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DEMUSEtool – user manual

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1. e inspect and edit the results attained by automatic decomposition e display graphs of decomposition results including plots of the MU discharge patterns instantaneous discharge rate motor unit action potentials MUAPs and their 2D and 3D animations e compare the original sEMG signals to the reconstructed MUAP trains e save and reload the decomposition results All the graphs are displayed as regular matlab figures and can be freely manipulated by standard matlab graphic tools i e figure resizing Zooming rotating printing etc User is referred to matlab documentation for further details on the use of matlab graphic user interface For further information on EMG acquisition tool see 2 Note The current version of the DEMUSEtool supports decomposition of isometric SEMG signals only i e the signals acquired during 9 isometric muscle contraction Intensive work on decomposition of dynamic sEMG signals is currently in progress and support for dynamic conditions will be built in the future versions of the DEMUSEtool 2 DEMUSEtool components DEMUSEtool represents the third layer in three tier system architecture Figure 1 The first two layers comprise the 128 channel EMG USB electromyographic signal amplifier 4 and the sEMG acquisition software 2 respectively SEMG signals under investigation are first acquired with a 2D matrix of electrodes The matrix is put on the surface of the skin above the investigat
2. Page 52 of 56 DEMUSE tool User Manual DEMUSE When o lt 1 and f t are limited on the interval 1 1 higher order terms of expansion in 8 decay rapidly and the first approximation of the update rule 7 yields EN HMC f HTC 9 t J yy t y which after using di it Ga ls finally yields dy di 90 HC HC f d 10 Now assume match filter d has converged to d e where e 0 0 1 0 0 is unity vector with element at the j th position equal to 1 and e is vector of errors e 1 Using the Taylor expansion of f A the updates of the j th and the i th rows i in 9 yield f e e 0 6 SO 2 ips Oef 11 f e 2 f0 21 ESO De According to 11 in the vicinity of local optimum convergence and stability of 10 depend on the values of the first few derivatives of AA at points 1 0 and t1 The values of the first few derivatives of cost functions f t tanh t fX0 texp 2 2 and 3 log 1 are depicted in Figure 73 Functions f t f t were proposed by Hyv rinen 5 and are implemented in the popular fastICA algorithm Function A was selected empirically and exhibits high robustness to outliers Among these three criteria functions fi M log 1 is least sensitive to errors in vicinity of O while its performance in vicinity of 1 is comparable to other two functions Ideally d has a large number of zeros of the order of several hundreds and a single value e
3. DEMUSE DEMUSE tool ioj Properties Load SIG file 20 ej 500 Hz T Plotsignals About DEMUSE i ___Saveresults _ Save MU discharges Load MU discharges _ Run decomposition _ f x log 1 x 2 xj A A A A A A A A A AAA ka r o o STRESS San OR S ane ap Whoa LA o o 000 ELIAS Soc C RRA O AS SRA RR IR PRESTR RARA TOMI A y PRA 100 50 Amplitude u pS AAN UT AMO PLA 6 y 00 PSR ASR p DOD 0 SR l 7 8 RRA SN RRE RRA ALTAR RAR LOWRY MARA To A Filter 20 500 Hz i CEL ER SRERSR RR ER TENE eje oe ep ce eco e eje o oe ec e oec oe o eco en coco pq e co coco oc oc ee o eses e ee DEMUSEtool user manual Version 3 0 31 10 2008 Page 1 of 56 SS MARIE CURIE ACTIONS This work was supported by a Marie Curie Intra European Fellowship within the 6th European Community Framework Programme DE MUSE Contract No 023537 Page 2 of 56 DEMUSE tool User Manual CONTENTS 1 o a 5 2 DEMUSEtool component occocccccconcnccconcncccononcccononncnonoononanoononanconenacinnens 5 3 DEMUSEtool installation cooccoccoonconcoccconioccconooncnonooncnacconcnccnonons 6 3 1 A o o PO 6 3 2 DEMUSE files and folders oocooccccccoccccncocconnconcononcncncnononanonnnnannnos T 4 USO DEMO SE TOO aen eee ee E E A 8 41 Staing DEMUSE TOO ecc 8 4 2
4. Figure 74 Top three panels vector di after the fifth iteration as calculated from theoretical approximation 9 red line and by direct numerical calculation 8 blue line Bottom panel estimated PS after the fifth iteration of 73 t log 1 7 Page 54 of 56 DEMUSE tool User Manual DEMUSE 7 Technical support DEMUSEtool is copyrighted by the Laboratory of Engineering of Neuromuscular System and Motor Rehabilitation LISIN from Politecnico di Torino Italy and System Software Laboratory SSL from University of Maribor Slovenia lts development was supported by a Marie Curie Intra European Fellowship within the 6th European Community Framework Programme DE MUSE Contract No 023537 For further technical assistance and support please contact ales holobar delen polito it or ales holobar Muni mb si Laboratory of Engineering of Neuromuscular System and Motor Rehabilitation LISIN 2008 Politecnico di Torino Italy System Software Laboratory SSL O 2008 University of Maribor Slovenia a 2 DEMUSE MARIE CURIE ACTIONS This work was supported by a Marie Curie Intra European Fellowship within the 6th European Community Framework Programme DE MUSE Contract No 023537 Page 55 of 56 DEMUSE tool User Manual DEMUSE References 1 Matlab the language of technical computing MathWorks Inc web address http matworks com 2 Acquisition Software User Manual v1 62 OT Bioelettroni
5. MU discharge is displayed The use of buttons which control the length and the scale of displayed MUAP template and portions of SEMG is explained in Figure 44 each pulse denotes a single MU discharge previc disch ha next discharge a delete discharge delete many dis ky y iD n Yo Pl ip Weg y p a 0 Qe s AS Oh y cn n gt hell PMH ibaa Y tise ik A i ie Pe ral il avin j iin 1 il iti o o 7 A time ruler in seconds lt y o e i E oni a oo o o o of eas 000 Ze o 00 4 15 CPM P SS ES Bo oO AS 0 Es oD 1 er x e o O o n O a IS instantaneous discharge rate each circle denotes a single in pulses per second MU discharge Figure 41 Lower panel of CKC inspector window with train of delta pulses as estimated by CKC method in the upper part of the panel and instantaneous discharge rate plot in the lower part of the panel In both plots horizontal ruler denotes the time in seconds Vertical axis of the lower plot denotes the instantaneous discharge rate in pulses per second move left move right previous discha next discharge add discharge di zoom in on time axis zoom out on time axis Figure 42 Same as in Figure 41 with the time axis zoomed in Delta pulses denoting the discharge times of single MU are clearly visible Base line noise is negligible and inter discharge interval exhibits regular behaviour Th
6. Matlab figure with selected sEMG channels Row 4 4 85 4 9 4 95 5 5 05 5 1 5 15 5 2 5 20 53 Time s Figure 13 Zoomed in version of Figure 12 Displayed figures can be manipulated by using standard matlab graphical tools for zooming in out for saving and printing the figure Figure 14 Figures can be closed by clicking on a corresponding buttons in the top right corner of each figure Figure 15 Page 13 of 56 DEMUSE tool User Manual DEMUSE Agure Mp Fle EM View Ireert Took Window Hep OSOS re ary il fpepr Figure 14 Matlab figure toolbar with tools for zooming in out on a figure and for saving and printing the figure Figure 15 Buttons for minimization maximization and closing of the figure To display power spectra of band pass filtered SEMG signals click on Plot spectra button Figure 11 right panel Matlab figure with spectra of selected sEMG channels appears Figure 16 Channels 100 200 300 400 500 600 700 Frequency Hz Figure 16 Matlab figure with power spectra of selected sEMG channels 4 4 sEMG signal decomposition DEMUSEtool uses the gradient Convolution Kernel Compensation gCKC decomposition technique see Appendix Il and 3 Decomposition is fully automatic minimally biased by the properties of investigated muscle and nonparametric The user specifies only the number of decomposition runs Figure 17 and optionally nonlinearit
7. function data DEMUSEtool_reader_5x13_5mm_telescopic_pins_ SD 4amplifiers filepath filename epoch_length function data DEMUSEtool_reader_5x13_5mm_telescopic_pins SD 4amplifiers filepath filename epoch_length description of a reader DEMUSEtool reader reads surface EMG acquired by a matrix of 5x13 anything before the electrodes with inter electrode distance of 5 mm and telescopic pins Acquisition board for 64 channels is made by synchronization of 4 keyword INPUT will 16 channel amplifiers appear in the reader description window INPUTS filepath directory with the SIG file to be loaded finename SIG file to be loaded Inputs to the reader epoch_length optional length of the epoch of signal to be loaded ins are standardized OUTPUT data structure with the following fields SIG two dimensional cell array with surface EMG channel in each cell SIG r c is the channel in row r and column c Missing electrodes are denoted by empty arrays e g SIG 1 1 fsamp sampling frequency of SEMG signal_length length of a surface EMG signals in samples montage montage of electrodes MONO for monopolar SD for Outputs are always single differential in the form of Matlab IED inter electrode distance in mm structure force measured force signal if avalable empty array otherwise AUXchannels auxilary chann
8. 5 2D MUAP Map animation ococcccccccnccccccncnccnnncononcncnncoconancnnnnannns 35 4 7 6 3D MUAP map animation jeesesccccosimcieubaceeveenonnstened etudeweusebesbodubieevods 37 4 1 1 Plots of reconstructed MUAP trains ooccoccccccociccncoccccnconccnnnnnos 40 4 7 8 MOAR SAU S IG a e EE ee ne eee eee ner 43 4 8 Saving and reloading of the decomposition results occoo 45 4 9 DEMUSEtool acknowledgement cccccccceceseeeseeeseeeeeeeaeeeaeeeaees 47 5 Appendix definition of DEMUSEtool reader cooccocccccccccccnconiocncocinnnnos 48 6 Appendix gradient Convolution Kernel Compensation ccocccoccoo 50 6 1 Data model conoser erecto era 50 6 2 Decomposition method ooccoccccccoccccnconcocnconcocnonnnononcnnonnononaninnnnanons 52 E Technical SUDDO a ones acid 55 REPEFENCES cece cecc cece eccececeeceeeseeceeceeecaeceeecaecseeseseeesueeaeeseesaeeseesaeeseeseesseeseeeaeeeas 56 Page 3 of 56 DEMUSE tool User Manual DEMUSE Page 4 of 56 DEMUSE tool User Manual DEMUSE 1 Introduction DEMUSEtool is a matlab 1 program for visualization and decomposition of multichannel surface electromyograms SEMG acquired by EMG acquisition software v1 32 2 or latter It runs on a standard PC and enables the user to e load and visualize the multichannel surface electromyograms e decompose the sEMG signals into contributions of individual motor units MUs
9. DEMUSE tool User Manual DEMUSE In the case of loading failure the Error Dialog Window will appear Figure 7 AMES About DEMUSE A A 4 A 4 4 4 4 4 4 A 4 Figure 5 Channel selection frame displaying relative spatial organization of surface electrodes grey rectangles By clicking the white triangles SEMG channels corresponding to specific row or column of surface electrodes can be selected for visual inspection Selected column row is denoted by blue rectangle getReaderDialogWindow NE 210 x Select reader DEMUSEtool reader 5x13 3 5mm _fixed pins SD 4amplifiers m DEMUSEtool reader 5x13_ Stim _telescopic_pins_ SD 4damplifiers mm DEMUSEtool reader 8x41 510m _ monopolar tri DEMUSEtool reader Aalborg 5x13 _2 Smm_single_differential_mat_tile m DEMUSEtool reader Aalborg 5x13 3 5mm SD new XML DEMUSEtool reader Aalborg _5 13_ 3 5mm SD_nevexML om DEMUSEtool reader_ alborg_5 13_3 Smm_sinole_differential_mat_file DEMUSEtool reader Aalborg 5x13 _3 m DEMUSEtool_ reader BEDREST YALDOLTRA_2007_5x13_ 6mm Mona Lom DEMUSEtool reader DynamicBiceps 5x13 Grom MONG im DEMUSEtool_ reader LISiM_Sx6_Sram_Minetta_SD om DEMUSEtool_ reader LISiN_tvwoSx6_Smm_Minetto_ MONO D mm DEMUSEtool reader Speshedica_Sx13_68raim_SD_permutator_64 out_of_128chs_old hML m DEMUSEtool_ reader Speshledica_Sx13_6rim_ SD _permutator_6b4chs_oldxML im DEMUSEtool reader reads surface EMG acquired by a matrix of 5x13 elect
10. MUAP shapes as estimated by a spike triggered averaging of each acquired sEMG channel Displayed MUAPs are spatially organized in rows and columns reflecting the relative position of pick up electrodes Plot MUAPs E Selected MU Mu 2 7 Figure 54 Plot MUAPs button left panel and Selected MU pup up menu right panel Page 34 of 56 DEMUSE tool User Manual DEMUSE 00 oO oO rT Td TITT TT Mr 0 25 0 25 0 25 time ms o N al o NO al Figure 55 Multichannel MUAPs of MU 4 estimated by spike triggered averaging of SEMG signals SEMG signals were recorded with a grid of 61 electrodes arranged in 5 columns and 13 rows The location of the innervation zone tendon regions and propagation of motor unit action potentials are visible 4 7 5 2D MUAP map animation DEMUSEtool offers two animations of MUAP generation propagation and attenuation process The first one so called 2D MUAP map is a pseudocolor plot of the estimated MUAP amplitude in a given time instant First MUAP templates are estimated by a spike triggered averaging of the SEMG channels SEMG channels are then spatially organized into a discrete 2D map reflecting the relative position of pick up electrodes The amplitudes of MUAP templates at a given time instant specify the colour on this 2D map of channels The missing intermediate points on the map are calculated by bilinear interpolation of the MUAP
11. amplitudes in four adjacent sEMG channels In the next animation frame the animation time is advanced by one sample and the 2D MUAP map is recalculated Figure 57 Page 35 of 56 DEMUSE tool User Manual DEMUSE Animate 20 MUAF map A eave i eee Selected MU Miu 2 x e Frames s 10 f f H Figure 56 Animate 2D MUAP map button left Selected MU pup up menu and slider for selection of frame rate right Amplitude LV Amplitude LV Amplitude LV Amplitude LV 10 20 x mm 10 0 10 20 30 40 200 x mm Figure 57 Pseudocolor animation of a MUAP generation propagation and attenuation process MUAP amplitudes on different SEMG channels black amp white circles specify the colours of corresponding points on the 2D map Page 36 of 56 DEMUSE tool User Manual DEMUSE Colours of intermediate map points are calculated by the bilinear interpolation of the MUAP amplitudes in four adjacent SEMG channels The MU and the animation frame rate are selected by the pup up menu and slider shown in Figure 56 right panel After clicking on the Animate 2D MUAP map button Figure 56 left panel animation window opens Figure 57 and the animation starts automatically The animation begins approx 5 ms before the actual generation of the multi channel MUAP and ends approx 5 ms after the MUAP attenuation During the animation the propagation of MUAP along the muscle fibers can be obser
12. k 27 s s 0 0075079 2 4 6 8 10 12 time s Decomp run 18 Cost 0 13 ma AMO il SSA D f ELU Ar y En li b re 0 5 a Lit lk tH mi Lp a 1559 nt sea HET 1 A p f A 4 il Dat RAE oh E MRT bi rita M MISA ia E thes Ly T fii fi mm j AK time s Figure 21 MU discharge pattern as reconstructed in the 27 iteration of the gradient CKC technique after reaching the stop criterion s s g 1 lt 0 01 Each pulse corresponds to a single MU discharge Average discharge rate and CoV of inter pulse interval are within the expected range of values Thus in the lower panel the selected MU discharges are depicted by green circles When the decomposition ends the total processing time is displayed Figure 22 We can now proceed to visualisation and saving of the results Sections 4 6 1 and 4 8 Alternatively we can change cut off frequencies of band pass filter toggle time differentiation or select different nonlinearity and rerun the decomposition by clicking on Rerun decomposition button Figure 23 Contrary to the Run decomposition button Figure 19 Rerun decomposition button Figure 23 keeps the record of already reconstructed MU discharge patterns and adds them to those reconstructed in the new decomposition run Run decomposition button Figure 19 automatically deletes previously reconstructed MU discharge patterns and s
13. pass filtering before running the decomposition The effect of time differentiations and band pass filtering can be examined by plotting sEMG channels and or their power spectra see Section 4 3 Figure 9 Check box for selection of time differentiator Time differentiator is a high pass filter which suppresses the activity of small background MUAPs and enhances the differences between the MUAPs from different MUs Differential mode should be selected in the case of high MU activity only DEMUSEtool automatically removes line interference and tests the acquired SEMG channels for presence of movement artefacts and bad skin electrode contacts However percentage of the sEMG channels to be included into the decomposition must be specified explicitly by changing the value of signal quality slider Figure 10 Setting the slider value to 95 for example means that 5 of the channels with the lowest signal quality estimation will be skipped by the CKC decomposition This selection does not influence the commands for plotting of SEMG channels and or graphical representation of decomposition results e g estimated motor unit action potentials By default all the available channels are included in all graphical presentations Page 11 of 56 DEMUSE tool User Manual DEMUSE Figure 10 Slider for definition of SEMG signal quality DEMUSEtool automatically removes line interference and tests the acquired SEMG channels for mo
14. plot of all reconstructed MU discharge patterns Figure 49 Each circle in the figure corresponds to a single MU discharge The horizontal position of the circle denotes the time of MU discharge whereas its vertical position reflects instantaneous MU discharge rate calculated as a quotient between the sampling frequency and the inter pulse interval preceding the given MU discharge Discharge patterns of different MU are depicted one above the other Plot MU discharges Figure 48 Plot MU discharge button Page 31 of 56 DEMUSE tool User Manual DEMUSE 10 a nf E L En Jis f 5 10 MU number O 2 3 0 e dh al 10 instantaneous discharge rate pps 6 time s Figure 49 Plots of reconstructed MU discharge patterns Vertical axis on the left displays MU IDs vertical axis on the right displays the instantaneous discharge rates in pulses per second pps The tick lines on the right denote the discharge rates of 5 10 and 15 pps respectively Discharge patterns of different MUs are depicted one above the other 4 7 2 Smoothed discharge rate plots Smoothed MU discharge rates are plotted by a click on a Plot discharge rates button Figure 50 A matlab figure opens Figure 51 with a different colour lines depicting the smoothed discharge rates of different MUs one line per each MU The thick grey line depicts the exerted muscle force when measured during the acquisition of SEMG signa
15. up menu Figure 38 and then clicking on the CKC inspector button Figure 39 Selected MU Figure 38 Select MU pup up menu allows selection of MU to be edited by CKC inspector i Figure 39 CKC inspector button CKC inspector window consist of two panels Figure 40 Lower panel displays discharge pattern of selected MU as estimated by gradient CKC method Two different versions of the same discharge pattern are depicted train of delta pulses as calculated by gradient CKC method upper part of the panel in Figure 41 and instantaneous discharge rate of estimated MU lower part of the panel in Figure 41 User can zoom in and zoom out on time axis by clicking on buttons Il and I l respectively Figure 42 By clicking buttons lt and gt Figure 42 the displayed portion of the MU discharge pattern is moved left and right respectively MU discharges can be added or deleted by clicking the add discharge and delete discharge buttons After each click on these buttons mouse pointer changes from arrow to full cross Drag the cross to the pulse to be added deleted and left click to add delete the MU discharge Figure 43 Several MU discharges can be deleted simultaneously by clicking on delete many discharges button Figure 42 In this case full cross pointer is used to determine the left and the right edge of the MU discharge Page 26 of 56 D
16. 2 cache or more 1 GB RAM To run DEMUSE tool following software should be properly installed e matlab 1 version 7 0 or higher Page 6 of 56 DEMUSE tool User Manual 3 2 DEMUSE files and folders DEMUSEtool comprises several matlab s m and fig files which are located in the directory DEMUSEtool programs Program documentation is located in the directory DEMUSEtool documentation DEMUSE To install DEMUSEtool copy both directories to your hard disk e g to c DEMUSEtool directory and set the path in matlab environment to ADEMUSEtool programs MATLAB File Edit View Web Window Help New Current Directory C Open Ctri O Close Ctrl Import Data Save Workspace s Set Path Preferences Page Setup Print Gtrl P Print Selection 1 E grams 4boutDialog m 2 plotMUAP_3DMap_black m 3 E rograms MUAPmap2D m 4E rograms MUAPmap3D m Exit MATLAB Ctrl Q Se Hl xh All changes take effect immediately MATLAB search path Add Folder Add with Subfolders Move to Top Move Up Move Down Move to Bottorn Remove id i Save Close Revert Default Page 7 of 56 IDEMUSEtoo CADEMUSEtooliprograms y C Matlab6 Sitoolbox local q C Matlab6 5Sitoolbox matlab general C Matlab6 Sitoolbox matlablops C Matlab6 Sitoolbox matlab lang q C Matlab6 Sitoolbox matlab elmat q C Matlab6 5Sitoo
17. EMUSE tool User Manual DEMUSE cancellation interval All the discharges between the aforementioned edges will be deleted File Edit View Insert Tools Desktop Window Help Figure 40 Window of CKC inspector with upper panel displaying multichannel MUAP of selected MU as detected by all surface electrodes and lower panel displaying the train of MU discharge times as estimated by CKC decomposition method Upper panel of the CKC inspector window displays multichannel MUAP template of selected MU as detected by all surface electrodes and estimated by spike triggered averaging of SEMG channels blue thick lines in Figure 40 All available MU discharges are used as triggers Displayed MUAPs are spatially organized in rows and columns reflecting the relative position of pick up electrodes By right clicking on a red circle in the lower panel Figure 41 portions of the original SEMG channels around that discharge are displayed in the upper panel of CKC inspector window red thin lines in Figure 40 and aligned with the displayed MUAP templates Selected MU discharge is depicted by black thick circle in the lower panel Page 27 of 56 DEMUSE tool User Manual DEMUSE Figure 40 This allows inspection of MUAP presence and MUAP superimpositions on all the sEMG channels simultaneously By clicking on previous discharge next discharge button Figure 42 sEMG portion around the previous next
18. Figure 59 enable the following actions e gt button re plays the animation e l button pauses the animation e I button stops the animation e lt P button animates the previous animation frame i e step backward e lt T animates the next animation frame i e step forward The current animation frame is displayed in the top right corner of the animation window Figure 59 The animation window is a regular matlab figure and can be freely manipulated by all available matlab graphical tools e g zooming coping printing etc Note Animation window cannot be closed during the run of animation i Stop the animation by clicking on or button before you close the figure During the 3D animation the axes of the 3D plot can be freely rotated To rotate a 3 D axes click on the axes and drag the cursor in the direction you want to rotate When you release the mouse button DEMUSEtool redraws the axes in the new orientation Figure 60 Frame 24 Frame 24 ae 200 O oes a a Amplitude LV 50 eee Aen ane IA pee aoe te 200 E Os OOO Otay 0 00 AROS i y mm Figure 60 3D rotation of the axes the axes of the 3D plot can be rotated by dragging the cursor Page 39 of 56 DEMUSE tool User Manual DEMUSE 4 7 7 Plots of reconstructed MUAP trains DEMUSEtool provides tool for plotting the sum of reconstructed MUAP trains Sup
19. SEMG Signal loading occcocccocccociccncconcncnconnnonnnnnnoncnnnronaronaronanonnnos 9 4 3 SEMG Signal visualization occoocccncocnnoconcccnconnnonnnnnonaronaronaronanonons 12 44 SEMG Signal decomposition cooccoccccoccconcoccnncnconnnnnnnnnonanonaronanenanonons 14 4 5 Editing of the decomposition results SEMG Editor 19 4 5 1 Plotting SEMG SIQNaAlsS ocoocccoccccccconccnnnocnconnnonnnoconaronanonanonanonons 20 4 5 2 Displaying instantaneous MU discharge rate ocoocconcoccoc 21 4 5 3 Adding anew MUAP occurrence occooccccccncncoconnoncononoconanonanenanonons 23 4 5 4 Moving and deleting MUAP occurrences ceeeeeeeeeeeeeeneees 24 4 5 5 Selecting sSEMG channel spatial filter and cut off frequencies 25 4 6 Editing of the decomposition results CKC inspector occcoccoo 26 4 6 1 Deleting of decomposition results ooccoccccccoccccnconcccnconinnnnnnos 30 4 7 Graphical results oocooccccccocccccconcocnccnnoniccnnonnnnncononnnnanonnonannnnonannnos 31 4 7 1 MU discharge patterns plot coccoccoccocnccnccnconconcnccaninncnnnos 31 4 7 2 Instantaneous discharge rate plotsS cooccocconncociocononincnnns 32 4 7 3 Inter pulse variabilily ooocoocconcconconcconioncconioncoononnnnnccanonanonos 33 4 7 4 Multichannel MUAP plotS ocoocconconcoccoccocconconccononnconcncnncnnnnos 34 4 7
20. Us are additionally sorted with respect to the aforementioned degree of decomposition reliability the first MU being the most reliable one lecomp runs 30 Decomp runs 30 SIG offset 0 Figure 17 Slider for selection of decomposition runs For practical reasons the user can also specify the initial signal offset and length of SEMG interval entering into the decomposition Figure 18 This allows discarding the initial signal portions where for example the contraction level is not yet stabilized etc The initial signal offset and interval lengths are measured in seconds Note Due to the large number of SEMG channels and high memory f consumption of gradient CKC method the length of decomposition interval should generally be limited up to 20s Longer signals should be divided into 20s long epoch which should be decomposed independently The optimal length of decomposition interval depends also on the amount available computer memory Page 15 of 56 DEMUSE tool User Manual DEMUSE The decomposition starts by clicking on Run decomposition button Figure 19 Figure 18 Sliders for selection of initial offset and length of decomposition interval of SEMG signals Processing time 0 Figure 19 Run decomposition button During the decomposition the reconstructed MU discharge patterns are displayed Figure 20 and the instantaneous MU discharge rate and inter pulse interval v
21. ac impulses AO AOL J 1 N 2 where the k th MUAP of the j th MU appears at time 7 x Fq 1 can be rewritten in a matrix form x n Ht n o n 3 where o n 0 n O n is a noise vector and the mixing matrix H comprises all the MUAPs as detected by the surface electrodes h 0 A 1 h 0 h L 1 MUAPs inmeasurement1 7 h 0 A L 1 h 0 h L 1 MUAPs in measurement 2 Mari 0 Ay L Dh y 0 Ay L 1 MUAPs in measurement M KN y AAA Y MUAPs of MU1 MUAPs of MU2 while the vector 114 1 1 1 t n L 1 ty 1 ty n L 1 4 stands for an extended form of t 1 m n For decomposition it is beneficial to further extend ho an a E K 1 delayed repetitions of each measurement x n x n x n 1 x n K 1 Xy n Xy n K D 5 This increases the number of observations with respect to the unknowns in Eg 3 The optimal value of the extension factor K is application dependent and is typically between 5 and 15 This factor is automatically selected by the DEMUSEtool Page 51 of 56 DEMUSE tool User Manual DEMUSE 6 2 Decomposition method The gCKC method fully automates the identification of MU discharge sequences in the Eq 3 In the first step the method blindly estimates the cross correlation vector e E t n x n between the j th pulse train and the extended measurements where E stands for mathe
22. ariability are automatically calculated The reconstructed discharge pattern is put into the set of reconstructed MUs if and only if the calculated values fall within the expected range of values i e average discharge rate between 5 and 60 pulses per second Coefficient of Variability CoV of inter pulse interval smaller than 50 The selected MU discharges of accepted discharge pattern are depicted by green circles Figure 21 The reconstructed discharge pattern with the calculated values outside the expected range of values is discarded 10 x File Edit View Insert Tools Desktop Window Help Deal eaan gln g Iteration k 14 st s9 0 017111 AUN ool APA 2 4 6 time s Iteration k 14 s s 0 017111 time s Figure 20 discharge pattern of individual MU reconstructed in the 14 iteration of the gradient CKC decomposition technique Each pulse i e delta function corresponds to a single MU discharge Upper panel displays the entire train of reconstructed MU pulses i e MU discharges the lower panel displays its zoomed portion Relative norm of difference between reconstructions of MU discharge pulses in two successive iteration s and s 1 divided by the norm of s is used as a criterion to stop the iterations of gradient CKC Page 16 of 56 DEMUSE tool User Manual DEMUSE O x File Edit View Insert Tools Desktop Window Help D amp S k RaDa Iteration
23. ca SIRIO Automazione srl and LISIN Bioengineering Center Politecnico di Torino February 2007 3 A Holobar D Zazula Gradient Convolution Kernel Compensation Applied to Surface Electromyograms ICA 2007 LNCS 4666 pp 617 624 2007 4 Holobar A and Zazula D Multichannel Blind Source Separation Using Convolution Kernel Compensation IEEE Trans Sig Process 55 9 4487 4496 2007 5 Hyv rinen A Fast and Robust Fixed Point Algorithms for Independent Component Analysis IEEE Trans on Neural Networks vol 10 1999 pp 626 634 6 EMG USB electromyographic signal amplifier User Manual v 1 32 OT Bioelettronica SIRIO Automazione srl and LISIN Bioengineering Center Politecnico di Torino September 2006 T McGill KC Lateva ZC Marateb HR EMGLAB an interactive EMG decomposition program J Neurosci Methods 2005 149 121 133 8 Farina D Muhammad W Fortunato E Meste O Merletti R Rix H Estimation of single motor unit conduction velocity from the surface EMG signal detected with linear electrode arrays Med Biol Eng Comput 2001 39 225 236 9 A Holobar D Farina M Gazzoni R Merletti D Zazula Estimating Motor Unit Discharge Patterns from High Density Surface Electromyogram Clinical Neurophysiology in press Page 56 of 56
24. d MU pup up menu right panel Page 33 of 56 DEMUSE tool User Manual DEMUSE MU 4 IDR cut off freq 3 Hz IPI Win 10 MU discharges 140 120 _ 207 V Q 100 gt 5 2 E 80 a oO QA 60 D 10 40 E o 5 20 mean std dev 0 l 0 0 2 4 6 8 10 2 4 6 8 10 time s time s CoV mean 19 SD 5 range 6 37 ee L a 35 l 20 oo i oe 30 k Ari A e o al n 2 15 E A var fi AS x El ak NA d f k a i i wo j n gt RRR 5g Sahar Wit GA gt A OS gt i y i Ai avy y i v i E 10 e x 5 eS i Oo y V a 5 e y v y OE gt Yx X 10 N Ts ep Y Bt 0 I i i I 0 i I 2 4 6 8 10 0 20 40 60 80 100 120 time s IPI mean ms Figure 53 Plots of inter pulse interval IPI of MU 4 upper left panel smoothed discharge rate upper right panel Coefficient of Variability CoV of IPI bottom left panel and IPI variability CoV versus IPI mean Smoothed discharge rate is calculated by low pass filtering the instantaneous discharge rate with cut off frequency of 3 Hz Standard deviation of IPI is calculated over 10 consecutive MU discharges 4 7 4 Multichannel MUAP plots Multichannel MUAP plots so called MU fingerprints can be plotted by clicking on a Plot MUAPs button Figure 54 left panel MU to be depicted is selected in a Selected MU pup up menu Figure 54 right panel A matlab figure opens Figure 55 with
25. d results button Figure 67 Load results dialog window opens Figure 68 Choose the x mat file and click on Open button Once reloaded into the DEMUSEtool results can be freely edited and displayed graphical representations and animations of the reloaded results are fully supported Save results button saves all the decomposition results including the original SEMG singals Save results Es Figure 67 Save results button left and Load results button right Look in lo signals e amp e EJ Subject1_offsetO_runs30 mat Files of type MAT files mat y Cancel Figure 68 Load results dialog window Page 45 of 56 DEMUSE tool User Manual DEMUSE To save just the discharge patterns of MUs click on a Save MU discharges button Figure 69 MU discharges are automatically saved into the directory containing the currently loaded SIG file The following file naming convention is used NameOfTheSIGfile MUPulses offsetN runsM mat the name of the Initial Number of Signal decomposition offset iterations currently loaded SIG file where NameOfTheSIGfile stands for the name of the currently loaded SIG file N is the initial signal offset in seconds and M is the number of decomposition runs see Section 4 4 for details MU discharges are saved into a Matlab cell structure MUPulses with discharge times in samples of single MU in eac
26. d side of the top panel determine the position and the size of the time window used for depicting the sEMG channel Buttons lt lt and gt gt move the window left and right with respect to the sEMG channel respectively Figure 29 Button zooms in out on a displayed signals decreases increases the length of the time window move left move right Cine s zoom in zoom out Figure 29 The top panel of sEMG editor window with buttons for moving left right and zooming in out on displayed signals Page 20 of 56 DEMUSE tool User Manual DEMUSE 4 5 2 Displaying instantaneous MU discharge rate The central panel of the sEMG editor window displays the MUAP templates of different MUs as estimated by spike triggering averaging of the selected sEMG channel Figure 30 The identified MU discharges are taken as triggers The length of the averaging window is set equal to 25 ms te selected MUAPs lt lt move selected MUAPs move selected MUAPs gt gt A gl MUAP template of MU 1 MUAP template of MU 8 estimated from the estimated from the selected SEMG channel selected SEMG channel Figure 30 The central panel of sEMG editor with MUAP templates estimated by spike triggered averaging of the selected SEMG channel The central panel allows the user to select a particular MU by clicking on corresponding MUAP template The MUAP occurrences of selected MUs are automa
27. dient Convolution Kernel Compensation gCKC technique 3 is fully automatic resolves MUAP superimpositions and relies minimally on anatomic properties of the investigated muscle Moreover it implicitly combines all the available information provided by all the sEMG measurements By compensating for the shapes of the detected MUAPs it directly estimates MU discharge patterns without reconstructing the detected MUAP shapes This significantly decreases the number of unknowns to be estimated and reduces computational time MUAP shapes can then be estimated by spike triggered averaging of SEMG measurements When compared to other currently available surface EMG decomposition techniques gCKC exhibits high accuracy efficiency and robustness in identification of MU discharge patterns and is specifically tailored to low quality noisy signals This extension is of paramount importance for clinical practice where recoding environment cannot be strictly controlled The accuracy obtained with the g KC decomposition technique is comparable to that obtained by decomposition of intramuscular recordings 9 In the DEMUSEtool reconstructed MU discharge patterns are automatically tested against the predefined ranges of physiological variables i e discharge rate variability of inter pulse interval etc and sorted with respect to the estimated degree of decomposition reliability with MU 1 having the highest decomposition reliability In the sequel
28. e 2D MUAP map Animate 3D MUAP map animations MU sound panel_ Frames 1 10 ff gt Plot MUAP trains Plot decomp residual calc MUAP stat Acquisition matrix configuration and channel selection frame Figure 3 Main DEMUSEtool window with explanations of different command groups Each group of commands is depicted in different colour Figure 3 Channel selection frame displayed on the right hand site in Figure 3 allows selection of different rows or columns of acquired sEMG channels Its detailed description is provided in Subsections 4 2 4 3 and 4 7 7 Page 8 of 56 DEMUSE tool User Manual DEMUSE 4 2 sEMG signal loading To load acquired sEMG into DEMUSEtool click on Load SIG file button Figure 4 left panel Load SIG file dialog window appears Figure 4 right panel Chose the SIG file and click on Open button on E 21x popat Look in E 00M aGaLi0705151518_2 e e EE Lead siGfile OOMaGaLi070515151813 siq Flanal naa law 4 E OOMaGaLio70515151814 sig El 00MacaLi070515151615 5iq Files of type SIG ka Cancel Figure 4 Load SIG file button left panel and Load SIG file dialog window right panel SEMG acquisition software 2 supports arbitrary configurations and numbers of surface electrodes up to 128 channels and stores the information about the acquisition modalities into so called measurement session abstract file XML DEMUSEt
29. ed muscle and connected to the EMG USB signal amplifier 4 which amplifies and band pass filters the signals and sends them to the SEMG acquisition software 2 The acquisition software acquires the sEMG signals displays them on the screen for immediate visual inspection of the signal quality and saves them into so called SIG files 2 Information about the measurement session including technical specifications i e number of channels sampling frequency gain etc is saved into purposely designed Page 5 of 56 DEMUSE tool User Manual DEMUSE abstract file 2 Finally SIG and abstract files are loaded into DEMUSEtool and processed off line Figure 1 Tier 1 Tier 2 Tier 3 Figure 1 Three tier architecture with indicated data flows of the sEMG decomposition system DEMUSEtool installation DEMUSEtool v3 0 is still a prototype and runs in the matlab programme environment 1 As such it is supported by several personal computer PC platforms including Windows Linux and Mac OS It does not require any special hardware configuration However in the case of large number of channels and long sEMG signals a sufficient amount of RAM 1 GB or more should be installed on the system in order to prevent extensive swapping of the memory space 3 1 Requirements Minimal hardware configuration e 1 GHz CPU 20 MB disk e 1GB RAM Recommended hardware configuration 2 GHz CPU or higher 100 Mb disk 2 MB L
30. elected MU move left selected move right selected discharge MUAP MU discharge MUAP MU discharge MUAP Figure 35 Manipulation of selected MUAP occurrence depicted by red thick line The selected MUAP occurrence can be moved left right or deleted Each user action results in an immediate update of a signal residual and MUAP templates Figure 36 Selected MUAP occurrence can be deselected by a single click Time s 4 44 4 46 4 45 45 4 52 4 54 4 56 12 Al Jus pea v fy V ASA NA VA eee E S Figure 36 Same as in Figure 35 with the selected MUAP occurrence moved to the left Increase of the sEMG channel residual signal grey line is clearly visible when compared to Figure 35 Note Several MUAP occurrences can be simultaneously selected This saves the users time and energy in the 8 case of intensive manual editing Page 24 of 56 DEMUSE tool User Manual DEMUSE 4 5 5 Selecting sEMG channel spatial filter and cut off frequencies The sEMG channel to be displayed can be selected by clicking on a radio button representing the corresponding channel in the left bottom corner of the sEMG editor window Figure 37 Electrode rows and columns are denoted by red numbers displayed at left bottom of the channel selection panel Text labels right above the sEMG channel selection panel display cut off frequencies of the 1st order Butterworth band pass filter Cut off frequencies can be modified by typing
31. els currently not used by DEMUSEtool AUXchannels_description cell array of texts describing the data in AUXchannels one cell per channel Copyright LISIN Politecnico di Torino Italy SSL FEECS University of Maribor Slovenia Author Ales Holobar ales holobar uni mb si Last modified 14 10 2008 Figure 72 Reserved head of a SEMG reader and its standardized interface All the DEMUSEtool readers must specify this initial structure and must use specified inputs and outputs Actual implementation of the loading method is left to the user Outputs of the reader are given in the form of Matlab structure with the following field requested SIG two dimensional cell array with surface EMG channel in each cell SIG r c is the channel in row r and column c Missing electrodes are denoted by empty arrays e g SIG 1 1 fsamp sampling frequency of SEMG signal length length of a surface EMG signals in samples montage montage of electrodes MONO for monopolar SD for single differential configuration IED inter electrode distance in mm force measured force signal if available empty array otherwise AUXchannels auxilary channels currently not used by DEMUSEtool AUXchannels description cell array of texts describing the data in AUXchannels one cell per channel Page 49 of 56 DEMUSE tool User Manual DEMUSE 6 Appendix Il gradient Convolution Kernel Compensation Gra
32. erimposed to the original SEMG signals This proves beneficial when evaluating the efficiency of the decomposition process In surface EMG there are many small and deep MUs which cannot be recognized They contribute the background physiological noise The second source of noise is so called instrumentation or thermal noise which originates from the instrumentation s parasite capacities line interference etc All together these sources add to the measurement noise and affect the efficiency of the SEMG decomposition By comparing the sum of the reconstructed MUAP trains to the original SEMG signal one can estimate the proportion of recognized SEMG components and hence speculate on the power and even on the nature of the measurement noise In the DEMUSEtool the reconstructed MUAP trains are calculated as follow Firstly the MUAP shapes are estimated by spike triggered averaging of the acquired SEMG channel using the identified MU discharge instants as triggers The estimated MUAP shapes are then convolved with the identified MU discharge patterns and summed together The sum of MUAP trains is subtracted from the original sEMG signals and the following signal to interference ratio SIR between the original SEMG signals and the residue after the subtraction is calculated El O n Za Od J 100 E Es n SIR i 1 where x n denotes the i th sEMG measurement z n stands for the j th MU s MUAP train reconstructed from t
33. gth MU conduction velocity CV Correlation coefficient between the MUAP shapes used for calculation of MU conduction velocity e MU conduction velocity on a selected triplet of SEMG channels triplet with highest correlation coefficient between the MUAP shapes is automatically selected for this metrics All these metrics are calculated over double differential spatial derivations of a raw SEMG signals MUAP peak to peak amplitude is defined as a distance between the highest positive peak and the lowest negative peak of MUAP MUAP energy is calculated as a Root Mean Square of a MUAP whereas MUAP length is defined as a maximal time distance between the points in which rectified MUAP surpasses the 5 of its maximal amplitude Conduction velocity is estimated with the multi channel algorithm described by Farina et al 8 from triplets of double differential derivations Triplet with highest correlation coefficient between the MUAP shapes calculated pair wise is automatically selected for calculation of MU conduction velocity on a selected triplet of SEMG channels MUAP statistics tool Figure 66 opens after clicking on calc MUAP stat button Figure 65 Upper panel displays MUAP shapes as estimated by a spike triggered averaging of each of double differential derivatives Displayed MUAPs are spatially organized in rows and columns reflecting the relative position of pick up electrodes Lower panel displays the MUAP statistics Fig
34. h cell For example discharge times of MU 1 are stored in cell MUPulses 1 discharge times of MU 2 in cell MUPulses 2 etc lag Save MU discharges Load MU discharges Figure 69 Save MU discharges button left and Load MU discharges button right Page 46 of 56 DEMUSE tool User Manual DEMUSE 4 9 DEMUSEtool acknowledgements Information about the DEMUSEtool version copyrights and author s acknowledgement are displayed by clicking on the About DEMUSE button Figure 70 About DEMUSE dialog window opens Figure 71 About DEMUSE Figure 70 About DEMUSE button AboutDialog Figure 71 About DEMUSE dialog window Page 47 of 56 DEMUSE tool User Manual DEMUSE 5 Appendix I definition of DEMUSEtool reader When loading the sEMG files DEMUSEtool prompts for selection of a proper reader Figure 6 There are several readers already implemented in DEMUSEtool supporting all main acquisition systems currently available in LISIN lab For more complex acquisition configurations or other acquisition systems specialized reader of the sEMG files can be implemented and added to the DEMUSE readers directory located in the main directory of the DEMUSEtool The name of the reader must start with the string DEMUSEtool reader but can continue with arbitrary name A good practice is to specify the main parameters of the reader in its name so the user can easily ident
35. he i th sEMG measurement and E stands for sample mean Finally the range of SIRs of sEMG channels is displayed together with the reconstructed MUAP trains Figure 62 To display reconstructed MUAP trains select the corresponding electrode row or electrode column Figure 61 left panel and click on Plot MUAP trains button Figure 61 right panel Matlab figure with selected sEMG channels and corresponding MUAP trains appears Figure 62 Note Due to the large number of acquired sEMG channels only p selected row column of SEMG channels can be displayed in a one figure The number of figures however is not limited You can display the MUAP trains on all the SEMG channels by consecutively selecting the different electrode columns for example Page 40 of 56 DEMUSE tool User Manual DEMUSE About DEMUSE Plot MUAP trains Plot decomp residual ue a Cr wa way war wae war War wa wae Figure 61 Channels selection frame left Plot MUAP trains button and Plot decomp residual button right Row 4 SIR 38 46 Channel 1 j 4 4 5 5 5 5 6 6 5 7 Time s Figure 62 Matlab figure of selected sEMG channels blue lines and corresponding reconstructed MUAP trains red lines The range of SIRs of the depicted channels is displayed on the top of the figure Plots of reconstructed MUAP trains are displayed as matlab figures and can be freely manipulated by matlab fig
36. ify it For example reader DEMUSEtool reader 5x13 IED5mm telescopic pins SD m denotes the reader which reads surface EMG acquired by a matrix of 5x13 electrodes with inter electrode distance of 5 mm and electrodes on telescopic pins EMG signals were acquired in single differential SD mode DEMUSEtool automatically loads all the files whose name starts with DEMUSEtool reader into the list of available readers and display their descriptions in the Reader Dialog Window Reader for specific files can also be specified in a text file Simply write the name of corresponding Matlab routine in the text file called DEMUSE reader Tag txt e g DEMUSEtool reader 2x19 TEDomm telescopic pins Dm and save the file into the directory with corresponding sEMG files DEMUSEtool will automatically check the directory with sEMG files for DEMUSE reader Tag txt file and if found use the reader specified therein for all the seMG files in the corresponding directory Structure of reader is exemplified in Figure 72 All the text before the reserved keyword INPUTS is considered as a description and displayed by DEMUSEtool in the Reader Dialog Window Figure 6 Inputs to the reader are limited to the path and name of the sEMG file and optionally the length of the signal to be loaded in seconds If no signal length is specified the reader should return the entire signal in the file Page 48 of 56 DEMUSE tool User Manual DEMUSE
37. in Section 4 6 To open sEMG editor window Figure 27 click on sEMG editor button Figure 26 PRE ASIA sEMGeditor Figure 26 sEMG editor button lol File Edit View Insert Tools Desktop Window Help a Time s me 2h 2 75 2 8 2 85 2 9 2 95 Filter 20 500 Hz 1 o ove amp amp l ossy eo osos POCECE le oso es r r e amp o osos osovo eee e Figure 27 sEMG editor window For details see Subsections 4 5 1 4 5 5 Page 19 of 56 DEMUSE tool User Manual DEMUSE 4 5 1 Plotting sEMG signals sEMG editor window comprises three panels Figure 27 The top panel displays original SEMG channel black line and the residual after subtraction of identified MUAPs gray line The ID of MU discharging at a particular time moment is also depicted Figure 28 ID of MU discharging at this particular time instant Time s 4 15 42 4 25 43 IET AAA his dl Ba A AA i r Ve tia ah Ay pow y poe residual after subtraction of identified MUAPs original SEMG channel Figure 28 The top panel of sEMG editor window with original SEMG channel black line and residual after subtraction of the identified MUAPs gray line MUAP templates of identified MUs are superimposed over the original SEMG channel their IDs are listed on the top of each template Buttons at the left and right han
38. into the aforementioned text labels Figure 37 The sEMG signals and corresponding MUAP templates are automatically recalculated when cut off frequencies are changed Default cut off frequencies values are set to 20 and 500 Hz respectively Filter a0 500 Ha LEE ME ME NE NL TE NE SESE NE C M 2 8 E E E 4 5 4 LME BRL ALLA NE SESE OE Figure 37 Command frame of SEMG editor with SEMG channel panel Butterworth band pass filter cut off frequencies and Electrode configuration panel for single differential electrode configuration right and Laplacian electrode configuration left Above the filter cut off frequencies there is the Electrode configuration panel Figure 37 It allows the user to choose among different spatial filters applied to acquired sEMG signals The following four spatial filters are currently supported monopolar longitudinal single differential default longitudinal double differential and Laplacian sEMG channel selection panel sEMG channel displayed in the top panel and corresponding MUAP templates are automatically updated whenever a new spatial filter is selected Figure 37 Page 25 of 56 DEMUSE tool User Manual DEMUSE 4 6 Editing of the decomposition results CKC inspector CKC inspector allows editing the raw outputs of the gradient CKC method i e trains of delta pulses Inspector is launched by first selecting the MU from the Selected MU pup
39. is gives us confidence in the results of CKC decomposition Buttons on the edges of the lower panel control the size and position of the displayed portion of the MU discharge pattern Page 28 of 56 DEMUSE tool User Manual DEMUSE Figure 43 Portion of a MU discharge pattern same as in Figure 42 before left panel and after cancellation of the central MU discharge right panel In the right panel full cross pointer used for selection of the MU discharge is partially visible MU discharge is deleted by clicking on the delete discharge button positioning the full cross pointer over the MU discharge i e pulse and clicking the left mouse button increase MUAP decrease MUAP amplitude amplitude Motor Unit 2 exit MY TN V VV aa YY i i l A A jj 5 A Il o A L i An A ra zoom out on zoom in on time axis time axis Figure 44 Buttons for controlling the length and the scale of the displayed multichannel MUAP template and raw sEMG portions Buttons and scale the MUAP sEMG amplitude Buttons II and I I zoom in and out on the time axis respectively Page 29 of 56 DEMUSE tool User Manual DEMUSE 4 6 1 Deleting of decomposition results Reconstructed discharge patterns of specific MU can be deleted by first selecting the MU in a Selected MU pup up menu and then clicking on a delete MU button Figure 45 A window opens for conforma
40. late of MU 12 in Figure 34 deselects the corresponding MU Time s 4 44 4 46 4 48 45 4 52 4 54 4 56 4 2 6 4 2 54 1 Sl AA Pe nee ae Lr A Da E a Os AN EN p ya BH OO ee OG ori te AIDA a 1 3 7 8 9 pa ie Ae a Po ia Figure 34 Double click on a MUAP template of MU 12 followed by a click on a add selected MUAP button adds the MUAP to the top panel The MUAP template selected by double click is depicted by a red rectangle Note Double click on a MUAP template could directly result in i adding of the new MUAP occurrence to the top panel 8 However this would cause errors in the case of unintentional double clicks on the central panel Therefore adding of a MUAP occurrence must be explicitly confirmed by clicking on add selected MUAP button Page 23 of 56 DEMUSE tool User Manual DEMUSE 4 5 4 Moving and deleting MUAP occurrences Each MUAP occurrence displayed in the top panel can be manually moved to the left moved to the right and deleted respectively The user must first click on the displayed MUAP occurrence in the top panel in order to select it The selected MUAP occurrence is denoted by a thick red line Figure 35 Afterwards the selected MUAP occurrence can be moved or deleted by clicking on a lt lt move selected MUAPs move selected MUAPs gt gt and delete selected MUAPSs button respectively Time s 4 44 4 46 4 48 delete s
41. lbox matlab elfun q C Matlab6 Sitoolbox matlab specfun q C Matlab6 Sitoolbox matlab matfun no gt lol xj y L Help DEMUSE tool User Manual DEMUSE Figure 2 Setting the path in matlab programme environment in this case DEMUSE tool was copied to the directory c DEMUSEtool1 4 Using DEMUSE tool 4 1 Starting DEMUSE tool To start the DEMUSEtool type the following command to matlab command window gt gt DEMUSEtool The main DEMUSEtool window appears Figure 3 This window comprises four frames with the following groups of commands e loading band pass filtering and visualization of the acquired SEMG signals saving and reloading of the decomposition results e decomposition of acquired sEMG signals and manual inspection of decomposition results e graphical plots and animations of the decomposition results e graphical schema of acquisition matrix configuration loads and visualizes sEMG signals oo Properties a Load SIG file ilt J 20 f 500 Hz M Differential modi Plot signals About DEMUSE Signal quality 1 low 100 high 95 gt Save MU discharges Load MU discharges Proc ss ng tim Lo Rerun decomposition Apply to entire signal sEMG editor CKC inspector decomposes Sete S E M G S Ig Na S Plot MU discharges Plot discharge rates Plot IPI variability saves and reloads the results displays PlotMUAPs graphs and Animat
42. ls Smoothed discharge rates are calculated by low pass filtering of the instananeous discharge rates 1 order Butterworth filter with cut off frequency set to 3 Hz a5 Plat discharge rates Figure 50 Plot discharge rates button Page 32 of 56 DEMUSE tool User Manual DEMUSE 30r N O1 NO O O Instantaneous discharge rate pps a al of l l l e time s Figure 51 Plot of instantaneous discharge rates coloured thin lines Vertical axis depicts the instantaneous discharge rates in pulses per second pps Thick grey line depicts the measured muscle force 4 7 3 Inter pulse variability Variability of inter pulse interval IPI of reconstructed MU discharge patterns is displayed by selecting the MU in a Selected MU pup up menu and clicking on a Plot IPI variability button Figure 52 A window opens with four different plots Figure 53 inter pulse interval upper left panel smoothed discharge rate upper right panel Coefficient of Variability CoV of IPI bottom left panel and CoV of IPI versus IPI mean bottom right panel Smoothed discharge rate is calculated by low pass filtering the instantaneous discharge rate with 1 order Butterworth filter cut off frequency of 3 Hz Standard deviation of IPI is calculated over 10 consecutive MU discharges Piet MU discharges Figure 52 Plot IPI variability button left panel and Selecte
43. matical expectation In the second step the unknown mixing matrix H is compensated by calculating the linear minimum mean square error LMMSE estimator of the j th pulse train A l n Cox e H HCH C HEC 6 where C E x n x n is the correlation matrix of extended measurements x n and c E t n t n is the vector of cross correlation coefficients between the IPT of the j th MU and the IPTs of all the MUs active in the detection volume Estimator 6 requires the cross correlation vector e to be known in advance This is never the case and Holobar and Zazula proposed gradient based procedure for its blind estimation 4 Let F t t m denote a cost function in the space of MU discharge sequences with arbitrary differentiable scalar function F t applied to each sample of the estimated pulse sequence n General iteration step for gradient optimization of e is then defined as k l e 0 a i a 7 where y k is the learning rate in the k th iteration step Denote f t 0F t 0t Then the second factor in the update rule 7 simplifies to A o TM Qp 1 2k g 2k k ES GIA HC Eas f a o where d H Co is a match filter of the j th MU in the space of MU discharge patterns o is standard deviation of b m d H m and fl stands for a vector function with the rth element defined as fe a af a la where f z is the n th derivative of ft
44. n the Animate 3D MUAP map button Figure 58 left panel the animation window opens Figure 59 and the animation automatically starts The animation begins approx 5 ms Page 37 of 56 DEMUSE tool User Manual DEMUSE before the actual generation of the MUAP and ends approx 5 ms after the MUAP attenuation During the animation the propagation of MUAP along the muscle fibers can be observed Figure 59 a Selected MU ML 2 i P Animate 3D MUAF map Frames 6 10 aa YN H Figure 58 Animate 3D MUAP map button left Selected MU pup up menu and slider for selection of frame rate right Il i Frame 19 Frame 21 PA LB YS FOSS SS LE 7 ESA SSA Mie LLL OS LULL LP OLE SRO RIOR RRRS lt ES TF OR SRO RR SRR HIS SID Amplitude uV Amplitude VW x mm 1 Frame 25 Il g E Frame 29 Amplitude LV Amplitude uV 80 35 80 35 90 xX mm 90 x mm Figure 59 3D animation of MUAP generation propagation and attenuation MUAP amplitudes on different SEMG channels red circles specify the height of corresponding points on a 2D map heights of intermediate map points are calculated by the bilinear interpolation of the MUAP amplitudes in four adjacent SEMG channels Page 38 of 56 DEMUSE tool User Manual DEMUSE Buttons on the top of the animation window
45. o decompose the signal epoch with highest expected number of active motor units i e the last ramp in Figure 25 and then click on Apply to entire signal button Figure 24 Apply to entire signal button exerted muscle y y a o RE 13 poo Lo lt Pa hd RS MA o eo EN P sed e on k 1 5 e N go a raj ee s les a ES n i ia 0 Om AOS A EA 12 N 7s ese E en pats eat e ee Agua ss os Fs e A a once 2 1 0 1 A ene E a ai ci ma aoe MS 2 10 d 10 Br x at a 70 ates on T O a ANEN r aain Pel aeS 10 O qv J g 2 sp rp os 0 e de sty e g lt by 5 4 ss a ai r pr ES gt Y PA ce e Zn YA oy maar oy bast e a an x nthe ae Fsh es Has os 12 1 0 m e e O e pa eo e ss g 8 as ike 4 cod Miia eee pt ae ee Epi er aie ie a a 0 ES q i e O gt oo E e A e o PL s ee 2 gt TUN ra A p penae A AN E e aaan w vA hna saat sta 0 1549 O gt be e Poot Me 5 2 gang Meet Pe e E on NAL aN a N ne wie gt as et a Fhe Ao 0 D e o e o om C Jac EN gach AK Reach aks y he cos aire Hoi ATA coa a Utes AN ee M15 10 S amp ae d eo 4 o gt e a e e D 4 AA ENA SU ou A es 4 AA o GATA ar 15 49 E e e er ee A o e e i 5 2 e 09 A ue i A 3 Pre PATO E ENEE nara E 4 Prt tated gions ty Eh Int teo Ao TA 12 1 0 het Sete ceo g gt a Cir YE oo wt tions 3 A JA 2 ENT i as A iano E
46. ool automatically loads this information e g sampling frequency dimensions of the acquisition system electrode configurations etc and displays the number of acquired channels and their relative spatial configuration in Channel selection frame Figure 5 When requested information is missing DEMUSEtool prompts for selection of a proper reader for sEMG files Figure 6 There are several readers already implemented supporting all main acquisition systems currently available in LISIN lab For more complex acquisition configurations or other acquisition systems specialized reader of the sEMG files can be implemented and added to the DEMUSE readers directory see Appendix DEMUSEtool will automa tically load all the available readers and display their descriptions in the Reader Dialog Window Figure 6 To select the specific reader click on the line with its name Corresponding reader description is automatically displayed in the Reader Description Panel To confirm the reader selection and to continue with loading of the signal press OK button Proper reader can also be specified in a text file called DEMUSE reader Tag txt see Appendix Simply write the name of corresponding Matlab routine in DEMUSE reader _Tag txt file and copy the file into the directory with corresponding sEMG files DEMUSEtool will automatically use the reader specified in DEMUSE reader_Tag txt for all the sEMG files in the corresponding directory Page 9 of 56
47. pson ds equ ie SAR eet x e a E az er 1 24 0 A E n e y 1 a pti Penn Aa de fe airs SN 124 0 e Ci f L I I bd a 0123456789 101112131415161718192021222324252627282930313233343536373830404142434445 time s Figure 25 Result of Apply to entire signal button on an example of SEMG signals recorded during four force ramps of abductor pollicis brevis muscle Only the first force ramp was decomposed by clicking on Run decomposition button whereas discharge patterns on other three ramps were reconstructed by clicking on Apply to entire signal button Each dot corresponds to a single MU discharge Different MUs are denoted by different colours Page 18 of 56 DEMUSE tool User Manual DEMUSE 4 5 Editing of the decomposition results sEMG Editor DEMUSEtool integrates two toolkits for visualization and inspection of decomposition results First one so called sEMG editor allows editing of single channels and mimics the user interface of EMGLAB a popular intra muscular decomposition tool 7 User can easily switch among different SEMG channels but only one channel is display at a time The second toolkit so called CKC inspector allows inspecting the raw outputs of CKC method i e trains of delta pulses and displays the multichannel MUAPs as detected by the entire acquisition matrix In the sequel features of SEMG editor are briefly explained whereas CKC inspector is discussed
48. qual to 1 This makes low sensitivity to errors in vicinity of zeros a crucial advantage of fi0 log 1 1 function This is further demonstrated in Figure 74 where the value of vector d after the fifth iteration as calculated from theoretical approximation 9 red line and by direct numerical calculation 8 blue line is depicted Compare the vector values close to zero among different functions f t h t and R Page 53 of 56 derivatives f 0 A ri a ih S 03 7 4 w O 0 2 5 F S 0 1 Bot XK tee DEMUSE tool User Manual DEMUSE derivatives f 1 m 1 6 14 h O log 1 12 oe f O texp P 2 0 d pi fL0 tanh t 06 gt gt 04 0 2 OL relative error 34 56 7 8 9 0 Figure 73 The first few derivatives of the cost functions 7 t f gt and f3 1 at points t 0 top left panel and t top right panel and the relative error contribution as defined by 11 to A0 bottom left panel and to A1 bottom 1 07 0 5 right panel for different values Ej Ao texp 2 2 Iteration 5 SNR 0dB 180 200 0 1 0 0 5 20 40 60 80 100 120 140 160 At tanh t Iteration 5 SNR 0dB 0 1 0 5 100 120 140 160 180 200 20 40 60 80 l fit log 1 Iteration 5 SNR 0dB o j 100 120 140 160 180 200 20 40 60 80 0 800 1000 1200 1400 1600 1800 2000 Samples 200 400 600
49. rodes wih inter electrode distance of 3 5 mm and fixed pins Acquisition board for 64 channels is made by synchroonization of 4 or Cools ess sles Ok Carcel Figure 6 Reader Dialog Window for selection of the reader for SEMG signals Upper panel displays all available readers lower panel displays description of currently selected reader Selection of the reader is confirmed by pressing the OK button Page 10 of 56 DEMUSE tool User Manual DEMUSE DEMUSEtool 4 Oo x ES Loading of file failed Inproper SIG file reader Figure 7 Error Dialog Window signalling the failure of SEMG loading DEMUSEtool uses 1 order Butterworth band pass filter to filter the raw SEMG signals Filters cut off frequencies can be controlled by typing new values into the text labels shown in Figure 8 Default cut off frequencies are set to 20 and 500 Hz respectively 1 20 Asco f Figure 8 Text labels controlling the cut off frequencies of built in Butterworth band pass filter When the number of MUs contributing to the sEMG signals is high it might be beneficial to turn on the time differentiation of the sEMG channels Figure 9 Time differentiator is a high pass filter which suppresses the activity of small background MUAPs and enhances the discrimination of MUAPs from different MUs Selection of time differentiator is optional and left to the user A good practice is to play a bit with the time differentiation and band
50. tarts the decomposition med O Elf EA LE i Rerun decomposition Appl te entire slanal Figure 22 Text label displaying the total processing time Takip SMS dtl S Rerun decomposition Figure 23 Rerun decomposition button Due to the large number of acquired sEMG channels and high memory consumption of gradient CKC method the length of decomposition interval should generally be limited up to 20s Longer signals should be divided into 20s long epoch which should be decomposed independently Alternatively Page 17 of 56 DEMUSE tool User Manual DEMUSE the MU signatures in the space of discharge patterns can be reconstructed on a portion of a signal i e by running the decomposition on the first 20s long epoch and them applied to the entire signal length This takes much less time than separate decompositions of different epochs but is limited to MUs identified in the first time epoch only MUs recruited at latter time moments i e not active during the first epoch will not be identified In other words if we decompose first out of four consecutive force ramps in Figure 25 for example and then click on Apply to entire signal button we will quickly retrieve entire discharge patterns of MUs identified during the first ramp Figure 25 but will fail to identify MUs that were recruited after the first ramp e in second third and or fourth ramp only A good practice is t
51. technical details of gradient CKC method are briefly summarized Text provided describes the main decomposition concepts only whereas theoretical derivations of mathematical formulas are skipped Interested reader is referred to manuscripts 3 and 4 for all the details 6 1 Data model Suppose the sEMG signals are observed in M detection points and denote their sampled vector as x n x n x where x n stands for the n th sample of the i th measurement In the case of isometric muscle contractions the measurements x n can be modelled as outputs of a linear time invariant LTI multiple input multiple output MIMO system 4 N L 1 WM X VA OGD 0 m 1 M 1 J where v n stands for zero mean additive noise samples Each model input t n is considered a sample of a motor unit innervation pulse train IPT while causal and finite channel response h h D 0 1 L 1 Page 50 of 56 DEMUSE tool User Manual DEMUSE corresponds to the j th L samples long motor unit action potential as detected by the i th measurement No a priori limitations are posed on the channel responses h Thus properties of the detected MU e g its depth in the muscle tissue action potential propagation velocity as well as the properties of the detection system are described by h The innervation pulse trains t n 4 m ty 1 represent MU discharge times only and are modelled as sequences of Dir
52. tically displayed in the top panel while the bottom panel displays the instantaneous discharge rate plot Figure 31 Several MUs can be simultaneously selected Figure 32 AA lolx Fie Edit View Insert Tools Desktop Window Help x Time s 415 42 4 25 43 4 35 44 5 5 5 5 5 A p A A A pa Par hw AAAA Filter 20 500 Hz 9 Mi N 5 eo g eee eee bi ee eer see Ea o ss ss o ss eee ee oyy 9 o Discharge rate pps S Figure 31 MU 5 is selected by clicking on its MUAP template in the central panel MUAP occurrences and instantaneous discharge rates of selected MU are depicted in the top and the bottom panel respectively Page 21 of 56 DEMUSE tool File Edit View Insert Tools Desktop Window Help User Manual DEMUSE 10l x Time s 1 4 15 AUR RN ES o D A ooo Gaye ASM WHA e ARAS Bod AS RARA SEMENE A Bren e 00 0 09 20 Oo SAA Dd 2 SANET O 2 ost ou Ogangeg ECO 0 a 00 SAS ARA RAR TURTON Y OY A TORK RD og D am Filter 20 500 Hz ojo ojo e e 2 ee e2 o eco e e o eee CEE ME NE SE eco ep ome o Jo coco eco p o o e ee e eje ejeje Figure 32 The same as in Figure 31 with all MUs selected Each circle in the bottom panel corresponds to a single MU discharge Figure 33 The horizontal position of the circle denotes the MUAP occurrence time whereas i
53. tion of MU cancellation Figure 46 To really delete the MU click on Yes button To return to DEMUSEtool without deleting the MU click on No or Cancel delete MU ele SelectedMU MU 2 ll Figure 45 delete MU button eft panel and Selected MU pup up menu right panel 15 x Figure 46 window for conformation of MU cancellation Page 30 of 56 DEMUSE tool User Manual DEMUSE 4 7 Graphical results DEMUSEtool includes several tools for graphical representation of the decomposition results The user can plot the discharge patterns of reconstructed MUs instantaneous and smoothed MU discharge rates multichannel MUAPs and reconstructed MUAP trains In addition MUAP generation propagation and attenuation can be animated for each identified MUs All the graphical results are depicted in Matlab figures and can be easily manipulated by standard Matlab s editing tools Background colour of all the plots can be selected in Properties menu Figure 47 In the sequel description of each aforementioned graphical representation is provided Signal quality 1 lew 400 high 95 Figure 47 Properties menu allows selection of a background colour of all the plots of CKC inspector and of SEMG editor 4 7 1 MU discharge patterns plot MU discharge patterns are plotted by a click ona Plot MU discharges button Figure 48 A matlab figure opens with a
54. ts vertical position reflects instantaneous MU discharge rate calculated as the quotient between the sampling frequency and the inter pulse interval preceding the selected MU discharge The position and the length of the signal window displayed in the top panel is also depicted grey rectangle User can move to the time of a particular MU discharge by simply clicking on the corresponding circle N O Discharge rate pps y vertical scale denotes the instantaneous discharge rate of selected MUs in pulses per second pps Page 22 of 56 o o o 9 O 099 A o gt 0 0 Ya JO O 000 o CO 550 o o O position and length of the time interval currently displayed in the top panel each circle depicts single MU discharge Figure 33 Bottom panel of the sEMG editor window with the instantaneous discharge rate plot of a selected MUs DEMUSE tool User Manual DEMUSE 4 5 3 Adding a new MUAP occurrence A double click on a MUAP template in the central panel followed by a click on the add selected MUAP button adds the MUAP of the selected MU to the top panel The optimal MUAP position is automatically determined by the minimum squared error between the residual signal Figure 34 gray line and the selected MUAP template In the central panel the selected MUAP template is denoted by a red rectangle Figure 34 central panel A further double click on the already selected MUAP template e g MUAP temp
55. ty MU CV corr and MU conduction velocity on a selected triplet of SEMG channels triplet denoted by red triangles in the upper panel Left bottom window displays statistics for an individual MU averaged over all surface channels Right bottom window reports statistics averaged over all the MUs Mean value standard deviation minimum and maximum are reported for each of aforementioned metrics User can move among different MUs by clicking on lt lt and gt gt buttons Page 44 of 56 DEMUSE tool User Manual DEMUSE 4 8 Saving and reloading of the decomposition results Decomposition results can be saved by clicking on the Save results button Figure 67 The results are automatically saved into the directory containing the currently loaded SIG file The following file naming convention is used NameOfTheSIGfile offsetN runsM mat the name of the Initial Number of currently loaded Signal decomposition SIG file offset iterations where NameOfTheSIGfile stands for the name of the currently loaded SIG file N is the initial signal offset in seconds and M is the number of decomposition runs see Section 4 4 for details For example the decomposition results of a SIG file Subject1 SIG with initial signal offset set equal to O and number of decomposition iterations set equal to 30 is saved in the following matlab file Sun Jectl OCEESELU cunsod mac Saved results can be reloaded by clicking on the Loa
56. ure 66 Left bottom window displays statistics for individual MU averaged over all surface channels Right bottom window reports statistics averaged over all the MUs Mean value standard deviation and minimum and maximum values are reported for each of aforementioned metrics Triplet of SEMG channels selected for calculation of MU conduction velocity on selected channels Is denoted by red triangles User can move among different MUs by clicking on lt lt and gt gt buttons A I calc MUAP stat Figure 65 calc MUAP stat button Page 43 of 56 DEMUSE tool User Manual DEMUSE eee mu 3 Statistics for all MUs mean mean MUAP p2p mV 0 08 0 06 i fi MUAP p2p mV 0 13 MUAP energy mV 0 01 0 01 1 MUAP energy mV 0 02 MUAP length ms 0 2 0 03 MUAP length ms MU CV mis 2 73 0 07 MU CV mis MU CY corr 0 93 0 03 MU CY corr MU CY on selected channels mis 2 76 MU CY on selected channels mis Figure 66 MUAP statistics window with upper panel displaying multichannel MUAP of selected MU as spatial double differential derivatives of SEMG channels Displayed MUAPs are spatially organized in rows and columns reflecting the relative position of pick up electrodes Lower panel displays the MUAP peak to peak amplitude MUAP p2p MUAP energy MUAP length MU conduction velocity MU CV correlation coefficient between the MUAP shapes used for calculation of MU conduction veloci
57. ure editing tools i e figure resizing zooming rotating printing etc Zoomed in portion of Figure 62 is depicted in Figure 63 The user is referred to matlab documentation for further details on the use of the matlab s graphic user interface Page 41 of 56 DEMUSE tool User Manual DEMUSE Row 4 SIR 38 46 o 1 is i di hi i A j M O pm Channel ity 5 15 5 2 5 25 53 5 35 5 4 5 45 Time s Figure 63 Matlab figure with selected sEMG channels and corresponding MUAP trains short signal segment from the signal shown in Figure 62 Click on Plot decomp residual button Figure 61 left panel opens the Matlab figure with selected SEMG channels and corresponding residuals after subtraction of estimated MUAP trains Figure 64 Range of SIRs of displayed sEMG channels is displayed at the top of the figure Row 4 SIR 38 46 Channel 4 4 5 5 5 5 6 6 5 7 Time s Figure 64 Matlab figure of selected sEMG channels blue lines and residual after subtraction of reconstructed MUAP trains red lines The range of SIRs of the depicted channels is displayed on the top of the figure Page 42 of 56 DEMUSE tool User Manual DEMUSE 4 7 8 MUAP statistics DEMUSEtool integrates a simple tool for calculation of MUAP statistics of individual MU Currently the following metrics are supported MUAP peak to peak amplitude MUAP energy MUAP len
58. ved Figure 57 Buttons on the top of the animation window Figure 57 enable the following actions e gt button re plays the animation e button pauses the animation e button stops the animation e lt P button animates the previous animation frame i e step backward e s lt animates the next animation frame i e step forward Current animation frame is displayed in the top right corner of the animation window Figure 57 Note Animation window cannot be closed while the animation is running Stop the animation by clicking on or button 9 before you close the figure 4 7 6 3D MUAP map animation The second animation provided by the DEMUSEtool includes a 3D plot of MUAP amplitude in time By analogy with the animation of 2D MUAP map MUAP templates are first estimated by a spike triggered averaging of SEMG channels SEMG channels are then spatially organized into a discrete 2D map reflecting the relative position of pick up electrodes The amplitudes of MUAP templates at a given time instant specify the height on this 2D map of channels Missing intermediate points on the map are calculated by bilinear interpolation of MUAP amplitudes in four adjacent sEMG channels In the next animation frame the time is moved forward by one signal sample and the 3D map is recalculated To start the 3D animation select the MU and the animation frame rate Figure 58 right panel After clicking o
59. vement artefacts and bad skin electrode contacts 4 3 sEMG signal visualization To display loaded time differentiated and or band pass filtered sEMG signals select first offset and the length of signal interval to be displayed Figure 11 left bottom panel select the corresponding electrode row or electrode column Figure 11 left panel and click on Plot signals button Figure 11 right panel Matlab figure with selected sEMG channels appears Figure 12 Zoomed in version of Figure 12 is depicted in Figure 13 Note Due to the large number of acquired sEMG channels only p selected row column of SEMG channels can be displayed in one figure The number of figures however is not limited You can display all the SEMG channels by consecutively selecting the different electrode columns for example Plot signals Vcomp Pane JU Ce ee er ee cr er Figure 11 Channel selection frame with selected 9 row of electrodes left panel and plot signals plot spectra buttons right upper panel and sliders for selection of offset and length of displayed signal interval right bottom panel Page 12 of 56 Channel Channel DEMUSE tool User Manual DEMUSE Row 4 Time s Figure 12
60. y used in gradient CKC optimization of estimated MU discharge patterns User can select among the following possible values see Appendix ll for details about selection of gCKC nonlinearity Page 14 of 56 rn e rr y iisas 800 DEMUSE tool User Manual DEMUSE Value of parameter Nonlinearity used by ir f x log 1 x2 f x oa 1 x04 f x x42 e f x 2 x 1 x 12 f x x log 1 x42 2 x 2 atan x x log 1 x 2 gt atan x The initial offset and the length of SEMG time interval to be decomposed can also be selected by dragging the sliders in Figure 18 gCKC is a sequential motor unit MU identification technique and requires one iteration run per each reconstructed MU The user can predefine maximal number of iterations by moving the slider Decomp runs Figure 17 As a general rule the number of iterations should be larger or equal to the number of expected MUs excluding the small and deep MUs which contribute the background noise only As the exact number of MUs is difficult to estimate the number of decomposition runs should be large default value is set to 30 DEMUSEtool automatically tests the reconstructed MU discharge patterns against the predefined ranges of physiological variables i e discharge rate variability of inter pulse interval etc and discards all the outliers As a result from 5 to 15 most reliably reconstructed MUs are taken into consideration Reconstructed M

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