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Lesion-Behavior Mapping in Cognitive Neuroscience: A Practical Guide to Univariate and Multivariate Approaches
Lesion-behavior mapping is an influential and popular approach to anatomically localize cognitive brain functions in the human brain. The present chapter provides a practical guideline for each step of the typical lesion-behavior mapping study pipeline, ranging from patient and imaging data, lesion delineation, spatial normalization, and statistical testing to the anatomical interpretation of results. An important aspect of this guideline at the statistical level will be to address the procedures related to univariate as well as multivariate voxelwise lesion analysis approaches.
KeywordsLesion analysis Univariate voxel-based lesion-symptom mapping Multivariate voxel-based lesion-symptom mapping Multivariate pattern analysis VLSM VLBM MLBM MVPA Brain behavior inference Stroke Human
Within the spectrum of neuroscience methods, the analysis of pathological behavior following brain injury is an important source of knowledge regarding the function and anatomy of the healthy brain. Lesion analysis belongs to the brain interference methods, i.e.—in contrast to correlative methods as, e.g., fMRI, EEG, or MEG—to those methods where inferences about the functional brain architecture are drawn from changes in behavior following focal brain lesions. The prominent advantage of these methods is that they allow us to determine whether a brain region is required for a specific task and function . If a stroke causes a behavioral deficit, we know that the brain territory affected is essential for the normal functioning of this behavior.
2 Patient Selection
Ideally, researchers should a priori decide on a reasonable patient recruitment time period and unselectively include all suitable patients that present during that time period in the study. For example, if the researcher is interested in a function known to be located in the human left hemisphere from previous work (e.g., language functions), all patients with a left-sided brain lesion are included over a certain time period (e.g., 2 years). Exclusion criteria are, e.g., dementia, psychiatric disorders, or additional diffuse brain lesions since it would be difficult to determine which aspect(s) of the behavioral deficit can be attributed to the newly occurred brain lesion or might instead be due to these additional disorders. In contrast, absence of the behavioral deficit of interest is not to be used as an exclusion criterion. The inclusion of patients that do not have the behavioral deficit of interest is essential, as this allows us to differentiate between areas of the brain where damage is associated with the deficit of interest and areas of the brain where damage merely reflects increased vulnerability to injury .
The appropriate etiology of brain damage in studies aiming at the understanding of the functional architecture of the healthy human brain is stroke. Other etiologies, e.g., traumatic brain injury and tumors, have also been used in this context, but a considerable body of work suggests that such etiologies are less suitable or might even derive misleading results [2, 3]. There is no doubt that for clinical research questions as, e.g., the evaluation of brain tumor treatment , lesion-behavior mapping can also be a useful tool but—as mentioned in the introduction section above—such clinical questions are beyond the scope of the present chapter.
Stroke lesions are well suited for lesion-behavior mapping analyses aiming at the healthy brain’s functional architecture because they go along with (1) structural imaging data which (in most cases) clearly reflect the area of infarcted and irretrievably lost neural tissue as well as (2) clear behavioral consequences that can, for the large part, be directly linked to the original function of the impaired part of the brain. This is particularly true for strokes in the acute phase in which the brain has not yet had time to functionally reorganize. Lesion-behavior mapping thus should prefer acute stroke patients, while chronic stroke patients should remain to investigate the neural correlate of chronic dysfunction. Importantly, combining both acute and chronic stroke patients in the same lesion-behavior mapping study is to be avoided. Lesion-behavior mapping analyses assume that each patient is assessed at the same point in time following stroke onset and that thus the contribution of a certain brain area to a certain cognitive function is directly reflected in the behavioral scores in each patient. Combining both acute and chronic stroke patients in the same lesion-behavior mapping study violates this assumption.
3 Imaging Data
Imaging data should be obtained in the acute stroke phase, regardless of whether the aim is to study the functional architecture of the brain or to study the neural correlates of chronic cognitive deficits. For the study of the functional architecture of the brain, it has been shown that only the combination of acute behavioral scores and acute structural imaging precisely identifies the targeted brain areas. In contrast, lesion-behavior mapping analyses based on chronic behavior, in combination with either chronic or acute imaging, hardly detected any of the targeted substrates . On the other hand, if combined with acute structural imaging, the behavioral data from chronic stroke patients allows us to make long-term clinical predictions based on the location of the acute brain damage [6, 7, 8].
In acute stroke patients, the lesion can be visualized using either CT or MRI. The development of CT templates for spatial normalization of individual patient images  has removed the main reason to disregard CT for lesion-behavior mapping studies. Moreover, modern spiral CT scanners provide high-resolution images, and in many clinical institutions, CT remains the dominant imaging modality of choice at admission. Importantly, the choice between administering CT and MRI to patients at admission is not random but follows specific clinical criteria. As a consequence, the systematic exclusion of patients with CT images only implements a selection bias, typically influencing important factors such as lesion size, general clinical status, severity of cognitive deficits, etc. (for a detailed discussion ). As such, lesion-behavior mapping studies aiming at the healthy brain’s functional architecture should unselectively recruit all suitable patients, irrespective of whether they have received CT or MR imaging at admission.
We suggest the following practical guideline: In patients with CT imaging only, use noncontrast CT images to visualize the brain lesion. In patients with MR imaging only, use diffusion-weighted images (DWI) to visualize the lesion if imaging is performed less than 48 h following stroke onset, and use T2FLAIR images if imaging is performed more than 48 h following stroke onset. In patients with both CT and MR images, the researcher is in the privileged situation to choose the best from both modalities, i.e., to use those images where the lesion is most conspicuous.
4 Lesion Delineation
Following CT or MR data acquisition, the lesion needs to be delineated on each slice of the patient’s brain image. Manual lesion delineation, which can be done using programs like MRIcroN (https://www.nitrc.org/projects/mricron; ) or ITK-SNAP (http://www.itksnap.org; ), is time-consuming and potentially observer-dependent. To address these disadvantages, both fully automated and semiautomated lesion delineation methods have been developed. Fully automated methods do not require any user interaction but also may be more susceptible to imaging artefacts (for discussion ). Given this downside, semiautomated lesion delineation methods that combine fully automated steps with mandatory user interaction provide an optimal compromise. While several semiautomated lesion delineation approaches exist (e.g., ), the semiautomated approach Clusterize (https://www.medizin.uni-tuebingen.de/kinder/en/research/neuroimaging/software/; ) has been shown to be capable of significantly speeding up lesion delineation, without loss of either lesion delineation precision or lesion delineation reproducibility in acute stroke patients scanned in both CT and a range of common MRI modalities . The principle of Clusterize is simple: On the basis of local intensity maxima and iterative region growing, the whole CT or MR brain image is fully automatically clusterized, including the lesioned area. The user subsequently manually selects those clusters that correspond to the lesion.
5 Spatial Normalization of Patient Brain and Lesion Map
We now have a 3D binary lesion map reflecting the voxels where brain function is impaired for each patient (see Fig. 1). However, all brains differ in orientation, size, and shape. As such, before we can perform statistical comparisons, we need to spatially normalize the patient brains and lesion maps into standard stereotaxic space. Spatial normalization can be performed with programs such as BrainVoyager (http://www.brainvoyager.com/; ), SPM (http://www.fil.ion.ucl.ac.uk/spm/), FSL (https://fsl.fmrib.ox.ac.uk/fsl/fslwiki; ), AFNI (https://afni.nimh.nih.gov/; [18, 19]), or ANTs (http://stnava.github.io/ANTs/; ). The analysis package SPM is widely used due to its platform independence, free obtainability, and availability of many add-ons. As such, we here focus on the spatial normalization routines of SPM, as implemented in the Clinical Toolbox (https://www.nitrc.org/projects/clinicaltbx/; ). This toolbox provides specialized templates that allow spatial normalization of both CT and MR brain images of elderly, stroke-aged populations. As such, the Clinical Toolbox is ideally suited to be used in lesion-behavior mapping studies where the patients included are typically older, and where different modalities, i.e., CT as well as MR images, are present in different patients. Moreover, the Clinical Toolbox provides both the traditional normalization procedure and the unified segmentation and normalization approach  which are required to process the different types of imaging data typically present in clinical patient samples.
Normalization of DWI Data
DWI data are usually collected with different b-values (typically b0, b500, and b1000). While the b1000 image best suited to visualize the lesion in acute stroke patients has a low radiometric resolution, the additionally collected b0 image often has a relatively high radiometric resolution. The typical approach thus is to first coregister the image best suited to visualize the lesion but with a low radiometric resolution (e.g., the b1000 DWI) to the image with a high radiometric resolution (e.g., the b0 DWI or—if available—a T1 image). Subsequently, the image with the high radiometric resolution is normalized using the unified segmentation and normalization approach . This approach has been shown to be superior to the traditional normalization approach [22, 23], but requires an image with a high radiometric resolution. The unified segmentation and normalization approach combines tissue classification (i.e., segmentation), bias correction, and image registration (i.e., spatial normalization) in a single model. Once the necessary image transformations have been estimated, they are applied to the patient’s brain image(s) and the lesion map, bringing all images in standard stereotaxic space. Since the average age in clinical stroke samples investigated for lesion-behavior mapping studies is typically above 60 years, the Clinical Toolbox provides template-based tissue probability maps for use with the unified segmentation and normalization approach  derived from elderly adults (mean age: 61.3 years).
Normalization of CT and T2FLAIR Data
If only CT or only T2 FLAIR data are available, we use the traditional normalization procedure in which linear (affine) and nonlinear (nonaffine) image transformations are applied to match the orientation, size, and shape of each patient brain to the orientation, size, and shape of a template brain in standard stereotaxic space. In these cases, the template image to be selected in the Clinical Toolbox  should ideally have the same image modality as the patient image that is spatially normalized, as the accuracy of this approach depends on how similar the voxel intensities of a given brain area are between the patient and the template image. Moreover, the template image should roughly match the population of the lesion mapping study. That is, if the lesion-behavior mapping study is performed in elderly stroke patients, the template or template-based tissue probability maps used should have been derived from an elderly population. The Clinical Toolbox provides a template for CT imaging data  derived from elderly adults (mean age: 61.3 years), as well as a template for T2FLAIR imaging data (https://brainder.org/download/flair/; ) derived from a wide range of adults (mean age 35.4, range 18–69 years) for use with the traditional normalization procedure.
In patients with MR acquisition at admission, sometimes T1 images, i.e., data providing high radiometric resolution, are available in addition to the T2FLAIR data. In these cases, we can apply the unified segmentation and normalization approach instead of the traditional normalization procedure to optimize the normalization result . The image with a low radiometric resolution, i.e., the T2FLAIR data, is coregistered to the image with a high radiometric resolution (the T1 image). The image with a high radiometric resolution then is normalized using the unified segmentation and normalization approach. The necessary image transformations are estimated and applied to the patient’s brain image(s) and the lesion map, bringing all images in standard stereotaxic space.
5.1 Correcting for the Lesion During Spatial Normalization
In both the traditional normalization procedure and the unified segmentation and normalization approach, the area of brain damage creates a large mismatch between the patient brain and the template brain. The two dominant solutions to this problem are cost function masking  and enantiomorphic normalization . The Clinical Toolbox provides both options to address this problem. During cost function masking, lesioned voxels are excluded during spatial normalization. As such, the image transformations necessary to bring the patient’s brain image(s) and the lesion map in standard stereotaxic space are derived from intact areas of the brain only. During enantiomorphic normalization, on the other hand, the lesion is “corrected” by replacing it with brain tissue from the lesion homologue in the intact hemisphere of the brain. As such, the image transformations necessary to bring the patient’s brain image(s) and the lesion map in standard stereotaxic space are effectively derived from a brain image without a lesion.
Logically, one can expect enantiomorphic normalization to perform better than cost function masking when lesions are large and unilateral, as spatial normalization with cost function masking becomes less accurate as lesion size increases (as the area from which the image transformations can be derived decreases with increasing lesion size), while enantiomorphic normalization does not. Cost function masking can, however, be expected to perform better than enantiomorphic normalization when lesions are bilateral and affect similar areas in both hemispheres, as enantiomorphic normalization would in this case replace the lesion with the likewise lesioned homologue. Moreover, as enantiomorphic normalization assumes that the brain is essentially symmetric, enantiomorphic normalization might be suboptimal in areas known to be considerably asymmetric (e.g., the planum temporale). The decision to use either cost function masking or enantiomorphic normalization for normalization thus should be made on an individual, patient-to-patient basis. A comparison of both methods, however, highlighted a generally better precision of enantiomorphic normalization . Thus, if no clear preference exists, enantiomorphic normalization should be chosen.
6 Voxelwise Lesion Analysis
Following lesion delineation and spatial normalization, we have a spatially normalized binary lesion map for each patient. Moreover, we have a behavioral measurement for each patient. With these two sources of information, we are ready to perform a voxelwise lesion-behavior mapping analysis to relate lesion location and patient behavior (see Fig. 1). Over the last decades, various techniques for lesion analyses evolved, spanning from subtraction plots over mass-univariate mapping to recently developed multivariate methods. The choice of one or the other of these techniques is largely depending on the fulfilment of specific prerequisites and own research interests. The simplest type of voxelwise analysis is a lesion subtraction analysis. In fact, this method is not a statistical but a descriptive method that should be reserved for studies aiming at rare disorders, i.e., for studies that a priori are expected to include only a small number of patients. If more patient data is available, it is possible to conduct either a mass-univariate or a multivariate lesion analysis. If we have good reasons to assume that the function of interest is represented in a widely distributed network in the human brain, multivariate approaches are to be preferred, as in these cases the ability of univariate techniques to detect all of the network modules might be limited [27, 28]. In the following, we introduce all three types of possible voxelwise analysis techniques.
6.1 Voxelwise Comparison by a Lesion Subtraction Analysis
6.1.1 Tools for a Lesion Subtraction Analysis
First the binary normalized lesion images need to be copied into a single directory.
It is recommended to convert these .nii files into .voi files. This can be done by selecting “Convert” (“NII->VOI”) from the “Draw” menu (if necessary, select “Show drawing tools” from the “Draw” menu to make all options in the “Draw” menu visible).
Create a lesion overlap image for each patient subgroup (usually one patient subgroup with the deficit of interest and a control patient subgroup without the deficit of interest) by selecting “Create overlap images” from the “Statistics” submenu of the “Draw” menu.
Once we have a lesion overlap image for each patient subgroup, we can perform a subtraction analysis by selecting “Subtraction Plots” from the “Statistics” submenu of the “Draw” menu. Under “Select POSITIVE overlap image,” select the overlap image of the patient subgroup with the deficit of interest, and under “Select NEGATIVE overlap image,” select the overlap image of the control patient subgroup without the deficit of interest. On non-Windows computers, saving the subtraction plot sometimes needs to be repeated several times (just keep reselecting the originally chosen filename and ignore the “overwrite” warning).
The resulting subtraction plot can be loaded as an overlay (over a suitable template image) by selecting “Add” from the “Overlay” menu. The range of values to be shown can be adjusted by modifying the lower bound and upper bound intensity value in the boxes to the right of the “Autocontrast” button ( Open image in new window ). Values between 1 and 100 show voxels more often damaged in patients with the deficit of interest than in patients without the deficit of interest, whereas values between −1 and −100 show the reverse. These values reflect relative frequency of damage, e.g., a value of 50 reflects that that voxel is damaged 50% more frequently in patients with the deficit of interest than in patients without the deficit of interest. Assuming n = 10 in both groups, this could mean that the voxel is damaged in 9 of 10 patients (i.e., 90%) with the deficit of interest and in 4 of 10 patients (i.e., 40%) without the deficit of interest (or 7 of 10 vs. 2 of 10, etc.).
6.2 Univariate Voxelwise Statistical Comparisons
Continuous Behavioral Data
When the behavioral data is continuous, the behavioral data of the group of patients in whom a given voxel is damaged is statistically compared to the behavioral data of the group of patients in whom that same voxel is intact. This is traditionally done with a two-sample t-test, which assumes that the behavioral data is normally distributed and measured on an interval scale. Unfortunately, however, behavioral data from patient populations is often not normally distributed. During behavioral assessment, patients without the deficit of interest will typically all demonstrate close to maximum performance, whereas performance in patients with the deficit of interest will typically be poorer and more variable over patients. As a consequence, the distribution of the behavioral data from patient populations is often negatively skewed. Moreover, behavioral data from patient populations is often not measured on an interval but on an ordinal scale. The use of the assumption-free rank order test proposed by Brunner and Munzel  is more appropriate in these situations. In fact, this so-called Brunner-Munzel test has been shown to have higher statistical power than the t-test while offering similar protection against false positives in situations where the distribution of the behavioral data is skewed . The Brunner-Munzel test is provided in the NPM software for lesion-behavior analyses (https://www.nitrc.org/projects/mricron).
Binomial Behavioral Data
When the behavioral data is binomial (i.e., when the deficit is either present or absent, as in, e.g., hemianopia), we statistically assess, for each voxel, whether the variables “voxel status” (voxel lesioned vs. voxel intact) and “behavioral status” (deficit present vs. absent) are associated or independent. The statistical test typically used in these situations is the Pearson’s chi-square test. In many lesion-behavior mapping analyses, however, expected cell frequencies are lower than five to ten in at least some voxels, resulting in inflated false-positive rates when using Pearson’s chi-square test. A statistical test more appropriate in these situations is the quasi-exact test proposed by Liebermeister . In a lesion-behavior mapping analysis with simulated data, observed false-positive rates for this so-called Liebermeister test closely approximated the set false-positive threshold . The Liebermeister test is provided in the NPM software for lesion-behavior analyses (https://www.nitrc.org/projects/mricron).
6.2.1 Tools for Univariate Voxelwise Statistical Comparisons
Univariate voxelwise statistical analyses can be performed with programs or toolboxes such as VLSM (http://aphasialab.org/vlsm; ), VoxBo (https://www.nitrc.org/projects/voxbo/; ), NPM (https://www.nitrc.org/projects/mricron; ), and/or NiiStat (https://www.nitrc.org/projects/niistat/). Of these, NPM and NiiStat are the most up-to-date and will thus be the focus of this section.
First the binary normalized lesion images need to be copied into a single directory.
It is recommended to convert these .nii files into .voi files. This can be done in MRIcron by selecting “Convert” (“NII->VOI”) from the “Draw” menu (if necessary, select “Show drawing tools” from the “Draw” menu to make all options in the “Draw” menu visible).
In NPM, we first need to specify the design. To do this, select “Design…” from the “VLSM” menu, and click the “Design IVs” button. The amount of predictors (i.e., the behavioral variables) and the predictor names can be adapted if necessary. It is important to realize that entering multiple predictors here simply means that the statistical test will be performed separately on each predictor (i.e., the program will not implement a regression approach). To select the lesion images, click the button “Select Images.” To ensure sufficient minimum lesion overlap, voxels damaged in a very low percentage of the patient sample should be excluded. Typically, voxels damaged in less than 5–10% of the patient sample are excluded. Finally, after clicking the “OK” button, the behavioral scores for each patient can be added. In NPM, higher behavioral scores are assumed to reflect better performance. In other words, e.g., binomial behavioral data, patients with the deficit of interest should be coded as “0,” and patients without the deficit of interest should be coded as “1.” To save this specified design as an MRIcron .val file, select “Save” from the “File” menu.
Under the “Options” menu, the amount of permutations used to control the family-wise error rate using permutation thresholding can be selected. It is recommended to set this to the maximum value (8000). Moreover, in the case of continuous behavioral data, the “Tests” submenu allows you to select whether you want to perform a two-sample t-test, a Brunner-Munzel test, or both.
To run the analysis, select “Binary images, binary groups (lesions)” from the “VLSM” menu when the behavioral data is binomial. When the behavioral data is continuous, select “Binary images, continuous groups (vlsm)” from the “VLSM” menu. Select the saved specified design (MRIcron .val file). When it asks for “Base Statistical Map,” enter a filename. The results from the analysis will then be saved as <filename><StatisticalTestUsed><Predictorname>. If desired, an explicit mask can be selected to restrict the analysis to a region of interest in the brain. If you do not want to restrict your analysis to a region of interest, simply press “Cancel.”
For each behavioral predictor and statistical test used, the program creates an unthresholded z-map (<filename><StatisticalTestUsed><Predictorname>.nii.gz). Additionally, for each behavioral predictor, the program creates a text file (<filename>Notes<Predictorname>.txt) containing the range of unthresholded z-values obtained for each statistical test, as well as the critical z-values for several commonly used p-values following different methods of correcting for multiple comparisons (using Bonferroni, FDR, or permutation-based thresholding). The unthresholded z-map can be loaded as an overlay (over a suitable template image) in visualization software packages such as MRIcron (see Sect. 6.1) by selecting “Add” from the “Overlay” menu. To visualize the statistically significant voxels in MRIcron, the range of values to be shown can be adjusted by modifying the lower bound and upper bound intensity value in the boxes to the right of the “Autocontrast” button ( Open image in new window ). The lower bound intensity value should be set to the critical z-value.
NiiStat (C. Rorden; https://www.nitrc.org/projects/niistat/)
After successful installation, run the following command in MATLAB to launch the toolbox:
Like NPM, NiiStat is capable of performing lesion analyses using either continuous behavioral data or binomial behavioral data. Unlike NPM, however, NiiStat comes with general linear model functionality, allowing the inclusion of nuisance covariates, as well as performing ANOVAs.
In situations where there is only a single dependent variable of interest per statistical test, NiiStat computes the Liebermeister test when the behavioral data is binomial and computes statistics using the general linear model when the behavioral data is continuous (in which case results will be identical to the results of a two-sample t-test). Thus, barring minor rounding error differences, when there is only a single dependent variable of interest, results will be identical to those generated using NPM.
To correct for multiple comparisons, NPM supports Bonferroni, FDR, and permutation-based thresholding (see Sect. 7.2.).
6.3 Multivariate Voxelwise Statistical Comparisons
6.3.1 Support Vector Regression-Based Multivariate Lesion-Symptom Mapping (SVR-LSM)
Several parameters are relevant in such analyses and need to be adjusted. First, machine learning algorithms often use parameters that define aspects of how models are generated. These parameters, so-called hyperparameters (e.g., C and γ in SVR with an RBF kernel), have to be chosen a priori. Generally, these hyperparameters can be optimized through grid search before the actual analysis. Optimization in SVR-LSM, however, has proven to be tricky, because a model with high fit does not necessarily provide generalizable beta-parameters. Therefore, unambiguous maximization/minimization strategies are not available (for more details see Zhang et al.  and Rasmussen et al. ). Another parameter to be adjusted is the number of permutations. Large numbers require computational power, but they should be chosen as high as possible. Permutation numbers of at least several thousands are required; 10,000 permutations should be an ideal number. Next, we need to control for lesion size. While the optimal approach for this control is still a matter of debate , it is clear that at least any kind of such control is required, such as nuisance regression or direct total lesion volume control . Further, it was shown that a correction for multiple comparisons is required . The reason is that statistical significance in the current implementation of SVR-LSM is assessed for each voxel individually, i.e., many statistical tests are performed at once. There is no consensus yet on what correction suits best; available software programs offer several approaches such as false discovery rate.
Tools for SVR-LSM Analyses
Various tools and strategies allowing to perform SVR-LSM analyses are available, differing in functionality and the analysis algorithms they are based on. Among those the MATLAB toolbox provided by Zhang and colleagues  is interesting because it contains a set of MATLAB scripts which can be easily adapted (by advanced MATLAB users) to one’s own needs, allowing a simple MLBM analysis but also more advanced research questions. The following section will also address two other toolboxes, SVR-LSM GUI  and NiiStat (www.nitrc.org/projects/niistat), which extended the initial toolbox from Zhang and colleagues , adding a graphical user interface, which will make the analysis technique more accessible to clinicians and non-experienced MATLAB users. As these two tools are well documented and are rather straightforward, we will not go into details.
SVR-LSM MATLAB Toolbox 
The SVR-LSM toolbox by Zhang and colleagues  can be downloaded from https://github.com/yongsheng-zhang/SVR-LSM or https://github.com/dmirman/SVR-LSM. The latter contains additionally a fivefold cross-validation routine for finding the optimal set of the SVR parameters and was added by Daniel Mirman. Requirements for the use of this toolbox include MATLAB (The MathWorks, Inc., Natick, MA; version 7.12 or higher), SPM (Wellcome Institute of Imaging Neuroscience, London, UK; version SPM8 or SPM12), and libSVM (http://www.csie.ntu.edu.tw/~cjlin/libsvm/; version 3.18 or higher). Note that libSVM comes already with the toolbox, but needs to be compiled before being able to be used. A common error during the compilation process involves the miss of a suitable compiler in MATLAB. In most cases the installation of a further compiler following the instructions in the MATLAB Add-On Explorer should solve the problem. As a detailed description of the toolbox and installation instructions can be found in the manual of the toolbox, we will only summarize the essential information and give some hints.
First the binary normalized lesion images (.nii files) need to be copied to the “\lesion_imgs” folder and the behavioral variable files (.csv file) need to be set up and copied into the “score” folder.
Open the main script called “SVR-LSM-toolbox.m” in the MATLAB editor. Here, all the required parameters for the analysis can be adapted to your needs. Follow the instructions in the manual to find out which parameters you need to specify.
Out of the box, the analysis is running an epsilon-SVR using an RBF (radial basis function) kernel. This type of regression is nonlinear and has proven its validity in the initial investigations. The “degree” of nonlinearity is largely dependent on several user-defined parameters, namely, C (for cost), ε (for epsilon-SVR), and ɣ (for the RBF kernel). These parameters define among others how the features (voxels) are treated and thus will contribute to the overall model quality.
- (d)The toolbox sets automatically the C, ε, and ɣ values to 20, 0.01, and 2 respectively. As the optimal parameters are related to the data in question, we can recommend to perform a grid search with k-fold cross-validation to find the optimal parameters for a specific dataset. The SVR-LSM toolbox from Daniel Mirman includes a function called “optimize_parameters.m” which is able to do that for C and ɣ. To do so, the “SVR_LSM_toolbox.m” script needs to be run until line 88, while omiting line 61. After completion, the necessary data is loaded in the MATLAB workspace and can be send to the optimize_parameters.m function by entering the following commands into the MATLAB command line:This will run a fivefold cross-validation grid search with a parameter range of 1–50 for C and 0.5–10 for ɣ in steps of 1. If another parameter range is needed, svr_cost and svr_gamma should be modified before running the “optimize_parameters.m” function. cost_best and gamma_best will return the best C and ɣ for the dataset. Additionally, the variable acc is returned which provides information about the prediction accuracy. After that, the final analysis can be run by first changing the general parameter variables for C and ɣ, running the following commands:
Now the rest of the “SVR_LSM_toolbox.m” script can be run from line 90 on.
If a different type of analysis is needed (e.g., a linear SVR) or a different kernel is required, the “run_svr_lsm_beta_map.m” function can be opened up in a text editor, and the values in line 10 can be changed. For a detailed description on what value corresponds to which setting, we refer to explanations given in the libSVM toolbox (https://www.csie.ntu.edu.tw/~cjlin/libsvm/). In this case, please do not forget to change also the values at line 21 in the “optimize_parameters.m” function accordingly.
As explained in Zhang et al. , it is important to control for lesion size. Without changing anything, the toolbox is running automatically direct total lesion volume control (dTLVC). Nevertheless, it is still possible to include lesion size as a covariate without using dTLVC and regressing out lesion size out of the behavioral score. If needed, the dTLVC correction can be turned off at line 23 setting the flag to 0 in the “SVR_LSM_toolbox.m” script while adding the name of the lesion size variable at line 19. Note that the lesion size variable should then be included as an additional column in the behavioral score (.csv) file.
Before running the analysis, we recommend to document the chosen parameters or to save a copy of the “SVR_LSM_toolbox.m” and the “run_svr_lsm_beta_map.m” scripts in case you modified something; the toolbox does not output any report of the chosen parameters.
The duration of the final analysis is largely dependent on the used hardware and the chosen permutation number and hence can take up to several hours.
Finally, the toolbox creates an unthresholded probability map which can be opened up in visualization software packages as MRIcron. If some voxels are surviving the FDR thresholding, the critical p is saved to the generated report. For visualizing the inverse probability map in, for example, MRIcron, you need to set the lower bound intensity to 1—critical p—and the upper bound to 1.
SVR-LSM GUI MATLAB Toolbox 
- (a)After successful installation, run the following command in the MATLAB command line interface to open up the GUI, allowing you to specify all necessary parameters by clicking through it:
In comparison to the SVR-LSM toolbox by Zhang et al. , the SVR-LSM GUI toolbox is currently only providing an epsilon-SVR with a nonlinear RBF kernel but might be extended with a linear kernel in future releases.
Another benefit of this tool is that it is able to use the MATLAB Parallel Toolbox and perform the analysis using a parallel pool, which provides a remarkable speed benefit. For additional information about timings, we refer to the original work by DeMarco and Turkeltaub .
In difference to the SVR-LSM toolbox by Zhang et al. , the SVR-LSM GUI is very flexible in what kind of correction for lesion size is required. Hence, the authors implemented all four techniques, dTLVC and nuisance regression on behavior, on lesion data, or on both.
Moreover, the toolbox does not support FDR thresholding but rather implements by default a permutation-based approach which first thresholds the output on a voxelwise level and additionally applies an FWE-corrected cluster threshold. This procedure has been adapted from functional neuroimaging analysis  and controls the rate of a single false-positive cluster, instead of a single positive voxel. This technique is relatively new for MLBM. For more details, see DeMarco and Turkeltaub  or Mirman et al. . Nevertheless, in a recent investigation from Mirman et al. , the authors showed—at least for univariate testing—that this correction technique can produce clusters that extend well beyond the correct region.
As FDR correction is not based on the individual permutations used for the transformation of the SVR beta-parameters to a probability map, there is always the option to use freely available scripts to apply FDR-based multiple comparison correction on the unthresholded probability maps after termination of the SVR-LSM GUI analysis. Note that FDR correction is kind of a trade-off between allowing some false positives and minimizing false negatives. Moreover, for the univariate setting, Mirman and colleagues  demonstrated that FDR tends to produce anti-conservative results for smaller samples and thus might be rather interesting for studies with larger samples.
Continuous family-wise error rate (FWER) is an additional implementation which has been developed and tested in the univariate field , but which has also been integrated into the SVR-LSM GUI toolbox for MLBM. This procedure uses a user-defined most extreme voxelwise test statistic (v) for setting the upper limit of how many false-positive voxels are tolerated. Inferentially, this procedure is similar to FDR correction, as it allows a certain number of false positives and hence a better trade-off between very conservative and very lenient thresholding. Nevertheless, this procedure is again based on a user-defined criterion, and as there is no gold standard on the choice of v, the selection might be modified until the desired outcome shows up. The selection of the exact v value should thus be carried out with caution to prevent “p-hacking.”
- (a)After successful installation, one can run the following command in the MATLAB command line interface to open up the GUI, allowing you to specify various parameters by clicking through it:
This toolbox currently runs an epsilon-SVR with a linear kernel as default and does not provide an optimization routine to find the optimal SVR-LSM hyperparameter cost (C). Hence, it relies on a default setting of 1 for C and 0.01 for ε.
NiiStat allows FDR or Bonferroni for multiple comparisons correction and performs dTLVC as default for lesion volume correction.
6.3.2 Sparse Canonical Correlation-Based Lesion-Symptom Mapping (SCCAN)
Besides the SVR-based MLBM, another well-validated technique exists based on sparse canonical correlations . SCCAN is a sparse solution for multidimensional canonical correlation analysis, which allows one to symmetrically relate sets of variables to each other, hence to find sets of variables that covary. In the context of lesion-behavior mapping, SCCAN is based on an optimization procedure that gradually selects a multivariate model of sets of voxels which maximize correlations with behavioral scores. The outcome of SCCAN largely depends on preselected parameters as, for example, sparseness, which should be selected carefully. Currently the only implementation of SCCAN in a MLBM tool (LESYMAP) is based on such optimization algorithm that finds the best set by evaluation of different parameter combinations via cross-validation. The final model is then calculated with the optimal parameter set and evaluated by assessing the model’s predictive performance which is then statistically tested for significance.
Tools for Performing SCCAN
SCCAN is implemented in the LESYMAP package (https://dorianps.github.io/LESYMAP/) and based on R programming language. The installation of the LESYMAP package can be burdensome, as it relies on a relatively high number of R packages. Requirements for the use of this toolbox include R (version 3.0 or above), OS (Linux, Mac, or Windows Linux Subsystem), and several R packages including their dependencies (ITKR, ANTsRCore, ANTsR). Most errors encountered during installation will probably be based on missing dependencies of different R sub-packages. Hence, in case of any installation errors, the first step would be to check the error output and to install the missing dependencies individually. In some cases, some of the packages cannot be built as you need to install a newer version of CMake (https://cmake.org/) through your OS. After successful installation the use of the toolbox is straightforward, as it comes with a well-documented manual and an example dataset. Note that this toolbox is also able to perform univariate lesion-behavior mapping and will be complemented by SVR-LSM in a future release.
7 Statistical Thresholding and Correction Factors in Lesion Analyses
7.1 Inclusion of Nuisance Covariates and Ensuring Sufficient Minimum Lesion Overlap
One variable known to correlate strongly with the severity of behavioral deficit in stroke populations is lesion volume: the larger the lesion, the more likely it is that a patient will show a behavioral deficit. Thus, to avoid identifying brain areas where damage is related simply to lesion volume instead of patient behavior, lesion volume should be controlled, e.g., as a nuisance covariate by using regression approaches. These or other approaches are implemented in most software packages both for univariate and multivariate lesion mapping. Moreover, to ensure sufficient statistical power, voxels damaged in a very low percentage of the patient sample should be excluded. Correcting for lesion volume as well as ensuring sufficient minimum lesion overlap has been shown to improve the anatomical validity in univariate voxelwise statistical analyses . Finally, similarly as done for lesion volume, other nuisance covariates can additionally be included, such as the severity of frequently co-occurring deficits that may correlate with the cognitive function of interest or fiber tract disconnection likelihood .
7.2 Correcting for Multiple Comparisons
During a voxelwise statistical lesion-behavior mapping analysis, the same statistical test is performed at many individual voxels. This is the case for all univariate approaches and likewise for SVR-LSM. A correction for multiple comparisons thus is needed. The traditional method to correct for multiple comparisons is the Bonferroni correction. While this method offers excellent control of the family-wise error rate, it is also considered as very conservative for neuroimaging data where individual voxels are not truly independent; it severely reduces the statistical power to detect an effect. As such, considerable efforts have been made to develop alternative, less conservative, ways to correct for multiple comparisons.
Such an attempt to control the family-wise error rate (FWER), but without sacrificing statistical power, is permutation thresholding based on the maximum statistic . The underlying logic is that if an observed test statistic is truly due to the difference in voxel status, similar or more extreme test statistics would be unlikely to arise in situations where the pairing of behavioral data and voxel status is scrambled. Modern computers allow to use large numbers of permutations, and several thousands (e.g., 10,000) should be done. Permutation thresholding offers the same control of the family-wise error rate as the Bonferroni correction. Importantly, however, in situations where the individual voxels are not truly independent, permutation thresholding offers better statistical power than the Bonferroni correction. So far, various ways of implementing permutation thresholding exist. For example, there are techniques based on cluster-wise or voxelwise correction. Further, a more recent approach called “continuous FWER” is available. It is also based on permutation thresholding and was mentioned in one of the toolboxes introduced above (see Sect. 184.108.40.206). For a detailed discussion about these different techniques, we refer to recent work by Mirman and colleagues .
Another less conservative approach to correcting for multiple comparisons is offered by false discovery rate (FDR) thresholding [47, 48, 49]. Here, the goal is not to control the family-wise error rate but to control the proportion of false positives among observed positives. As a consequence, a false discovery rate threshold of 5% means that up to 5% (e.g., 1 out of 20) of the observed positives might be false positives. In situations where no positives are observed, false discovery rate thresholding will provide the same control of the family-wise error rate as the Bonferroni correction. However, in situations where positives are observed, false discovery rate thresholding will result in more positives surviving the correction for multiple comparisons than either the Bonferroni correction or permutation thresholding. In fact, as the amount of observed positives increases, the false discovery rate threshold decreases. This adaptiveness of false discovery rate thresholding, however, comes at the price of reduced control of the family-wise error rate (as up to 5% of the positives surviving the correction for multiple comparisons could be false positives). In situations where control of the family-wise error rate is paramount, permutation thresholding should thus be preferred to correct for multiple comparisons.
8 Anatomical Interpretation of Lesion Analysis Results
Following a univariate or a multivariate voxelwise statistical lesion-behavior mapping analysis, we obtain a statistical map highlighting the voxels where voxel status (lesioned vs. non-lesioned) and patient behavior are significantly related. In the case of a lesion subtraction analysis, on the other hand, we obtain a map highlighting areas of the brain where lesions are descriptively more frequent in patients with than in patients without the cognitive deficit of interest (often thresholded to isolate those percentage relative frequency difference values thought to be meaningful [with typical threshold values of 20–50%]). Anatomical interpretation then consists of describing the location of these significant or meaningful voxels, typically with the help of a brain atlas. For practicability, coordinates of peak voxels or a coordinate range can be provided to characterize the findings resulting from the voxelwise lesion-behavior mapping analysis or subtraction analysis results. However, it should be noted that all voxels identified as “statistically significant” in statistical lesion-behavior mapping analyses or as “meaningful” in lesion subtraction analyses have the same impact and thus should be given the same weighting when interpreting the results.
Nowadays, there are many different cortical atlases to choose from. Whereas atlases derived from single-subject data remain popular (the Brodmann atlas or the AAL atlas by Tzourio-Mazoyer et al. ), probabilistic atlases derived from multi-subject data should be preferred, as these are able to quantify the intersubject variability in location and extent of each anatomical area. Within these multi-subject atlases, a second division can be made based on the brain characteristics used to parcellate distinct areas in different atlases. Whereas some probabilistic multi-subject atlases are based on macroscopical landmarks such as gyri and sulci [51, 52], others are based on histology  and on functional connectivity patterns  or are created via surface-based registrations of multimodal MRI acquisitions . Finally, in addition to these cortical atlases, multi-subject atlases exist for white matter fiber tracts, based on either DTI fiber tracking [56, 57] or on histology . Which atlas to choose for the anatomical interpretation of the results of a lesion-behavior mapping study is not a trivial issue. It is important to realize that different atlases might result in very different anatomical interpretations of the same lesion-behavior mapping results . A pragmatic solution to this problem may be to interpret the data resulting from a lesion-behavior mapping analysis with respect to more than only one atlas. For example, due to the marked variance between DTI- and histology-based white matter atlases , Wiesen et al.  recently decided to interpret a multivariate voxelwise statistical lesion-behavior mapping analysis according to a probabilistic cytoarchitectonic atlas  and a DTI-based probabilistic fiber atlas  simultaneously, using a common threshold of p ≥ 0.3 before overlaying the data on the statistical topographies.
This work was supported by the Deutsche Forschungsgemeinschaft (KA 1258/23-1). Daniel Wiesen was supported by the Luxembourg National Research Fund (FNR/11601161).
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