac Surg 1989 47 4 p 524 7 discussion 527 8 Kreindel M S W A Schiavone H M Lever and D Cosgrove Systolic anterior motion of the mitral valve after Carpentier ring valvuloplasty for mitral valve prolapse Am J Cardiol 1986 57 6 p 408 12 Yacoub M H and L H Cohn Novel approaches to cardiac valve repair from structure to function Part II Circulation 2004 109 9 p 1064 72 183 25 26 27 28 29 30 31 92 33 34 35 36 37 Yoganathan A Cardiac Valve Prostheses in The Biomedical Engineering Handbook 1995 CRC Press Boca Raton Hashim S R A Fontaine S He R A Levine and A P Yoganathan A three component force vector cell for in vitro quantification of the force exerted by the papillary
55. e specimens from the peak membrane tension to the same membrane tension observed after the three hour duration of the stress relaxation experiments Figure 52 The results of this analysis showed that the specimen stretches for the relaxation experiments were markedly different from those seen in the quasi static unloading cycles Specimen stretches observed in the relaxation experiments were statistically different from those observed in the quasi static unloading cycles in both the circumferential p 0 02 and radial p lt 0 01 directions As expected the quasi static results showed a negative change or decrease in stretch to reach the relaxed membrane tension Conversely the stretches over the duration of the stress relaxation experiment actually increased slightly The increase in stretch was quite small however it did occur in all but one specimen 117 0 008 Siress relaxation 0 006 Quasi static unloading 0 004 0 002 0 000 0 002 0 004 Change in Stretch 0 006 0 008 0 010 0 012 Circumferential Radial Figure 52 Changes in stretch over the three hour duration of the stress relaxation experiments compared to the changes in stretch required to reach the same membrane tension in quasi static unloading cycle The increased stretches over the stress relaxation duration indicate that a portion of the total specimen stretch may be redistributed into the central mar
56. een both of the surgical staple attachments for the attached suture loop Both pulleys are mounted symmetrically on either side of a central stainless steel ball bearing 141 This mechanism distributes the total force applied by the positioner equally between both pulleys Leaflet deformations are measured optically with a digital camera see background material for references on biaxial stretch measurement Load measurements are acquired by the device control computer from a pair one on each device axis of load cells Model 31 Honeywell Sensotec Columbus OH via an analog digital converter PCI 6036E National Instruments Austin TX 142 Section 3 Biaxial Testing Software Screens 3 1 Load Cell Calibration Load Control 4 0 vi Ele Edit Operate Tools Browse Window Help Load Cells g Tes igs Run Tes igh Speed Test 1 1 Load Cell Tab Load Cell Voltages 4 07 1 2 Load Cell Voltage Readings 1 3 Low amp High Indicators 1 4 Loads Graph Voltage 1 Voltage 2 1 5 Save Button 2 1 6 Load Button Loads o 5 1714606 Load 1 0 533 9 Load 2 0 532 g Calibration Load Units Newtons N SET 0 00 g _ ig y High SETI 9116 50 g X mi High sr 9116 50 g Calibration File Save Program Status acere 6 95 spe E 143 3 2 Image Setup ix Load Control 4 0 vi ianl xi Ele Edit Operate Tools Br
57. ements of the final quasi static loading cycle If anything is unusual with the final quasi static cycle it is not recommended to proceed with the high speed test It is Strongly recommended that all high stretch rate tests are preceded by a standard quasi static biaxial protocol to ensure that no abnormal characteristics are present in the test sample The Axis Retum Factors 2 8 allow the userto multiply the retum stroke during the high speed testing by the appointed retum factor in orderto account forovershoot or instabilities in the high speed protocols Though these factors are present no correction was ever needed retum factors 1 in the mitral valve testing Take care that a large numberis not accidentally input into one of these fieldsasthis could be devastating to your sample and the device if the limit switches are improperly installed The Recalibrate LC button allowsthe userto recalibrate the load cells between high speed cycles This wasfound to be unnecessary and this toggle should not be used since it wasnever fully qualified The Apply Preload toggle causesthe testing software to reapply the specified preload See Specimen Positioning in the Biax Manual between high speed cycles Better results were obtained in mitral valve testing when thisfeature wasdisabled indicator light black Protocol 1 2 3 Input the desired quasi static test settings Refer to Biax Manual for instructions Click the Hi
58. en 6 Click the green Start Test button 6 3 at the top of the tab 7 When prompted entera base file name forthe test The software will automatically write test data foreach test cycle in a file named user entered base file name cycle gt bx 8 When prompted select a reference file to use forthe test 9 St backand watch the show 158 Section 5 Biaxial Tester Output Files BX Files Each file that is automatically generated during the biaxial test procedure bx file isa tab delimited file that can be opened in Microsoft Excel or most other spreadsheet programsortext editors The headings for thes files are Time ms Stretch 1 Stretch 2 Shear Angle Load 1 9 Load 2 g Tension 1 N m Tension 2 N m Stress 1 kPa Stress 2 kPa x1 x2 x3 x4 x5 x6 x7 x8 x9 yl y2 y3 y4 y5 y6 y7 y8 y9 REF Files REF files are saved reference files that are saved by the user and used by the Biax software during test protocols Each REF file isa tab delimited file that can be opened in Microsoft Excel or most other spreadsheet programs or text editors if further analysis is necessary The field order is X1 X2 XA X5 X6 X7 X8 X9 Y1 Y2 Y4 Y5 YO Y7 Y8 Y9 159 Section 6 Software Drivers and Virtual Channels Software amp Drivers Manufacturer Name Version National Instruments Measurement amp Automation Explore
59. en perfectly taut The original prototype specimen window was thin and level with the bottom of the bath but it was discovered in testing that small vertical specimen motions could cause problems with image focus and could introduce some stretch measurement error since from the camera viewpoint the markers appeared to move apart as the specimen moved closer to the camera thus increasing the size of the specimen in the camera image 2 1 2 5 Stretch and load measurement Leaflet deformations were measured optically with a dual camera digital imaging system Figure 29 The first camera XCD X700 Sony Tokyo Japan acquired images with a pixel resolution of 1024 x 768 at an acquisition rate of 15 frames per second These images were stored in the device computer memory in real time via a Firewire IEEE 1394 port and were used for control purposes during quasi static preloading cycles and to acquire data in the later portions of stress relaxation and creep experiments During high speed cycles and the initial loading phases of stress relaxation and creep experiments an auxiliary high speed digital imaging system FastCamera 13 Fast Vision 60 Nashua NH was engaged This imaging system made use of a 4 megapixel complementary metal oxide semiconductor CMOS image sensor with a maximum resolution of 1240 x 1024 and acquisition speed of 1000 frames per second This high speed camera was controlled with a second PC that contained 3 high speed fra
60. ential direction and independent of stretch rate in the radial direction Overall the stretch rate sensitivity of soft tissues appears to be highly tissue specific and dependent on the specific experimental protocol The variation in the findings of these studies underscores the necessity for characterization of the MV leaflet mechanical properties under the physiologic condition 1 9 7 Creep and stress relaxation in soft tissues In addition to the stretch rate sensitivity the creep and relaxation aspects of MV leaflet mechanical behavior remain to be explored These tests are particularly relevant to the 300 millisecond constant stretch phase observed in the leaflet surface during valve closure Of particular relevance to this study is a recent study by Liao and Vesely 40 in which uniaxial stress relaxation experiments were performed on the porcine MV chordae tendineae This study reported relaxation percentages between 30 and 60 after 100 seconds and went on to link the amount and rate of relaxation to the glycosaminoglycan GAG content of the individual chordae Although the investigations into the stress relaxation and creep response of the MV leaflets are non existent to the author s knowledge the creep and relaxation literature for soft tissues reveals some interesting behaviors that should be investigated in the MV 44 Provenzano et al 47 explored the relaxation and creep behavior of the rat medial collateral ligament MCL a
61. erefore planar biaxial testing can be used to quantitatively characterize its mechanical properties 51 In the work by May Newman and Yin discussed previously 34 quasi static stretch rates of 4 to 12 second biaxial experiments were performed on the MV leaflets This work provided biomechanical data by subjecting MV leaflet specimens to a range of biaxial stretch based protocols and this data was later used to develop a stretch energy based constitutive model for a generalized loading state 52 This study provided a valuable data but was performed before a complete understanding of MV surface stretches was available The recent study by Sacks et al 32 in which the surface stretches of the leaflet were measured in a left heart simulating flow loop showed that the stretch rates of the MV anterior leaflet were on 46 the order of 1000 per second more than an order of magnitude greater than the maximum stretch rates employed in the May Newman study In addition to the stretch rate analysis the study by Sacks and colleagues reported the stretch states of the leaflet under physiological conditions thus providing the necessary data to reasonably replicate the in vivo loading condition of the valve leaflet under controlled conditions in a biaxial stretching mechanism It is critical to determine if previously reported quasi static biomechanical data can be used to model the behavior of the valve in the physiological condition since the appli
62. ersely this result differed from those detailed in the work of Leeson Deitrich 42 for aortic and pulmonary valves who reported significant differences in the stress stretch response at different stretch rates Our results also differed from the results reported by Lee et al 60 who observed stretch rate sensitivity of the glutaraldehyde stabilized porcine aortic valve in the circumferential axis only Lee et al linked the explanation of this behavior to the presence of major collagen bundles which were observed to span the valve parallel to the circumferential leaflet axis It should be noted that a similar collagen arrangement has been observed in the anterior MV leaflet 58 and we observed no directional differences in stretch rate sensitivity It is unclear whether the differences between our results and those reported in these two studies 115 were derived from differences in material or if they were a product of the differences in loading condition biaxial tension versus uniaxial tension The hysteresis of the MVAL was difficult to compare between different loading unloading cycle times due to the extremely small amount of energy stored within the MVAL The traditional definition of hysteresis the difference between the areas beneath the loading and unloading curves may not be appropriate for biaxially loaded specimens because due to coupling effects one axis may actually contract at high tension levels creating an undefined integrat
63. et f heating element maintained bath temperature at 37 C g high speed digital camera h standard digital camera i beam splitter j sub specimen mirror 55 2 1 2 2 Actuation components The new biaxial stretching device was designed to meet the displacement requirements while accelerating smoothly and stopping precisely in order to prevent overstretching and to minimize excessive vibrations associated with rapid accelerations and decelerations that could potentially result in specimen damage and generally decrease the levels of test repeatability and validity To accomplish this four ball screw driven linear positioners 404XR Parker Hannafin Corp Irwin PA each equipped with a 20mm lead capable of achieving a maximum carriage velocity of 1 m s and maximum carriage acceleration of 25 m s were mounted in an opposing fashion such that one pair of positioners was aligned to stretch a centered tissue sample along one device axis and a second pair of positioners was aligned with orientation orthogonal to the first pair to stretch the sample along the second device axis These linear positioners were coupled with rotary stepper motors OS22B SNL10 Parker Hannafin Corp Irwin PA Each stepper motor was driven with a microstepping drive E AC Parker Hannafin Corp Irwin PA that provided a step resolution of 50 800 steps per revolution which when coupled to each aforementioned linear positioner resulted in a spatial resolution of ap
64. et and their performance has not been qualified for other materials It is strongly suggested that anyone who uses these programs have a good knowledge of LabView programming so that adjustments to the programs can be made as necessary The high speeds involved in these tests increase the need for the user to be familiar with the device and its capabilities Always make sure that limit switches are properly installed to avoid device damage 12 Program Descriptions Each of the three high speed testing programs works in a manner very similar to the quasi static load control biaxial testing program Load Control 1 0 Generally each program is set up to run through a series of quasistatic test cycles exactly like those in Load Control 1 0 then to perform a designated high speed test at the end of the quasi static testing based to the displacements determined in the quasi static cycles 169 Load Control 2 0 Stress Relaxation This program runs a series of quasi static cycles to user defined load limits After the final quasi static cycle the program can be set to perform a stress rela xation test in which the specimen will be stretched from the preload state to the displacements that were determined to correspond to the load limits in the final quasi static cycle The specimen will be loaded in a user defined time and the carriage positions will then be locked forthe duration of the experiment This program triggers the high speed camera t
65. f the Run Test tab 6 1 2 Atest can be cancelled by clicking the cancel button 6 3 atthe top of the Run Test tab If the device doesnotrespond to thisaction and the device needsto stop immediately shut off powerto the motors 3 During or before a test you can choose to view the data forthe current test cycle only orforall test cycles with the toggle 6 2 in the upperright comer of the Run Test tab Protocol 1 Click the Test Settings tab 4 1 or 5 1 at the top of the screen 2 Input all test parameters a b Specimen dimensions 4 2 or 5 2 insert the specimen dimensions in mm Number of Cycles 4 3 or 5 3 15 Cycle Time 4 3 or 5 3 The time secondsthatthe specimen will be loaded orunloaded The duration of one cycle will be 2 1 2 Cycle Time Correction Gain 4 8 or 5 8 The testing device makes corrections between cycles based on the assumption that the material is linear The more nonlinear your material is the lower your correction gain should be to prevent overshoot A typical correction gain for valve materials is 0 3 3 Parametersin Load Control Only 4 1 a b C d Control 4 5 Determine the units and type of control forthe load test Axis 1 amp Axis 2 4 6 Inputthe desred peakloadsforeach axisin the units specified in Control Estimated Stretch 1 amp 2 4 7 Initial guessesforthe stretchesthat will be required to stretch the specimen to
66. figuration tension limits In a typical quasi static loading and unloading cycle the device carriages moved with constant velocities for the prescribed loading period in order to stretch the centered specimen from the tare configuration to the peak tension limit reversed direction after the prescribed loading period then stopped after returning to their original location Pairs of opposing carriages always moved with the same velocity in order to prevent the specimen from moving out of the camera view but the two pairs of carriages usually had different velocities in order to account for anisotropic specimen behavior In the first quasi static cycle of a given specimen the carriage velocities were calculated based on stretch estimates input by the user In this study these guesses were based on pilot studies of other leaflets as well as experience with other test specimens within the study Because the carriage velocities required to reach the 90 N m tension state were highly variable it was rare that the initial carriage velocity guesses were sufficient For this reason automated corrections were made to the carriage velocities between cycles Corrections for each axis were made independently without considering the correction made on the opposing axis If the desired peak tension was not reached for a given specimen axis in the desired loading period the following correction was made to the carriage velocity peak desired T uk C Ve bd V
67. flet stretch states 34 In this study MV leaflets were mounted in a biaxial stretching mechanism Figure 18 using a series of suture loops on 3 of the four leaflet edges and directly tethering the leaflet chordae tendineae on the final edge In this study cyclic stretching was applied with displacement ramp times of 10 seconds corresponding to stretch rates of 4 12 per second Results of this study showed that the mechanical properties of the valve leaflets were highly anisotropic with the circumferential axis much less distensible than the radial axis Additionally this study revealed that the mechanical behavior each specimen axis was highly dependent on the stretch state of the alternate specimen axis Figure 19 The stress stretch responses of both specimen axes were found to be highly nonlinear The authors of this study attributed this nonlinear behavior to the stretch dependent recruitment of collagen fibers 31 Figure 18 Experimental setup for biaxial mechanical testing of the MV leaflet Reproduced from May Newman and Yin Biaxial Mechanical Properties of the Mitral Valve leaflets American Journal of Physiology 1995 32 8 E 150 Q o g e w 100 o 50 0 0 0 2 0 4 0 6 0 8 Strain 200 B 2 150 uU 9 100 i 2 E 50 z Strain Figure 19 Membrane stress stretch relations from porcine anterior A and posterior B leaflets comparing equibiaxial open symbols
68. gh Speed Tes Tab 2 1 Enter 1 0 in both of the Axis Retum Factor Inputs 2 8 177 Verify that the Recalibrate LC 2 7 and Apply Preload 2 9 toggles are deactivated indicator lights blac k Click the High Speed Test toggle 1 5 such that the indicator light tums to bright green Clicking thistoggle will direct the biaxial testing software to perfom the high stretch rate tests after completing the quasi static protocol Make sure to disable this toggle by clicking the toggle again such that the indicator light is black before proceeding with any additional quasi static only experiments Select the Test Settingstab and run a quasi static experiment as detailed in the Biax Manual Afterthe quasi static protocol is completed the software will wait forthe userto click the Trigger Test button 1 3 on the High Speed Test tab Before you triggerthe test checkthe final cycle of the quasi static protocol to ensure that nothing abnormal occured and that the carriage displacements resulted in a condition very close to the desired loads If you are using the high speed camera to track stretchs during the high speed cycles ensure that the camera isready to receive the analog trigger signal from the biaxial testing software Pressthe Trigger Test button The specimen should be loaded and unloaded in 1sand the load vstime curve should be plotted on the screen afterthe motion hascompleted 10 If everything in
69. gramming level The creep algorithm automatically loadsthe specimen to the peak levels defined in the Test Settings Tab See Biax Manual This was convenient for the mitral valve since the valve wasstretch rate insensitive but this may need to be modified forother materials since loading the specimen in 100ms instead of quasistatically may result in much higher load levels Protocol 1 Input the desired quasi static test settings Refer to Biax Manual for instructions 179 Clickthe High Speed Test Tab 3 1 Enterthe desired duration forthe creep portion of the experiment in the test duration input 3 6 Enterthe desired Creep Stretch Limits 3 7 Thisisa safety function If these limits are reached the software will automatically stop the test Clickthe High Speed Test toggle 3 5 such thatthe indicator light tums to bright green Clicking thistoggle will direct the biaxial testing software to perform the creep test after completing the quas static protocol Make sure to disable thistoggle by clicking the toggle again such thatthe indicator light is black before proceeding with any additional quasi static only experiments Select the Test Settingstab and run a quasi static experiment as detailed in the Biax Manual Afterthe quasi static protocol is completed the software will wait forthe userto click the Trigger Test button 3 3 on the High Speed Test tab Before you triggerthe test checkthe fi
70. hner and J Leeson Dietrich Bioprosthetic Valve Tissue Viscoelasticity Implications on Accelerated Pulse Duplicator Testing Annals of Thoracic Surgery 1995 60 p S379 383 Sacks M S Biaxial mechanical evaluation of planar biological materials Journal of Elasticity 2000 61 p 199 246 May Newman K and F C Yin A constitutive law for mitral valve tissue J Biomech Eng 1998 120 1 p 38 47 Hoffman A H and P Grigg A Method for Measuring Strains in Soft Tissue Journal of Biomechanics 1984 10 p 795 800 Sacks M S and W Sun Multiaxial Mechanical Behavior of Biological Materials Annu Rev Biomed Eng 2003 Butler D L S A Goldstein and F Guilak Functional tissue engineering the role of biomechanics J Biomech Eng 2000 122 6 p 570 5 Lanir Y Constitutive Equations for Fibrous Connective Tissues journal of biomechanics 1983 16 p 1 12 Lanir Y A Structural Theory for the Homogeneous Biaxial Stress Strain Relationships in Flat Collageneous Tissues Journal of Biomechanics 1979 12 p 423 436 Kunzelman K S M S Sacks R P Cochran and R C Eberhart Mitral Valve Leaflet Collagen Distribution by Laser Analysis in Seventh Southern Biomedical Engineering Conference 1988 p 82 85 Naimark W A J M Lee H Limeback and D Cheung Correlation of structure and viscoelastic properties in the pericardia of four mammalian species American Journal of Physiology 1992 263 32 p H1095 H11
71. hours A Creep percentage C was calculated as C A 99ms A 1 84 2 3 5 Statistical methods For all tests the circumferential and radial data groups were considered separately and the uniaxial and biaxial stress relaxation groups were considered separately To determine the effects of stretch rate on each biomechanical parameter in the stretch rate sensitivity protocols i e A AP and hysteresis comparisons between all loading times were performed using one way Analysis of Variance ANOVA The Holm Sidak method was then used to perform pair wise comparisons between loading time groups to further elucidate any significant differences Student s t test was used to assess any directional differences between specimen axes in both creep and relaxation experiments and to compare uniaxial and biaxial relaxation percentages Additional comparisons between creep percentages at 100 ms 300 ms 1s and 3 hr were performed using one way ANOVA for both the circumferential and radial creep data sets All tests were performed with a commercial statistics software package SigmaStat SPSS Inc Chicago IL All data values are presented as the mean the standard error of the mean SEM 85 3 1 1 The stretch measurement system was found to be accurate to within a stretch of 0 001 Table 3 1 CHARACTERIZATION OF DEVICE PERFORMANCE 3 0 RESULTS Stretch Measurement Accuracy 2 and shear angle was measured to wi
72. i vw hyaluronan molecule fo i v in iti kerat chondroitin sulfate sulfate Figure 6 Picture illustrates the extensive branching characteristic of GAG molecules which account for their ability to attract and retain water molecules to enhance their molecular volume Reproduced from Alberts Molecular Biology of the Cell 1994 13 1 3 4 Small angle light scattering analysis of collagen architecture The orientation of collagen fibers within the MV anterior leaflet has been examined using a small angle light scattering SALS technique Figure 7 This technique consists of directing a helium neon laser through dehydrated tissue specimens and recording the subsequent beam diffraction 10 According to the principles of Fraunhofer Diffraction the laser light scatters in a direction orthogonal to the fibers within the beam envelope Based on this principle the collagen fiber orientations can be reconstructed from the recorded diffraction pattern 14 25 31 36 41 46 51 56 61 65 Figure 7 A map of the collagen fiber architecture of the MV anterior leaflet Colors from red highly aligned to blue randomly aligned represent the degree of collagen alignment 15 1 4 MITRAL VALVE DISEASE Diseases of the MV can be logically separated into two categories those that cause left ventricular inflow obstruction termed MV stenosis and those that allow retrograde flow from the left
73. iage velocity used in the final 15 second quasi static cycle by the ratio of quasi static cycle time to the high speed cycle time or 15 in this case This control method ensured only that the specimen would be loaded and unloaded over the desired high speed duration to the same carriage displacements reached at the peak of the final quasi static cycle and back to the tare configuration Only if the specimen under test did not exhibit any stretch rate sensitivity would this control method load the specimen to the 90 N m equitension state 2 1 3 5 Stress relaxation testing The algorithms used to control the stress relaxation test were very similar to those used to control the high stretch rate testing As in the high speed 70 cycles a stress relaxation experiment always followed a set of quasi static cycles and the carriage velocities used in the final quasi static cycle were simply scaled to calculate the carriage velocities required to load the specimen in the 0 1 second rise time The difference between the stress relaxation and high speed loading unloading cycles was that after loading the specimen the carriages were simply held at the peak load configuration for the duration of the test in the case of stress relaxation 2 1 3 6 Creep testing As in the high speed loading unloading and stress relaxation tests the creep test was always performed after a set of quasi static cycles The carriage velocities required for the initial 0 1 sec
74. iangles radial axis Reproduced from May Newman and Yin Biaxial Mechanical Properties of the Mitral Valve leaflets American Journal of Physiology 1995 rosa etd uen 33 Figure 20 Pressure areal stretch relationship of the MV anterior leaflet measured in left heart simulating flow loop Reproduced from Sacks et al Surface stretches in the anterior leaflet of the functioning mitral valvezi onis oben cies cactus es 34 Figure 21 a The seven loading protocols used to characterize the biaxial stress stretch response and b response to all loading protocols for an AV cusp open circles along with the structural model fit demonstrating an excellent fit 0 0 eee sese 35 xii Figure 22 b The stress relaxation responses to three different stretch histories a Reproduced from Wineman AS Rajagopal KR Mechanical Response of Polymers Cambridge Umversity Press DO eei bees e ar Nite teet aste ms tto etre 38 Figure 23 The creep responses b to three different stress histories a Reproduced from Wineman AS Rajagopal KR Mechanical Response of Polymers Cambridge University Press 2000 aieo caesi p brat oa eR tad d caters oleh sale nui cress dpa tad 39 Figure 24 The high speed biaxial testing device mounted on a vibration isolation table 53 Figure 25 Overhead schematic of the high speed biaxial testing device a step
75. ibers This coiling is hypothesized to allow the elastin fibers to retain elastic mechanical properties even when highly distended 1 3 2 3 Glycosaminoglycans Glycosaminoglycans GAGs are composed of a series of are negatively charged unbranched polysaccharides attached to a protein core Figure 6 The negative charges of the GAGs cause these molecules to be highly hydrophilic This property allows GAGs to retain a relatively large volume of water given their molecular weight Because of the GAG content valve leaflets typically contain a large amount of water which enables them to resist compressive forces due to the incompressibility of water 11 1 3 3 Active components of the mitral valve In addition to the previously mentioned passive components the MV leaflets contain cells that may actively contribute to the leaflets mechanical properties such as myocardium smooth muscle and contractile interstitial cells These cells are supplied with blood by a sparse arrangement of blood vessels which runs throughout the leaflets The MV leaflets are innervated with both adrenergic and cholinergic nerves 8 9 and recent evidence has shown that neural control may play a role in controlling some of the finer motions of the leaflets such as regulating the precise leaflet deformations necessary for proper leaflet coaptation 12 aggrecan aggregate 6 1 um NUI 2 Wy i JN N D TT NW 4 core protein
76. ience and practice You can do it The suture attachment pulley pieces can be removed by unscrewing the thumbscrew located above each pulley attachment When twisting the thumbscrew on a that containsa load cell be careful to hold the metal load cell contacting arm away from the load cellto prevent from accidentally applying a force to the load cell It may be helpful to tum the powerto the motors off in orderto allow manual position adjustment during the mounting procedure Protocol 1 2 Steps 2 5 can be completed before preparing the specimen if desired Fill the specimen bath with the appropriate fluid Begin extemal bath flow loop if applicable Wait forbath parameters i e temperature gas concentrations to reach appropriate stable condition Attach suture loopsto device pulleys by lifting pulley caps looping suture around pulley and dropping pulley cap over suture line Once the specimen is successfully mounted make sure the powerto the motors is on Click the Positioning tab 3 1 atthe top ofthe software screen Adjust the motorspeed on the Motor Speed mm s scroll bar 3 3 Using the Free Movement buttons 3 2 centerthe specimen within the bath Note that the free movement directions should correspond to directions relative to the image window 153 4 5 Setting Up the Imaging System Notes 1 If the markers are lost by the software at any time after they are ini
77. igure 38 Relaxation of the biaxial test system and sutures Both device axes open symbols device axis 1 closed symbols device axis 2 showed minimal relaxation and were indistinguishable from each other 91 3 2 EFFECTS OF STRETCH RATE 3 2 1 Device Control Tension and stretch vs time loading curves were similar among the full range of cycle periods Figure 40 demonstrating that the biaxial device was able to accurately control loading and unloading time for the different cycle periods Additionally the level of test repeatability was found to be quite high as displayed by the close agreement between the first and final 1 second loading unloading protocols Figure 39 Between these two protocols the mean change in AP was found to be 0 006 0 002 and the mean change in was 0 01040 005 demonstrating a high degree of accuracy and reproducibility 92 120 Circumferential Radial 100 Circumferential Verification Radial Verification 80 60 Tension N m 40 20 EAM Ad ALi a M A ASYA A A e 1 0 Ki 1 2 1 3 1 4 Stretch Figure 39 Typical tension stretch curves for the initial and final 1s loading unloading protocols 93 1s 0 1s 14 14 a Circumferential o Circumferential Radial oe Radial 000000000 oo P re c of c 134 13 4 c oe o o o o S q o E 13 om
78. illary Muscles Figure 33 Diagram of the native mitral valve Square specimens were taken from the anterior leaflet with sides parallel to the circumferential and radial axes of the leaflet centered circumferentially and extending radially from just below the annulus to just above the first chordae tendineae attachment site 79 2 3 2 Quasi static biaxial testing Specimens were mounted in the biaxial testing device with the circumferential and radial specimen axes aligned with the device axes Figure 35 within a specimen bath which was filled with PBS and maintained at a temperature of 37 C for the duration of testing Each leaflet underwent 20 preconditioning cycles Figure 34 in which the specimen was stretched such that the membrane tension T defined as the force per unit length of tissue over which it was applied along each specimen edge was increased to 90 N m over a cycle period of 15 seconds then was returned to its original configuration over an additional period of 15 seconds To increase test repeatability all loading cycles were initiated at a tare load of 0 5g and all presented stretch data were referenced to the preconditioned tare configuration which was taken at the 0 5g tare load after the 20 preconditioning cycles After the preconditioned tare reference was recorded specimens underwent either a high speed stretch rate sensitivity testing protocol a stress relaxation protocol or a creep protocol 80
79. imits For This Test 9 9 File Settings Display File Settings You will be prompted to enter these when you start a test Test Name 4 Reference File 147 3 6 Running a Test f Load Control 4 0 vi 5 xj File Edit Operate Tools Browse Window Help eae uj Load Cells Imaging Positioning Test Settings Run Test High Speed Tes 6 1 Run Test Tab Update Image Display Current Cycle Only lt 2 alll Cycles Stretch vs Time ms 1 143 1 123 1 103 TE 6 3 Start Test Cancel Test and Update Image Buttons 6 2 Cycle Display Toggle 6 4 Stretch Graph 6 5 Shear Angle Display 6 6 Loads Graph 10000000 1200000 6 7 Loads vs Stretches Graph 37 697 2 46 103 lg Load g vs Stretch 70 0 6 8 Current Cycle Display 60 0 50 0 6 9 Acquisition Rate Display 40 0 30 0 6 10 Image Load Alias Display 20 0 10 0 0 1 0 990 1 000 1 010 1 020 1 036 1 040 1 050 1 060 1 070 1 080 1 090 1 100 1 110 1 120 1 1304 Current Cycle 1 Acquisition Rate 6 Hz Image Load Alias ms Program Status wes se 6 95 spe 4 gt 148 Section 4 Biaxial Testing Protocols 4 1 General Notes 1 The program can be run by pressing the LabView arrow in the upper left comerof the program window 2 In order to properly shutdown the program press the Stop Program button at the bottom of the screen while the program isin an id
80. ings of Sacks et al in their left heart simulating flow loop 32 In this study the mean circumferential and radial stretches were 1 11 and 1 33 respectively refer to INTRODUCTION as necessary To calculate the maximum stretches for the device requirements the standard deviations of the circumferential and radial stretches 0 07 and 0 16 respectively were multiplied by three and added to the mean values This stretch range was chosen in order to encompass 99 of the MVAL specimens The specification for the maximum specimen stretches calculated in this manner were 1 31 circumferential and 1 80 radial To translate the maximum stretches into displacements they 49 were multiplied by the appropriate maximum expected specimen dimension Maximum specimen dimensions were estimated to be 3 cm x 3cm based on previous experience These dimensions resulted in maximum displacements of 0 93 cm circumferential and 2 40 cm radial These displacements were divided by two to account for the fact that each specimen axis would be stretched by two actuators one on each free edge for maximum displacements of 0 47 cm circumferential and 1 20 cm radial per actuator Using the calculated displacements the maximum necessary displacement rates were calculated by dividing the necessary displacements by the shortest required loading time The in vitro data showed the physiological opening and closing times to be approximately 0 07 seconds so the shorte
81. ion of the stress versus stretch relationship Differences in the stretch energy beneath the stress stretch curves were different for the circumferential and radial specimen axes due to the relatively higher distensibility of the radial axis The slight differences in the areas beneath the loading and unloading curves for the 0 1 second loading time were not significant and furthermore could have been a reflection of the hysteresis of the load cells themselves which was specified as 0 5 percent 116 4 4 STRESS RELAXATION The stress relaxation exhibited in the MVAL was consistent with findings for other collagenous soft tissues 47 48 50 61 62 including findings for the MV chordae tendineae 40 However due to the relatively large change in membrane tension that corresponded to extremely small changes in stretch on both axes near the 90 N m equitension level i e high stiffness further analysis of the results is necessary The main goal of this analysis is to show that the observed stress relaxation was real and was not an artifact caused by small changes in the specimen attachments 1 e specimen sutures pulling out slightly from the specimen edges that could cause minute reductions in the specimen stretches To do this the change in stretch observed over the three hour duration of the biaxial stress relaxation experiments was compared to the change in stretch observed in the unloading phase of the final preconditioning cycle for the sam
82. ism distributed the total force applied by the positioner equally between both pulleys This attachment mechanism was based on the previously reported suture attachment pulley system but improved on that mechanism by ensuring that the orientation of each suture line was aligned with the specimen plane 58 Figure 27 A CAD model of one suture attachment arm A Custom suture attachments were designed to balance the force applied by each carriage through all four suture lines B Specimens were mounted to these attachment arms in a trampoline fashion by attaching two loops of 000 nylon suture to each side of the specimen via four stainless steel surgical staples C Specimen 59 2 1 2 4 Specimen bath The cross shaped specimen bath Figure 28 was designed to allow room for the carriage arm specimen attachment travel required to achieve the necessary specimen displacements The cross shape was used because it minimized the volume of the bath while still allowing adequate travel lanes for the portions of the specimen attachments that reached into the bath The central portion of the bath base contained a custom acrylic specimen viewing window Unlike the rest of the bath this window was highly polished allowing a clear image to be taken from beneath the bath The window doubled as a specimen stand This stand supported the specimen so that it did not move vertically when the applied membrane tensions were not high enough to keep the specim
83. istories a Reproduced from Wineman AS Rajagopal KR Mechanical Response of Polymers Cambridge University Press 2000 39 1 9 3 Hysteresis Hysteresis represents the energy lost when a material is loaded Hysteresis is typically calculated as the ratio of the change in energy between the loading and unloading cycles to the total energy stored in the loading cycle Energy storage is usually determined by calculating the area beneath the loading versus displacement curves 1 9 4 Modeling viscoelastic behavior the Boltzmann superposition principle The superposition principle developed by Boltzmann states that the total stretch response of a material to the application of individual stress histories is the sum of the effect of applying each stress separately In the one dimensional case we may consider a simple bar subjected to a force F t and elongation u t The elongation u t is caused by the total stress history before the current time t If the function F t is continuous and differentiable then in a small time interval dt at time x the increment of loading is dF dt dt This increment acts on the bar and contributes an element du t to the elongation at time t with a proportionality constant c dF z du t c t 7 ds dr 1 If the origin of time corresponds with the beginning of motion and loading then by the contributions of all loading for all time we obtain M dF z u t fett de 2 40
84. ius Acute rheumatic fever Cardiovasc Clin 1993 23 p 3 23 182 13 14 15 16 17 18 19 20 215 22 23 24 Glower D D K P Landolfo R D Davis Y Y Cen J K Harrison T M Bashore J E Lowe and W G Wolfe Comparison of open mitral commissurotomy with mitral valve replacement with or without chordal preservation in patients with mitral stenosis Circulation 1998 98 19 Suppl p 120 3 Baptist Health Foundation I The Autonomic Disorders Mitral Valve Prolapse Center 2003 Webspace Enterprises Kontos J V Papademetriou K Wachtell V Palmieri J E Liu E Gerdts K Boman M S Nieminen B Dahlof and R B Devereux Impact of valvular regurgitation on left ventricular geometry and function in hypertensive patients with left ventricular hypertrophy the LIFE study J Hum Hypertens 2004 18 6 p 431 6 Pierard L A and P Lancellotti The role of ischemic mitral regurgitation in the pathogenesis of acute pulmonary edema N Engl J Med 2004 351 16 p 1627 34 Alfieri O and F Maisano An effective technique to correct anterior mitral leaflet prolapse J Card Surg 1999 14 6 p 468 70 Borer J S and K Kupfer Mitral Regurgitation Current Treatment Options and Their Selection Curr Treat Options Cardiovasc Med 2004 6 6 p 509 517 El Khoury G P Noirhomme R Verhelst J Rubay and R Dion Surgical repair of the prolapsing anterior leaflet in degenerativ
85. ker region as the specimen relaxes For comparison a similar analysis was done using the uniaxial stress relaxation and quasi static unloading data As seen in the biaxial analysis stretch levels for specimen axes 118 under tension increased over the duration of the stress relaxation tests while the quasi static unloading cycles showed decreased stretch levels for the equivalent relaxed membrane tension state Interestingly the stretches on the unloaded axes in the stress relaxation experiments all decreased Figure 53 over the duration of the stress relaxation experiments This result was expected due to the mechanical coupling between specimen axes however and also showed that the stretch measurement system was not biased towards positive changes in stretch in the stress relaxation experiments The changes in stretch observed while extremely small were within the capabilities of the optical measurement system which was able to calculate stretches to with 0 001 see RESULTS This result underscores the importance of performing biaxial experiments on membranous tissues The difference between the change of stretch of the free and loaded axes indicates that the mechanism of relaxation may be different in uniaxial and biaxial experiments In uniaxial experiments increases in stretch level on the loaded axis may be due to time dependent Poisson like effects minimizing the areal tissue stretch while this cannot be the case in biaxial experime
86. l 0 9 0 8 Nomalized tension 0 7 0 6 663 661 D period 659 697 0 7200907405 9017 60 70 80 905 100 Time Minute Figure 56 Normalized membrane tension versus stress relaxation test duration top Collagen D spacing as a function of stress relaxation test duration for the same specimen bottom Reproduced from Liao J Unpublished Communication 128 4 8 STUDY LIMITATIONS One limitation of this study was the optical stretch measurement system This system could only track four or nine markers in the central belly region of the leaflet A more thorough analysis of the stretch state in the entire specimen would provide insight into both the stress relaxation and creep mechanisms In addition to the stretch measurement system the actuation components provided some study limits While these actuation components provided a major improvement over previous biaxial testing devices the component stability at the extremely high speeds necessary for the 0 05 second loading unloading cycles was not sufficient In addition to limits of the device itself in the current study it was assumed that the mechanical properties of the MVAL leaflet were dominated by its passive structural elements collagen elastin and polysaccharides which constitute 85 95 of the leaflet dry wt 64 65 No attempt was made to maintain cell viability within any of the test samples nor was there any effort to trigger an active respo
87. l Testing Software Screens 2 1 Load Control 2 0 Stress Relaxation 10 File Edt Operate Tools Browse Window Help E an Load Cells Imaging Positioning Test Settings Run Test High Speed Test 1 7 HigirSpead Test Tap Bigtg SpeedTest Trigger Teg Stop est ff DiPlacemont 1 0 mm Displacement 2 0 1 2 Stop Test Button Loading Time gio Do Stop Test After 0 s 1 3 Trigger Test Button Stretch vs Time ms 1 50 z 1 407 1 4 Test Statistics Display 1 304 1205 1 5 High Speed Test Toggle 1 107 1 0071 1 U 0 0 1000 0 2000 0 3000 0 4000 0 1 6 Loading Time Input Stretch 1 0 0000 Loads vsTime ms Stretch 2 0 0000 1 7 Test Duration Input 1 8 Stretch vs Time Graph 1 g 1 1 1 0 1 1 1000 0 2000 0 3000 0 4000 0 6000 0 7000 0 8000 0 9000 0 10000 0 11000 0 1 9 Load vs Time Graph Load 1 0 0000 i Load 2 0 0000 i Program Status 172 2 2 Load Control 3 0 High Stretch Rate Testing Eile Edit Operate Tools Browse Window Help 2 1 High Speed Test Tab Load Cells Imaging Positioning Test Settings Run Test High Speed Tes C High Speed Test Trigger Te TET Displa Displacement 2 0 00 mm Speed 1 6 0000 m s Speed 2 0 0000 m s Motor Delay 0 0000 ement 1 0 00 mm 2 2 Stop Test Button Disabled 2 3 Trigger Test Button Loads v
88. laxation data using quasilinear viscoelastic assumptions 49 In contrast to our study in which the observed behavior occurred after stretching the MVAL through the transition phase of the stress stretch relationship Thornton et al observed this relaxation creep imbalance at low stress and were able to properly relate creep and relaxation by incorporating fiber recruitment Our findings suggest that the mechanisms responsible for creep and relaxation in the MVAL may be functionally independent 124 4 7 COMPARISONS TO SMALL ANGLE X RAY SCATTERING RESULTS Recent small angle x ray scattering studies SAXS 63 also from the University of Pittsburgh by Liao et al may shed some light on the microstructural mechanisms responsible for the behavior observed in this study For quasi static loading of the MVAL SAXS results Figure 54 show that the D spacing see INTRODUCTION on collagen structure of the collagen molecules does not increase until the specimen has been stretched into the stress stretch transition zone and collagen fiber uncrimping has been initiated This suggests that components other than collagen itself are primarily responsible for bearing specimen loads at low stretch levels In addition to dynamic loading this study included SAXS analysis of biaxial creep Figure 55 and stress relaxation behavior Figure 56 Our finding that the MVAL did not creep was supported by this SAXS study which also found no appreciable creep in the MV
89. le state 3 In case of an emergency tum off power to the motors and stop the program by clicking the LabView arrow in the upper left comer of the program window 4 Throughout the manual gray numbers in parentheses comespond to labels in the Biax Software Screens section 149 4 2 Setting up the Biaxial Testing Device Notes 1 This protocol assumesthat the device is properly installed and affixed to the testing tabletop During this protocol care should be taken to limit contact and forces applied to the load cells Applying forces greaterthan 150 of full scale to the load cells will result in permanent damage Caution should alwaysbe used around the biaxial testing device Limit switches are in place to prevent the device from damaging itself not you Powerto the motors may be tumed off to allow the device cariagesto be moved manually Powerto the motors must be restored before setting either the low or high calibration points Protocol 1 on powerto all components computer motors light load cells and camera Tum on device computer Launch Biax software a Load Control 1 0 load based test b Stretch Control 1 0 stretch based test Clickon the Load Cell tab 1 1 atthe top ofthe screen Perform steps 6 10 independently on each load cell Checkto make sure that nothing istouching the load cell and proceed to adjust the zero foreach load cell within the inline amplifier u
90. llowing each chamber to function as a positive displacement pump The right atrium fills with blood from the systemic and coronary circulation via the superior and inferior vena cava From the right atrium blood moves into the right ventricle which in turn pumps the blood into the pulmonary circulation where it is oxygenated in the lungs The left atrium fills with blood returning from the pulmonary circulation via the pulmonary veins This blood is pumped into the left ventricle which in turn pumps the blood through the systemic and coronary circulation via the aorta and coronary arteries Each cardiac chamber pumps blood through a one way valve The mitral and tricuspid valves are known as the atrioventricular valves due to their location between the atria and ventricles These valves prevent retrograde flow from the left and right ventricles respectively during ventricular contraction or systole The mitral valve has two leaflets while the tricuspid valve as its name denotes has three leaflets The leaflets of the atrioventricular valves are tethered to papillary muscles located within the respective ventricles via thin tendinous structures known as chordae tendineae A second pair of valves the aortic and pulmonary valves are known as the semi lunar valves These valves each have three leaflets but the leaflets lack the chordal attachments present on the atrioventricular valves The aortic valve is located between the left ventricle
91. ltiplying by unit conversion factor of 101 97 g N to yield peak loads in grams of 275 32 Because the stretch rate sensitivity of the MV tissue was unknown at this point in the design process this value was rounded up to 1000g to account for any stretch rate sensitivity in the stress response of the leaflets 211 3 Stretch amp load measurement frequency Using the 0 05 second minimum loading unloading time the maximum necessary stretch and load measurement frequencies were calculated by dividing the minimum number of data points desired by the 0 05 second duration The minimum number of desired data points was estimated at 25 Approximating the stretch response of the MV leaflet to be roughly linear with respect to time during loading and unloading see INTRODUCTION 25 data points would allow a maximum stretch step of 0 032 between image acquisitions Dividing 25 by the 0 05 second minimum loading duration yielded a necessary stretch measurement frequency of 500 Hz The load frequency was calculated by multiplying the stretch acquisition frequency by 10 This was done to allow each load data point to represent the average of 10 load acquisitions 51 This technique was employed successfully on the previous biaxial testing device to reduce noise levels in the load signal 52 2 1 2 Device design The following section describes the specific components used in the design of the testing apparatus in order to meet the design specifi
92. markers and r and s are the isoparametric coordinates The spatial derivatives of u with respect to r and s can then be calculated as m ou ou Of E gt Un Ae 8 ug Os n n 1 10 which can be substituted into du or or OX Ou as s Os 0 11 to calculate the spatial derivatives of u with respect to x These spatial derivatives form the basis of the deformation gradient tensor F from which and can be determined by fp X 0 X 1 0 ES Ay K So dup EE zn ox 12 This procedure was used to calculate the stretch state of at the center of the marker array 0 0 is the isoparametric coordinate system All reported stretch levels were the levels interpolated at this location For this study four markers a 2 by 2 array were used providing a bi linear interpolation of the displacement field It should be noted that although it was not used the biaxial device also included provisions for 9 marker 3 x 3 array interpolation that could allow bi quadric variation of the displacement field 67 2 1 3 3 Quasi static control Due to the non linear and highly variable mechanical properties of the MV anterior leaflets the only variables that could realistically be controlled in the quasi static testing were the loading and unloading time and the upper peak tensions and lower tare con
93. me grabbers FastFrame 1300 Fast Vision Nashua NH Figure 26 Because of the high frame rates images from the high speed imaging system were not available in real time and could not be used for control purposes Figure 28 A CAD model of the cross shaped specimen bath with specimen window stand 61 Figure 29 The dual biaxial testing device dual camera system These images were downloaded after each test and analyzed separately Both cameras were equipped with 55mm telecentric lenses H52 271 Edmund Optics Barrington NJ which were focused through a 60 40 beam splitter in order to ensure that both cameras maintained identical specimen views The greater portion 6096 of the light was directed towards the high speed 62 imaging system since this system was more sensitive to light intensity levels due to the rapid image acquisition rates it employed The specimens were mounted with an orientation parallel to the specimen plane and a sub specimen 45 angled first surface mirror was used to direct the camera views to the lower specimen surface In addition to acquiring images the high speed frame grabbers received an image acquisition trigger signal from an analog digital converter PCI 6036E National Instruments Austin TX within the device control computer This trigger signal served to synchronize the acquired images with load measurements that were acquired by the device control computer from a pair one on each device axis
94. n System EN E Initialization Quasi Static Quasi Static High Speed Manual Specimen Loading Loop Unloading Loop Functions Positioning Auto Loading High Speed functions are present only in Load Control 2 0 3 0 and 4 0 164 Section 8 System Specifications 0 1kg per carriage Actuator Max Speeds Actuator Acceleration 25 m s 2 165 APPENDIX C HIGH SPEED BIAXIAL TESTING MANUAL 166 Biaxial Testing Manual High Speed Testing Supplement Author s Jonathan Grashow Version 1 0 Original Release Date 3 16 05 Last Revision Date N A 167 Contents Section 1 General Information 1 1 Waming 1 2 Program Descriptions Section 2 High Speed Biaxial Testing Software Screens 2 1 Load Control 2 0 Stress Relaxation 2 2 Load Control 3 0 High Stretch Rate Testing 2 3 Load Control 4 0 Creep Section 3 High Speed Biaxial Testing Protocols 3 1 Stress Rela xation 3 2 High Stretch Rate Testing 3 3 Creep Section 4 High Speed Biaxial Tester Output Files Need to Add 168 Section 1 General Information 1 1 Waming Please note that the high speed biaxial testing programs Load Control 2 0 Stress Relaxation Load Control 3 0 High stretch rate testing and Load Control 4 0 Creep are much more involved than the standard quasi static Biaxial Testing programs These three programs were all used to complete high speed testing on the native Mitral Valve leafl
95. nal cycle of the quasi static protocolto ensure that nothing abnormal occured and that the camage displacements resulted in a condition very close to the desired loads If you are using the high speed camera to track stretc hs during the initial loading phase ensure that the camera isready to receive the analog trigger signal from the biaxial testing software Pressthe Trigger Test button The specimen should be loaded in the user defined duration and the stretches and loads should be plotted in real time on the screen 10 The test will continue for the user specified duration unless you select the Stop Test button 1 2 180 Section 4 High Speed Biaxial Tester Output Files Stress Rela xation lt ilename gt _first_second hsbx This file contains the first second of data from stress rela xation test File column headings are Time ms Load 1 units selected in Test Settings Tab Load 2 units selected in Test Settings Tab Hlename entire testhsbx This file contains all data from the stress relaxation test File column headings are Time ms Stretch 1 Stretch 2 Shear Angle degrees Load 1 N or g Load 2 N or g Tension 1 N m Tension 2 N m Stress 1 kPa Stress 2 kPa High Stretch Rate Testing Each data file for the High Stretch Rate testing includes time and load data for approximately 2 x the half cycle time 1 additional second of data all at the noted acquisition rate File Heading
96. nd found that the rate of relaxation was nonlinearly inversely proportional to the stretch level and that the rate of creep was nonlinearly directly proportional to the applied stress Dunn and Silver 48 showed that the amounts of relaxation in aorta skin tendon dura matter and pericardium were all dependent on stretch level In contrast to these two studies Lee et al 46 found that the percentage of stress remaining in glutaraldehyde stabilized porcine aortic valve strips after a 1000 second uniaxial stress relaxation test was independent of initial load In their study of the rabbit MCL Thornton et al observed an imbalance between stress relaxation and creep rates of MCL specimens initially loaded to the same level 49 To quantify their results Thornton et al fit the MCL relaxation data with a quasilinear viscoelastic QLV model and used this model to predict the MCL creep behavior A comparison to the actual creep data showed that the QLV formulation predicted much higher creep percentages than those actually observed 150 predicted versus 115 observed These findings were supported by the findings of the previously mentioned study by Provenzano et al 47 in which the rate of stress relaxation proceeded approximately two times faster than the creep rate in the rat MCL when contralateral ligaments were tested simultaneously Vesely et al 50 expanded on these findings by showing that the stress relaxation behavior of porcine aortic valve cusp
97. nd posterior leaflets known as commisures in order to create a larger mitral orifice Replacement of the MV with a prosthetic valve may be superior to repair in this case Patients who undergo MV replacement have a reduced need for additional procedures in the first ten years following implantation 13 1 4 2 Mitral valve regurgitation The most common valve disorder affecting five to twenty percent of the population 14 is mitral valve prolapse MVP Figs 8 9 in which the MV leaflets coapt improperly and allow leakage from the ventricle into the atrium during systole In MVP one or both of the leaflets typically extend above the plane of the atrioventricular junction during ventricular contraction In the United States MVP results in 4000 mitral valve surgical procedures 25 of all cases 1000 cases of endocarditis 10 of all cases and 4000 cases of sudden death 3 Symptoms of MV prolapse may include chest pain palpitations dyspnea fatigue and dizziness Acute cases of MV leakage may trigger the onset of cardiogenic shock while chronic mitral regurgitation may affect the geometric structure of the ventricle 15 and may lead to pulmonary edema 16 MVP is often correlated with symptoms of myxomatous mitral valve disease such as opaque and thickened leaflets and chordal elongation thinning and rupture Current treatment for the diseased MV includes surgical repair and valve replacement Repair techniques include partial leaflet
98. ng and unloading phases with different cycle times essere 102 Figure 46 Typical membrane tension versus time curves for the first 500 ms of a biaxial stress relaxation experiment The biaxial stretching mechanism was able to load the specimens within the allotted 100 ms rise time with minimal vibrations and overshoot 104 Figure 47 Membrane tension versus time curves for a typical stress relaxation experiment Membrane tension levels at 3 hours were statistically less than those immediately after loading 100 ms Tor both specimen axes 106 xiv Figure 48 Relaxation percentage for different test groups and specimen axes Relaxation was observed in both uniaxial and biaxial experiments however the amount of radial relaxation was significantly greater in the biaxial experiments and the circumferential and radial relaxation percentages were not statistically different in the uniaxial experiments as they were in the biaxial experiments dans ciu eR ER EAT IA Eae D HARUM RU Ud 107 Figure 49 The one phase reduced relaxation model fit both the uniaxial pictured and biaxial relaxation data very well for both the circumferential and radial pictured axes 109 Figure 50 Stretch versus time curves for a typical biaxial creep experiment Minimal relaxation was observed on either axis Note the anisotropic leaflet behavior exhibited by the relatively higher
99. nomenon is called hysteresis These behaviors are all features of a mechanical property called viscoelasticity 36 On its most basic level viscoelasticity suggests that the time dependent mechanical properties of a material are dependent on the deformations to which the particular specimen has been previously subjected a classification often termed stretch history dependence Currently the viscoelastic properties of the MV leaflets remain largely unstudied mainly due to the complexity of the necessary experimental protocols 36 Generally one of three main theories is used to describe the viscoelastic mechanisms in soft tissues 1 Time dependent reorientation of collagen fibers within a viscous matrix 2 Molecular relaxations within the GAG matrix 3 Molecular relaxations within the collagen fibers themselves The following subsections give information on viscoelastic testing in general 1 9 1 Stress relaxation testing Stress relaxation experiments Figure 22 typically include a rapid loading phase to a desired stretch level after which the material stretch state is held constant The maintenance of a constant stretch state has special implications for typical biological materials including the MV leaflet the lack of change in the stretch state of the material limits the ability of the fibers within a tissue to reorient themselves for the duration of the test Thus changes in the specimen loading state require
100. nse from the leaflet with an appropriate chemical stimulus It was recently demonstrated in flexure that native aortic valve interstitial cells can contribute to leaflet stiffness 66 However the forces generated here are at several orders of magnitude lower than those experienced by the MVAL ECM components However changes in leaflet deformation in an in situ preparation 8 suggest some contribution by the leaflet cells While additional work in this is required to clarify issue it is unlikely that cellular forces contribute substantially to the MVAL mechanical response We note finally that only equitension protocols were performed in the present study However given the close agreement with normal physiologic stretches this should be sufficient for characterizing the physiologically relevant viscoelastic properties of the MVAL 129 4 9 CONCLUSIONS The results of this study highlight the need to perform creep tests on soft tissues Although generally more difficult to perform creep experiments are more representative of the physiologic conditions of most soft tissues and as demonstrated by our results creep behavior may be radically different from relaxation behavior Furthermore our results underscore the importance of performing mechanical tests on soft tissues using the appropriate loading condition which in the case of membranous soft tissues usually consists of a biaxial loading state This study has provided insight into the
101. nt with the stretches observed by Sacks et al 32 in a left heart simulating flow loop The close agreement of the peak stretches observed at the 90 N m equitension state and the peak stretches observed in the left heart simulating flow loop when the MVAL was in the closed configuration suggested that the 90 N m peak equitension biaxial loading state was reasonably representative of the maximum physiologic stress state The close agreement observed between the ratio of circumferential and radial stretches at the 90 N m equitension state compared to those observed in vitro for the functioning MVAL was of particular importance because it implied that 114 the rotational kinematics of the underlying fiber structure were comparable to those of the MVAL in vivo 4 3 STRETCH RATE EFFECTS One of the primary findings of this study was that the stress stretch behavior of the anterior MVAL was independent of stretch rate in both the circumferential and radial directions over the full range of cycle periods from 15 seconds to 0 05 seconds studied This result was in close agreement with the results reported by Naimark et al 59 that showed no significant stretch rate dependence in the stress stretch relationship of mammalian pericardia for stretch rates between 1 and 100 second Naimark suggested that the lack of stretch rate dependence may be due to the pseudo plastic shear thinning of the glycosaminoglycan matrix surrounding the collagen fibers Conv
102. ntil the voltage 1 2 forthe cell reads 0 Using the calibration arm hang a weight and adjustthe load cell gain within the amplifier See amplifier manual for details such that the span of the load cell output voltage is maximized forthe load range for yourtest a If itisnecessary itis possible to mechanically amplify the load signal by mounting the load cell closerto the carriage arm pivot Rough 150 amplifications are from upperto lower mounting position 1 1 1 14 1 1 33 1 1 6 1 8 With no force on the load cell check to make sure that 0 is entered next to the low indicator 1 3 forthe appropriate axisand click the set button 9 Hang an appropriate weight from the calibration arm enterthe weight next to the high indicator 1 3 forthe appropriate axisand clickthe set button 10 Repeat steps 8 and 9 until the loadsdisplayed in the Loads graph 1 4 are correct and repeatable 11 Click the Save button 1 5 to save the calibration file If you choose not to save the calibration file and the computer crashes or freezes you will have to repeat the load cell calibration a You can reload any calibration file by click the Load button 1 6 and selecting the desired calibration file 151 4 3 Preparing the Specimen Notes 1 The biaxial tester is designed to test specimensthat range in size from 0 7 x 0 7c m to 4 0 x 4 0 cm 2 Specimens should be properly hydrated throughout preparation procedu
103. nts since the stretch on both axes increases In biaxial experiments the observed relaxation was greater in the radial direction than the circumferential direction This discrepancy may be linked to the higher distensibility of the MVAL in the radial direction in order to achieve the desired 90 N m equitension state the required stretches in the radial direction were generally approximately 3 times greater than those required in the circumferential direction 119 0 015 Circumferential Specimen Axis 555 Radial Specimen Axis 0 010 0 005 0 000 Change in Stretch 0 005 0 010 0 015 Circumferential Stress relaxation Radial Stress relaxation Figure 53 In uniaxial stress relaxation experiments stretch levels increased for axes under tension and decreased on the free axis Data presented as mean SEM In their study on ligament viscoelasticity Provenzano et al 47 found that the uniaxial relaxation of the rat medial collateral ligament MCL was highly dependent on stretch level However in contrast to our findings the observed relaxation decreased as the initial stretch level increased Additionally the results of Provenzano et al showed that the influence of stretch level on the relaxation behavior diminished after stretch levels increased to a level beyond the transition phase generally attributed to collagen recruitment in collagenous soft tissues as shown in our earlier work the 90 N m equitension s
104. o T measured f 13 68 In this formulation v is the corrected carriage velocity Ve is the corrected carriage velocity Tpeak is the peak membrane tension and C is a user defined correction factor typically 0 3 for the MV leaflet The correction factor was used in many of the correction algorithms as a method to decrease the magnitude of the correction This factor allowed the user to tune the correction algorithms and was very helpful when making corrections to the MV leaflet due to its highly nonlinear mechanical behavior In essence the correction factor allowed this linear velocity correction to incrementally make the necessary nonlinear correction over a number of cycles while reducing the propensity of the correction algorithm become stuck in over and under correction patterns that are common when linear corrections are made and nonlinear corrections are necessary Additionally this correction factor helped reduce the propensity of the correction algorithm to become stuck in over and under correction patterns due to the simultaneous corrections and therefore related coupling effects on both specimen axes If instead of underestimating the system overestimated the required carriage velocities a different correction was made Ifthe carriage velocities were too high the specimen was not stretched for the entire prescribed loading period Instead the carriages were stopped once one or both of the specimen axes reached the desired pe
105. o acquire stretch data in the loading phase of testing then engagesthe standard digital camera to measure stretchs forthe remainderof the test Load Control 3 0 High Speed Loading Unloading This program runs a series of quasi static cyclesto user defined load limits After the final quasi static cycle the program can be set to rapidly load and unload the specimen from the preload state to the displacements that were determined to correspond to the load limits in the final quasi static cycle The specimen will be subsequently loaded and unloaded in 1s 0 5s 0 25s 0 1s 0 05s and 15 cycle times This program triggers the high speed camera to acquire stretch data during the high speed testing Load Control 4 0 Creep 170 This program runs a series of quasi static cyclesto user defined load limits After the final quasi static cycle the program can be set to perform a creep test in which the specimen wil be stretched from the preload state to the displa cements that were determined to correspond to the load limits in the final quasi static cycle The specimen is loaded in a user defined time after which a loading algorithm is engaged to maintain the specimen loads at user defined levels forthe duration of testing This program triggersthe high speed camera to acquire stretch data in the loading phase of testing then engagesthe standard digital camera to measure stretchsforthe remainder of the test 171 Section 2 High Speed Biaxia
106. o measure the performance of the stretch measurement system artificial marker arrays with known deformations were created using SolidWorks CAD software The prescribed stretches were chosen to be representative of the physiologic stretch levels observed in the MV anterior leaflet These marker arrays were printed onto paper and the individual printed paper marker arrays were placed on the specimen window facing down All of the marker tracking methods that were used on actual specimens see Marker tracking were carried out on the paper marker arrays The specimen stretches calculated by the biaxial testing software were then compared to the prescribed stretches to evaluate the accuracy of the marker tracking method 72 2 2 2 Load cell calibration Load cells were calibrated using a custom calibration fixture Figure 32 which allowed weight standards to be applied to the specimen attachments This custom fixture attached to the side of the specimen bath and contained 2 pulleys Using these two pulleys the weight of a standard could be redirected via suture similar to that used in actual testing to the specimen attachment suture pulleys A two point calibration procedure was carried out using weights of 1 kg and no weight 0 load condition until the calibration was repeatable then the linearity of the load cells was tested by hanging a 500 g weight The weight of the paper clip attachment was 1 3 g and was compensated for in the calibration and
107. o track 4 or 9 Move to step 3 ofthe image setup boxand click the initialize button to launch the subregion initialization Using the mouse draw a boxaround each markerin the image window that appears clicking the OK button afterdrawing each box A textual 154 description of the marker you should be selecting is written in the upper right hand comer of the marker initialization window Note that the marker subregions should not overlap and the markers should be the only objects each subregion Upon retuming to the main screen after completing the marker initialization the marker subregions that you drew should be ovenayed in green on the image window Move to step 5 of the image setup boxand click the tum on marker tracking button Move to step 6 of the image setup box and adjust the upperand lower marker size thresholds until the software recognizes all markers You can tell if the software recognizesa marker by looking forthe presence ofa small green crossin the center of the marker Additionally recognized markers should be plotted on the Marker Positions graph 2 3 10 Move to step 7 ofthe image setup boxand clickthe Lock Subregions button This will centerthe marker subregions on the markers and force the marker subregionsto translate with the markers such that the markers remain centered within their respective subregions 155 4 6 Setting a Preload Notes 1 The automatic preload
108. ond loading in the creep test were again calculated by appropriately scaling the quasi static carriage velocities The difference between the creep experiment and the stress relaxation experiment was that after the initial loading was completed another algorithm was used to move the device carriages such that the 90 N m equitension state was maintained for the duration of the test The creep algorithm recalculated this carriage velocity approximately 10 times per second using the following formula V x 90 EE T iuba XS 15 where V is the carriage velocity Tmeasurea is the current membrane tension and S is a scaling factor that converts the membrane tension difference into the appropriate velocity In this formulation negative carriage velocities corresponded to compressions while positive carriage velocities corresponded to stretches As in the quasi static tension control the carriage velocity 71 for each axis was evaluated separately ignoring any mechanical coupling effects between specimen axes The creep algorithm relied heavily on the fact that the MV was not sensitive to stretch rate Had this not been the case the initial loading would not have brought the specimen to the desired 90 N m equi tension state and the effectiveness of the creep control algorithm to effectively correct such a possibly large discrepancy is questionable 2 2 CHARACTERIZATION OF DEVICE PERFORMANCE 2 2 1 Stretch measurement system In order t
109. operties of soft tissues 4 5 CREEP The results of our creep experiments showed that despite the observed relaxation behavior the MVAL did not exhibit a functionally significant degree of creep The small amount of creep that was observed over the three hour time period was statistically insignificant for all time points except 3 hours on the radial specimen axis only However creep at this distant time point is irrelevant to the physiologic loading cycle of the valve which occurs over approximately 0 5 seconds during ventricular systole The lack of creep observed in the MVAL was inconsistent with previous findings for ligament 47 49 pericardium 62 and AV leaflet 46 which all exhibited a much greater degree of creep than that observed in the MVAL It should be noted again that these experiments were all performed under uniaxial tension and that it is unclear whether the differences observed in our creep experiments are due to material differences or due to differences in loading condition 123 4 6 RELATIONSHIP OF STRESS RELAXATION AND CREEP The presence of disproportionate degrees of creep and relaxation behavior has been observed although to a lesser degree than was observed in this study previously Provenzano et al observed that the rate of relaxation proceeded faster than the rate of creep in contralateral ligaments while Thornton et al reported a similar finding and showed that ligament creep could not be predicted from re
110. or the relaxation and creep protocols the device carriages 82 were returned to displacements required to stretch the specimen to the 90 N m equitension state in the preconditioning cycles in a rise time of 0 1 seconds The 0 1 second rise time was chosen because it was very close to the physiologic rise time and was slow enough that any vibrations associated with rapid carriage decelerations at the peak loading state were limited 2 of the peak load In the stress relaxation protocol the device carriages were then locked in the displaced positions and the specimens were allowed to relax for 3 hours For the creep protocols after reaching the 90 N m equitension state the membrane tensions in both the circumferential and radial directions were sustained for 3 hours by adjusting the carriage positions at a rate of approximately 10 Hz in order to maintain the desired membrane tensions This was accomplished by displacing each axis independently at a rate V given by V C 90 Tm where C is a tuning constant and Tm is the measured membrane tension on the axis to be adjusted For this formulation positive values of V corresponded to stretches while negative values of V corresponded to compressions Satisfactory maintenance of the 90 N m equitension state see RESULTS Table 4 was achieved by evaluating and adjusting each axis independently ignoring any mechanical coupling between the circumferential and radial specimen axes Each specimen was used
111. owse Window Help CN aaen Load Cells Imaging Positioning Test Settings Run Test High Speed Test 2 1 Imaging Tab Image Setup 2 2 Image Setup QE wie 2 Number of Markers 9 gt 2 3 Marker Positions Graph 3 Initialize Marker Subregions 2 4 Set References 4 Marker Color Dark C_ Light 5 Turn on Marker Tracking GD 2 5 Save Reference File 8 6 Define Marker Size OTTO OT ETT o 1000 200 7 Lock Subregions gt 2 6 Compare References Program Status Loading Specimen Spe 6 95 Spe a 144 3 3 Specimen Positioning Load Cells Imaging Positioniig Test Settings Run Test High Speed Test 3 1 Positioning Tab Free Movement ee ee eme D 3 2 Free Movement Buttons X1 C Dp C 3 CC n 3 3 Motor Speed Scroll Bar id t ic i 3 4 Reset Motors Button Motor Speed mm s GEM amm RI 0 1 2 3 4 5 3 5 Preload Units Preload Settings Enter specimen dimensions before applying tension a ESS Preload Units Load 9 Allowable Error 20 050 g 3 6 Allowable Error amp Preload Inputs Load N Tension N m Stress kPa al X2Preload X1 Preload Jj 0 500 3 7 Apply Load amp Cancel Buttons 3 8 Loads Graph 3 9 Program Status Display 145 3 4 Test Settings Load Control gt Load Control 4 0 vi Bile Edt Operate Tools Browse Window Help
112. pair of positioners is aligned to stretch a 140 centered tissue sample along each device axis Each linear positioner is driven by a rotary stepper motor OS22B SNL10 Parker Hannafin Corp Irwin PA and each stepper motor is controled with a microstepping drive E AC Parker Hannafin Corp Irwin PA that provides a step resolution of 50 800 steps per revolution which when coupled to each aforementioned linear positioner results in a spatial resolution of approximately 0 394 um for each positioner camage All the microstepping drives are controlled via a 4 axis PCI motion controller card DMC 1740 Galil Motion Control Inc Rocklin CA that is installed in the device control PC Precision 550 Dell Inc Round Rock TX Custom attachment arms are mounted onto the carriage of each linear positioner in order to provide a mechanism for specimen attachment Leaflet specimens are mounted to these attachment arms in a trampoline fashion by attaching two loops of 000 nylon suture to each side of the specimen via four stainless steel surgical staples see specimen mounting procedure attachment arms are designed to fasten the two specimen suture loops and to transmit the total load applied by each actuator evenly through all of the attached suture lines To accomplish this each attachment arm is fumished with a pairof custom stainless steel pulleys which are free to rotate ensuring that the forces applied through each pulley are balanced betw
113. paring the Specimen 4 4 Mounting the Specimen in the Biaxial Testing Device 4 5 Setting Up the Imaging System 4 6 Setting a Preload 4 7 Running a Test Section 5 Bia xial Tester Output Files Section 6 Software Drivers amp Virtual Channels Section 7 System Dia grams 7 1 System Overview 7 2 System Orientation 7 3 Motor Wiring Diagram 7 4 Load Cell Wiring Diagram 7 5 Software Overview Section 8 System Specifications 138 Section 1 Background Material Biaxial testing and analysisisa complicated and delicate process The following articles are strongly suggested for anyone planning to perfom biaxial experiments For General Information on Biaxial Testing 1 Sacks MS Sun W Multiaxial mechanical behavior of biological materials Annu Rev Biomed Eng 2003 5 251 84 Epub 2003 Apr 18 Review 2 Sacks MS A method for planar biaxial mechanical testing that includes in plane shear J Biomech Eng 1999 Oct 121 5 551 5 For Information on Optical Stretch Measurement Technique 1 Hoffman AH Grigg P A method for mea suring stretches in soft tissue J Biomech 1984 17 10 795 800 For Examples of Biaxial Experiments 2 Gloeckner DC Sacks MS Fraser MO Somogyi GT de Groat WC Chancellor MB Passive biaxial mechanical properties of the rat bladder wall after spinal cord injury J Urol 2002 May 167 5 2247 52 3 Billiar KL Sacks MS Biaxial mechanical properties of the natural and glutaraldehy
114. per motors b screw driven linear actuators c load cells d specimen bath outlet e specimen bath inlet f heating element maintained bath temperature at 37 C g high speed digital camera h standard digital camera 1 beam splitter j sub specimen mirror 55 Figure 26 Two computers used to control the biaxial testing device 57 Figure 27 A CAD model of one suture attachment arm Custom suture attachments were designed to balance the force applied by each carriage through all four suture lines B Specimens were mounted to these attachment arms in a trampoline fashion by attaching two loops of 000 nylon suture to each side of the specimen via four stainless steel surgical Staples C Specimen eq orici aeter ed c aan ot ebbe ule t cd oie t ce qx iosa 59 Figure 28 A CAD model of the cross shaped specimen bath with specimen window stand 61 Figure 29 The dual biaxial testing device dual camera system sse 62 Figure 30 A sample bitmap showing four markers black and the user defined marker s bregions NOT CEN seeded eat midst 64 Figure 31 Marker coordinates were mapped into an isoparametric coordinate system 66 Figure 32 A photograph of the calibration fixture mounted on the bath 74 Figure 33 Diagram of the native mitral valve Square specimens were taken from the an
115. proximately 0 394 jum for each positioner carriage All stepper motors were controlled via a 4 axis PCI motion controller card DMC 1840 Galil Motion Control Inc Rocklin CA that was installed in the device control PC Precision 550 Dell Inc Round Rock TX Figure 26 56 Stepper Motion Motors Controller Load Analog Digital PERO Converter M High Speed Camera Trigger High Speed Digital Camera High Speed Camera Computer Figure 26 Two computers used to control the biaxial testing device 57 2123 Specimen attachments Custom attachment arms Figure 27 were mounted onto the carriage of each linear positioner in order to provide a mechanism for specimen attachment Leaflet specimens were mounted to these attachment arms in a trampoline fashion by attaching two loops of 000 nylon suture to each side of the specimen via four stainless steel surgical staples The attachment arms were designed to fasten the two specimen suture loops and to transmit the total load applied by each actuator evenly through all of the attached suture lines To accomplish this each attachment arm was furnished with a pair of custom stainless steel pulleys which were free to rotate ensuring that the forces applied through each pulley were balanced between both of the surgical staple attachments for the attached suture loop Both pulleys were mounted symmetrically on either side of a central stainless steel ball bearing This mechan
116. r 3 0 0 3014 National Instruments IMAQ Vision 6 0 National Instruments IVI Engine 1 6 National Instruments Labview Run Time 6 0 National Instruments Labview 6 0 National Instruments NI Spy 2 0 0 16 National Instruments NI 488 2 Software 1 60 National Instruments NI DAQ 6 9 3f3 National Instruments NI IMAQ Software 2 5 5 National Instruments NI IMAQ for 1394 1 5 National Instruments NI PAL Software 1 6 3f0 National Instruments NI VISA 3 0 Galil Motion Control DMC 18x0 Motion Controller Driver 4 0 3 0 Virtual Channels Channel Type Name Description Analog Input X Axis Load Cell Differential Channel 0 Analog Input Y Axis Load Cell Differential Channel 1 Channel 0 DACOOUT Analog Output negative trigger High Speed System Only Channel 1 DAC1OUT Analog Output positive trigger High Speed System Only Biaxial Software Versions Load Control 1 0 Quas static load control Load Control 2 0 Quasistatic load control Stress Relaxation Load Control 3 0 Quas static load control High stretch rate testing Load Control 4 0 Quasi static load control Biaxial Creep Stretch Control 1 0 Quasistatic stretch control 160 Section 7 System Diagrams 7 1 System Overview Biaxial Testing Device Device Control PC a Load Cell Data Acquisition Amplifiers Card Stepper Motors Motor Drivers ICM AMP
117. radial axes were fit quite well Figure 49 with the one phase reduced relaxation model with an value of 0 996 0 002 for all specimens Model parameters for all specimen fits are presented in appendix A Experimental data 0 83 0 67 Gr 05 0 33 0 17 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 1 104 Time s Figure 49 The one phase reduced relaxation model fit both the uniaxial pictured and biaxial relaxation data very well for both the circumferential and radial pictured axes 109 3 3 5 Creep The high degree of mechanical anisotropy in the leaflet as seen in the stretch rate sensitivity protocols was also observed in the creep experiments Specifically peak stretches at the 100 ms time point were 1 12 0 014 in the circumferential direction and 1 36 0 048 in the radial direction In sharp contrast to the relaxation results the observed creep was minimal in both the circumferential and radial specimen axes Figure 50 Mean stretches in the circumferential direction stayed constant over the entire three hour test duration and were minimal in the radial direction Creep percentages Figure 51 were not statistically different from zero at any time point in the circumferential direction and were statistically different from zero only for the 3 hour time point in the radial direction Table 5 110 14 1 3 1 2 1 1 1 0 0000000000000000000000 R0IIm d o Pr ARIA IAAT 0 5
118. radial stretch required to maintain the 90 N m membrane tension 111 Figure 51 Creep percentages were not statistically different from zero for any time point on the circumferential or radial ARCS ceo ioe edocuit he men DU Soo itd dint ume dne 112 Figure 52 Changes in stretch over the three hour duration of the stress relaxation experiments compared to the changes in stretch required to reach the same membrane tension in quasi Static nloadine Cy Cle sae dae nb S toda Mea cer LE iam Nl a enon M UE 118 Figure 53 In uniaxial stress relaxation experiments stretch levels increased for axes under tension and decreased on the free axis Data presented as mean SEM 120 Figure 54 Changes in collagen D spacing as a function of membrane tension left Membrane tension versus areal stretch 96 for the same MVAL specimen Reproduced from Liao J Unpublished ite e haa daas 126 Figure 55 D spacing as a function of creep experiment duration left Areal stretch as a function of creep test duration for the same specimen right Reproduced from Liao J Unpublished Communication ter etr t meer reden etr etx ute eel ev et eder eo ERA aeneus 127 Figure 56 Normalized membrane tension versus stress relaxation test duration top Collagen D spacing as a function of stress relaxation test duration for the same specimen bottom Reproduced from Liao J Unpublished
119. rate protocols on a single leaflet are shown in the four separate panes of Figure 43 Stretch energy storage during loading and dissipation during unloading were minimal due to the extremely nonlinear mechanical behavior of the MV leaflet As shown in Figure 44 larger amounts of energy were stored in the leaflet at lower tension levels due to the relatively higher level of extensibility of the leaflet tissue at lower stretch levels The area beneath the membrane tension versus areal stretch curves Figure 45 were not statistically among different cycle times for either the loading or unloading phases Hyteresis levels loading energy minus unloading energy were significantly greater than zero for the 15s and 0 1s cycle times only p 0 01 98 15 seconds 100 4 e g 80 4 v 91 o 2 id x 1 40 4 E A D td A 2 54 0 F me 1 0 14 12 1 3 us Stretch 1 second 100 4 v e A 5 y 60 4 z v z 40 4 v v A 20 4 9 vA 4 ow T T T 1 0 14 12 1 3 14 Stretch 99 0 5 seconds 100 8 i e 80 v s A 60 vA 2 w ke vA 40 5 A VA e MS Q v 20 M WA Q X vna yyy 1 0 1 1 1 2 1 3 1 4 Stretch 0 05 seconds 100 4 A 6 ie 80 4 6 MA v g vA ES w ES 9 SE 2 d 8 vA 40 4 vA 3 Y a s A 20 4 v E 0 MNT T T T 1 0 1
120. re by submerging them in the appropriate fluid asneeded Protocol 1 Prepare specimen for dissection e Thaw frozen specimens atthe appropriate temperature e Rinse and clean specimens if needed 2 Cutout region for biaxial testing from sample e Biaxial specimens should be rectangular in shape 3 Insert suture staples along each side of the specimen e 2suture loops consisting of a total of 4 suture staples should be attached to each side of the specimen e Care should be taken to space the 4 suture staples evenly across each specimen edge e Insert suture staplesatleast 1 mm away from the edge to prevent sutures from ripping out during testing This spacing recommendation isa general rule and may have to be increased for materialsthat rip easily 4 Glue orotherwise attach markersto the central region of the biaxial testing sample e The biaxial software can track either 4 in a 2x2armay or9 in a 3x 3 array markers e The markerarray should be applied to the central region of the sample spaced away from the suture staples to ensure an even stress distribution within the marker region e Markerscan be dark on a light specimen orlight on a dark specimen Adequate contrast between the specimen and the markers is crucial to the successof the experiment 152 4 4 Mounting the Specimen in the Biaxial Testing Device Notes 1 2 The mounting processis considered by many to be the crux of biaxial testing It requires pat
121. re plotted in green on the device computer monitor specimen image display in real time so that marker tracking could be visually confirmed Once markers were located their precise image coordinates were calculated as the center of area of the pixels below the image intensity threshold 2 1 3 2 Stretch calculation The stretch calculation method used is well documented for soft tissues 53 54 First consider this generalized homogenous biaxial deformation A 4X1 k1X 2Xo Kk2X1 8 where X and x are the location of a particular material particle in the reference and deformed configurations respectively is the stretch ratio and describes the in plane shear angle 65 C151 1 1 1 1 1 1 Figure 31 Marker coordinates were mapped into an isoparametric coordinate system In the biaxial testing protocol X where n is the marker number are the pixel coordinates of the marker positions in the reference configuration and x are the time dependent marker coordinates calculated during the test Shape functions are used to map the real pixel coordinates into an isoparametric coordinate system Figure 31 such that the marker displacements u can be calculated as the linear sum of the isoparametric shape functions u r falr s us n l 9 66 where f is the set of isoparametric shape functions m is the total number of markers n denotes a specific marker in the set of m
122. relaxation in the radial direction may be due to the fact that a relatively larger percentage of the total stress on the radial axis is borne by the GAGs suggesting that interfibrillar GAG connections may preferentially resist shearing forces between individual fibrils related to circumferential relaxation in the MVAL and may be weaker when stressed orthogonally to the preferred collagen orientation as they would be in response to radial stretch Additional support for this idea may be supplied by our uniaxial stress relaxation data In the uniaxial case we observed significantly less radial relaxation than was observed for the biaxial relaxation protocols This may be due to the fact that fiber rotations were not restricted in the uniaxial experiments allowing fibers to reorient themselves in a direction more parallel to the loaded specimen axis This fibrillar reorientation would also reorient the proteoglycan linkages allowing them to resist shearing relaxations Another hypothesis is that the GAG resistance to relaxation is not directionally dependent at all but instead is dependent on areal stretch level If this is the case uniaxial stress relaxation may not be as sensitive to stretch level because the free dimension may contract as the tissue is loaded effectively minimizing the areal stretch In either 122 case it is clear that the proper biaxial loading condition is critical when evaluating the physiologically functional viscoelastic pr
123. resection chordal transplantation chordal shortening insertion of artificial chordae and edge to edge leaflet apposition 17 21 These methods are 17 usually accompanied with annuloplasty 22 23 which is thought to increase the durability of the repair by stabilizing the valve 24 18 DIASTOLE SYSTOLE 4 Figure 8 A B 2D echocardiographic images of mitral valve regurgitation in diastole and systole respectively C Color flow Doppler image showing the eccentric jet of regurgitation Reproduced from Otto CM Valvular Heart Disease Elsevier Inc 2004 19 ESPVR Aortic regurgitation Mitral regurgitation Pressure Passive diastolic pressure volume relation Figure 9 Typical Pressure Volume loops for the normal heart mitral regurgitation and aortic regurgitation Reproduced from Otto CM Valvular Heart Disease Elsevier Inc 2004 20 1 5 PROSTHETIC VALVE REPLACEMENTS In many instances damage to the MV is too severe for the valve to be effectively repaired and the valve must be replaced with a prosthetic valve Mechanical valves are completely fabricated from synthetic materials Figure 10 These implants pose an increased risk of thromboembolism so that patients require continuous anticoagulation therapy for the lifetime of the implant Additionally the hemodynamic characteristics of mechanical valves do not perfectly duplicate those of the native valve often causing hemolysi
124. s Figure 10 On X bileaflet pyrolytic carbon mechanical aortic valve MCRI Inc 21 Bioprosthetic alternatives Figure 11 made of biologically derived chemically modified collagenous tissues greatly reduce the risks associated with mechanical valves but have limited durability and may require anti calcification treatment to prevent material failure 25 Figure 11 Porcine aortic valve Edwards Lifesciences 22 1 6 VALVULAR COORDINATE SYSTEM The coordinate system used to describe orientation with respect to the valve is typically based on the circumferential and radial specimen axes Figure 12 The circumferential direction describes the axis that would be created by following the mitral orifice about its circumference while the radial direction is defined as the direction orthogonal to the circumferential axis which typically is parallel to the path from the atrium into the ventricle radial Cut here Anterior Leaflet Posterior Leaflet Figure 12 A drawing looking down on the mitral orifice showing the circumferential and radial specimen axes Reproduced from Reproduced from May Newman and Yin Biaxial Mechanical Properties of the Mitral Valve leaflets American Journal of Physiology 1995 23 1 7 MITRAL VALVE DYNAMICS The proper and coordinated action of each of the components of the MV apparatus Figure 13 is critical to the normal function of the valve 26 28 The majority of blood flow
125. s was highly dependent on the initial rise time As seen in the stretch rate sensitivity literature it is clear that the creep and relaxation responses in different studies are highly tissue specific Additionally the experimental factors such as initial rise time initial stretch load level and test duration heavily influence the results 45 1 10 MOTIVATION FOR THE CURRENT STUDY amp STUDY AIMS The ultimate goal for any MV repair or replacement is to permanently reproduce the functional properties of the native valve Studying the mechanical properties of the native valve will provide the necessary data for the qualification of suitable prosthetic materials Additionally an in depth understanding of the relationship between the valvular function macrostructure and microstructure may provide motivation for the progression of novel repair techniques as well as the development of suitable tissue engineered replacement materials The primary objective of any biomechanical study should be to first describe the functional properties of the valve The investigation of biomaterial behavior under non physiologic conditions does supply useful information and may provide insight into the inner workings of a given material but this information is of much greater value when it complements a complete understanding of the physiologically relevant material properties In the case of the MV the valve leaflet is a thin and nearly incompressible membrane Th
126. s Time ms 80 0 2 4 Test Statistics Display 70 0 60 0 50 0 2 5 High Speed Test Toggle 40 0 30 0 20 0 2 6 Load vs Time Graph 10 0 0 0 2 7 Recalibrate LC Button 10 0 i 1 1 1 1 1 1 1 1 i 1 1 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 2 8 Axis Return Factor Inputs Recalibrate LC 2 Return Factor 0 00 C Apply Preload xe mH des sin 2 9 Apply Preload Toggle C Time Remaining 0 00 Program Status of 173 2 3 Load Control 4 0 Creep E tood Contro sovi O zix Ele Edt Operate Tools Browse Window Help gt een Load Cells Imaging Positioning Test Settings Run Test High Speed Test 3 1 High Speed Test Tab I High Speed Test Displacement 1 0 00 mm Displacement 2 Stop Test Stop Test After 0 00 3 2 Stop Test Button Creep Stretch Limit 1 Creep Stretch Limit 2 10 3 3 Trigger Test Button Stretch vs Time ms 1 605 1 505 1 405 1 305 1 20 1104 3 4 Test Statistics Display 3 5 High Speed Test Toggle I 4000000 0 6000000 0 8000000 0 Stretch 1 0 0900 hear Angle 55 3 6 Test Duration Input Loads g vsTime ms Stretch 2 0 0000 3 7 Creep Stretch Limits 3 8 Stretch vs Time Graph 8000000 0 10000000 0 12000000 Load 1 0 0000 2 Load 2 0 0000 3 9 Load vs Time Graph Program Status ae gt 6 95 spe 4 174
127. s for each file are Time ms Load 1 units selected in Test Settings Tab Load 2 units selected in Test Settings Tab lt Filename gt _HS O hsbx 1 second cycle time 50 Hz acquisition rate lt gt HS Lhsbx 0 5 second cycle time 100 Hz acquisition rate Hlename HS 2 hsbx 0 1 second cycle time 500 Hz acquisition rate Hlename HS 3 hsbx 0 05 second cycle time 500 Hz acquisition rate lt gt HS 4 hsbx 1 second cycle time 50 Hz acquisition rate Creep lt Filename gt _first_second hsbx This file contains the first second of data from creep test File column headings are Time ms Load 1 units selected in Test Settings Tab Load 2 g orN lt gt entire test hsbx This file contains all data from the creep test File column headings are Time ms Stretch 1 Stretch 2 Shear Angle degrees Load 1 N org Load 2 N org Tension 1 N m Tension 2 N m Stress 1 kPa Stress 2 kPa 181 10 11 12 BIBLIOGRAPHY Lam J H N Ranganathan E D Wigle and M D Silver Morphology of the human mitral valve I Chordae tendineae a new classification Circulation 1970 41 3 p 449 58 Ormiston J A P M Shah C Tei and M Wong Size and motion of the mitral valve annulus in man I A two dimensional echocardiographic method and findings in normal subjects Circulation 1981 64 1 p 113 20 O
128. scalloped texture Figure 2 A photograph of the MV leaflets A anterior leaflet P posterior leaflet Reproduced from Otto CM Valvular Heart Disease Elsevier Inc 2004 Membranous Septum e i Right fibrous Central Dor 3 trigone fibrous body CUN G Non Hp Left coronary coronary Left cor leaflet leaflet A leaflet A leaflet Mitral valve X Muscular V septum Left fibrous trigone Figure 3 Diagram from a pathological perspective with division of the septum illustrating the fibrous continuity between the mitral and aortic valves Reproduced from Anderson RH Wilcox BR The anatomy of the mitral valve in Wells FC Shapiro LM eds Mitral Valve Disease Oxford England Butterworth Heinemann 1996 1 3 MITRAL VALVE HISTOLOGICAL STRUCTURE 1 3 1 Tri layered leaflet structure The MV leaflets are composed of three membranous layers 6 Beginning on the atrial side the first layer termed the spongiosa consists of proteoglycans elastin and a variety of connective tissue cells The spongiosa contains a relatively small number of collagen fibers when compared to the other two layers The core of the leaflets is named the fibrosa due to its large collagenous content This layer is thought to bear the majority of the loads applied to the leaflets evidenced by the fact that collagen fibers from this layer have been shown to ex
129. sed porcine mitral valve leaflets Am J Physiol 1995 269 4 Pt 2 p H1319 27 Billiar K L and M S Sacks Biaxial mechanical properties of the native and glutaraldehyde treated aortic valve cusp Part II A structural constitutive model Journal of Biomechanical Engineering 2000 122 4 p 327 35 Fung Y C Biomechanics Motion Flow Stress and Growth 1990 New York Springer Verlag 569 Fung Y C Biomechanics Mechanical Properties of Living Tissues 1981 New York Springer Verlag 184 38 39 40 41 42 43 44 45 46 47 48 49 Woo S L Gomez and W H Akeson The time and history dependent viscoelastic properties of the canine medical collateral ligament J Biomech Eng 1981 103 4 p 293 8 Nagatomi J D C Gloeckner M B Chancellor W C DeGroat and M S Sacks Changes in the biaxial viscoelastic response of the urinary bladder following spinal cord injury Ann Biomed Eng 2004 32 10 p 1409 19 Liao J and I Vesely Relationship between collagen fibrils glycosaminoglycans and stress relaxation in mitral valve chordae tendineae Ann Biomed Eng 2004 32 7 p 977 83 Lim K O and D R Boughner Low frequency dynamic viscoelastic properties of human mitral valve tissue Cardiovasc Res 1976 10 4 p 459 65 Leeson Dietrich J D Boughner and I Vesely Porcine Pulmonary and Aortic Valves A Comparison of Their Tensile Viscoelastic Properties at Ph
130. sing frequency This finding was supported by a study by Leeson Deitrich et al 42 who used a uniaxial tension testing mechanism to test porcine pulmonary and aortic valve leaflet strips and reported that the average leaflet stiffness increased with stretch rate Results for other soft tissues have revealed varying behaviors among different tissues Naimark et al 43 explored the effects of uniaxial loading rate on mammalian pericardia and showed that the stress stretch relationship for pericardia was not dependent on stretch rate Woo et al 38 found that the stress stretch relationship for the canine medial collateral ligament was only slightly affected by stretch rate while a study by Lydon et al 44 measured the affects of elongation rate on the rabbit anterior cruciate ligament and found that the stress stretch response of the ligament was highly dependent on elongation rate Haut and Little 45 explored the effects of stretch rates on rat tail tendon and observed that the stiffness of the tendon was affected slightly by stretch rate but that the failure stretch increased dramatically with stretch rate 43 Additional studies have explored the effects of loading rate on biologically derived valvular materials again with varying results Lee et al 46 performed uniaxial experiments on glutaraldehyde stabilized porcine aortic valve leaflet strips and found that the stress stretch relationship was dependent on stretch rate in the circumfer
131. st desired loading time was chosen to be 0 05 seconds to provide sub physiological loading rates This resulted in maximum required displacement rates of 0 093 m s circumferential and 0 24 m s radial per actuator These displacement rates were then multiplied by a safety factor of 2 in order to account for the influence of edge effects on the overall loading This provided a final displacement rate specification of 0 19 m s circumferential and 0 48 m s radial for each actuator 2 1 1 2 Maximum loads The maximum loads on the device carriages were calculated by estimating the membrane tension T defined as the load per unit length over which it is applied on the leaflet under physiological conditions Assuming the valve was roughly spherical with a radius of 10 mm when loaded the Law of Laplace was used to calculate T peck 2 7 50 where P is the transvalvular pressure and R is the radius Substituting a transvalvular pressure value of 120 mmHg 3 into this equation yielded a T 79 99 N m It was preferable for this estimate to slightly overestimate the physiological condition because this would make it more likely that the physiologic condition would be included in the load range so this estimate was rounded up to 90 N m 10 This peak membrane tension level was converted to axial load by multiplying by the largest expected specimen dimension 3 cm This yielded a peak load value of 2 7 N This was converted to grams by mu
132. tate was achieved in the MVAL well after this 120 transition phase In accord with this finding Lee et al 46 observed that the amount of relaxation in the glutaraldehyde stabilized porcine aortic valve leaflet was independent of initial load Interestingly this study noted relaxation differences between specimens tested in uniaxial tension in the circumferential and radial directions but these differences were opposite to our findings possibly due to the large amount of collagen cross linking that resulted from the glutaraldehyde treatment In contrast to the studies by Provenzano and Lee a study by Dunn and Silver 48 reported increased relaxation levels in several soft tissues including parietal pericardium with increased stretch level However comparisons with this study are less direct since relaxations were calculated at 5 sequential stretch increments without returning to the original unloaded stretch state between relaxations Another factor that could potentially play a role in the relaxation behavior observed in our study is the stretch rate differences between specimen axes Due to the relatively greater stretch required to load the MVAL to the 90 N m membrane tension in the radial direction and the fact that the rise times for the circumferential and radial axes were the same the stretch rate in the radial direction was necessarily higher than that observed in the circumferential direction In their study on the uniaxial relaxation
133. tend directly into the chordae tendineae Both the spongiosa and the fibrosa are wrapped in a thin fibrous layer composed of densely packed elastin fibers On the atrial side of the leaflet covering the spongiosa this layer is termed the atrialis while on the ventricular side of the leaflet this layer is termed the ventricularis The ventricularis predominantly covers the anterior leaflet and contains higher collagen content than the atrialis Additionally the ventricularis may thicken with age due to increases in collagen and elastin content 1 3 2 Passive components of the mitral valve 1 3 2 1 Collagen The term collagen fiber describes an intricately arranged set of tropocollagen molecules Three single chains are wound around each other in a left handed a helix Each of these chains contains approximately one third glycine one third proline and hydroxyproline and one third other amino acids These left handed helices are then wrapped together to form a right handed super helix Figure 4 The integrity of this helical structure is maintained by the interactions of proline and glycine amino acid residues Additionally hydroxylated proline and lysine residues serve to further stabilize the structure via hydrogen bonding interactions These tropocollagen molecules are then assembled into collagen fibrils Figure 5 which are organized fibers with diameter on the scale of a single micrometer ds y 1680 A BELA e
134. terior leaflet with sides parallel to the circumferential and radial axes of the leaflet centered circumferentially and extending radially from just below the annulus to just above the first chordae tendineae attachment site tet nie sidine ai tuc d uidens 79 Figure 34 Biaxial stretch rate sensitivity creep stress relaxation and uniaxial stress relaxation PLOT CONS CS 81 Figure 35 Specimens were mounted in the biaxial testing device with the circumferential and radial specimen axes aligned with the device axes ceccceesscceseceeeceeeceeeeceseceeeeeeeeeseeeaeens 82 xiii Figure 36 Load versus time curves for the loaded axis closed symbols and unloaded axis open symbols showed that the load cell on the unloaded axis was not affected by rapid THOLIOISS areata seh C neat oor datus et UL Ja Sao ata Me 89 Figure 37 Residuals versus time for the unloaded axis showed no clear trend further indicating that the unloaded axis was not affected by rapid motions ssssssssssesss 90 Figure 38 Relaxation of the biaxial test system and sutures Both device axes open symbols device axis 1 closed symbols device axis 2 showed minimal relaxation and were imdistinguishable from each other sce cipi et eta ko PAIN OREL NUR USE REA UR RI ERE UI 9 Figure 39 Typical tension stretch curves for the initial and final 1s loading unloading protocols
135. the desired peak loads Allowable Stretch 1 amp 2 4 4 Safety limits forthe stretches on each axis If an axisis stretched beyond the allowable stretch the test will be stopped immediately 157 4 Parameters in Stretch Control Only 5 1 a b Stretch Ratio 5 4 the ratio of stretch1 1 to stretch2 1 desired for the peak stretches Use Load Limits forthis Test 5 5 If thisoption is selected the test protocol will consist of the specimen being stretched at the ratio specified in Stretch Ratio until one of the load limits is reached on one axis or both simultaneously Thisoption cannot be used in conjunction with Use Stretch Limits for this Test and should be unselected before selecting that option i MaxLoads 5 5 select the units for the max loads Axis 1 amp 2 5 6 the load limits that will be used if Use Load Limits for this Test is selected Use Stretch Limits for this Test 5 7 if this option is selected the test protocol will consist of the soecimen being stretched at the ratio specified in Stretch Ratio until the stretch limit isreached on one axis or both simultaneously Thisoption cannot be used in conjunction with Use Load Limits for this Test and should be unselected before selecting that option i Stretch 1 amp 2 5 7 stretch limits that will be used if Use Stretch Limits for this Test is selected 5 Click the Run Test tab 6 1 at the top of the scre
136. the high speed cycle went normally repeat steps 7 10 for each high speed protocol Make sure to setup the high speed camera to receive the analog trigger before triggering each test 178 3 3 Creep Notes 1 Load Control 4 0 is simply an expansion of Load Control 1 0 All quasi static protocols can be run using Load Control 4 0 The displacements used in the creep initial loading are based on the displa cements of the final quasi static loading cycle If anything is unusual with the final quasi static cycle it is not recommended to proceed with the creep test Itisstrongly recommended that all creep tests are preceded bya standard quasi static biaxial protocol to ensure that no abnormal characteristics are present in the test sample Currently a bug in the software causes every creep experiment to stop prematurely Forthis reason it is recommended that you save all necessary calibration files and reference files and manually shut down and restart the program between sequential creep experiments orfix this bug The creep loading algorithm is used afterthe initial loading phase to maintain the desired specimen loads This algorithm wastuned to prevent large loading oscillations forthe mitral valve and may require adjustment for other materials Unlike the stress rela xation software the creep software doesnot allow the userto define the loading time All loading is done in 100ms unless modified on the pro
137. thin 0 1 degrees Table 2 Stretch measurement accuracy Stretch 1 Stretch 2 Shear Angle Prescribed Measured Prescribed Measured Prescribed Measured 1 200 1 199 1 600 1 600 30 0 29 9 1 200 1 200 1 600 1 600 30 0 29 8 1 200 1 199 1 600 1 600 30 0 29 9 86 3 1 2 Load cell calibration After a repeatable calibration was completed the mean load measurement of the 500g standard was 501 3 0 4 g 3 1 3 Ability to reach peak loads The ability of the device to reach the desired equibiaxial tension state of 300 g using a latex test sample is presented in Table 3 The first two cycles were not close to the desired peak loads due to the initial guesses used for the first cycle These results show the ability of the device correction algorithms to correct for inaccurate initial displacement guesses see METHODS for details After the second cycle the peak loads were reached with a high degree of accuracy The mean absolute differences between the desired and measured peak loads were 0 94 0 83 g circumferential and 0 12 0 12 g radial 87 Table 3 Peak loads for the ten cycle test using a latex test sample Peak Load g Cycle Axis 1 Axis 2 1 210 3 215 9 2 290 8 295 5 3 299 3 301 5 4 301 1 299 7 5 298 8 300 9 6 301 0 299 9 7 299 0 300 8 8 298 9 299 4 9 301 2 299 6 10 299 8 298 0 3 1 4 Load cell momentum sensitivity The unloade
138. tialized disable the lock subregions feature 2 2 and repeat steps 5 10 Once the imaging system is propeny setup you can save a reference file X amp Y marker positions for reference orto use in yourtesting protocols by clicking the Save Reference File 2 5 in the lower right comer of the imaging tab 3 The Compare References button 2 6 allows you to automatically calculate the stretches between two reference files that you will be prompted to select afterclicking the Compare References button Clicking any of the Set buttons 2 4 next to the Marker Positions graph 2 3 allows you to plot marker positions on the graph for comparison It doesNOTsave the marker positions asa reference file and will not allow you to use the current marker positions asa reference fora test See note for details on saving reference files Protocol 1 Position and focusthe camera such that the markers are centered in the image window and leave enough room so that the markers will not move out of the camera field of view during testing Select the Imaging tab 2 1 atthe top of the screen Click the Threshold Image button in step 1 of the image setup box 2 2 and adjust the threshold value using the scroll baruntil the markers are Clearly visible and the thresholded image isclean and free of noise and image specks Move to step 2 ofthe image setup boxand select the number of markers you would like t
139. tto C M Valvular Heart Disease 2nd ed 2004 Philadelphia Saunders Ranganathan N J H Lam E D Wigle and M D Silver Morphology of the human mitral valve II The value leaflets Circulation 1970 41 3 p 459 67 Silverman M E and J W Hurst The mitral complex Interaction of the anatomy physiology and pathology of the mitral annulus mitral valve leaflets chordae tendineae and papillary muscles Am Heart J 1968 76 3 p 399 418 Wells S Mitral Valve Disease 1996 Oxford Butterworth Heinemann Fulchiero G S M Wells T L Sellaro E Rabkin F J Schoen and M S Sacks Alterations in Collagen Fiber Crimp morphology with Cyclic Loading in Zero and Low Pressure Fixed porcine bioprosthetic heart valves Biomaterials in press Curtis M B and D V Priola Mechanical properties of the canine mitral valve effects of autonomic stimulation Am J Physiol 1992 262 1 Pt 2 p H56 62 Marron K M H Yacoub J M Polak M N Sheppard D Fagan B F Whitehead M R de Leval R H Anderson and J Wharton Innervation of human atrioventricular and arterial valves Circulation 1996 94 3 p 368 75 Sacks M S D B Smith and E D Hiester A small angle light scattering device for planar connective tissue microstructural analysis Ann Biomed Eng 1997 25 4 p 678 89 Wood P An appreciation of mitral stenosis I Clinical features Br Med J 1954 4870 p 1051 63 contd Burge D J and R J DeHorat
140. ventricle during systole termed MV regurgitation 1 4 1 Mitral valve stenosis The most widely recognized symptoms of MV stenosis are associated primarily with pulmonary venous congestion or low cardiac output Additionally systemic thromboembolism may occur In general thromboembolic events are much more common in patients with MV stenosis or a combination of MV stenosis and regurgitation than they are in patients with MV regurgitation alone The most common cause of MV stenosis is rheumatic heart disease which causes occlusion of the mitral orifice due to structural changes such as scarring to the valve leaflets 11 20 million cases of rheumatic fever are reported annually with this condition being particularly prevalent in third world countries 12 It is believed that rheumatic MV stenosis typically begins before the age of twenty but may take up to thirty years to fully develop into a clinically important condition Other causes of MV stenosis include MV calcification congenital mitral valve deformities thrombus formation within the left atrium and certain inherited metabolic diseases Although this condition develops with a relatively long time course preemptive treatment is generally not performed since the primary treatment is surgical intervention Surgical options 16 include both valvular repair and replacement In order to repair the stenotic valve a surgeon typically removes the leaflet like regions between the anterior a
141. were left free To provide a basis for optical stretch measurement 4 small graphite markers 250 um in diameter were glued to the specimen center using a cyanoacrylate adhesive Permabond Somerset NJ in a 2 x 2 array formation with dimensions of approximately 3mm x 3mm 77 Table 1 Specimen database Specimen Test Circ mm Rad mm Thickness mm HS2 High Stretch Rae 9 9 0 63 HS5 High Stretch Rate J A 9f 0762 HS6 High Stretch Rate 9 X 8 06096 HS7 High Stretch Rate 9 07112 BSH BiaxialStresselaxation 9 0 80 BSR2 jBiaxialStressrelaxaion 9 072 BSR3 Biaxial Stress relaxation 0 69 BSR5 Biaxial Stress relaxation 9 078 BSR6 jBiaxialStressrelaxaion 9 9 9080 BSH7 jBiaxialStressrelaxaton 9 079 BSR8 10 9 0 65 CSR jCircumferentialStress relaxation 9 10 0 81 CSR2 jOircumferentialStress relaxation 9 10 076 RSR jJRadialStressrelaxaion 9 10 083 RSR3 jRadialStressrelaxation 11 _ 9 078 Creep 9 J O74 5 Creep 89 9 oe jeep _ 9 9 oo 78 Annulus Anterior Leaflet Specimen Location Posterior Leaflet Chordae Tendineae Pap
142. xial Biaxial Figure 48 Relaxation percentage for different test groups and specimen axes Relaxation was observed in both uniaxial and biaxial experiments however the amount of radial relaxation was significantly greater in the biaxial experiments and the circumferential and radial relaxation percentages were not statistically different in the uniaxial experiments as they were in the biaxial experiments 107 3 3 3 Uniaxial Stress Relaxation Specimens tested uniaxially also exhibited relaxation on both the circumferential and radial specimen axes As observed in the biaxial stress relaxation experiments the peak membrane tensions in both the circumferential and radial directions were statistically greater than the membrane tensions measured at the 3 hour time point P lt 0 001 for each specimen axis However unlike the biaxial relaxation experiments the relaxation percentages observed in the circumferential 25 2 2 2 and radial 28 5 1 8 experimental groups were not statistically different from each other P 0 305 and a comparison between the uniaxial and biaxial relaxation percentages revealed that the biaxial relaxation was significantly greater p 0 05 in the radial direction while the uniaxial and biaxial relaxation percentages were not statistically different in the circumferential direction p 0 78 108 3 3 4 Reduced Relaxation Function Fit Both the uniaxial and biaxial relaxation data for both the circumferential and
143. ysiological Strain Rates The Journal of Heart Valve Disease 1995 4 p 88 94 Naimark W A Structure function relations in mammalian pericardial tissue implications for comparative and developmental physiology 1995 University of Toronto Lydon C J Crisco M Panjabi and M Galloway Effect of elongation rate on the failure properties of the rabbit anterior cruciate ligament Clin Biomech Bristol Avon 1995 10 8 p 428 433 Haut R C Age dependent influence of strain rate on the tensile failure of rat tail tendon J Biomech Eng 1983 105 3 p 296 9 Lee J M D W Courtman and D R Boughner The glutaraldehyde stabilized porcine aortic valve xenograft I Tensile viscoelastic properties of the fresh leaflet material J Biomed Mater Res 1984 18 1 p 61 77 Provenzano P R Lakes T Keenan and R Vanderby Jr Nonlinear ligament viscoelasticity Ann Biomed Eng 2001 29 10 p 908 14 Dunn M G and F H Silver Viscoelastic behavior of human connective tissues relative contribution of viscous and elastic components Connect Tissue Res 1983 12 1 p 59 70 Thornton G M A Oliynyk C B Frank and N G Shrive Ligament creep cannot be predicted from stress relaxation at low stress a biomechanical study of the rabbit medial collateral ligament J Orthop Res 1997 15 5 p 652 6 185 50 51 22 53 54 55 56 YI 58 59 60 61 62 Vesely I D R Boug

Evaluation of the Biaxial Mechanical Properties of the Mitral Valve

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