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LYNGBY Matlab toolbox for functional neuroimaging analysis

1. Woh1 Ti 2Zh 1 211 32 oo 22 1 22 C 33 lLars Kai Hansen et al 1997 Section C 1 Neural Netvvork 83 The derivative for the errorfunction is Np No 0 He 1 l m in ig 22h 1 34 S yo Soo Yo Wo ho 1 2 Ziz Wohi 1 z 5 C 35 ES 5 Yo to Woh Ohy ho 22h 1 za C 36 Np S Yo Soo Yo Won 1 za Won 1 s l C 37 o No No r Titis 25232 Yo to wWon zn 1 Zh C 38 Yo doo Yo Wo ho 1 2 Woh 1 2 C 39 VVith diagonal approximation the derivative becomes No No PE T T aa 5 12 y E Yo to Woh Zh 1 za C 40 hi p o o TYo doo o Yo Woh Woh 1 2 C 41 C 1 3 Numerical stabil computation of softmax The softmax function has an exponential divided by an exponential which makes it prone to congest the range of the data type and divide Inf with Inf For 64 bit double data type this happens a bit over 700 gt gt log realmax ans 709 7827 To cope with this problem the softmax function can be reformulated _ explo explgo k C 42 yoxe exp dy 1 Sm explo 4 1 exp k E exp dy k expl And by setting k max we can make sure that the exponential in the numerator does not saturate against Inf and it does not matter that the denominator saturate against Inf for comp
2. 1970b Ridge regression Biased estimation for nonorthogonal problems Technometrics 12 1 55 67 Jackson J E 1991 A user s guide to principal components Wiley Series in Probability and Mathematical Statistics Applied Probability and Statistics John Wiley amp Sons New York Lange N Hansen L K Pedersen M W Savoy R L and Strother S C 1996 A con cordance correlation coefficient reproducibility of spatial activation patterns In Belliveau et al 1996 page S75 Lars Kai Hansen et al 1997 BIBLIOGRAPHY 94 Lange N and Zeger S L 1997 Non linear fourier time series analysis for human brain mapping by functional magnetic resonance imaging with discussion Applied Statistics Journal of the Royal Statistical Society Series C 46 1 1 29 Le Cun Y Denker J S and Solla S A 1990 Optimal brain damage In Touretzky D S editor Advances in Neural Information Processing Systems Proceedings of the 1989 Conference pages 598 605 San Mateo CA Morgan Kaufmann NIPS 2 Liptrot M Adams K H Matiny L Pinborg L H Lonsdale M N Olesen N V Holm S Svarer C and Knudsen G M 2003 Cluster analysis in kinetic modelling of the brain A noninvasive alternative to arterial sampling NeuroImage In press Locascio J J Jennings P J Moore C I and Corkin S 1997 Time series analysis in the time domain and resampling methods for studies of functional magnetic
3. b a z r ils ee GLA to Geb 4 2 4 1 How Lyngby Reads in Data 2 4 2 Setting up the Conversion Files for Non supported Data Formats 2 4 3 Examples of the Data Conversion Files 2 5 Using the Lyngby Windows Interface o 2 5 1 The Workflow in the Lyngby Toolbox 2 5 2 A Typical Analysis Session 2 5 3 Exporting Variables Printing and Saving Results 2 6 Using Lyngby from the commandline 2 61 Data Lord a to er aes Mace s Ow A ae s fa 2 60 2 Pre Processing aa a a M R AO Pe 2 6 3 Global Variables tutelar a ee a byt tae a a bee 2 7 Writing Scripts to Run Lyngby Automatically 2 2 8 Adding New Algorithms to the Toolbox O oNN 10 10 11 11 11 12 12 12 CONTENTS 3 Data Formats Masking and Pre Processing Jl AntrOductiOn s ca EA 77 ne 32 Volume file formats z Maskingizi e aa Bok cite AA Seni Sd 34 Preprocessing Steps 225 2 a ea a a eo a SAL Genterin areri a o a a ne as 3 4 2 Variance Normalization sofaer Donie Analysis The Modeling Algorithms 4 1 Cross correlation ee 4 1 1 Our implementation 4 27 PIR filter site Pane 4 2 1 Estimation of the Activation strength in the FIR filter 4 2 2 Estimation of th
4. lLars Kai Hansen et al 1997 88 Once the calculations have finished as shown in the status line then the results can be viewed The control window initially shows two lay ers The lower one controls the right hand time based window while the upper one is used to control the left hand volume based window The Time window shows the time series for whichever voxel is selected in the Volume window The current voxel location is shown above the time series in the form x y z Note how the data in the top left of the image x 32 34 y 1 z 34 corre lates better with the paradigm than that at the bottom right x 14 20 z 40 45 Note also how the FIR model red line matches the data far more closely in these highly activated regions For the FIR filter there are several results for both the volume and time windows The Activation Strength shows better contrast be tween the activated and non activated re gions The time display can also display other types of data that are voxel dependent For in stance the FIR filter algorithm generates a range of results displaying histograms of the greyscales of a voxel through the time series The different areas in the volume have dif ferent greyscale distributions Note that the distribution in activated areas has a bi modal distribution reflecting the two dis tinct grey levels that occur during the ac tivated and non activated states whilst the distribut
5. T y Kronecker s delta Output of the neural network before the softmax is applied Errorfunction for the classifier neural network Index for hidden units Index for input units Number of outputs Number of patterns i e examples or scans Index for output unit Index for pattern Probability Training set Target output for the neural network Weights parameters in the neural network Input layer weights first layer weights Output layer weights second layer weights Input for the neural network Predicted Output of the neural network after the softmax is applied 79 Section C 1 Neural Netvvork 80 z The hidden unit value after the activation function has been applied In the following the index for pattern has been omitted so that what should have been written as al z ob yb and 4 or in an equivalent notation is written as i Zh Po Yo and to C 1 2 The errorfunction for the classifier neural network and its derivatives The errorfunction for the classifier neural network is developed from the conditional probability Np No p Tlu I y x u y C 1 p o The error function is constructed as the normalized negative log likelihood of the parameters u and with the two layer feedforward neural network with an added softmax layer and a 1 of c 1 coding scheme or rather 1 of no 1 coding scheme we get E C 2 3 toas C 4 1 1
6. U TU A kl 4 46 1 2 U A a kx kx 4 47 If kx 0 as in ordinary CVA we will get a simpler equation 1 2 1 2 a ka GTG kal GT UA TAC 4 48 U A A 1 4 49 U 4 50 U is an orthonormal matrix it is a matrix containing eigenvectors eigensequences of the original datamatrix Such a matrix does not contain any principal direction All directions are equally strong 1 e the eigenvalues have the same magnitude Multiplying with another orthonormalized matrix e g the designmatrix part of equation 4 50 will not bring up any new principal direction When there are no principal directions in the matrix the eigenvectors eigenimages cannot be said to represent anything but an arbitrary direction Lars Kai Hansen et al 1997 Section 4 13 The SOP model Strother Orthonormalized PLS 61 4 12 1 Our implementation The main function that implements the SCVA model is called lyngby_scva_main Before the datamatrix is singular value decomposed it is doublecentered The actual canonical variate analysis function is called lyngby_cva The number of components singular values maintained in the final singular value decom position can be varied by the user Usually only three or less components are significant The function will only return eigenvectors with eigenvalues that are different from zero i e larger than a tolerance set to account for numerical round off errors In t
7. each of which may have several runs The spatial data which could be 2D or 3D available at each time point Sometimes this is referred to as a scan or volume A portion of a window in the Lyngby toolbox that contains buttons that are related to each other The main Lyngby window consists of a separate frame for each of the processing stages A term used in image processing to describe individual images put together to form a single composite image viewed on common axes Part of each image will be transparent allowing the images under neath to show through It is rather akin to the building up of a cartoon frame from different cells a character or item is drawn on clear plastic The majority of the layer is transparent allowing anything underneath to show through However individual items are not transparent and will obscure those directly underneath A portion of a window in the Lyngby toolbox that contains buttons that are related to each other The Load New Data window has three panes for the data parameters external influences and the window control buttons The activation signal usually binary that indicates when the subject in a functional imaging experiment is performing some task The stage that comes after the analysis of the data It usually con sists of some form of analysis of the results sets such as clustering of all the result parameters Pre processing Sagittal slice Transversal slice
8. 9 2 10 2 11 2 12 2 13 3 1 4 1 4 2 4 3 4 4 4 5 The main control window in Lyngby 22 The file load window in Lyngby 24 The time window in Lyngby 25 The volume window in Lyngby showing three orthogonal views and a 3 dimensional 0150600101 26 The External influences window in Lyngby 27 The run window in Lyngby 27 The paradigm window in Lyngby 28 The preprocessing window in Lyngby 28 The Neural Network Saliency parameter window in Lyngby 29 The Neural Network Saliency results window in Lyngby 30 The Concept of Layers in the Result Windows 2 31 Volume result window in mosaic mode 34 Meta K means parameters 35 The data matrix a aa da al A A Go td a 44 Time series assignment l Clustered VEROS a sala iz sa daya s m yi a e 52 The gamma density kernel 54 The gamma density kernel 54 Comparison of errorfunctions 56 List of Tables 21 2 2 2 3 24 3 1 B 1 D 1 E 1 Direction of the axes in Talairach coordinate space o oo aa 2 18 Architecture Independent Variables 19 Global variabl
9. A parameterized convolution model with a grid search of optimal parameters with zoom built in The same as above but a non iterative grid search scheme for estimating the parameter is used The model estimates three parameters that have easy physical interpretation Tterative Lange Zeger model A parameterized convolution model with an iterative scheme for estimating the model parameters The model estimates three parameters that have easy physical interpretation The Ardekani t test A linear transform of the time series mapped to a subspace controlled by the paradigm In this method the activation estimator can be approximated to be Student t distributed hence a statistical measure of the correlation to the paradigm is found The method has been described by Babak Ardekani and Iwao Kanno Ardekani and Kanno 1998 Ardekani F test A linear transform of the time series mapped to a subspace controlled by a finite size Fourier based subspace In this method the activation estimator can be approximated to be F distributed hence a statistical measure of the energy in the subspace relative to the energy lying outside of this subspace is found The method has been described by Babak Ardekani and Iwao Kanno Ardekani and Kanno 1998 Ardekani F test with nuisance subspace A variation of the Ardekani F test where a nui sance subspace is identified and extracted from the signal The method is described in Ardekani et al 1999 Ordinary t test Fro
10. All the functions associated with the graphical interface to lyngby are called lyngby_ui_ Furthermore functions to each algorithm also have a special prefix For example the FIR filter algorithm uses the files lyngby_fir_ and lyngby_ui_fir_ A Lars Kai Hansen et al 1997 Section 2 4 Data Setup 15 very useful index of all the toolbox function files and their inter dependencies can be found on the Lyngby website Within the GUI there are Help buttons at various stages Clicking on a Help button will bring up a single dialog box explaining the purpose of the different windows and the options within them In addition most of the windows have a Tooltips option invoked from the Options window menu or with the lt Ctr1 T gt key combination These Tooltips will pop up handy explanations for any button over which the mouse pointer rests temporarily They are meant for the new user although they are set to be off by default as they can become distracting after a short while 2 4 Data Setup This section will deal with getting data into Lyngby It will cover the file formats that Lyngby can currently read and will also explain how your own data format even highly custom or non standard formats can be read in 2 4 1 How Lyngby Reads in Data There are two ways to get new data into Lyngby either by the file formats already supported or via a conversion process that will allow any non supported file format to be read For the s
11. Initialize K cluster centers co Of same dimensionality as the time series iteration 0 2 Assign each data vector x to the cluster with the nearest center cl Currently we use the ordinary Euclidean distance metric rene x l Lars Kai Hansen et al 1997 Section 4 6 K means Clustering 52 Data vectors are assigned closest cluster center Figure 4 2 In a high dimensional space the data vectors are clustered to the nearest cluster center 3 Set new cluster centers cur to the center of gravity of each cluster i 1 cl eco 4 19 This formula can also be modified to use the median and or to include an inertia term 4 Goto step 2 until convergence 4 6 1 Our implementation Instead of using the time series directly as the input to the K means algorithm we have made it possible to use the cross correlation of the fMRI time series and the paradigm This has a major impact of the results of K means algorithm which will make it far easier to find the activated voxels Toft et al 1997 When clustering on the cross correlation function or the raw time series the final clusters centers will be affected by the amplitude level and a possible lag For instance if two spatially separated regions have similar response strength but different delays then they will be clustered into two different clusters according to their delay values The toolbox enables clustering using K means or K median K mediod Th
12. Neurolmage volume 5 Academic Press Friston K J Frith C D Frackowiak R 5 J and Turner R 1995a Characterizing dynamic brain responses with fMRI A multivariate approach NeuroImage 2 2 166 172 Friston K J Holmes A P Worsley K J Poline J B Frith C D and Frackowiak R S J 1995b Statistical parametric maps in functional imaging A general linear approach Human Brain Mapping 2 4 189 210 Friston K J Jezzard P and Turner R 1994 The analysis of functional MRI time series Human Brain Mapping 1 2 153 171 92 BIBLIOGRAPHY 93 Gold S Christian B Arndt S Zeien G Cizadlo T Johnson D L Flaum M and Andreasen N C 1998 Functional MRI statistical software packages A comparative analysis Human Brain Mapping 6 2 73 84 Goutte C Nielsen F and Hansen L K 2000 Modeling the haemodynamic response in fMRI using smooth FIR filters IEEE Transactions on Medical Imaging 19 12 1188 1201 Goutte C Nielsen F Svarer C Rostrup E and Hansen L K 1998 Space time analysis of MRI by feature space clustering In Paus T Gjedde A and Evans A C editors Fourth International Conference on Functional Mapping of the Human Brain Neurolmage volume 7 page S610 Academic Press Goutte C Toft P Rostrup E Nielsen F and Hansen L K 1999 On clustering fMRI time series Neurolmage 9 3 298 310 Hansen P C 1996
13. ROI to Full volume Normalize in vertical direction of a datamatrix Normalize Preprocess a datamatrix Returns the masked number of scans volume Returns the paradigm Global variables for preprocessing Initialize global variables for preprocessing Returns the begin and end index of the volume Transform ROI definition to masking matrix Returns the run specification Number of runs and scans within runs Returns indices for a specified slice Swap the xyz order in a volume Returns Talairach brain plot in the style of SPM Return time mask from indices Prints which temporary files was opened by lyngby Get sequence from temporary file of data matrix Get volume in temporary file for all voxels mitialize temp file for datamatrix Read Write Section B 1 Available Functions lyngby_tmp_putseq lyngby_tmp_putvol Matrix Operations lyngby_std lyngby_test_wilrank Statistics Tests lyngby_ts_ftest lyngby_ts_global lyngby_ts_init lyngby_ts_main lyngby_ts_pttest lyngby_ts_ttest lyngby_ts_uttest lyngby_ui_ts_init lyngby_ui_view_ts lyngby_uis_ts lyngby_uis_ts_v General User Interface Functions lyngby_ui_credit lyngby_ui_global lyngby_ui_loadfile lyngby_ui_loadsetup lyngby_ui_main lyngby_ui_message lyngby_ui_movie lyngby_ui_option lyngby_ui_para_draw lyngby_ui_paradigm lyngby_ui_preproc lyngby_ui_resinfo lyngby_ui_run lyngby_ui_run_no lyngby_ui_saveresult lyngby_ui_time lyngby_ui_time_be lyngby_ui_view lyngby_ui_view_dfl
14. Trial as in single trial Volume OLars Kai Hansen et al 1997 66 The stage after the data has been loaded into the toolbox but before the data analysis is started It is an initialization stage used to get the data into the correct form for analysis by the usual algorithms It usually involves some form of mean removal nor malisation and or removal of any unwanted scans The part of a time series of functional images where a certain task is performed A run usually consists of several cycles of a paradigm A single experiment can consist of several runs A slice taken through a spatial volume For the example of a person this would be like looking at them from the side As such the slice index goes from left to right Derived from the Latin word for arrow due to the direction of the cutting plane indicated by the angle of an arrow striking a person from the front A spatial volume one voxel thick i e a 2 D image Usually refers to an entire time series e g trial or run and as such can be thought of as a volume with time as the third dimension A slice taken through a spatial volume For the example of a person this would be like looking at them from above As such the slice index goes from inferior superior or bottom to top An experiment where only one task is performed usually repeated several times A spatial volume of slices usually spatially adjacent with a time reference It can be thought of
15. ae 2 exp 6v 3 eu C 19 et no 1 no 1 o o g z 20 2 ye ae C 20 no 1 o o gt Yo Soo Men C 21 We can now use equation C 21 in C 16 arriving at PE 5 E d Bho ot doo 22 Np 2 9 dm The partial derivatives for the 6 output are the same as for the quadratic neural network For the output weights w we have d OWoh Zp C 23 lLars Kai Hansen et al 1997 Section C 1 Neural Netvvork 82 Combining equations C 14 and C 23 makes the derivative for the errorfunction to DE b t 24 Fae o C 24 For the input weights v we have Woh 1 Zh Ti C 25 DE LE m A y Yo to Won 1 za Ti C 26 The second order derivative the Hessian is more complex and it can unfortu nately luckily be approximated in a number of ways using only the Gauss Newton term and diagonalizing it The derivative for the output weights is relatively simple O d y 777 700102 27 l hi OWooho Pha Pha E bS Np y Yo to Zhi Zhe Yor 50102 Yoz h Zha C 28 Tip m ye Yo Yoz 260102 Yo Sor02to Zhi C 29 p The diagonal approximation is PE a 3 3 w np SN y a 2Yo gt to z l C 30 For the input weights we have ao 2 w 1 zp Le C 31 OVhoin OUR Whois i
16. and then the filter for each value of u can be generated from the linear transform h TY 4 11 This type of regularization is the same as principal component regression Jackson 1991 Note that for the FIR filter with a symmetric paradigm symmetric with respect to rise and fall flange the response will also be symmetric This means that if you have for example an on off square wave paradigm then a positive spike at the rise flank will force a negative spike at the fall flank Lars Kai Hansen et al 1997 Section 4 2 FIR filter 48 4 2 1 Estimation of the Activation strength in the FIR filter Using the estimated FIR filter an activation strength can be defined as the standard deviation of the data estimate normalized by the standard deviation of the paradigm A u 4 12 where V is a variance estimator 4 2 2 Estimation of the delay from the FIR Filter Dealing with a FIR filter makes it easy to derive several descriptors One is the group delay e g Oppenheim and Schafer 1989 pp 205 defined as H v H o yar H w 5 E where index r and i denote the real and the imaginary part respectively N H w Y h n e d n cos wn j sin wn 4 14 n 0 OH t jwn 1 alu y nh n e 1 sin wn j cos wn 4 15 which means that the delay has a frequency dependence and given that the paradigm functions often are dom
17. autocorrelation in the noise Lars Kai Hansen et al 1997 Chapter 5 Post Processing Revision 1 8 Date 2002 08 14 12 44 33 This chapter covers the post processing or meta analysis stage within the toolbox This is where the results of the previous analysis stage are then themselves analysed in an effort to gain more insight and robustness into the location of stimulations within functional images Currently only one post processing algorithm has been implemented within the toolbox although more are in the pipeline Any suggestions for expanding this section will also be greatly received 5 1 K means Clustering on the Modelling Results As described in section 4 6 the K means clustering algorithm can be used to cluster from the time series or the cross correlation function It can also be taken a step further and be used as a post processing tool Here the result of the modelling method is fed into the K means algorithm regardless of the number of parameters generated For the Kolmogorov Smirnov test the clustering could be made solely on the maximum test size but with the FIR for example the whole filter could be fed to the clustering algorithm The K means will then cluster the similar results into the same bins hence a label is generated for each of the voxels Note that this strategy can be questioned If for instance a measure of activation and a delay measure are generated for each voxel and fed into the post
18. data Both of these documents are available on the Lyngby website for seperate download and are also included in this book as Appendices D and E respectively 2 2 2 Using Lyngby On Your Own Data If you want to use Lyngby to analyse your own data there are two main approaches If the data is in one of the supported formats Analyze Vapet Stimulate or Raw then you can simply load the data directly into the toolbox However if you data is in any other format you will need 13 Section 2 3 Using Lyngby 14 a few simple conversion files to act as format translators These are very simple to write and once stored alongside the data will allow seamless loading of your data with little or no user intervention required These files the supported data formats and detailed instructions on how to load data into the toolbox are given later on in this chapter and in the next 2 3 Using Lyngby From this point we will assume that the user has followed the Getting Started guide and installed Lyngby correctly It may also be advantageous for the user to have worked through the Example Analysis guide to see how the Lyngby toolbox can be used to analyse fMRI data 2 3 1 Starting Lyngby Lyngby can be run either through the graphical interface or through the Matlab commandline The toolbox consists of over 300 Matlab script m files which can all be executed from the Matlab prompt This allows the advanced user great flexibility and th
19. follows the time series Once the results have been analysed you will probably want to save them In Matlab you are able to save the entire variable and re sult set into a single file which can then be reloaded at a later date without having to re specify all the data loading parameters Alternatively you may want to save a subset of the results The toolbox has a new save layer which can be used for this purpose As an example we will save the time sequence for the current voxel Other options allow you to save the present slice or the en tire volume Click on the button and the lyngby main window will disappear On the command line type gt gt 1yngby ui global In the command line type gt gt whos Lars Kai Hansen et al 1997 Once you have finished using the GUI just close it All the variables will still be accessi ble from the command line To make the results and variables visible to the command line you will need to make them all global You can also do this whilst the GUI is still open This will then display all the variables as used in the calculations You can now access the individual results and variables 91 Bibliography Aguirre G K Zarahn E and D Esposito M 1998 A critique of the use of the Kolmogorov Smirnov KS statistic for the analysis of BOLD fMRI data Magnetic Resonance in Medicine 39 500 505 Alldredge J R and Gilb N S 1976 Ridge r
20. layer and select the Cluster mean seg from the pop up list The Time window will now show an additional red line representing how the mean of the cluster that the selected voxel is a member of varies with time In the main window click on the button in the seventh pane The entire workspace is then saved into the file lyngby_workspace mat located in the directory from which lyngby was started Click on the button to bring up the standard four layers plus the extra Save layer Click on the first button on the Save layer and select the Sequence option On the sec ond button select the Matlab Binary option Type in a filename into the edit box and then press the Save here lLars Kai Hansen et al 1997 90 Next we can cluster the actual parameters of the FIR filter a Meta K means clustering of the results This enables us to look for patterns in the result dataset The post processing analysis can then be started with feedback on the progress given on the status line The results are viewed in the same way as the main analysis results The data can then be analysed using the same techniques as for the main anaylsis results The Volume window shows the voxels in their correct locations but with the colour indi cating their cluster membership Note how the voxels near the upper left of the image around x 31 y 1 2 34 are members of the same cluster and that the mean of this cluster most closely
21. lyngby_ui_viewvol lyngby_ui_volume lLars Kai Hansen et al 1997 71 Store a sequence in a temporary file of data matrix Store volume in temporary file for all voxels Take the standard deviation of a matrix Wilcoxon sign rank test F test for two samples Global variables for TS analysis method Initialize globals for t test analysis method Whole volume Student s t test for equal variances Student s paired t test Two sample Student t test equal variances Student s t test for unequal variances User interface for initialization of t test t test viewing function Script executed for t test analysis Script for t test view Display a credit Defines global for the user interface Opens a window for specifying file parameters Opens a window for specifying file parameters Main function for the GUI for lyngby Display a message User interface for movie Option setup for user interface Jser interface for paradigm viewing and specification Jser interface for paradigm viewing and specification JI for setting up preprocessing parameters Defines global for the user interface User interface for run viewing and specification User interface for time mask specification Opens a window for specifying file parameters Jser interface for time mask specification Jser interface for time mask specification Jser interface for viewing results Default viewing function View full volume timeserie and specify ROI and voxelmask
22. network output diag 2nd 2nd order der of regularization for weights Classifier neural network input 1st der Classifier neural network output 1st der Neural network regularization 1st der Classifier neural network error Classifier neural network forward Main functions for classifier neural network Cost function error regularization Classifier neural network OBD pruning Classifier neural network soft linesearch Softmax for neural network classifier Classifier neural network training 2nd order entropic input diag sym Entropic neural network output diag 2nd 2nd order der of regularization for weights Entropic neural network input 1st der Entropic neural network output 1st der First order derivative Regularization Neural network entropic error Hodge Lehmann Neural network entropic error median Calculate cross entropic error Entropic neural network feed forward Main function for Entropic Neural network Pruning by Optimal Brain Damage entropic Soft linesearch with the entropic cost function Soft linesearch with the quadratic costfunction Normalize target for entropic neural network Entropic neural network training Initialize weights in neural network Neural network plot the network weights Pruning by Optimal Brain Damage 2nd der quad all weights gauss approx Section B 1 Available Functions lyngby_nn_qddevds lyngby_nn_qddevs lyngby_nn_qddewds lyngby_nn_qddews lyngby_nn_qddru lyngby_n
23. of the delay from the Lange Zeger model The Lange Zeger model is in principle a constrained version of the FIR model hence a delay can be estimated just as it was in subsection 4 2 2 In the Lange Zeger case the spectrum has a rather simple expression olay 1 a 4 22 Kai Hansen et al 1997 Section 4 8 Lange Zeger 54 The convolution kernel for 02 1 and a set of values of 9 Figure 4 3 The gamma density kernel as a function of the time t for 6 1 and 02 1 for a set of 01 The convolution kernel for 8 5 and a set of values of 8 Figure 4 4 The gamma density kernel as a function of the time t for 6 1 and 6 5 for a set of hence the delay for very low frequencies w 0 ends up in a very simple form 4 23 Kai Hansen et al 1997 Section 4 9 Neural netvvorks 55 4 8 2 Our implementation Compared to the original algorithm our algorithm does not perform any noise estimates as suggested in Lange and Zeger 1997 Furthermore we have experienced that the iterative way of estimating the model parameters suggested in Lange and Zeger 1997 is often unstable which cannot be explained with the lack of a better noise model In certain situations the noise makes the iterative algorithm diverge resulting in extreme values of the model parameters In our implementation the original iterative algorithm is available though currently not in the GUI as w
24. processing K means clustering algorithms Meta K Means then the magnitudes of the two parameters are very different which naturally will bias the results In our implementation the Matlab matrix fed into K means is called RESULT this is generated by each of the modelling algorithms If rescaling of the rows of the RESULT matrix is required before this clustering e g multiplication of the first row by two then from the Matlab commandline simply type gt gt global RESULT gt gt RESULT 1 2 RESULT 1 and then run the Meta K means from the GUI as normal 63 Appendix A Glossary Revision 1 3 Date 2002 08 14 13 20 17 Table A 1 An Explanation of Lyngby Toolbox fMRI and Related Terms 64 Analysis Axial slice Coronal slice Experiment Paradigm Post processing OLars Kai Hansen et al 1997 65 The core stage of the investigation of functional images within the toolbox usually involving statistical algorithms acting upon a time series of volumes It comes directly after the pre processing stage and before the post processing one See Transversal slice A slice taken through a spatial volume For the example of a person this would be like looking at them from the front As such the slice index goes from posterior anterior or back to front A term used to describe the entire set from which results are de rived An experiment can consist of several trials over different days
25. significant The function will only return eigenvectors with eigenvalues that are different from zero i e larger than a tolerance set to account for numerical round off errors In the present implementation it is only possible to do the analysis on a run basis not within a run e g if you have a repeated stimulus function in a run and not with longer periods than a run The run specification is used to make the designmatrix 4 13 2 References SVD and CVA is usually explained in most multivariate analysis textbooks e g Mardia Mardia et al 1979 For PLS and orthonormalized PLS see the compact explanation in Worsley et al 1997 The SOP model orthonormalized PLS combined with Strother s designmatrix is not described anywhere else than here 4 14 The Ordinary t test A common test in functional brain modeling is the t test For a given voxel the fMRI signal is split into two sections the activated part and a baseline part The difference in means of the two parts divided by a measure of the standard deviation for the two parts can be modeled by the Student t distribution Hence a t value and or a probability measure for the two parts being identical can be derived If a Gaussian assumption is made about the noise and it is independent and identically dis tributed then a P value can be derived The noise from fMRI BOLD is usually not independent due to the hemodynamic response function and unmodelled confounds
26. the common file stem and the scope of the file index Lars Kai Hansen et al 1997 Section 2 5 Using the Lyngby Windows Interface 24 Lyngby Load setup Figure 2 2 The file load window in Lyngby Image Dimensions Specifies the size of the full data volume in spatial terms i e for a single time point before any region of interest is selected Image Word Size The size of the individual words in the datafile File Byte Ordering The order of the bytes within the file Data Endian Intel Pentium and DEC Alpha usually use big endian while Sun and SGI usually use little endian when storing data on disk Data Orientation allows the user to change the orientation of the displayed image Note that this refers to the mirroring around each of the three orthogonal axes and not to the way the data is stored within the file that is catered for by the Ordering option Greyscale How the greyscales are mapped to the colourmap Vozel Dimensions Specifies the real world size of the image voxels to allow for calibration etc Location of Origin Vozel Allows spatial calibration of the brain Plane angle to horizontal Compensates for non orthogonal orientation of the slice planes Repeat period The frame rate allows the calculations to be calibrated in seconds instead of in frames Lars Kai Hansen et al 1997 Section 2 5 Using the Lyngby Windows Interface 25 File Offset The number of bytes to skip in the d
27. values last For the Jezzard data the file looks like function V data_readdata index fid fopen sprintf jezzard0716phot1_unwarp 03d index r ieee be if fid 1 error readdata Could not open file end fread fid 8 char V fread fid int16 V reshape fliplr flipud reshape V 64 64 1 64x64 fclose fid Let s look at this in more detail The first thing to do is open the file with fid fopen sprintf iezzard0716phot1 unvarp 03d index r ieee be The fid is the file pointer Note that the filename is actually the file stem of the relevant data files and that the individual datafile is specified by the index parameter This index is passed to the data_readdata function when it is called and so this function will be called for each volume that is to be read in The number of times that data_readdata is called is given by the difference between the Start and Stop scan indices as specified in the Load Data window or in the data_init m file The former takes preference Note that some data formats don t use a different file for each time point or frame and instead the whole time series is contained Kai Hansen et al 1997 Section 2 4 Data Setup 19 within a single file When this is the case the File Pattern field and the Start and Stop indices are not used The r means that the files are to be opened read only while
28. 30 h To be able to interprete the output as a probability we use a softmaz layer i oy expl 1 4 31 Vo o 1 00 Yv ifo no The neural network is optimized by adjusting the weights in an iterative scheme either with gradient or with Hessian based methods see e g Ripley 1996 appendix A 5 The term back propagation is usually used to denote gradient based optimization 4 9 1 Our implementation All neural network functions have the prefix lyngby_nn In the present implementation there are two types of neural networks A regression type with least square fitting and a classification type with a cross entropic cost function suitable for binomial distributions The functions in connection with the regression neural network have the prefix 1yngby_nn q where the q stands for quadratic The second group of functions has the prefix Iyngby nn e where the e is for entropic Functions that are common do only have the prefix lyngby_nn 4 9 2 References There are a number of good books for that introduce neural networks e g Chris Bishop s Neural Networks for Pattern Recognition Bishop 1995 and Brian Ripley s Pattern Recognition and Neural Networks Ripley 1996 Others are Haykin 1994 and Hertz et al 1991 The two layer feed forward neural network is described in several papers from our depart ment the first important one being Svarer et al 1993a followed by Hintz Madsen e
29. 85 2090 M rch N J S and Thomsen J R 1994 Statistisk analyse af positron emission tomografier Master s thesis Electronics Institute Technical University of Denmark Lyngby Denmark In danish Nielsen F 1996 Visualization and analysis of 3D functional brain images Master s thesis Department of Mathematical Modelling Technical University of Denmark Lyngby Denmark Nielsen F Hansen L K Toft P Goutte C M rch N J S Svarer C Savoy R Rosen B R Rostrup E and Born P 1997 Comparison of two convolution models for fMRI time series In Friberg et al 1997 page 473 Lars Kai Hansen et al 1997 BIBLIOGRAPHY 95 Oppenheim A V and Schafer R W 1989 Discrete Time Signal Processing Prentice Hall Englewood Cliffs New Jersey Ripley B D 1996 Pattern Recognition and Neural Networks Cambridge University Press Cambridge United Kingdom Sonka M Hlavac V and Boyle R 1993 Image Processing Analysis and Machine Vision Chapman amp Hall Computing Series Chapman amp Hall London United Kingdom Strother S C Lange N Savoy R Anderson J R Sidtis J J Hansen L K Bandettini P A O Craven K Rezza M Rosen B R and Rottenberg D A 1996 Multidimen sional state spaces for fMRT and PET activation studies In Belliveau et al 1996 page S98 Strupp J P 1996 Stimulate A GUI based fMRI analysis software package I
30. 997 Section 2 5 Using the Lyngby Windows Interface 23 Note that we use the following convention for the menus Accept the values currently shown in the display and close the window e Apply Accept the values currently shown in the display Don t accept the values currently shown in the display note that pressing Cancel after Apply will first accept the current values and then close the window 2 5 2 A Typical Analysis Session A typical analysis procedure would progress as follows 2 5 2 1 Data Loading The first stage of the process is to get some data into the toolbox This is done by either loading an existing worksheet from a previous session or loading new data from scratch A previously saved worksheet usually mat is recalled by pressing the button This brings up a standard Matlab file chooser starting from the directory where lyngby was started New data is loaded by pressing the button This then displays a window called Load setup shown in Fig 2 2 allowing specification of the number of scans the file format voxel masking etc To aid this process there is a button This attempts to probe the header files for the chosen file format or the data_readinfo m file in the case of the Lyngby format and place any extracted information about the datafiles into the correct fields in the Load Setup window Any fields successfully read are indicated by the change of the respective status box to Header There are
31. Analysis guide demonstrates how Lyngby can be used to analyse one of the sample datasets extract some meaningful results and then interpret them Both these documents are included in this manual as appendices Section 1 1 The Purpose of the Lyngby Toolbox 8 1 1 1 Models Available in the Toolbox Currently the toolbox includes the following modelling methods The exact details of the algo rithms are covered later on in the manual Cross Correlation Cross correlation with the paradigm The activation function which usu ally is a square shaped design function A well established method suited for estimation of delay and activation strength from a given paradigm FIR filter A general linear regression model of finite length The time series are modelled as a convolution between the paradigm and a linear filter of a finite length on a per voxel basis Exhaustive FIR filter The same as the FIR filter but using an exhaustive search of all FIR models up to a specified filter length The optimal filter is found from generalization theory K means Clustering A non linear statistical method for clustering labelling the data using either the raw time series or the cross correlation with the paradigm This method is suited for identification of areas with similar activation and delay The method is described in Bishop 1995 pp 187 189 and has been used for fMRI in Toft et al 1997 Goutte et al 1999 Grid Search Lange Zeger model
32. CHANGE 1e 4 LZ2_ITERATIONS 90 RESULT_LZIT lyngby_lzit_main PN XN Iterations LZ2_ITERATIONS MinChange LZ2 MINCHANGE StepSize LZ2 STEPSIZE Thetallnit LZ2 THETA1INIT Theta21lnit LZ2 THETA2INIT RESULT RESULT_LZIT STRENGTH_LZIT RESULT_LZIT 1 DELAY_LZIT RESULT_LZIT 2 RESULT_LZIT 3 session_save_lz Save LZ results m dl datevec now s sprintf d 02d 02d y m d t pud Lars Kai Hansen et al 1997 Section 2 8 Adding New Algorithms to the Toolbox 41 t t length t eval sprintf save RESULT LZ BETA s txt STRENGTH_LZIT ASCIT s t eval sprintf save RESULT LZ DELAY 2s 4s txt DELAY_LZIT ASCII s t 2 8 Adding New Algorithms to the Toolbox The Lyngby toolbox is meant as a development platform as well as an analysis one and as such we encourage you to add your own functions and models If you have any you think would benefit other researchers we would be happy consider it for the next release of the toolbox The process of adding your own functions is straightforward and you need only follow the steps outlined below 1 In lyngby_ui_main m Add the new main algorithm m file to the list in the header under See also Add the variables returned from the new method to the ones in 1yngby_ui_global m often RESULT_ NAME where NAME is the identifier for the new method Both in t
33. I can be used to make changes to the paradigm function if required data_run m This specifies which time points belong to which run within a given experiment or session As for the paradigm file this too can be specified through the GUI although only if the lengths of all the runs are equal But once again it is far easier to keep the information in a file that is loaded automatically Changes to the function can also be made from within the GUI if required data_init m This file contains all the parameters that the user would normally enter in the Load new data window As such it also is not essential but it makes life easier because it then saves the user specifying the parameters every time data is loaded It is simply a file of variable assignments specifying such parameters as the size and shape of the volume the number of scans and runs and a TIME_MASK variable which can be used to remove unwanted scans Note that the latter three files can be used for all data formats and it is only the first two which are specific to custom data Lars Kai Hansen et al 1997 Section 2 4 Data Setup 17 2 4 3 Examples of the Data Conversion Files This section looks at how to write the actual code within the data conversion files It uses the Jezzard dataset as a basis for the code examples This is a single trial single slice fMRI experiment with 64 volumes i e time points or frames each of size 64 by 64 by 1 2 4 3 1 The data_rea
34. LYNGBY Matlab toolbox for functional neuroimaging analysis Peter Toft Finn rup Nielsen Matthew G Liptrot and Lars Kai Hansen IMM Informatics and Mathematical Modelling DTU Technical University of Denmark Version 1 05 August 14 2006 Contents 1 Introduction 1 1 The Purpose of the Lyngby Toolbox 1 1 1 Models Available in the Toolbox 1 2 Organisation of this Book 0 0 0 0 0 1 3 Explanation of the Typographic Conventions 1 4 fMRI Analysis Matlab and the Lyngby Toolbox 1 4 1 Definitions and Glossary 1 5 Support on the Web and Downloading the Toolbox T 6 Other Software Z a pe YA vz ed 1 7 The Lyngby Development Team 1 7 1 Acknowledgments 17 25 Contech Ms Lo E pihaa soz it a a 2 User Manual Introduction a cs gave eno da ee da 2 2 Installation and Getting Started o 221 First time Users a ceed as a Ee le ae ae eS 2 2 2 Using Lyngby On Your Own Data 2 3 USNE Lyne by lt ear kos eh e Bee Gp E Bas See aah a an OS 2 9 1 Starts Lyngby s geh esate a ala he Ges 2 3 2 Getting ea Be eee ee ee 2 4 Data Setup amp fate aad
35. READING_TYPE 2 DISCRIM_TMASK lyngby_index2tmask lyngby_dropedge TIME_MASK lyngby_paradigm 4 4 length TIME_MASK lyngby_paradigm The data paradigm n file data paradigm m function P data paradigm P kron ones 8 1 zeros 12 1 ones 24 1 zeros 12 1 The data run n file data_run m function R data_run R kron 1 8 ones 48 1 The data_readdata m file data_readdata m function V data_readdata index fid fopen data simfmri 1 r X fscanf fid f fclose fid offset index 1 x288 V XC 1 288 4offset Then the main script file may look something like this session load Load data lyngby_init lyngby_ui_global Set up X data_readx Set up design Lars Kai Hansen et al 1997 Section 2 7 Writing Scripts to Run Lyngby Automatically 40 P lyngby_paradigm R lyngby_run session_prep Compute data pre processing lyngby_ui_global Preprocessing lyngby_prep_global PREP_CENTERING 1 PREP_RUNCENTERING 0 PREP_IMAGECENTERING 0 PREP_NORMALIZATION 0 XN X_MEAN X_STD X_SEQMEAN X_SEQSTD lyngby_normalize X Centering PREP CENTERING RunCentering PREP_RUNCENTERING gt ImageCentering PREP_IMAGECENTERING Normalization PREP_NORMALIZATION PN P mean P session_1z Compute Lange Zeger lyngby_1lzit_global LZ2_THETA1INIT 10 LZ2_THETA2INIT 2 LZ2_STEPSIZE 1 LZ2_MIN
36. Rank Deficient and Discrete Ill Posed Problems Polyteknisk Forlag Lyngby Denmark Doctoral Dissertation Hartigan J A and Wong M A 1979 Algorithm AS136 a K means clustering algorithm Applied Statistics 28 100 108 Haykin S 1994 Neural Networks Macmillan College Publishing Company New York Hertz J Krogh A and Palmer R G 1991 Introduction to the Theory of Neural Compu tation Addison Wesley Redwood City Califonia 1st edition Santa Fe Institute Hintz Madsen M Hansen L K Larsen J Olesen E and Drzewiechi K T 1996a Detec tion of malignant melanoma using neural classifiers In A B Bulsari S K and Tsaptsinos D editors Proceedings of International Conference on Engineerings Applications on Neural Networks pages 395 398 Hintz Madsen M Hansen L K Larsen J Olesen E and Drzewiecki K T 1995 De sign and evaluation of neural classifiers application to skin lesion classification In IEEE Workshop on Neural Networks for Signal Processing NNSP 95 Hintz Madsen M Pedersen M W Hansen L K and Larsen J 1996b Design and evalua tion of neural classifiers In S Usui Y Tohkura S K and Wilson E editors Proceedings of the IEEE Workshop on Neural Networks for Signal Processing VI pages 223 232 Hoerl A E and Kennard R W 1970a Ridge regression Application to nonorthogonal problems Technometrics 12 1 69 82 Hoerl A E and Kennard R W
37. View full volume timeserie and specify mask Section B 1 Available Functions lyngby_uis_none_v Script for original view Analysis Functions and Modelling Algorithms Ardekani F Test lyngby_baf_global lyngby_baf_init lyngby_baf_test lyngby_ui_baf_init lyngby_ui_view_baf lyngby_uis_baf lyngby_uis_baf_v Ardekani F Test with Nuisance Subspace lyngby_baf2_global lyngby_baf2_init lyngby_baf2_main lyngby_baf2_test lyngby_ui_baf2_init lyngby_ui_view_baf2 lyngby_uis_baf2 lyngby_uis_baf2_v Ardekani T Test lyngby_bat_global lyngby_bat_init lyngby_bat_test lyngby_ui_bat_init lyngby_ui_view_bat lyngby_uis_bat lyngby_uis_bat_v Cross correlation lyngby_cc_global lyngby_xcorr lyngby_ui_cc_init lyngby_ui_cc_view lyngby_ui_view_cc lyngby_uis_cc lyngby_uis_cc_v lLars Kai Hansen et al 1997 72 Global variables for Ardekani f test analysis method Initialize globals for Ardekani F test Barbak Ardekani s F test Ardekani s F test GUI for init of param Viewing BAF filter results Script executed for Ardekani s F test Script for Ardekani F test view Global variables for Ardekani nuisance signal f test Initialize globals for Ardekani F test with nuisance Barbak Ardekani s F test with nuisance estimation Barbak Ardekani s F test with nuisance estimation Ardekani s nuisance F test init of param Viewing function for Ardekani s nuisance F Script executed for Ardekani s nuisance F Script for Arkani s F test w
38. _v Lange Zeger Iterative lyngby_Izit_algo lyngby_Izit_beta lyngby_Izit_conv lyngby_lzit_cost lyngby_Izit_ftlamb yngby lzit global yngby lzit init lyngby_Izit_main yngby lzit noise lyngby_Izit_pickf lyngby_Izit_thopt lyngby_ui_lzit_init lyngby_ui_view_lzit lyngby_uis_lzit lyngby_uis_lzit_v Meta K Means lLars Kai Hansen et al 1997 74 Kolmogorov Smirnov test Kolmogorov Smirnov probability Kolmogorov Smirnov test of two arrays KS GUI for initialization of parameters Kolmogorov Smirnov viewing function Script executed for Kolmogorov Smirnoff Script for Kolmogorov Smirnov view Lange Zeger residual signal Quadratic error The Lange Zeger hemodynamic response function Returns the masscenter of the Lange Zeger Kernel Plot Paradigm data and Lange Zeger model Plot Lange Zeger thetal against theta2 Global variables for LZ Grid Search analysis Initialize global variables for LZGS Lange Zeger model with grid search Lange Zeger main algorithm for grid search Lange Zeger GUI init of parameters Viewing Lange Zeger results Script executed for Lange Zeger Grid Search Script for Lange Zeger gridsearch view Lange Zeger optimization of model Lange Zeger Estimate beta parameter Lange Zeger Convolve kernel with the input The cost function used in the Lange Zeger model Lange Zeger Fourier transformed of lambda Global variables for iterative LZ Initialize global variables for iterative LZ Main function for Lange Zege
39. alyse and model the data and do any post processing all without any user intervention Obviously this allows you to set up a whole selection of jobs running overnight on different data using different modelling parameters and Lars Kai Hansen et al 1997 Section 2 7 Writing Scripts to Run Lyngby Automatically 38 X The original datamatrix XN The preprocessed datamatrix RUN The original run series PARADIGM The original paradigm series P The paradigm variable after the time mask has been ap plied R The run variable after the time mask has been applied PN The preprocessed paradigm zero mean Mean of each scan Standard deviation of each scan The results from algorithms that include a measurement of temporal shift between the paradigm and the voxel s response RESULT_ The main results from the different algorithms See below for examples STRENGTH_ The results from algorithms that include a measurement of the strength of the voxel s response RESULT_FIR The result from the FIR analysis RESULT_BAT The result from the Ardekani t test RESULT_BAF The result from the Ardekani f test RESULT_LM_ASSIGN The assignment labels from the K means analysis RESULT_KM_CENTER The cluster center in K means analysis RESULT_CC The result from the Cross correlation analysis RESULT_TS The result from the ordinary t test t measure TS_PROBMAP The result from the ordinary t test probability map RESULT_LZ The result from the Lange Zeger a
40. ar transformation we apply to the voxel datamatrix X to project it onto a subspace containing the data described by the subspace datamatrix X X XB 4 32 The vectors x from the subspace matrix X are used as input to a two layer feed forward neural network see section 4 9 When the neural network is fully optimized to best generalization the full costfunction from the voxel to the output of the neural network is Taylor expanded with respect to the components in the linear transformation B For an entropic neural network the first order derivative and the diagonal approximation of the second order derivative yield Np Nh EP yP won 1 Ay ma 4 33 P h Np nh 2 oe Y 1 5 Esa 1 p ni xP 4 34 p The symbols are i 1 n is indicing over inputs to the neural network i e the output of the linear transformation and 1 n indices over voxels The rest of is the same as the symbols of section 4 9 Entering the derivatives in the Taylor expansion yields Np Nh Ni Co e YY Y won 1 MY 4 35 p h Np nj m 5 2 won 1 ni ih ef P h lLars Kai Hansen et al 1997 Section 4 12 The SCVA model Strother Canonical Variate Analysis 59 Similar calculations can be performed for the costfunction to the quadratic neural network Here the derivatives become ac Np No Nh ALI when 1 07 ma 4 36 2C o 22 2 Substituting these derivati
41. as a 4 D set with three spatial dimensions and one time dimension An element of a spatial 3 D volume usually with a time reference It can be thought of as a 1 D time signal Appendix B Functions Revision 1 3 Date 2002 08 14 13 32 23 B 1 Available Functions This appendix provides a list of all the functions that are available within the Lyngby package This is meant for users who wish to write scripts to automatically process their data Users of the GUI will not normally need to access these functions directly Help on each function can be obtained from the Matlab command line by typing gt gt help lt functionname gt For instance to obtain help on the lyngby_getdata function gt gt help lyngby_getdata This will then return the following lyngby_getdata Returns the masked datamatrix function X lyngby_getdata ROI voxelMask timeMask Input ROI Optional Region of Interests 3x2 matrix voxelMask Optional Sparse masking matrix timeMask Optional Sparse masking matrix Output X The datamatrix This function loads the datamatrix The voxel is in the horizontale direction as columns and the time is in the vertical direction as rows To save memory a Region of Interest can be specified and further a voxel or and a time mask can be specified If the input arguments are missing TIME_MASK VOXEL_MASK and ROI_VOXELS are used 67 Section B 1 Available Functions 68 Which volume
42. atafile in order to get past the header info and into the data Very useful for loading in raw data without creating any seperate translation files Compression method The file compression used on the datafiles The toolbox is capable of decompressing the files on the fly allowing the data to be kept compressed and thus saving space It also allows the data to be read compressed straight from a CDROM Extract to dir The temporary directory used for on the fly decompressing of the data as it is loaded in 2 5 2 3 The Load Window Bottom Right Frame This frame controls some of the external factors that affect the loading in of the data Other external influences such as the Run and Paradigm variables don t affect the way the data is loaded in and as such are seperated off into a later stage Time Mask Before actually loading the data a time mask can be specified by pressing the button This is convenient if you want to discard transient scans or scans at the start that behave badly such as highly saturated T1 scans The associated global variable is TIME_MASK and the window is shown in figure 2 3 Bi lyngby Time View time mask Figure 2 3 The time window in Lyngby Voxel Mask This allows the exclusion of specific voxels within the selected region of interest ROI to be loaded It is usually in the form of a sparse matrix At the moment the front end interface for this feature is not yet finished but the suppor
43. atlab commandline will have the Matlab prompt in cluded on the left hand side e g gt gt help lyngby Any Lyngby variables or Matlab files mentioned in running text such as PARADIGM or data paradigm m will also be in bold monospace Any reference to a particular in the Lyngby GUI will have a box around it whilst Window Titles and Window Menus will be shown in italics 1 4 fMRI Analysis Matlab and the Lyngby Toolbox The Lyngby toolbox was created for the analysis of fMRI images using advanced mathemat ical and statistical methods in a way that was easily accessible to researchers from all fields fMRI is still a relatively new field and this is reflected in the continually growing number of analysis routines available Originally methods developed for the analysis of PET images were adapted to work on fMRI data and some of these are still present in the toolbox However we have also added a considerable number of innovative analysis methods and are continually developing more One of the purposes of the toolbox is to enable researchers to add their own algorithms with relative ease without having to worry about handling the data input image display statistics or saving of results By writing the toolbox in the universally adopted Matlab package and allowing the code to be open we hope that other researchers will be able to add their own algorithms with ease We also hope that they will consider submitting to us any they think woul
44. ave space Edit your Matlab startup m file to inform Matlab where it can find the lyngby executable files Start Matlab as normal Within Matlab change to the direc tory containing the sample data Start lyngby by simply typing lyn gby from the command prompt The lyngby main window should pop up Appendix E Example Analysis Revision 1 2 Date 2002 08 14 13 08 46 How To Load and Analyse Data Using the Sample Dataset Table E 1 A Simple Example Analysis How To Use The Lyngby GUI Keyboard mouse action Explanation Press Load new data A new window ti tled Load data will pop up Press the Apply button at the bottom of the new window Press the Load Data button The window will close Press the Create Edit External Influences button bringing up a new window Press Setup design Press Process design 86 First we need to load the sample dataset The data parameters should all be set auto matically as lyngby will have read in a con version file specifying them The values of the GUI will be written to global variables needed for the loading The data will now be read in from the files In the main window it should display Finished loading data at the bottom This is were you e g can specify a stimulus function The first pre processing step is to mask out those unwanted timepoints from the paradigm and run structures Next the mean i
45. by tar gz Note that currently the software and documentation is password protected Please fill in the form on the Lyngby homepage or contact the authors regarding access We use CVS to control the code revisions which enables very easy updating and automatic generation of the web documentation On the Lyngby homepage it is also possible to see which files have changed and view the change logs over the last 7 days and last 30 days The closed mailing list lyngby isp imm dtu dk can be joined by sending an email to majordomo isp imm dtu dk with the only line in the body being subscribe lyngby The mailing list is used for discussions problems and announcements 1 6 Other Software Other software packages for the analysis of functional neuroimages do also exist most notably SPM from Wellcome Department of Cognitive Neurology Friston et al 1995b and Stimulate developed by John P Strupp from University of Minnesota Medical School Strupp 1996 Gold et al 1998 gives a review of these two together with several other software packages Lars Kai Hansen et al 1997 Section 1 7 The Lyngby Development Team 12 1 7 The Lyngby Development Team Lyngby has been designed and implemented by a modeling group at Informatics and Mathe matical Modelling IMM formerly called Department of Mathematical Modelling Technical University of Denmark DTU The head of this group is Lars Kai Hansen The programming has been carried out mainl
46. d prediction Poisson filter Global variables Poisson filter Initialize global variables Main function for Possion filter Possion kernel optimization GUI Poisson filter initialization Viewing poisson filter results Script executed for Poisson filter analysis Script for Poisson filter view Global variables for SCVA analysis Initialize global variables for SCVA analysis Strother Canonical variate analysis GUI for init of Strother CVA Viewing function for Strother CVA Script executed for SCVA analysis Script for SCVA view Strother design matrix set intersection S1 S2 set difference S1 S2 set thining all elements different Global variables for SOP analysis Initialize global variables for SOP analysis Strother OPLS SOP with SVD on the residual GUI of init of SOP model Viewing for Strother OPLS Script executed for SOP analysis Script for SOP view Function to find the indices of the on off scans Singular value decomposition Global variables for SVD analysis Initialize global variables for SVD analysis Filtering by SVD GUI for initialization of SVD model Section B 1 Available Functions 78 lyngby_ui_view_svd Viewing for Strother OPLS lyngby_uis_svd Script executed for SVD analysis lyngby_uis_svd_v Script for SVD view Lars Kai Hansen et al 1997 Appendix C Derivations Revision 1 5 Date 2002 08 14 13 17 05 C 1 Neural Network C 1 1 Symbol table o gt No w
47. d be useful to other people in the field so that we may include them in a subsequent release of the Lyngby toolbox Of course any other suggestions for developments of the toolbox will also be greatly welcomed Lars Kai Hansen et al 1997 Section 1 5 Support on the Web and Downloading the Toolbox 11 1 4 1 Definitions and Glossary It would probably be useful at this point to define some of the terms used throughout this book Although the fMRT field is developing rapidly some of the terms used are still ambiguous and those coming into the field for the first time may not appreciate the difference betvveen for example volume when it refers to a 2D slice with time vs a spatial 3D volume For consistency and clarity we will define what we mean by the standard terms along with some Lyngby specific terms These are all in the Glossary at the back of the book see Appendix A 1 5 Support on the Web and Downloading the Toolbox The Lyngby toolbox has a mailing list where the latest development is announced and its own homepage http hendrix imm dtu dk softvare lyngby The parts of the Lyngby homepage relating to downloading of software and documentation is updated automatically every day The Lyngby toolbox can either be downloaded file by file more than 300 files or you can get the compressed tar file that contains all the files You can download the latest version from http hendrix imm dtu dk softvare lyngby code lyng
48. d have been pulled into a common pre processing step The most common step is the substraction of the mean for each of the time series Furthermore it is becoming more and more clear that the pre processing steps are very important examples could be motion correction and correction for field inhomogeneity Currently we have chosen to concentrate our efforts into the modelling of the data and to only supply basic pre processing steps and leave other preprocessing to other packages However we are open to contributions 3 2 Volume file formats Given that many have designed their own best file format we cannot support all formats and currently the toolbox can read fMRI data in the formats show in table 3 1 The Custom option allows Lyngby to read any data format with a little help from the user The interface conversion files that are required to help Lyngby understand the user s own data are very simple and straightforward to write and should only take a few minutes to construct Full details and examples on how to write these files are given in the previous chapter see section 2 4 2 If your format cannot be read automatically and you don t want to use the custom option tell us about the format and maybe it can be incorporated in the toolbox soon Currently we would like to support AnalyzeSPM slightly changed Analyze format the VorelView format and the XPrime format 43 Section 3 3 Masking 44 Files Extension Usage Analyze h
49. d the fMRI data The initial parameters for the FIR Filter can be set within a dedicated window The Pa rameters window will be different for each algorithm reflecting the different variables used in each case Note that each algorithm will have a sensible set of defaults within its Parameters window For this example we can use default settings The calculation is then started with feedback given on the status line within the main win dow Note that once the calculation is fin ished the symbol adjacent to the algorithm name changes to a indicating that re sults for this algorithm are ready to be ex amined A indicates that no calculation has been performed whilst a indicates that the parameters have been changed but not yet used in a calculation Press the View these results button A set of three windows labelled Control Volume and Time will pop up Click on different voxels in the Volume win dow Note how the Time window displays the relevant time series Click on Sum of Coefficients in the Data Layer and pick Activation Strength from the pop up list Click on in the Time Layer select ing the Histogram of Data option The Time window will change from displaying a time series to showing a histogram of the greylevels for the selected voxel Click on different voxels and note that the general shape of the histogram is different for the activated and non activated areas
50. ddata m and data_readinfo m Files The contents of the data_readinfo m file are read when the user wants to pass the header information contained within the file into the Load Setup window This is achieved by pressing the Try to setup button An example of the file is shown below function siz vdim name datatype data readinfo index siz 64 1 64 vdim 0 003 1 0 003 name jezzard datatype short Pressing the button then attempts to locate the file in the current directory and read the contents These are then placed in the correct fields of the Load Setup window and the relevant status boxes are set to Header For all the other file formats pressing the button ignores any data_readinfo m file and instead the relevant header files for the chosen format are attempted to be read and the extracted parameters again passed into the relevant fields in the Load Setup window with the associated status boxes also being changed to Header The other function data_readdata is the function that should return the actual data The data has to be flipped because in this case the original ordering is not the same as that used by Lyngby The Lyngby toolbox will always assume that the vector data returned from data_readdata is of the following form V Pio Pega Pee es where P refers to an individual data point x y z refers to the location in 3D space of the data point x refers to the sagittal slice i e ea
51. dr img Widely used SPM AIR and ANALYZE Analyze 4D hdr img All the time frames are in a single file SDT sdt spr Stimulate format Vapet Used at the Minneapolis Veterans Medical Center PET Center RAW Support for raw binary data with several options of orientation and type Custom Support for other data where the user writes a small interface file that returns the volume at a given time step Table 3 1 Data formats read by Lyngby 3 3 Masking The core of this toolbox lies in the composition of a datamatrix named X in our Matlab code where a certain row is the volume at that particular time and a certain column corresponds to the time series for that particular voxel This is shown in figure 3 1 voxel number _ y time The data matrix X Figure 3 1 The data matrix X The toolbox has the potential to mask in both time and space although currently the user only has a GUI interface with which to specify a box region A mask in time Trmemsx the variable TIME_MASK in the code is multiplied from the left of the full data matrix And likewise a mask in space Svoxe msx the variable VOXEL_MASK in the code is multiplied from the right Before the VOXEL_MASK is applied a further masking step can be made A box region can be specified with the limits defined in the variable ROLVOXELS X Terme X full O hor voxELs O yoxeLmask 3 1 We use sparse matrices for the TIME MASK and the VOXEL_MASK so these e
52. e ability to add and alter the code as desired as well as the option of writing batch scripts to run Lyngby automatically or on large jobs However it can be difficult to remember all the different script names and their required parameters so the novice user will find that the graphical interface is far easier to use Here the user is prompted for all the required information removing the need to call anything from the commandline once the toolbox is started To start the graphical interface change directory within Matlab to the directory that contains the data files that are to be processed and then type gt gt lyngby If you get an error saying Undefined function or variable lyngby it is prob ably because you haven t set up the path to the 1yngby functions To fix this assuming that you have placed the lyngby code in the directory usr local lyngby simply type gt gt path path usr local lyngby You can put this command in your matlab startup m file Details on how to use Lyngby via each method are given in Sections 2 5 and 2 6 respectively 2 3 2 Getting Help An overview of all the functions in the toolbox can be obtained through the standard matlab help function gt gt help lyngby You can also get help for each individual function for example gt gt help lyngby_fir_main To distinguish the functions in this toolbox from other Matlab toolboxes all the functions have the prefix lyngby_
53. e delay from the FIR Filter 4 2 3 Our Implementation 25 s en ee Rg AS es 42 4 References a eee a Park ee ar do Diab oe a a a eee R 4 3 Exhatstive FTR Tilter ici bow ae ie ee eS oe ee ae a ADA 4 341 Que Implementation ta 24 6 eee noq A BD References since sos Brin he es Boke Sean BR ei wats ue eet a 4 4 The Ardekani t test 4 4 1 Our Implementation 4 4 2 ReTeTehe 8 ay qala rra WBA ce di 4 5 Ardekani F test 4 5 1 Our Implementation 0 0 0 0 010 010 0 0 4 02 References Bisa a R oa s ER Bela ee a Sie es se dees 4 6 Clustering css tg aaz ad e a R se A L 4 6 1 Our implementation 4 6 2 References Bok ee Lan adad Bee Seba dun a eS 4 7 Kolmogorov Smirnov test ee 4 7 1 Our implementation 4 7 2 Referentes on m a ie l R d el eS a R E 4 6 a nia ate a ae ee da Bebe bo a eS 4 8 1 Estimation of the delay from the Lange Zeger model 4 8 2 Our implementation 4 9 Neural networks ioe mooni aru xa Bala OTUR ee ee A asa g l n a 4 9 1 Our 2 2 2 419 25 References pte ines oe EA
54. e range of the variables can be standardized normalized to unit variance or standardized according to the min max range The cluster centers can be initialized randomly In Toft et al 1997 it has been found that this strategy works rather well for the cross correlation clustering or according to the correlation with the paradigm function The variable to cluster on can be set to the raw time series or the cross correlation function It is implemented in the lyngby_km_main matlab function 4 6 2 References The K means clustering algorithm was first described in MacQueen 1967 Other non neuro imaging descriptions of this algorithm are available in Ripley 1996 section 9 3 Sonka et al 1993 section 7 2 4 or Hartigan and Wong 1979 Our approach in connection with functional neuroimaging is published in Goutte et al 1999 and described shortly in Goutte et al 1998 Kai Hansen et al 1997 Section 4 7 Kolmogorov Smirnov test 53 Toft et al 1997 In Liptrot et al 2003 it was applied to extract the time activity curve from dynamic PET scans in connection with the 5H T gt A receptor ligand Different kinds of clustering methods have been applied in functional neuroimaging Some of the references are collected at http www inrialpes fr is2 people goutte fmriclusterefs html 4 7 Kolmogorov Smirnov test Most standard text books in statistics show the Kolmogorov Smirnov test where the maximal di
55. e same three windows are used to explore the results For the Neural Network Saliency algorithm these result windows are shown in Fig 2 10 Jiral network sali 0 xlm EX File Edit Tools Window Help File Edit Tools Window Help DIH lRAZ Z 882 Data ll Paradigm Prediction i 00500 00 G Neural network saliency Control File Edit Tools Window Help Options Figure 2 10 The Neural Network Saliency results window in Lyngby Let s go through the features of these windows in more detail e There is always one control window underneath two data viewing windows which usu ally show spatial voxel information and time series information respectively The control window is arranged in layers to reflect the concept of overlapping data layers in the spa tial window This is perhaps illustrated more clearly with the aid of a diagram see figure 2 11 e Clicking on a voxel in the volume window will automatically update the other window to show the time series for the chosen voxel plus the result of any modelling algorithm for that particular voxel Kai Hansen et al 1997 Section 2 5 Using the Lyngby Windows Interface 31 Figure 2 11 The Concept of Layers in the Result Windows e The control window can be expanded to show extra layers with the button These allow the addition of a contour overlay a background underlay and data masking features Time Di
56. e selected modelling algo rithm and as such the window that pops up after pressing it will be different for each one For the Neural Network Saliency algorithm the parameter window is shown in Fig 2 9 Once the required parameters have been chosen then click Apply followed by Close Neural network saliency Figure 2 9 The Neural Network Saliency parameter window in Lyngby The Calculate button will then run the algorithm and the progress of the processing is shown on the status line at the bottom of the main window e Finally pressing the button shows the result of the analysis e The two LI buttons adjacent to the and Caleculatel buttons will display in the command window the actual code script that will be run when their neighbouring buttons are pressed This allows the user to easily keep track of what variables will be Lars Kai Hansen et al 1997 Section 2 5 Using the Lyngby Windows Interface 30 modified and displayed at each stage Note that the popup menu showing the algorithms will have a or a alongside each one indicating whether or not the results of that algorithm are available for visu alization indicates no result indicates a new result and indicates that the parameters have been changed and the algorithm has not yet been run with these new variables The next step is the actual viewing of the modelling results Whichever modelling or analysis method is chosen th
57. e zero i e zero taps in the filter In the Exhaustive FIR filter the idea is to find the optimal filter length in each voxel The optimal model is chosen by using the mean generalization error as a measure based on a training and test scheme this scheme is especially used in artificial neural networks see section 4 9 The basic idea is that each run in a time series is considered as an independent time series Using resampling without replacement with that prior it is possible create a new dataset that gives good statistics in the generalization error The mean generalization error for a given model is defined as T N Egen u x Vito t x 4 i U t 4 18 t 1 i 1 where denotes the resample index and t is the time The new dataset created with the resampling is split into a training and a test set The ratio between the size of these two datasets is used in the algorithm as a variable The Exhaustive FIR filter uses a varying filter length combined with the SVD regularization This means that for each filter length there is a filter length of singular values that can enter the pseudo inverse So for each filter length there is a model using the largest singular value and another model using the two largest singular values etc The number of models is now given Lars Kai Hansen et al 1997 Section 4 4 The Ardekani t test 50 by 1 2 Maxorder l n n models being tested The job is now to calculate the genera
58. ed integer 32 bits uint64 integer 8 unsigned integer 64 bits float32 real 4 floating point 32 bits float64 real 8 floating point 64 bits Table 2 2 Architecture ndependent Variables We now have a single volume of the full data i e a spatial volume for a given time point in the form of a 1D vector The next bit re orders this data so that it will appear in the correct order for Lyngby as specified earlier This is the most complex bit V reshape fliplr flipud reshape V 64 64 1 64 64 Looking at this function in more detail OLars Kai Hansen et al 1997 Section 2 4 Data Setup 20 First of all the vector V is reshaped into a 2D matrix 64 by 64 Note that this case is relatively easy because the Jezzard data is only single slice so the volume is 64 by 64 by 1 For a multiple slice dataset you would have to use the reshape function with an extra parameter Type help reshape at the Matlab prompt for more information reshape V 64 64 Next the matrix is flipped about the horizontal axis flipud matrix and then about the vertical axis fliplr matrix Finally this re ordered matrix is put back into the vector V with another reshape command V reshape matrix 1 64x64 This results in a vector V that has been re ordered so that the elements appear in the same order that Lyngby is expecting them i e X Y Z X Y Z X etc with the Z indices changing the quickest Finally
59. eft to select an earlier slice before choosing the mosaic view Once selected the mosaic view will display up to 20 slices from the current volume You can move the slice slider as before to move through the volume The result sets all use the same colourmap i e the colourmap has been scaled to the maximum and minimum of the current result set so individual colourbars are not necessary and the slices update far quicker wiith them turned off A single colourbar for this view will be added very shortly You can turn the mosaic view off again with the same menu or keyboard shortcut that turned it on 2 5 2 7 Data Post Processing After the data analysis the user can perform some post processing on the results data This post processing allows the analysis of the previous result sets in a formal way At the moment Lars Kai Hansen et al 1997 Section 2 5 Using the Lyngby Windows Interface 34 orrelation Volume Figure 2 12 The volume result window in mosaic mode only one post processing algorithm Meta K means clustering is included in the toolbox but more are due to be added later To use this feature one first has to have a collection of result parameters that require analysis This result dataset is presently acquired by using either the FIR Filter or the Iterative Lange Zeger routines Once this has been created then the post processing can be done The procedure is exactly the same as for the main analysis routines w
60. egression An annotated bibliography Interna tional Statistical Review 44 3 355 360 Andersen L N Larsen J Hansen L K and Hintz Madsen M 1997 Adaptive regular ization of neural classifiers In Principe J editor Proceedings of the IEEE Workshop on Neural Networks for Signal Processing VI Florida USA pages 24 33 Piscataway New Jersey IEEE Ardekani B A and Kanno 1 1998 Statistical methods for detecting activated regions in functional MRI of the brain Magnetic Resonance in Imaging 16 10 1217 1225 Ardekani B A Kershaw J Kashikura K and Kanno 1 1999 Activation detection in func tional MRI using subspace modeling and maximum likelihood estimation IEEE Transaction on Medical Imaging 18 2 101 114 Belliveau J Fox P Kennedy D Rosen B and Ungeleider L editors 1996 Second International Conference on Functional Mapping of the Human Brain volume 3 Academic Press Bishop C M 1995 Neural Networks for Pattern Recognition Oxford University Press Oxford UK Fletcher P C Dolan R J Shallice T Frith C D Franckowiak R 5 J and Friston K J 1996 Is multivariate analysis of PET data more revealing than the univariate approach Evidence from a study of episodic memory retrieval NeuroImage 3 209 215 Friberg L Gjedde A Holm S Lassen N A and Nowak M editors 1997 Third Inter national Conference on Functional Mapping of the Human Brain
61. ell as a version where the 61 92 space is grid searched and the value of 8 is determined directly in every grid point Furthermore is it possible in the grid search version to use regularization on the value of 6 penalizing the extreme values It should also be mentioned that the Lange Zeger kernel shown in equation 4 20 is a con tinuous function of time t which needs to be sampled in time as indicated in equation 4 21 This implies that the number of samples taken from equation 4 20 should at least include the maximum point of the kernel which is found at Oi 4 24 t arg max hz 4 9 Neural networks By neural networks we mean artificial neural network They have little to do with biologic neural network we are not trying to simulate the biological neural circuit The name neural network has arisen because the first versions of these mathematical models was highly inspired by the biological neural circuits We use neural networks solely as general purpose non linear statistical models In some sense the neural network is a non linear generalization of the linear model see the FIR model in section 4 2 The main type of neural network we employ is the two layer feed forward neural network It consists of two layers of weights the neural network name for the model parameters and two or three layers of neurons or units The first layer of neurons is not usually counted as a layer It is the input to the neural net
62. ely you can save the entire worksheet by using the button near the bottom of the main window This will bring up a file chooser allowing you to store all the data the variables and all the results obtained into a single file usually of the form mat To print a window of the lyngby toolbox in Matlab 5 0 you can use the print function in the window frame or you can use the ordinary matlab function print gt gt print deps MyFilename eps An alternative is to save the data from the Result View Control window To specify which data to save click on the button towards the bottom right of the window This will expand the window to five layers the normal four layers and an extra red framed Save layer Changing the choices in the first button on the Save layer specifies which layers and hence which data is to be saved These layers are also highlighted in red The other buttons in the Save layer allow the choice of the Save options the file format file compression filename and file location Lars Kai Hansen et al 1997 Section 2 6 Using Lyngby from the commandline 36 2 6 Using Lyngby from the commandline You may prefer to use Lyngby from the command line instead of using the window interface As the GUI simply calls individual Matlab m files then these can also be called directly from the command line However if you are working without the GUI you must setup the parameters in the data_init m file In addition it may hel
63. es 400 ao a e deat hae D M SoBe aw R is mo 37 Some Examples of the Global GUI variables 38 Data formats read by Lyngby 44 An Explanation of Lyngby Toolbox fMRI and Related Terms 64 Functions Available in the Lyngby Toolbox 69 Installed Up and Running in Two Minutes 84 A Simple Example Analysis How To Use The Lyngby GU1 86 Chapter 1 Introduction Revision 1 26 Date 2002 08 14 16 52 07 1 1 The Purpose of the Lyngby Toolbox Lyngby is a Matlab toolbox for the analysis of functional magnetic resonance imaging fMRI time series The main purpose of the toolbox is to model four dimensional fMRI data i e 3D spatial volume over time and to derive parameter sets from them that will allow easy interpreta tion and identification The toolbox was primarily written for the analysis of experimental data obtained from controlled multicentre trials The Human Brain Project Spatial and Temporal Patterns in Functional Neuroimaging carried out by the International Consortium for Neu roimaging All of the methods have low level modelling functions and a graphical user interface GUI interface for easy access to the data and modelling results It is important to realize that no single model can grasp all the features of the data Each of the models have their own contributions and the assumptions underlying
64. et al 1996 4 11 Neural network saliency Contrary to the neural network regression analysis section 4 10 the Neural Network Saliency does not analyze the fMRI signal as time series Rather the neural network treats each scan as an individual object that is used in a classification or regression and the saliency map estimates each voxel s importance for this prediction Each scan is after an SVD projection or other linear transformation used as the input to the neural network The state of the paradigm corresponding to the scan is used as the target The SVD projection is usually necessary because the weight optimization problem will be highly ill posed if the number of parameters is not heavily reduced After the neural network has been optimized for best generalization the actual saliency computation is performed The saliency resembles the saliency from OBD Le Cun et al 1990 but where the OBD saliency is for the weights the saliency in connection with the saliency map is for the variables i e each individual voxel The saliency describes the change in the generalization error when a voxel is deleted The method to derive the change in generalization error is based on a Taylor expansion of the neural network costfunction and regarding the effect of the small perturbation when deleting a weight There are several levels of approximation from the generalization error to the actual estimate Let the matrix B denote the line
65. fMRI data Human Brain Mapping 5 4 254 258 Worsley K J Poline J B Friston K J and Evans A C 1997 Characterizing the response of PET and fMRI data using multivariate linear models Neurolmage 6 4 305 319 Lars Kai Hansen et al 1997
66. fference between two histograms is used as a measure of match between the two signals Hence a very small difference indicates that the two signals are nearly identical Note that the method only uses the histograms hence the temporal placement is not used here 4 7 1 Our implementation As mentioned in section 1 1 1 each of the time series is split into an activated part and a baseline part determined from the paradigm function In order to compensate somewhat for the hemodynamic response time we have made it possible to drop a number of samples after each transition from the baseline to an activated state and vice versa The Kolmogorov Smirnov test requires the histograms hence some sorting of signal values is needed This implies that the function might be slow if the fMRI data has many time elements 4 7 2 References A critique of the Kolmogorov Smrnov test used for MRI has been made in Aguirre et al 1998 4 8 Lange Zeger The Lange Zeger model Lange and Zeger 1997 fits a three parameter gamma density function hz as the convolution filter hrz u t BU O2 exp 02 ut T 01 1 4 20 The gamma density function is convolved with the paradigm to give the voxel value y u t 2 h u t T x u 7 4 21 Note that the Lange Zeger kernel is normalized so that the 6 is the power amplitude of the hemodynamic response The dependence on the two parameters can be seen from fig ures 4 3 and 4 4 4 8 1 Estimation
67. ful for viewing a thresholded activation result over a background image This masking process is only activated when the second button initially labeled None is switched to some other value Next to the first button which chooses which of the result sets to use to create the mask is the button which selects the threshold type The choice is between j z absolute or integer equals The first is a simple threshold The second is an absolute threshold to remove both positive and negative values greater than a certain value and the third is used only with a few result sets to pick out a particular level for instance in the K Means clustering you may want to extract the results of just the 3rd cluster The next two buttons are used to select the threshold level either via typing it into the edit box or by moving the slider The final button controls whether the threshold level is an absolute one or is done on a percentage bssis within the current slice Contour Layer This is the left side of the top layer and controls the addition of a contour overlay on top of the current volume view It is turned on and off via the radio button to the left Next to this is the popup button allowing the selection of the result set to use for drawing the contours The adjacent button specifies whether the contour is drawn using the current slice of the chosen result set or using its mean or maximum values along the current direction Backgr
68. gby toolbox is easy to use due to a graphical user interface GUI front end embedding the numerical routines The main window that pops up when starting Lyngby is shown in figure 2 1 Lars Kai Hansen et al 1997 Section 2 5 Using the Lyngby Windows Interface 22 Figure 2 1 The main control window in Lyngby 2 5 1 The Workflow in the Lyngby Toolbox As seen from figure 2 1 a top to bottom flow is intended The main window is split into sections or frames according to their purpose as follows Title frame The name of the Toolbox Data This shows the name or location of the current dataset being used Data Input Data is loaded into the toolbox here External Influences This is where the Run and Paradigm variables are loaded in and or edited Pre processing and Design Any set up of the data including removal of unwanted scans or the subtraction of the mean across each time series can be performed here Data Analysis The heart of the toolbox this allows the data to be analysed by any of the built in algorithms and viewing of the subsequent results Post Processing Once a result dataset has been created further analysis such as clustering of the results can then be performed Close The worksheet is saved and the toolbox closed from here Status Feedback on what process is currently running is shown here and the toolbox copyright infomation can also be obtained by pressing the status line Lars Kai Hansen et al 1
69. gby_cdf_gauss lyngby_cdf_t lyngby_cdf_wilrank lyngby_fs_cdf lyngby_fs_invcedf lyngby_idf_chi2 lyngby_idf_t lyngby_pdf_bin lyngby_pdf_gauss lyngby_pdf_poisson Data Loading and Writing lyngby start Calls lyngby_ui_main Draw a circle Classification error Lin s concordance correlation coefficient for reproducibility Normalized cumulated periodogram Canonical variate analysis Canonical Ridge n a Drop scans at the paradigm shifts function for averaging volumes Test function File defining global variables Perform histogram equalization Plot a slice Initialize the global variables Kronecker add Log Geometric mean Hodges Lehmann estimator Modulus function Perform meta svd comparison of selected models Orthonormalized PLS Plot paradigm data and model Binomial distribution function X2 cumulated distribution function Gaussian normal distribution function Student t distribution Wilcoxon sign rank distribution Returns the cumulative F disttribution Returns the inverse of the cumulative F dist Invers X2 distribution function Inverted Student t distribution Binomial probability density function Gaussian normal density function Poisson probability density function lyngby_filefind Find the position of a string in a file lLars Kai Hansen et al 1997 Section B 1 Available Functions lyngby_read_header lyngby_read_volume lyngby_readanahdr lyngby_readanavol lyngby_readvahdr4 lyngby_readva
70. gt exp n ln 2 v 2 to ln oe C 5 6 A exp o s E Ena 7 E 6e xil 25 toto no 1 F C 8 2 to In Dor 1 no 1 no 1 tA todo 2 to In exp o 1 no 1 2 In Y expl w 1 Y vs 0 9 no 1 no 1 n b exp o 1 x tade C 10 In order to optimize the neural network with gradient or newton methods the derivatives have to be found The first order derivative of the classifier neural network errorfunction with Np 1 1 m gt jo exp o 1 no 1 Lars Kai Hansen et al 1997 Section C 1 Neural Netvvork 81 respect to the weights is an m gt 2 in x zi S C 11 np 1 no 1 EE Y to e 0 14 The second order derivative of the classifier neural network errorfunction with respect to the weight is PE 4 Np 2 s Np No 1 2 EY uq m k 0 16 Tip For the first order derivative we only need to compute the derivative for the two ordinary layer not the softmax layer However for the second order derivative we need to have the derivative through the softmax y _ 0 o C 17 u yr Texp 69 1 no 1 eXp 6o Odo E expl d Ode a 1 exp o y 2000000 v I 0 18 expl Po o 1 1
71. he conversion by use of an example To do this we will use the Jezzard Turner Friston Friston et al 1994 dataset Visual stimu lation and a single coronal slice This is one of the sample datasets available from the Lyngby website The data is stored in a filetype that is not recognized by Lyngby so we have to make our own functions that read the data data_readinfo m and data_readdata m the latter of the two being the most important These files are called from the Load new data window of the GUI Several Lyngby internal functions are called once the data is required to be loaded The first of these is Kai Hansen et al 1997 Section 2 4 Data Setup 16 lyngby_getdata m This then calls lyngby_getvolume m which for non supported data then calls the user created file data_readdata m This acts as the actual data reader returning the data to the program in the form of a vector Details about the actual shape and order of the volume are not specified in this file though of course they will be required in order to write the data reading function within it that will actually return the data However Lyngby itself will not know the shape of the data the number of runs volumes time points etc This information has to be entered into the GUI or can be stored in a matlab file data_init m to save the user typing in the relevant details each time the data is loaded In summary then there is only one file that is absolutely
72. he help text and the global settings In lyngby_ui_main m Add a line under the line Globals with the name lyngby_ NAME _global Add the file Lyngby NAME global m where the control variables of the new algorithm are made global See lyngby_fir_global mas an example The control variables should be named NAME _ SOMETHING where SOMETHING describes the variable contents In lyngby_ui_main m under the line Method Identifiers add an identifier for the new method am_ NAME NEXT where NEXT is the next available number It is ok to insert and shift the remaining In lyngby_ui_main m under the line Initialize add the line Iyngby NAME init Lars Kai Hansen et al 1997 Section 2 8 Adding New Algorithms to the Toolbox 42 7 Add the file lyngby_ NAME _init m where the variables used in 8 10 11 12 13 14 lyngby_ NAME _global m are initialized to suitable values In lyngby_ui_main m add a new line under the line Analysis Buttons which should look like 5 EXPLAINING TEXT Note that the order should match the selection from 5 In lyngby_ui_main m locate the line elseif command 500 and add two lines elseif AnalysisMethod am NAME lyngby_log EXPLAINING TEXT chosen Locate the line elseif command 501 add two lines elseif AnalysisMethod am NAME lyngby_ui_ NAME _init Add the file lyngby_ui_ NAME _init m Here a GUI interface t
73. he present implementation it is only possible to do the analysis on a run basis not within run e g if you have a repeated stimulus function in a run and not with longer periods than a run The run specification is used to make the designmatrix 4 12 2 References SVD and CVA is usually explained in most multivariate analysis textbooks e g Mardia Mar dia et al 1979 An short overview of multivariate analyses is available in Worsley et al 1997 or Worsley 1997 The special canonical ridge technique is described shortly in Mardia et al 1979 which reference the original article Vinod 1976 Furthermore the canonical ridge analysis has a special case in PLS see section 4 13 The SCVA model with the special designmatrix which we here call the Strother s design matrix was used in Strother et al 1996 CVA has also been used in Friston et al 1995a Fletcher et al 1996 and Van Horn et al 1996 4 13 The SOP model Strother Orthonormalized PLS The SOP model consists of a preliminary SVD on the datamatrix a orthonormalization of a designmatrix followed by a partial least square analysis PLS between the SVD ed datamatrix and the orthonormalized designmatrix The outcome of this analysis is eigenimages eigenvalues and the corresponding eigensequences are represent a dependency between the datamatrix and the designmatrix The designmatrix is constructed in a special way as in Strother et al 1996 where
74. inated by the low frequencies a simple approximation is to neglect the frequency dependence and only consider the delay for w 0 BEE Yth u t TFIR Ho Ea Rt 4 16 For some combinations of filter coefficients the denominator of equation 4 16 can be very small which will influence the delay estimate dramatically This problem can be explained from the fact that equation 4 16 is based on a low frequency dominance and in case of a very high noise level the assumption is in general not valid and the estimate should rather be disregarded A simple way to check whether the assumptions is fulfilled is to evaluate b h u t gt y Y h u t 4 17 where y should at least be larger than 0 5 More details can be found in Nielsen et al 1997 4 2 3 Our Implementation Currently the user has to choose to parameters depending on whether the inversion type is done using equation 4 9 or equation 4 7 e The order of the filter can be varied e The regularization parameter Lars Kai Hansen et al 1997 Section 4 3 Exhaustive FIR filter 49 For SVD The lowest level of singular values accepted ksy p For ridge regression the weight decay parameter k Ridge The order of the filter should depend on the number of scans in the time series and the magnitude of the regularization With a too high order the model will mainly fit the noise in the data with a too small order it will not be able to fit the data Current
75. ion for Neural network Regression User interface for NNR method Viewing NNR filter results Script executed for Neural network regression Script for neural network regression view Saliency map with entropic cost function Global variables for NNS analysis Initialize global variables for NNS analysis Main function for Neural network saliency GUI for Neural network saliency Viewing of NNS results Script executed for Neural network saliency Script for neural network saliency view PCA test for equal eigenvalues Main PCA analysis Reduce the dimension or filter a matrix with PCA filtering Section B 1 Available Functions Poisson lyngby_pois_error lyngby_pois_forward lyngby_pois_forwn lyngby_pois_global lyngby_pois_init yngby pois main lyngby_pois_toptim lyngby_ui_pois_init lyngby_ui_view_pois lyngby_uis_pois lyngby_uis_pois_v SCVA lyngby_scva_global lyngby_scva_init lyngby_scva_main lyngby_ui_scva_init lyngby_ui_view_scva lyngby_uis_scva lyngby_uis_scva_v lyngby_sdesign lyngby_set_and lyngby_set_diff lyngby_set_unique SOP lyngby_sop_global yngby sop init lyngby_sop_main lyngby_sopressvd lyngby_ui_sop_init lyngby_ui_view_sop lyngby_uis_sop lyngby_uis_sop_v yngby splitonnoff SVD lyngby_svd lyngby_svd_global lyngby_svd_init lyngby_svdfilter lyngby_ui_svd_init lLars Kai Hansen et al 1997 77 Poisson residual signal Quadratic error Possion kernel forward prediction Possion kernel forwar
76. ion of non activated areas is gener ally monomodal Click on the button to expand the control window to display an additional two rows The upper row contains two new vi sual layers Contour and Background whilst the Masking Layer underneath is an interme diate processing layer that affects the data layer below it See Fig 2 11 for a graphical explanation In the Masking Layer click on the second button from the left showing None and select the gt option Click on the Sum of Coefficients button in the Masking layer and select Activation Strength from the pop up list Using the slider control in the Masking layer adjust the threshold to around 0 96 You can use the edit box immediately to the left to type in 0 96 if you prefer In the Background Layer click on the first button to the right of the Background la bel This turns the layer on Now click the button and select the Mean data dataset to display the anatomi cal data Click on the button immediately to the right of the Contour label to activate the contour layer Then click on the Sum of Coefficients button and select the Activation strength dataset from the pop up list OLars Kai Hansen et al 1997 89 The toolbox can also display concurrent spa tial information by the use of overlays layers that sit above or below the data Now we can mask the Data layer by using the Masking layer above This creates a mask from a gi
77. ion that the error is Gaussian the minimization of the error function E Y 0 0 44 u can be identified directly through the so called normal equation XTY 4 5 h XTX XTY 4 6 If the model is too complex if the model is allowed to use too many filter coefficients the model will not only fit to the signal within the data but also to the noise In the toolbox two ways of estimating the inverse matrix have been implemented for handling the often ill posed inversion problem The first method for reducing the model complexity without reducing the lag size is to introduce regularization One regularization technique is the ridge regression controlled by a single parameter Kridge Note that the neural network community calls this weight decay and that this technique biases the filter coefficients towards zero h XT X Kpidgel 1X7 Y 4 7 where I is the unity matrix The other estimation technique computes the singular value decomposition SVD of the matrix to invert In this case the U and V will be equal so that cheaper and equivalent numerical methods can be used XT X 4 8 hence XT X 1VX UT 4 9 where a threshold ksyp controls how many singular values enter the pseudo inverse f 4 j x e if oyu 5 and i j 4 10 ij 0 if cii sy 0777 Note that this inversion does not depend on the voxel position u hence a transformation matrix T XT X 1X7 can be generated once
78. is only interesting around lag zero and the user can decide how many lags that should be computed and stored Note that people often only compute the cross correlation for lag zero which can lead to unreliable results in regions with long delays so we maintain the temporal information as well In the display of the cross correlation function we have enabled the display of the maximal value of the cross correlation function as well as the delay defined as the position of the maximal value and the energy of the cross correlation function 4 2 FIR filter The finite impulse response FTR filter is the same as a regression model or an ARX 0 n model that is an autoregressive model with exogenous input The voxel denoted by u is regarded as a linear system with the input x the paradigm the filter transformation function to be estimated h and the output fMRI data y which is disturbed by additive noise L 1 y u t X h u t eu t 4 1 T 0 The algorithm fits the parameters h r so that the error is the least square solution This 46 Section 4 2 FIR filter 47 assumes that the noise is gaussian distributed In that case the model y is L 1 9 u 2 Y h u t r e u 7 4 2 T 0 or in matrix vector notation for each value of u Y Xh 4 3 where Y ylu 0 u 1 G u N 1 and X contains the time shifted values of the paradigm where each row of the matrix has L samples From the assumpt
79. it was used in connection with CVA canonical variate analysis All the scans that correspond to a specific period in a run are given their own class e g the designmatrix of a tiny study consisting of 2 runs each with four scans will have the following structure 1 0 0 010 0 0010 00 0 1 7 Qas 0100 0010 00 0 1 It is of course important that the stimulus function the paradigm is the same for all runs We use partial least square not as in introduced by McIntosh McIntosh et al 1996 but in the orthonormalized version as suggested by Worsley Worsley et al 1997 where the designmatrix is made invariant to linear transformations Lars Kai Hansen et al 1997 Section 4 14 The Ordinary t test 62 2 UAV 4 52 Here X is the SVD projection X 4 53 And V is the eigenimage of X X 4 54 The eigensequence U and the eigenimage of V of equation 4 52 are the interesting parts These are sorted according to descending eigenvalues The first eigenimage and eigensequence will usually have a direct relationship with the stimulus function 4 13 1 Our implementation The main function that implements the SOP model is called lyngby_sop_main Before the datamatrix is singular value decomposed it is doublecentered The number of components singular values maintained in the final singular value decom position can be varied by the user Usually only three or less components are
80. ith nuisance view Global variables for Ardekani t test analysis method Initialize globals for Ardekani t test t test using the Ardekani t method User interface for init of Ardekani s t test Viewing Ardekani t test results Script executed for Ardekani s t test Script for Ardekani t t test view Global variables for cross correlation analysis method Cross correlation User interface for init of cross correlation User interface for viewing Cross correlation results Viewing Cross correlation results Script executed for cross correlation anal Script for cross correlation view Section B 1 Available Functions 73 Exhaustive FIR lyngby_efir_global Global variables for Exhaustive FIR analysis method lyngby _efir_init Initialize global variables for EFIR analysis yngby efir main Main exhautive FIR function lyngby_ui_efir init UI for initialization of EFIR model lyngby_ui_view_efir Viewing EFIR filter results lyngby_uis_efir Script executed at the EFIR analysis lyngby_uis_efir_v Script for exhaustive FIR viewing lyngby_plotfilter Plot FIR response FIR lyngby_fir_convolve Convolve the FIR kernel with the input lyngby_fir_error FIR residual signal Quadratic error lyngby_fir_global Global variables for FIR analysis method lyngby_fir_init Initialize global variables for FIR analysis lyngby_fir_main Regularized FIR filter main function yngby fir masscent Returns the masscenter of the FIR kernel yngby fir plot Plot
81. ith the user setting the initial parameters of the algorithm via the button shown in Fig 2 13 and then starting the calculation by pressing the button The results are also viewed using the same interface as before accessed via the button The Meta K Means algorithm attempts to cluster for example the parameters of the filters used to model each of the voxels in effect looking for commonality of filter types instead of common voxel time series In this way it is a higher level of analysis and should provide another viewpoint on the data 2 5 3 Exporting Variables Printing and Saving Results Generally the result variables are not available from the commandline as they are global vari ables However it is easy to access them by issuing the command gt gt lyngby_ui_global You can then list all the variables by doing Lars Kai Hansen et al 1997 Section 2 5 Using the Lyngby Windows Interface 35 lt means initialization Figure 2 13 The parameter options for the Meta K Means post processing algorithm gt gt whos This allows you to both see the size of the result variables and save them directly from the command line For example gt gt save MyFilename txt RESULT LZ ascii This will export the Lange Zeger result to an ASCII file named MyFilename txt Note that you might want to change to another directory first you are in the data directory while working with the Lyngby package Alternativ
82. lization error test error which depends of the dif ferent models and the split ratio for splitting the dataset The model with the smallest mean generalization error is chosen as the optimal model for the voxel When the optimal model for each voxel has been estimated the activation strength can be found from equation 4 12 Note also that the number of filter coefficients will vary across the volume and this might also be of interest to investigators which can lead to several hundred different 4 3 1 Our Implementation All exhaustive FIR functions have an infix of efir The two parameters that can be set are the filter length and the reshuffle amount The reshuffle amount determines how many times the data set resampling is done 4 3 2 References We can not make any direct references in connection with the exhaustive FIR model Consult section 4 2 4 for reference in relation to the architecture of the model Generalization and train test set are terminology from the artificial neural network society and reference to that can be found in section 4 9 2 4 4 The Ardekani t test In Ardekani and Kanno 1998 another type of t test is described The method is rather different than the one described in section 4 14 and it is actually closer to the cross correlation method The basic idea is to project each of the time series onto a subspace driven by the paradigm function The t statistics are obtained by dividing by the es
83. lobal Variables The Lyngby toolbox has to use a set of global variables that under normal conditions are hidden from the user The user can make the these variable available to the workspace by calling lyngby global A list of the Lyngby global variables is given in table 2 3 Furthermore the result variables and the data matrix are also global but are seperate from the ones shown above You can make the these variables available to the workspace by calling lyngby_ui_global An example list of these global variables is given in table 2 4 X and P will be defined once the data have been loaded normally done upon pressing the button XN and PN will be defined once the pre processing has been done and the RESULT will first be defined once an analysis has been performed via the button The next section gives more details on how to run the analysis algorithms from the com mandline Lars Kai Hansen et al 1997 DATATYPE DEFAULT SAVE DISCRIM TMASK FILENAME PATH FILENAME PATTERN FILENAME STARTINDEX FILENAME WORKSPACE FILE_READING_TYPE LOGFILENAME NUM_RUNS NUM_SCANS NUM_SUBJECTS NUM_VOXELS ORDERING ORIENTATION ORIGIN ROI_VOXELS TIME_MASK UI_ON VOXELSIZE VOXEL_MASK Section 2 7 Writing Scripts to Run Lyngby Automatically Type of data e g float double short byte long The default location in the file chooser when sav ing data Path to the data file String wi
84. ly although a suitable order must be chosen manually this does not seem to degrade the results significantly If an automatic determination of the order is required then the more time consuming algorithm described in section 4 3 should be used 4 2 4 References The standard linear regression we employ here should be described in most books about time series analysis The ridge technique in regression was first applied by Hoerl and Kennard 1970b Hoerl and Kennard 1970a For an annotated bibliography see Alldredge and Gilb 1976 Ridge regresion is a form of Tikhonov regularization for linear models Tikhonov 1963 Tikhonov and Arsenin 1977 Hansen 1996 Principal component regression is described in Jackson 1991 The application of the FIR filter on fMRI is described in Goutte et al 2000 and shortly in Nielsen et al 1997 Another type of linear time series analysis on fMRT is described in Locascio et al 1997 4 3 Exhaustive FIR filter In the FIR filter method section 4 2 the user has to make the choice about the length of the filter In principle the filter length is a parameter that can be varied as a function of the voxel index In voxels where the signal is complex and there is a high signal to noise ratio many filter coefficients may be needed On the other hand in voxels where only noise is observed none of the estimated filter coefficients are stable and the best stable signal estimator is a constant of valu
85. m a square wave activation function each of the time series is split into an activation part and a baseline part In this model the difference in means relative to a deviation measure is given a statistical interpretation Lars Kai Hansen et al 1997 Section 1 2 Organisation of this Book 9 The Kolmogorov Smirnov test In the Kolmogorov Smirnov test each of the time series is split into an activated part and a baseline part The maximal distance between the his tograms of the two parts is taken as a measure of match A probabillity measure is also derived Neural Network regression A feed forward artificial neural network is trained to predict the time series for each voxel If the neural network is better at predicting the time series than a null model for a specific voxel that voxel can be said to be activated The neural network regression is a non linear generalization of the FIR filter model Neural Network Saliency A feed forward artificial neural network is trained to classify the scans according to the paradigm After the training the neural network is analyzed to reveal which voxels were the most important in the prediction Poisson Filter An fMRI time series model Singular value decomposition SVD The same as principal component analysis PCA Independent component analysis ICA A multivariate methods to find independent not necessarily orthogonal components with an implementation of the simple Molgedey Schuster algo
86. n Belliveau et al 1996 page S607 Svarer C Hansen L K and Larsen J 1993a On the design and evaluation of tapped delay lines neural networks In Proceedings of the IEEE International Conference on Neural Networks San Francisco California USA volume 1 pages 46 51 Svarer C Hansen L K Larsen J and Rasmussen C E 1993b Designer networks for time series processing In Kamm C et al editors Neural Networks for Signal Processing III pages 78 87 Piscataway NJ Baltimore 1993 IEEE Tikhonov A N 1963 Solution of incorrectly formulated problems and the regularization method Soviet Math Dokl 4 1035 1038 Tikhonov A N and Arsenin V Y 1977 Solution of Ill Posed Problems Winston Washing ton D C Toft P Hansen L K Nielsen F Strother S C Lange N M rch N J S Svarer C Paulson O B Savoy R Rosen B R Rostrup E and Born P 1997 On clustering of fMRI time series In Friberg et al 1997 page S456 Van Horn J D Esposito G Weinberger D R and Berman K F 1996 Volume based multivariate discriminant and canonical correlation analysis of neurophysiological measures of brain function In Belliveau et al 1996 page S103 Vinod H D 1976 Canonical ridge and econometrics of joint production Journal of Econo metrics 4 147 166 Worsley K J 1997 An overview and some new developments in the statistical analysis of PET and
87. n_qdev lyngby_nn_qdew lyngby_nn_qdru lyngby_nn_qerror lyngby_nn_qforward lyngby_nn_qmain lyngby_nn_qpruneobd lyngby_nn_qtrain lyngby_nn_reg2reg lyngby_nn_setsplit lyngby_nn_tanh lyngby_nn_u2vw lyngby_nn_vw2u Neural Network Regression lyngby_nnr_global yngby nnr init lyngby_nnr_main lyngby_ui_nnr_init lyngby_ui_view_nnr lyngby_uis_nnr lyngby_uis_nnr_v Neural Network Saliency lyngby_nns_esalmap lyngby_nns_global lyngby_nns _init lyngby_nns_main lyngby_ui_nns_init lyngby_ui_view_nns lyngby_uis_nns lyngby_uis_nns_v PCA Analysis lyngby_pca_eqtest lyngby_pca_main lyngby_pcafilte lLars Kai Hansen et al 1997 76 2nd der quadratic input diag gauss 2nd der quadratic input gauss approx 2nd order der quadratic output diag gauss 2nd order der quadratic output gauss approx 2nd order der of regularization for weights Quadratic neural network input 1st der First order derivative quadratic Output weights Quadratic neural network 1st der reg Quadratic error Neural network forward with linear output function Main function for quadratic neural network Pruning by Optimal Brain Damage quadratic Quadratic neural network training Standardize regularization Split the data into training and validation set Faster hyperbolic tangent Vectorize neural network weights Vectorize neural network weights Global variables for NNR analysis method Initialize global variables for NNR analysis Main funct
88. nalysis KS_PROBMAP The result from the Kolmogorov Smirnov test probability map RESULT_KS The result from the Kolmogorov Smirnov test analysis Table 2 4 Some Examples of the Global GUI variables then look at the results the next morning It is very straightforward to write scripts for Lyngby although it will be easier once you are familiar with using the GUI You will then know the order in which the data is processed and the range of possible choices e g the different pre processing options and algorithms available A full list of all the functions within the Lyngby toolbox and their purpose is given in Table B 1 of Appendix B In addition you may want to have a look at the Lyngbywebsite where there is ahyperlinked index of all the toolbox files giving details of its purpose and its interdependencies with the other files When using the commandline you must have a data_init m file to specify the initial data parameters as well as the data_run m data_paradigm m and data_readdata m files These are set up in exactly the same way as would be required when using the GUI see Section 2 4 2 for details and examples For example for a particular dataset the initialisation and conversion files would be as shown below Lars Kai Hansen et al 1997 Section 2 7 Writing Scripts to Run Lyngby Automatically 39 The data_init m file data_init m function data_init lyngby_global NUM_VOXELS 24 12 1 NUM_SCANS 384 FILE_
89. necessary when reading in non supported data data_readdata m although up to four others may be used These others are optional but do make life easier Any file that is to be supplied by the user will have a filename stem of data_ m Their individual purposes are summarized below data_readdata m The only necessary file required for reading in non supported file formats it contains a few lines of matlab code that actually return the non supported data as a vector It is also where the user will put in any re organisation of the data in order to get the byte read order correct The user must use the standard Matlab functions to re organise their data to match this ordering An example of how to do this is given later data readinfo m This file is only required if the user wants to use the facility within Lyngby to check the headers of their data files This is accessed by pressing the button in the Load new data window It is therefore not an essential requirement for loading in non supported data formats and indeed may become redundant in future versions of the toolbox data paradigm m This is used to specify the paradigm the external reference function which is used in the actual analysis stage It can be specified within the GUI but it is far easier to keep it within a file that is loaded in automatically It is simply a 1D vector indicating on and off time points and as such usually only requires a single line of code The GU
90. o setting the parameters from 7 is made Look at the other lyngby_ui_ OTHERNAME _init m for examples In lyngby_ui_main m locate the line The actual analysis Add a new block for the new algorithm which maybe look like elseif AnalysisMethod am NAME RESULT_ NAME lyngby_ NAME _test XN PN R Something NAME _ SOMETHING RESULT RESULT_ NAME XN is the normalized data matrix at this point PN is the activation function with mean subtracted and R is the run structure In lyngby_ui_main m locate the line elseif command 503 Add a new block for visualization of the new method Add the file lyngby_ NAME _test m which returns the result of the method The file lyngby_ui_main m will turn the RESULT into activation strength delay etc Lars Kai Hansen et al 1997 Chapter 3 Data Formats Masking and Pre Processing Revision 1 11 Date 2002 08 14 14 21 24 3 1 Introduction These next three chapters are reference texts covering the different stages of data input analysis and post processing in more detail than in the previous user manual This chapter deals with the issues of data formats and preparation before the analysis stage The next chapter describes the different analysis algorithms available within the toolbox whilst the one after it covers the post processing or meta analysis algorithms Each of the modelling algorithms needs to do several processing steps Some of them are common an
91. od Gp BERG ann Brin ada 4 10 Neural network regression 4 10 1 Our implementation 4 10 2 References ic Hn a Re a S 4 11 Neural network saliency 4 11 1 Our implementation 4 11 2 References ner s a adad azm dk da 4 12 The SCVA model Strother Canonical Variate Analysis 4 12 1 Our implementation 4 12 2 References 4 13 The SOP model Strother Orthonormalized PLS 4 13 1 Our implementation Lars Kai Hansen et al 1997 43 45 45 44 44 44 45 CONTENTS 4132 RETERCN CESS oot 7 4 14 The Ordinary t test esa eos iog ace da 5 Post Processing 5 1 K means Clustering on the Modelling Results A Glossary Functions 1 AyalableF ncii6BS u s ci at eh oe ee ee A Mu S C Derivations Cul Neural Network tidad oe ok ee eR Se l Symbol tables eg hon A AN C 1 2 The errorfunction for the classifier neural network and its derivatives C 1 3 Numerical stabil computation of softmax D Getting Started E Example Analysis Lars Kai Hansen et al 1997 63 63 64 67 67 79 79 79 80 83 84 86 List of Figures 21 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2
92. odelling stage by way of meta analysis algorithms Finally the appendices cover any derivations of modelling algorithms and other similar details refererred to in the main part of the book In summary Chapter 1 Introduction to Lyngby what is it who wrote it and what is it for Chapter 2 The main user manual a step by step guide to the user interface Chapter 3 Details of the preliminary steps the data formats and the pre processing stages Lars Kai Hansen et al 1997 Section 1 3 Explanation of the Typographic Conventions 10 Chapter 4 Details of the analysis algorithms in the toolbox Chapter 5 Details of the post processing stages meta analysis Appendix A Glossary of MRI and Lyngby terms Appendix B Detailed list of all the functions and script files within the toolbox Appendix C Derivations of the algorithms used in the toolbox Appendix D The Getting Started Guide useful for first timers Appendix E Example Analysis An step by step example of how to to use the toolbox to analyse fMRI datasets 1 3 Explanation of the Typographic Conventions Within this manual we have tried to improve the readability of the text by using certain typographic conventions For instance Any reference to Matlab code either on the commandline at the gt gt prompt or within a Matlab script m file will be written in monospace with all the inherent formatting included In addition commands written at the M
93. ound Layer This is the right side of the top layer and it controls the underlay of a background image At the moment this background image must be chosen from the cur rent result set We are hoping to incorporate the option of loading in a seperate anatomical background image soon although this raises several questions regarding registration and resolution For the moment though a very good approximation to an anatomical image Lars Kai Hansen et al 1997 Section 2 5 Using the Lyngby Windows Interface 33 can be obtained by use of the mean image which is automatically included in all result sets Once again the radio button to the left controls the activation of the layer and the next button allows the choice of which result set to use as a background The final button specifies whether the background is taken as the values in the current slice or as a mean or maximum of the volume along the current direction Save Layer This appears on top of the other four layers and has a red background to highlight it In addition the layers upon which the save layer is acting are also coloured red The first button controls what is to be saved e g the whole volume the current slice or the time series of the current voxel The next button specifies the format in which to save the data The options depend on what is to be saved For instance the volume has a choice of ASCII Matlab Analyze STD or VAPET More choices will be added in fut
94. p to have the run and paradigm files setup as for the GUI If your data is a non supported format then it may also be easier to put the data loading functions into the data_readdata m file rather than having to enter them on the commandline each time 2 6 1 Data Loading e Change to the relevant data directory Setup the global variables This is usually done within data_init m data_paradigm m and data_readdata m e X lyngby_getdata 2 6 2 Pre Processing Pre processing has been used with different meanings in neuroimaging In terms of the Lyngby toolbox by pre processing we mean the step after loading the data but before the actual data analysis In the GUI the setup of the pre processing is managed by lyngby_ui_preproc This is called from lyngby_ui_main upon pressing the button The function and its associated window are used to setup the global variables in lyngby_prep_global These variables are used by lyngby_ui_main in its call to lyngby_normalize the function that does the actual pre processing This is normally done by pressing the Apply Pre Processing and Close button in the Data Setup window The loaded data held in the global variable X is passed to the pre processing step which then outputs the global variables XN X MEAN and X_STD You do not have to use the lyngby_normalize function and you can set these variable yourself directly from the command line XN X X_MEAN mean X X_STD std X 2 6 3 G
95. paradigm data and FIR model lyngby_ui fir init User interface for FIR filter analysis lyngby_ui_view_fir Viewing FIR filter results lyngby_uis_fir Script executed at the FIR analysis lyngby_uis_fir_v Script for FIR view lyngby_plotfilter Plot FIR response Gaussian Mixture Models lyngby_gmm_error Gaussian mixture model error lyngby_gmm_fit Gaussian mixture model fitting lyngby_gmm_plot Plot gaussian mixture model K Means lyngby_km_error K means error lyngby_km_global K means Global variables declarations lyngby_km_init K means Global variables initialization lyngby_km_main Main function for K means clustering lyngby_km_plot K means plot lyngby_ui_km_init GUI for K means parameter initialization lyngby_ui_view_km Viewing K means filter results lyngby_uis_km Script executed for K means analysis lyngby_uis_km_v Script for K means view Kolmogorov Smirnov lyngby_ks_global Global variables for KS analysis method lyngby_ks_init Initialize globals for KS test analysis lLars Kai Hansen et al 1997 Section B 1 Available Functions lyngby_ks_main lyngby_ks_prob lyngby_ks_test lyngby_ui_ks_init lyngby_ui_view_ks lyngby_uis_ks lyngby_uis_ks_v Lange Zeger lyngby_lz_error yngby lz lambda lyngby_lz_masscent yngby lz plot yngby lz plottheta Lange Zeger Grid Search lyngby_lzgs_global lyngby_Izgs_init lyngby_Izgs_main lyngby_lzgs_search lyngby_ui_lzgs_init lyngby_ui_view_lzgs lyngby_uis_lzgs lyngby_uis_lzgs
96. pethdr lyngby_readvapetvol lyngby_readvavol4 lyngby_readxpihdr lyngby_readxpivol lyngby_vmask2index lyngby_write_ana lyngby_write_sdt lyngby_write_vapet Data Formatting and Information lyngby_full2mask lyngby_getdata lyngby_getinfo lyngby_getslice lyngby_getvolume lyngby_index2tmask lyngby_index2vmask lyngby_mask2full lyngby_normalize lyngby_normalize lyngby_numscan lyngby_paradigm lyngby_prep global lyngby_prep _init lyngby_roi lyngby_roi2vmask lyngby_run lyngby_runinfo lyngby_sliceindex lyngby_swaporder lyngby_talaimg lyngby_tmask2index lyngby_tmp files lyngby_tmp getseq lyngby_tmp getvol lyngby_tmp init lLars Kai Hansen et al 1997 70 Reads header information of a volume file Reads a volume from a recognized file Reads an ANALYZE header Reads an ANALYZE img file Reads the header information in a 4 dimensional VAPET file Reads the header information in a VAPET file Reads a VAPET volume from a file Reads a 4 dimensional VAPET structure from a file Read header from EC flexible format Read data from EC flexible Xprime format Return Indices from voxel mask Write a volume to ANALYZE files Write a volume datamatrix to SDT SPR file Write a volume to VAPET file Convert indices from Full volume to ROI volume Returns the masked datamatrix Get volume info from a file Extracts a slice from a volume Get a volume from a file Return time mask from indices Return voxel from indices Convert indices from
97. r estimation Noise estimate in the Lange Zeger model Pick frequencies out from the data matrix Lange Zeger Optimize theta parameters GUI for iterative Lange Zeger initialization Viewing Lange Zeger results Script executed for Lange Zeger Iterative Script for Lange Zeger iterative view Section B 1 Available Functions lyngby_mkm_global lyngby_mkm_init yngby ui mkm init lyngby_ui_view_mkm yngby uis mkm yngby uis mkm v Neural Netvvork lyngby_nn_cddevds lyngby_nn_cddewda lyngby_nn_cddewds lyngby_nn_cddru lyngby_nn_cdev lyngby_nn_cdew lyngby_nn_cdru lyngby_nn_cerror lyngby_nn_cforward lyngby_nn_cmain lyngby_nn_cost lyngby_nn_cpruneobd lyngby_nn_csoftline lyngby_nn_csoftmax lyngby_nn_ctrain lyngby_nn_eddevds lyngby_nn_eddewd lyngby_nn_eddru lyngby_nn_edev lyngby_nn_edew lyngby_nn_edru lyngby_nn_eehl lyngby_nn_eemedian lyngby_nn_eerror lyngby_nn_eforward lyngby_nn_emain lyngby_nn_epruneobd lyngby_nn_esoftline lyngby_nn_esoftline lyngby_nn_etarget lyngby_nn_etrain lyngby_nn_initvw lyngby_nn_plotnet lyngby_nn_pruneobd lyngby_nn_qddeus lLars Kai Hansen et al 1997 75 Meta K means Global variables declaration Meta K means Global variables initialization GUI for Meta K means initialization Viewing of meta K means results Script executed for Meta K means analysis Script for Meta K means viewing 2nd order entropic input diag sym Classifier neural network output diag 2nd Classifier neural
98. r to ear left right y refers to the coronal slice i e back to front z refers to the transaxial slice i e bottom to top and so this is the order into which the user must reshape their own data The X index changes quickest followed by the Y index with the Z index changing the slowest Thus the data cycles through the X s first then the Y s and finally through the Z s So for a 10 by 10 by 10 cube the data should be in the order Lars Kai Hansen et al 1997 Section 2 4 Data Setup 18 P x1 y1 z1 P gt x2 y1 z1 Py x3 y1 z1 as ig Pio 10 y1 z1 Pir x1 y2 z1 Pip x2 y2 z1 Pis x3 y2 z1 aot oo 10 y2 z1 Pioi x1 y10 z1 Pio x2 y10 z1 Pio3 x3 y10 z1 eiae 5 Pio x10 y10 z1 Pin 11 922 Pi x2 yl 22 3 1 22 Pioo x10 yl 22 Po91 x1 y10 210 Po92 x2 y10 210 Po93 3 yl0 z10 Piooo x10 y10 z10 Note that the direction along each of the three orthogonal axes is also important The Lyngby toolbox uses the Talairach co ordinate space as its reference The origin of this space is located at the centre of the brain with the directions of the axes as given in Table 2 1 Table 2 1 Direction of the axes in Talairach coordinate space The Lyngby toolbox will assume that the data is written with the most negative values first increasing through the origin and up to the most positive
99. resonance brain imaging Human Brain Mapping 5 5 168 193 Lundsager B and Kristensen B L 1996 Line r og ulineser modellering af positron emission tomografier Master s thesis Department of Mathematical Modelling Technical University of Denmark Lyngby Denmark In Danish MacQueen J 1967 Some methods for classification and analysis of multivariate observations In Le Cam L M and Neyman J editors Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability volume 1 pages 281 297 Berkeley Califonia University of California Press Mardia K V Kent J T and Bibby J M 1979 Multivariate Analysis Probability and Mathematical Statistics Academic Press London McIntosh A R Bookstein F L Haxby J V and Grady C L 1996 Spatial pattern analysis of functional brain images using Partial Least Square NeuroImage 3 3 part 1 143 157 Merch N J S Hansen L K Strother S C Law I Svarer C Lautrup B Anderson J R Lange N and Paulson O B 1996 Generalization performance of nonlinear vs linear models for 5O water PET functional activation studies In Belliveau et al 1996 page S258 M rch N J S Kjems U Hansen L K Svarer C Law I Lautrup B Strother S C and Rehm K 1995 Visualization of neural networks using saliency maps In Proceedings of 1995 IEEE International Conference on Neural Networks volume 4 pages 20
100. rithm Strother CVA Canonical variate analysis Strother Orthonormalized PLS The PLS partial least square method finds the images and sequences that explain the majority of the variation between two matrices The two matrices in the Strother orthonormalized PLS are the datamatrix and a designmatrix that is constructed by putting the scans in the same period in each run into the same class 1 2 Organisation of this Book This book fulfills several requirements The first explaining what the Lyngby toolbox is for what it can do who developed it and other related information is here in the first chapter The second the user manual element is contained in Chapter 2 It explains how to go about using the toolbox including getting your own data into it and shows you how to do the different analyses Consider it as a How to guide The following three chapters explain the different stages of using the toolbox in more detail and provide more background information The first of these covers the different data formats that Lyngby supports how data is loaded and stored in the toolbox and the pre processing that is usually done to the data before any analysis is performed The second Chapter 4 looks at the actual data analysis stage and considers each of the modelling algorithms in detail The final chapter of this group Chapter 5 covers post processing of the data This involves the analysis of the results from the previous m
101. s is loaded is determined by global variables and through calls to consecutive calls lyngby_getvolume for each volume See also LYNGBY LYNGBY_GETVOLUME LYNGBY_UI_LOADFILE Id function appendix tex v 1 3 2002 08 14 13 32 23 fnielsen Exp The last line is the concurrent revision system CVS text The first number indicates the revision number and the date is the date of the last revision You can also use the helpwin Matlab command gt gt helpwin lyngby_getdata A new help window should popup and you can click between related functions listed at the button next to See also The following table lists all the functions available Not that the list is not complete Some will never need to be called directly as they will be called from other functions All the functions with a lyngby_ui_ stem are concerned with the GUI controls and as such are unlikely to be called from a script Kai Hansen et al 1997 Section B 1 Available Functions 69 Table B 1 Functions Available in the Lyngby Toolbox General Lyngby Functions lyngby lyngby_circle lyngby_classerr lyngby_corrlin lyngby_cumperiodo lyngby_cva lyngby_design lyngby_dropedge lyngby_filter lyngby_frame lyngby_global lyngby_histeq lyngby_image lyngby_init lyngby_kronadd lyngby_log lyngby_meangeo lyngby_meanhl lyngby_mod lyngby_msvd_main lyngby_opls lyngby_plotmatch Statistical Distributions lyngby_cdf_bin lyngby_cdf_chi2 lyn
102. s removed from the paradigm structure i e the paradigm signal is trans formed from 0 1 0 1 0 1 to 1 2 1 2 1 2 1 2 1 2 1 2 as required by some analysis algorithms Press Close The window should disappear Press the Data setup button in the main window A new window titled Data Setup will pop up If not already highlighted select the first options normalization on the left hand pane and press Setup design and run A new window Pre Processing will appear Select the first and third option and press the Apply Pre Processing and Close button Press in the Data setup window Click on the top button of the Data Analy sis frame initally labeled Original From the pop up list select the FIR Filter algorithm Press the button to bring up a new window Once you have finished exam ining the settings press the button to shut the window Press the Calculate button to start the cal culation Lars Kai Hansen et al 1997 87 The next stage is to perform any pre processing of the data The next stage is to select the pre processing methods that will be applied to the data The Pre Proceesing window will close and the status of the pre processing will be shown on the status bar within the main window This will close the window Next the actual analysis of the data can take place As an example we will do a FIR Filter analysis of the paradigm an
103. several options within the Load Setup window The majority of the fields are used to set up the file structure and image size etc whilst the bottom right frame is used to specify some external factors such as specifying a region of interest ROT and the removal of any unwanted scans 2 5 2 2 The Load Window Data Fields There are many fields in this window and the various file formats support a different number of these fields Those that are not supported or are yet to be fully implemented are greyed out and hence cannot be used note how the accessibility of the fields changes as you change the file format File Format lyngby can load in several different file formats Apart from its own native format lyngby can also read Vapet Analyze Stimulate and Raw formats The lyngby format requires some additional small conversion files to be written that describe how the data should be read examples were given earlier in Subsection 2 4 3 on how to create your own Once this has been done for your dataset the 1yngby format then becomes the easiest to load as the image parameters have already been specified The other formats will require the user to specify the location of the data the image size the size of each data unit the ordering of the data etc It is usual for the data to be split across many individual files and this is catered for by the File Pattern Start Index and No of Scans choices which allows the user to specify
104. splay Layer The lower layer controls the right window which usually displays the time series of the currently selected voxel However some algorithms also produce histograms error curves periodograms etc either voxel based or full volume based which can be selected from the left most button in this layer and displayed in the right window The button controls the scaling of the bottom axis and so allows temporal zoom ing The next button switches the vertical axis scaling between fixed and automatic Adjacent to this the slider controls the temporal location of the time series display and is used in conjunction with the horizontal zoom button to move through the time series It is disabled when the full time series is displayed The next four buttons apply to all three windows The Close all button closes all three windows The results are still kept though and can be accessed again by pressing the View these results button in the main window The button displays the Save Layer allowing specific volumes or results to be selected for saving This is covered again later The button brings up help for all three windows and the or button adds removes the extra layers for masking background display etc Lars Kai Hansen et al 1997 Section 2 5 Using the Lyngby Windows Interface 32 Data Layer This controls the main results of the modelling algorithm As in the other three voxel related layers Masking Conto
105. splaying 8 adjacent slices volume view Window 1777777 A E m z IX File Edit Tools Window Help File Edit Tools Window Help DSH Figure 2 4 The volume window in Lyngby showing three orthogonal views and a 3 dimensional one Once all the loading parameters have been set press the Apply button to ensure that they are all stored and then press the Load Data button to start the loading in of all the data The Load Setup window is closed and the status bar at the bottom of the main window indicates the progress of the loading 2 5 2 4 Data External Influences In the main window there were links to create edit and load external influences on the data that affected the way or the amount of data loaded into the toolbox This section covers the external influences on the data that are applied once the data is loaded To access this stage press the button in the main window This will bring up the External Data Influences window as seen in figure 2 5 Most of these external influences are usually specified in external files first and then altered here if necessary Guidelines for writing these files are given later e The run structure can be verified by pressing the Create of edit the Run function button Each of the runs is given a unique number so the graph should be a staircase as shown in figure 2 6 You will only need this structure if you plan to make a pre proce
106. ssing step or analysis type that requires run information e g run centering The global variable associated with the run structure is called RUN Like the paradigm this function can be altered here but is usually defined in an external file Lars Kai Hansen et al 1997 Section 2 5 Using the Lyngby Windows Interface 27 lyngby Run setup Figure 2 6 The run window in Lyngby The paradigm can be verified by pressing the button The global Matlab variable associated with this window is called PARADIGM The GUI allows alteration of the paradigm function that is usually defined in an external file data_paradigm located at the same place as the data The Paradigm window is shown in Fig 2 7 2 5 2 5 Data Pre Processing Before the actual modelling the data should be pre processed By pressing the Data Setup button the window shown in Fig 2 8 pops up This window has a left and right pane which serve different purposes The user should do any work on the left pane first before selecting the Lars Kai Hansen et al 1997 Section 2 5 Using the Lyngby Windows Interface 28 p DOSBIT Figure 2 7 The paradigm window in Lyngby relevant options on the right pane and then pressing the Apply button On the left the top button is used to remove unwanted scans by applying the TIME MASK variable which was previously specified in the Load Setup window to the PARADIGM and RUN variables The lower button removes the
107. strive for uniformly minimum variance thus we can use the mean square error for the measure Np No 2 53227 4 26 p o In the case of two class classification a more appropriate measure is the two class cross Jentropy error Np No 1 1 6 1 1 6 Ee 14 20 1 1 5 1 4 27 yir ez ari r 4 27 The cross entropic errorfunction of equation 4 27 requires the target to be t 1 or t 1 3 r 4 Square x Entropic 2 5 A 4 Errorfunction 1 0 8 0 6 0 4 0 2 0 0 2 0 4 0 6 0 8 1 Neural network output Figure 4 5 Comparison of the square and the cross entropic errorfunction The target is t 1 The cross entropic errorfunction is penalizing large deviation from the target value much more than the square errorfunction Another type of errorfunction is the cross entropy for multiple classes Bishop 1995 We use a so called c 1 variation where the number of output neurons in the neural network is one less than the number of classes Andersen et al 1997 1 1 Es Um b 2 a gt todo 4 28 This errorfunction is developed for a neural network with neural network function as follows The hidden layer neurons have a hyperbolic tangent as the activation function hy tanh gt Uno 4 29 h Lars Kai Hansen et al 1997 Section 4 10 Neural netvvork regression 57 The second layer has linear activation functions nr Po x Wonh Who 4
108. t al 1995 Hintz Madsen et al 1996a Hintz Madsen et al 1996b and Svarer et al 1993b 4 10 Neural network regression The Neural network regression is a neural network generalization of the FIR model For the input to the neural network we use the paradigm and the weights are adjusted to target the output to the fMRI time series signal One neural network is trained for every voxel The ability of the neural network to predict the MRI time series is used as a measure for the strength of the signal in a voxel If this signal can be predicted from the paradigm signal then the voxel is activated 4 10 1 Our implementation The functions that belong to the neural network regression analysis method have the prefix lyngby nnr The optimization of a single neural network is usually a tedious affair and when one neural network has to be optimized for every single voxel the computational effort of this analysis method is enormous The neural network regression analysis is currently under implementation and it does not provide any means for assuring that the neural network is generalizing well so it is presently dangerous to use the neural network regression Lars Kai Hansen et al 1997 Section 4 11 Neural netvvork saliency 58 4 10 2 References To our knowledge using neural networks in connection with fMRI time series regression is not described anywhere yet A first application was in a comparison between models Lange
109. th the filename pattern Example volume 602d Start index for use with the FILE NAME PATTERN The name of the workspace loaded in lyn gby_workspace mat is the default 1 Analyze Vapet obsolete 2 Lyngby i e custom 3 Raw 4 Analyze 5 Analyze4D 6 SDT Stimulate 7 VAPET4D File name to write log information into not currently used Number of runs in the data matrix Number of scans in the data matrix Number of subjects in data not used at the moment Number of voxels in the datamatrix 3x1 vector The file order of the voxels xyz yxz etc How the data is mirrored to display it the correct way around Ir pa is Centre voxel Number of voxels in the rectangular ROI 3x1 vector Mask in time to discard unwanted scans If ULON 1 then the program is run from the GUI interface if 0 then text based not up to date Voxelsize Spatial mask e g to remove non brain voxels 37 Table 2 3 Global variables 2 7 Writing Scripts to Run Lyngby Automatically The functions in Lyngby do not need to be run from the GUI and can easily be run from the commandline although the structure and ordering in which everything is done is not as obvious This is the advantage of using the GUI But the commandline approach does have an advantage also and that is the ability to write and run scripts equivalent to batch files This means you can load your datafiles perform the pre processing an
110. the file is closed with fclose fid 2 4 3 2 The data paradigm m and data_run m files The data paradigm function for the Jezzard data is function P data_paradigm P kron ones 3 1 zeros 10 1 ones 10 1 zeros 4 1 Another example of a data_paradigm function is function P data_paradigm P lyngby_kronadd zeros 8 1 zeros 24 1 ones 24 1 zeros 24 1 1 This function was created for an 8 run study with 72 scans in each run first are 24 base line scans then 24 activation scans and finally 24 base line scans Note that as well as using this compact way of specifying the paradigm it is also valid to type the paradigm as a long vector i e specify the paradigm in long hand function P data_paradigm P 000111000 BI The total length of the paradigm vector must be the same as the whole time series i e before the time mask is applied This is also true for the function defining the run structure data_run Lars Kai Hansen et al 1997 Section 2 5 Using the Lyngby Windows Interface 21 function R data_run The Jezzard dataset contains three runs The first with 24 scans then one with 20 and the last also with 20 R ones 4 1 ones 20 1 2xones 20 1 3 ones 20 1 Another example of a data_run m file is function R data_run R lyngby_kronadd 0 7 ones 72 1 Both examples define a staircase function with one level per run Two of the examples use the con
111. the ieee be specifies that they are in big endian format As a rule files stored on Intel Pentium and DEC Alpha machines are little endian ieee le whilst those stored on Sun and SGI machines are big endian ieee be Make sure that the correct format is chosen for your architecture The next few lines check that the file was actually there and that it could be opened returning an error if not if fid 1 error readdata Could not open file end The next line skips the header in each data file The Jezzard data files have an 8 byte header fread fid 8 char Next the data in the file is read into a single vector V Remember that this is only one volume at a time The size of the individual data points must be specified a 2 byte signed integer in this case It is probably wise to specify the data size in architecture independent form as shown in Table 2 2 e g use int16 instead of short V fread fid int16 MATLAB char char 1 character 8 bits uchar unsigned char unsigned character bits schar signed char signed character 8 bits ints integer 1 integer 8 bits int16 integer 2 integer 16 bits int32 integer 4 integer 32 bits int64 integer 8 integer 64 bits uint8 integer 1 unsigned integer 8 bits uint16 integer 2 unsigned integer 16 bits uint327 integer 4 unsign
112. the models are very different in nature The Lyngby toolbox can import data in various different formats and it is also able to cope with non supported formats with very little user intervention In addition to the large set of data modelling strategies there is also a choice of pre processing steps and routines and the ability to perform post processing on the modelling results The toolbox was developed on Linux and SGI platforms and should work on all platforms with Matlab version 5 2 Lyngby was previously supported with Matlab 4 2 and some of the functions will still work with this version There are still some teething problems with running the toolbox under MS Windows however due to some differences in the way Matlab operates between the Unix and Windows flavours We are working to overcome these problems but as they are due to subtle undocumented Matlab inconsistencies it is something of a trail and error process For the time being we encourage people to use the toolbox in Matlab under Linux where the majority of our development is now carried out Any advice regarding the development of the toolbox in Matlab for MS Windows is of course welcomed In addition to this manual there are also a few other pieces of documentation to aid use of the toolbox A Getting Started guide has been written to show the first time user how to download install and run the toolbox as quickly and simply as possible In addition an Example
113. timate of the standard deviation found from the part of the energy in the time series that is not explained by the paradigm 4 4 1 Our Implementation Our implementation follows the paper rather closely and as suggested in the paper we have implemented a delay option so that the paradigm can be delayed a number of samples compared to the time series in order to adapt to a possible delay in the data 4 4 2 References Babak Ardekani s t test is described in Ardekani and Kanno 1998 4 5 The Ardekani F test In Ardekani and Kanno 1998 an F test has been presented to identify activated regions The strategy has some common ideas with the Ardekani t test described in the same article The basic idea is to project each of the time series onto a subspace driven by a truncated Fourier expansion of the data The power of the data in the subspace driven by the expansion is divided by the power of the data that lies outside of the Fourier subspace Thus an F statistic is obtained without using requiring any knowledge of the paradigm Kai Hansen et al 1997 Section 4 6 K means Clustering 51 In Ardekani et al 1999 the F test is extended with the modeling of a nuisance subspace A subspace orthogonal to the subspace spanned by the Fourier expansion is found and this subspace is then extracted from the original signal The dimension of the subspace is found by using Akaike s information criterion 4 5 1 Our Implementation F
114. ting code is in place and as such you may load in a voxel mask from the command prompt Details of how to do this are given later Volume ROI The ROI can be specified by pressing the Volume ROI button In order to edit the volume it must first of course be loaded in This requires the data parameters to be specified first so once this is done press the Apply button at the bottom and this will then unshade the Volume ROI button Note that the whole data matrix is not loaded at this point only the relevant volume In this window a rectangular ROI can be specified by the user who can also browse through all the data in OLars Kai Hansen et al 1997 Section 2 5 Using the Lyngby Windows Interface 26 both time and space As can be seen in Fig 2 4 the user has the choice of five different viewing layouts to examine the data The first one simply shows a single slice of the data with the choice of the three orthogonal directions and the ability to move along each of these axes The second choice allows two slices to be shown alongside one another either from the same or different viewpoints There is also the ability for linking the two views if they are of the same direction allowing for easy stepping through the volume The third choice is the standard triple orthogonal view This is also repeated in the fourth option alongside a 3 dimensional view of the data The final option is for view multiple slices from the same viewpoint di
115. unctions belonging to the Barbak Ardekani F test have the infix baf and function for the Ardekani F test with nuisance have the infix _baf2_ Our implementation follows the paper rather closely It is also intended to implement alternatives to the Fourier expansion 4 5 2 References Babak Ardekani s F test is described in Ardekani and Kanno 1998 The F test with nuisance parameters extension is described in Ardekani et al 1999 4 6 K means Clustering The K means algorithm is a simple non parametric clustering method The idea behind K means clustering here is to classify the individual voxel in the volume with respect to their time series This is indicated in figure 4 1 After the clustering the individual clusters may be analyzed further The method is currently sensitive to the initial cluster positions and the algorithm converges fast pray rare sk al Gl n n A ro Au aa NA YAA Figure 4 1 The time series are each assigned to the cluster center with the best match In the K means algorithm K cluster centers have to be chosen The dimension of the space is equal to the size of the time series length Then the distance from each voxel to each cluster center is calculated Each voxel is then assigned to the cluster which is the minimum distance away as shown in figure 4 2 lastly before iterating the new cluster center is calculated as the mean of all the voxels assigned to that cluster 1
116. upported formats nothing needs to be done outside the GUI in order to read in the data all the required information is extracted from the header files and from details entered into the GUTs Load New Data window Non supported file formats can be read in by the use of conversion files data readdata m and data_readinfo m These are small matlab files which act as header and data reading files for the Lyngby program so that it can understand the data These are very simple to write and detailed examples of how to do this are given later For all file formats there may be external influences on the data that you will also need for your analysis For instance the paradigm and run signals any previous voxel masking or a time mask to remove unwanted scans These can be specified through the GUI but it may be easier to save this information as small matlab files that can then be loaded in at the same time as the data Examples include data_paradigm m and data run m In addition it may be easier to save the parameters that specify the data such as image size and data location in a seperate file as well Then the user does not have to enter them every time data is to be loaded This file will work for any data format This file is called data_init m Details on how to create all these files are also given later 2 4 2 Setting up the Conversion Files for Non supported Data Formats It is easiest to explain how to set up the files that perform t
117. ur and Background the result set being used is chosen from the leftmost button s popup list Some algorithms only have a few result sets whilst others may have dozens The beauty of this layering approach is that it allows you to display one result set filtered by another over a background of a third whilst overlaying a contour plot of a fourth The next button specifies the slice direction for observing the data volume This is only really interesting if the data is a 3D spatial volume The adjacent slider controls the position of the slice plane within the volume Note that these also alter the viewing direction of the other layers as well it is no use plotting the transversal activation over a sagittal background Next to this is a button controlling what each voxel represents There is a choice of the current slice as selected by the previous two buttons the mean of the volume or the maximum voxel value both measured along the current direction Next comes a button specifying the colourmap to be used for this layer The Default setting uses the default colourmap as set in the file lyngby_ui_option m Finally the last button controls whether the colourbar on the spatial plot should be dis played or not Masking Layer This layer creates a binary mask from the selected dataset and then applies it to the Data Layer below Thus the only parts of the result set that are visible are those that occur where the mask allows This is use
118. ure as will more flexible saving options These will be located in the next button which is currently unavailable The next button allows choice of a compression algorithm This currently only works on Unix type systems as it employs the unix compress and gzip routines The filename to save the file under can be typed into the next box and saved in the current working directory by pressing the adjacent button If you want to choose a different directory simply use the button instead Mosaic View Originally most MRI studies were single slice but as the amount of volume studies has grown we have added in a mosaic slice viewer This allows the display of mutliple adjacent slices of a volume so the whole result set can be viewed at once To turn this on select the Toggle Mosaic View from the View Options menu in the volume window Alternatively use the Control M keyboard shortcut when the volume window is the selected window An example of the mosaic view can be seen in figure 2 12 The mosaic view requires a minimum of 3 slices of the current view plane In addition it won t work if you are looking at the mean or maximum result values as this would lead to multiple copies of the same image The current slice is used as the first slice in the mosaic list and so there must be at least two more slices left after it for the mosaic view to work So if you are currently looking at the last slice of a 16 slice volume move the slider to the l
119. uter with IEEE arithmetic since exp Inf yields Lars Kai Hansen et al 1997 Appendix D Getting Started Revision 1 3 Date 2002 08 14 13 03 16 Table D 1 Installed Up and Running in Two Minutes Keyboard mouse action Explanation Installation Click on the link to the toolbox file lyngby tar gz Choose Download the lyngby Toolbox and a suitable place to save the file Save the sample dataset the sample dataset from the web sampledata tar gz in the same way site at http hendrix imm dtu dk software lyngby cp lyngby tar gz usr local Copy the file to a suitable location such as usr local where a program directory will be created gunzip lyngby tar gz Uncompress the file tar xv lyngby tar Unpack the file which automatically creates a lyngby directory rm lyngby tar gz Remove the original distribution file to save space cp sampledata tar gz usr local lyngby Copy the sample dataset to the lyn gby directory gunzip sampledata tar gz Uncompress the sample dataset tar xvf sampledata tar Unpack the sample dataset auto matically creating a sampledata directory in the process 84 gt rm sampledata tar gz Setup 5 emacs startup m Add the line path path usr local lyngby Starting lyngby gt matlab gt gt cd usr local lyngby sampledata gt gt lyngby Lars Kai Hansen et al 1997 85 Remove the original distribution file to s
120. variate analysis With the ridge regression parameters on the highest level the canonical ridge will become PLS see section 4 13 The ordinary canonical correlation analysis canonical variate analysis is the singular value decomposition of a normalized cross correlation matrix 1 2 UAVT 4 39 1 2 Gta ex x Tx Here X is the SVD projection see also the equivalent equation 4 53 X XV U A 4 40 Lars Kai Hansen et al 1997 Section 4 12 The SCVA model Strother Canonical Variate Analysis 60 The equality sign only holds if there are more variables than objects more voxels than scans V is found through a normal singular value decomposition X U A V T 4 41 Ordinary canonical variate analysis can be extended to canonical ridge Canonical ridge is usually written as de kal M atx xx kxI UR UAVT 4 42 A different way to write the canonical ridge equation is by using another form of scaling 1 2 1 2 keg GTG kel GTX a HD kxI UAV 4 43 This has the advantage that the ridge parameters ka and kx are morphing between ordinary CVA and PLS via orthonormalized PLS kx ke ordinary CVA 0 0 ordinary PLS 1 1 orthonormalized PLS 0 1 Equation 4 40 can be used to eliminate X 1 2 1 2 kg GTG G xxx kx 4 44 179 U A a kx U A 7U A kx 4 45 1 2 U A a kx A
121. ven dataset and then applies it to the dataset in the Data layer We will choose to define the mask using the Activation Strength dataset although any of the others could be used to give different masks We can now adjust the size of the mask by adjusting the thresholding limit This can be done by specifying either an absolute or fractile value We ll use the latter which is the default It would be more useful if we could now see this thresholded data overlaid onto the origi nal data To see how far this threshold is from the rest of the data we can now overlay a contour layer of the full Activation strength dataset Note how you can now see that if you de creased the mask threshold then the peak at x 31 y 1 z 27 will be the next to show up The contour layer can also be used to compare different variables from the same result set This allows a comparison of meth ods for highlighting the activated regions In the main window below the Analysis pane is the Post processing section Meta K means should already be selected Click on the button to bring up the options dialog box Make sure that the Pa rameter Variables Set is set to the FIR fil ter results The other initial settings should should already be sensible Click once you have finished Click on the button Once the calculation is finished click on the button to bring up the triple set of viewing windows Click on the button in the Time
122. venient 1yngby_kronadd function which is actually a kro necker addition It works like the kronecker tensor product the matlab kron function just with addition instead of multiplication Alternatively instead of defining functions you can define mat files data_paradigm mat and data_run mat with a PARADIGM and RUN variable in them or you can define an ascii file data_paradigm txt and data_run txt When you start Lyngby two functions are automatically called lyngby_paradigm and lyngby_run These will call your data_paradigm and data run function files and setup the global variables PARADIGM and RUN 2 4 3 3 The data_init file A data_init function is created to setup some of the global variables These variables could also have been setup through the command line However it is convenient to have them in a file so you will not need to set them up every time For the Jezzard data function data_init lyngby global NUM_VOXELS L 64 1 64 ROI_VOXELS 29 46 1 1 14 43 A list of the general global variables is given in Table 2 3 on page 37 and a list of the user interface related global variables is given in Table 2 4 on page 38 If another program has masked the volumes so that non brain voxels are already zero we will take advantage of this by setting a VOXEL_MASK reading in the first volume and extracting only the voxels that are different from zero 2 5 Using the Lyngby Windows Interface The Lyn
123. vertical offset DC component from the PARADIGM variable This is necessary for those analysis algorithms which require a zero mean paradigm The right pane focuses only on the data Three of the choices involve the removal of the mean from the data over the whole time series the whole volume and over each run respectively The remaining choice normalizes the variance The relevant choices should be selected by pressing the toggle buttons and then these are applied by pressing the Apply button at the bottom of the window This also closes the pre processing window Lyngby Data setup Figure 2 8 The preprocessing window in Lyngby Lars Kai Hansen et al 1997 Section 2 5 Using the Lyngby Windows Interface 29 2 5 2 6 Data Analysis and Modelling The next step is to select the actual data modelling algorithm from the Data analysis frame The top button in this frame determines the analysis algorithm that will be used Pressing this button causes a list to pop up of all the available algorithms Simply select the desired one and the list will disappear and the button will display the name of the chosen algorithm The Original option simply displays the un analysed data which is also the input data used by all the other analysis algorithms The actions of the associated buttons are then dependent on the choice of algorithm but always follow a standard pattern e The button is used to choose the parameters for th
124. ves into the Taylor expanded saliency yields 1 13 7 si xP 4 37 h Np No Nh mi Car 2303037342 E won 1 7 viba 4 38 p h i Np No Ni Nh 2 ELE Eo 1 07 l sey h 4 11 1 Our implementation The functions that are specific for the neural network saliency all have the infix nns_ The optimization of the neural network is performed with the functions calls nn_ 4 11 2 References The first description of the neural network saliency was in Merch M rch et al 1995 and M rch et al 1996 It has also been the subject of three master s thesis within our depart ment Lundsager and Kristensen 1996 M rch and Thomsen 1994 and Nielsen 1996 The method is still under development i e the mathematical form of the saliency is not yet fully justified 4 12 The SCVA model Strother Canonical Variate Analysis The SCVA model is directly related to the SOP model section 4 13 It uses the same designma trix equation 4 51 Using the same terminology as Mardia Mardia et al 1979 the analysis method should not be called canonical variate analysis but canonical correlation analysis CVA together with SVD on a datamatrix with degenerate rank is ambiguous The canonical correlation coefficients will all be one thus the canonical correlation vectors will have no unique orientations A technique to cope with this problem is canonical ridge which is a variation of ridge regression within canonical
125. work The second layer is the hidden layer The neurons in this layer have an activation function and it is necessary for the non linearity of neural network that this activation function is non linear The final layer is the output layer These will also have an activation function This might be linear or non linear With x as the input y as the output with v as the first layer of weights the input to hidden weights and w as the second the hidden to output weights and with i h o and p as the indices for the input hidden and output neurons and the examples respectively we get the following neural network function rae Sons ta a a Here g and g are the activation functions and and woo are the biases The activation function is usually of the sigmoidal type and we use the hyperbolic tangent In connection with classification the output activation function is this hyperbolic tangent to get a restricted output that can be interpreted as a probability In connection with regression the output activation function is linear The neural network is optimized to predict to a target i e to make the numerical difference between a desired target t and the computed output of the neural network y as small as possible Lars Kai Hansen et al 1997 Section 4 9 Neural netvvorks 56 As a measure for the discrepancy how well we have optimized the network we can use different kinds of cost functions In regression we usually
126. x It is a How do I guide showing in a step by step manner how data is loaded in how a typical analysis would be carried out what results can be obtained and how these results can be viewed and saved More information on each of the stages such as a description of the available data formats and the different modelling algorithms can be found in the later chapters 2 2 Installation and Getting Started 2 2 1 First time Users It is recommended that if you have not yet installed Lyngby you first read a seperate document entitled Getting Started which takes the user step by step through downloading installing and running the toolbox The aim is to have a first time user able to start experimenting with real data within a couple of minutes of downloading the Lyngby toolbox As an additional help the Lyngby toolbox also comes with a sample dataset that allows the first time user to quickly get started with using Lyngby without first spending time working out how to get their own data loaded in It is highly recommended that first time users then read the follow up document entitled Example Analysis This takes the user through a typical MRI analysis session from loading in the data and ensuring all the pre processing steps are done to performing some modelling of the data and finally through to analysing the results obtained This will give the user a good overview of how Lyngby can help them in the analysis of their own
127. xtra matrices only require a modest amount of memory Note that if all the data is to be used then the two masks can be set to 1 3 4 Preprocessing steps 3 4 1 Centering Currently we have support for the following steps for removal of mean in various ways Subtraction of mean from each voxel 1 e the mean of each time series is forced to zero OLars Kai Hansen et al 1997 Section 3 4 Preprocessing steps 45 e Subtraction of mean from each scan i e the mean of each volume at a certain time step is forced to zero Subtraction of mean from each run i e the mean of each run in each of the time series is forced to zero Note that this makes the first substraction meaningless 3 4 2 Variance Normalization Algorithms such as neural networks in general use data normalization to unit variance in order to improve the stability of the algorithms Note that this option might lead to unreliable results in other algorithms Kai Hansen et al 1997 Chapter 4 Analysis The Modeling Algorithms Revision 1 46 Date 2004 01 21 10 54 40 4 1 Cross correlation The Cross correlation measures the temporal cross correlation between the paradigm and the measured data 4 1 1 Our implementation In the toolbox the paradigm can be cross correlated with the time series This produce a cross correlation function i e a function that is approximately twice as long In general the cross correlation function
128. y by Finn rup Nielsen Peter Toft and Matthew Liptrot as well as Carsten Helbo Peter Toft and Carsten Helbo are now involved in other work 1 7 1 Acknowledgments Furthermore Cyril Goutte Lars Kai Hansen Ulrik Kjems and the student Pedro Hgjen Sorensen have supplied methods and code for the package Jan Larsen should also be mentioned for his long term support and discussions Much valuable input has come from the HBP partners especially Stephen Strother Nick Lange and Babak Ardekani This work has been supported by the The Danish Research Councils through the programs Functional Activation in the Human Brain 9502228 CONNECT Computational Neural Network Center 9500762 the US Human Brain Project Spatial and Temporal Patterns in Functional Neuroimaging P20 MH57180 and the European Union project MAPAWAMO 1 7 2 Contact us Besides the mailing list 1yngbyCisp imm dtu dk we can also be contacted by email directly see the list in the table below Lars Kai Hansen Associate Professor lkhansen isp imm dtu dk Finn rup Nielsen Post Doc fn imm dtu dk Matthew G Liptrot Research Assistent mgl imm dtu dk Peter Toft can be contacted via pto sslug dk however he is no longer employed at IMM or officially involved with Lyngby lLars Kai Hansen et al 1997 Chapter 2 User Manual Revision 1 30 Date 2002 08 14 15 54 22 2 1 Introduction This chapter deals with everyday usage of the toolbo

LYNGBY Matlab toolbox for functional neuroimaging analysis

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