Classification of Schizophrenia from Functional MRI Using Large-scale Extended Granger Causality
CClassification of Schizophrenia from Functional MRI UsingLarge-scale Extended Granger Causality
Axel Wism¨uller, a,b,c,d and M. Ali Vosoughi aa Department of Electrical and Computer Engineering, University of Rochester, NY, USA b Department of Imaging Sciences, University of Rochester, NY, USA c Department of Biomedical Engineering, University of Rochester, NY, USA d Faculty of Medicine and Institute of Clinical Radiology, Ludwig Maximilian University,Munich, Germany
ABSTRACT
The literature manifests that schizophrenia is associated with alterations in brain network connectivity. Weinvestigate whether large-scale Extended Granger Causality (lsXGC) can capture such alterations using resting-state fMRI data. Our method utilizes dimension reduction combined with the augmentation of source time-seriesin a predictive time-series model for estimating directed causal relationships among fMRI time-series. The lsXGCis a multivariate approach since it identifies the relationship of the underlying dynamic system in the presence ofall other time-series. Here lsXGC serves as a biomarker for classifying schizophrenia patients from typical controlsusing a subset of 62 subjects from the Centers of Biomedical Research Excellence (COBRE) data repository. Weuse brain connections estimated by lsXGC as features for classification. After feature extraction, we performfeature selection by Kendall’s tau rank correlation coefficient followed by classification using a support vectormachine. As a reference method, we compare our results with cross-correlation, typically used in the literatureas a standard measure of functional connectivity. We cross-validate 100 different training/test (90%/10%) datasplit to obtain mean accuracy and a mean Area Under the receiver operating characteristic Curve (AUC) acrossall tested numbers of features for lsXGC. Our results demonstrate a mean accuracy range of [0.767, 0.940] and amean AUC range of [0.861, 0.983] for lsXGC. The result of lsXGC is significantly higher than the results obtainedwith the cross-correlation, namely mean accuracy of [0.721, 0.751] and mean AUC of [0.744, 0.860]. Our resultssuggest the applicability of lsXGC as a potential biomarker for schizophrenia.
Further author information: (Send correspondence to Ali Vosoughi)Ali Vosoughi: E-mail: [email protected] a r X i v : . [ q - b i o . N C ] J a n eywords: machine learning, resting-state fMRI, Granger causality, functional connectivity, feature space,schizophrenia disorder
1. INTRODUCTION
Schizophrenia is a psychiatric disorder characterized by thoughts or experiences that are out of touch withreality, decreased participation in daily activities, disorganized speech or behavior, and (probably) difficultywith concentration and memorization may also be present. The current diagnosis of schizophrenia is by usingclinical evaluations of symptoms and behaviors; nevertheless, measurable biomarkers can be beneficial. Recentstudies on brain imaging data have shown that information can be extracted non-invasively from brain activity.Despite these studies’ promising results, there is still scope for improvement, especially using more meaningfulconnectivity analysis approaches [1].Extensive evidence has demonstrated that schizophrenia affects the brain’s connectivity [2]. Biomarkers fromresting-state functional MRI (rs-fMRI) for schizophrenia can be derived using Multi-Voxel Pattern Analysis(MVPA) techniques [3]. MVPA is a framework based on pattern recognition that extracts differences in brainconnectivity patterns among healthy individuals and individuals with neurological disease. Cross-correlation iscommonly used in most MVPA studies to obtain a functional connectivity profile. For instance, one such studyhas obtained an accuracy of 0.79 on the slow frequency bands (0.01-0.1 Hz) [4]. As a result, one can argue thatconnectivity analysis of fMRI data can be used to learn meaningful information. However, cross-correlation is notfit to obtain directed measures of connectivity. Therefore, there may be more relevant information in the fMRIdata that is not being grasped by cross-correlation. Several methods have been proposed to capture directionalrelations in multivariate time-series data, e.g., transfer entropy [5] and mutual information [6]. However, asthe multivariate problem’s dimensions increase, the density function’s computation becomes computationallyexpensive [7,8]. Under the Gaussian assumption, transfer entropy is equivalent to Granger causality [9]. However,the computation of multivariate Granger causality for short time series in large-scale problems is challenging[10, 11].Large-scale Extended Granger Causality (lsXGC) is a recently proposed method for estimating directed causalrelationships among fMRI time-series that combines dimension reduction with source time-series augmentationand uses predictive time-series modeling [12]. In this work, we investigate if alterations in directed connectivityevident in individuals with schizophrenia and if such directed measures enhance our ability to discriminatebetween schizophrenia patients and healthy controls. To this end, we apply lsXGC in the MVPA framework forestimating a measure of directed causal interdependence between fMRI time-series.This work is embedded in our group’s endeavor to expedite artificial intelligence in biomedical imaging by meansf advanced pattern recognition and machine learning methods for computational radiology and radiomics, e.g.,[ 13–70 ].
2. DATA2.1 Participants
The Centers of Biomedical Research Excellence (COBRE) data respiratory contains raw anatomical and func-tional MR data from 72 patients with schizophrenia and 74 healthy controls (ages ranging from 18 to 65 in eachgroup). All subjects were screened and eliminated if they had; a history of mental retardation, a history ofneurological disorder, history of severe head trauma with more than 5 minutes of loss of consciousness, historyof substance dependence or abuse within the last 12 months [2]. Diagnostic information was collected using theStructured Clinical Interview used for DSM Disorders (SCID) [2].
A multi-echo MPRAGE (MEMPR) sequence was used with the following parameters: TR/TE/TI = 2530/[1.64,3.5, 5.36, 7.22, 9.08]/900 ms, flip angle = 7 ◦ , FOV = 256 x 256 mm , slab thickness = 176 mm, matrix = 256 x256 x 176, voxel size =1 x 1 x 1 mm , number of echos = 5, pixel bandwidth = 650 Hz, total scan time = 6 min.With 5 echoes, the TR, TI and time to encode partitions for the MEMPR are similar to that of a conventionalMPRAGE, resulting in similar GM/WM/CSF contrast. Resting-state fMRI data was collected with single-shotfull k-space echo-planar imaging (EPI) with ramp sampling correction using the intercomissural line (AC-PC)as a reference (TR = 2 s, TE = 29 ms, matrix size = 64 x 64, 32 slices, voxel size = 3 x 3 x 4 mm ).Functional connectivity measurements were generated from a subsample of the COBRE dataset [71], a publiclyavailable sample which we accessed through the Nilearn Python library [72]. All subjects of healthy controls anddiseased patients under the age of 32 were selected, including 33 healthy and 29 diseased subjects, totaling 62individuals. The images were already preprocessed using the NIAK resting-state pipeline [73], and additionaldetails can be found in the reference [71]. The number of regions of interests has been selected to be 122 withfunctional brain parcellations [74].
3. METHODS3.1 Large-scale Extended Granger Causality (lsXGC)
The Large-scale Extended Granger Causality (lsXGC) method has been developed based on 1) the principle oforiginal Granger causality that quantifies the causal influence of time-series x s on time-series x t by quantifyingthe measure of improvement in the forecast of x t in the presence of x s . 2) the idea of dimensionality reduction,hich solves the problem of tackling an ill-posed system, which is often challenged in fMRI analysis since thenumber of acquired temporal samples usually is not sufficient for estimating the model parameters [10, 65].Consider the ensemble of time-series X ∈ R N × T , where N is the regions of interest (ROIs or number) oftime-series and T the number of temporal samples. Let X = ( x , x , . . . , x N ) T be the whole multidimensionalsystem and x i ∈ R × T a single time-series with i = 1 , , . . . , N , where x i = ( x i (1) , x i (2) , . . . , x i ( T )). To overcomethe ill-posed problem, first X will be decomposed into its first p high-variance principal components Z ∈ R p × T using Principal Component Analysis (PCA), i.e., Z = W X , (1)where W ∈ R p × N represents the PCA coefficient matrix. Subsequently, the dimension-reduced time-seriesensemble Z is augmented by one original time-series x s yielding a dimension-reduced augmented time-seriesensemble Y ∈ R ( p +1) × T for estimating the influence of x s on all other time-series.Following this, we locally predict X at each time sample t , i.e., X ( t ) ∈ R N × by calculating an estimate ˆ X x s ( t ).To this end, we fit an affine model based on a vector of m vector of m time samples of Y ( τ ) ∈ R ( p +1) × ( τ = t − , t − , . . . , t − m ), which is y ( t ) ∈ R m. ( p +1) × , and a parameter matrix A ∈ R N × m. ( p +1) and a constant biasvector b ∈ R N × , ˆ X x s ( t ) = A y ( t ) + b , t = m + 1 , m + 2 , . . . , T. (2)Now ˆ X \ x s ( t ), which is the prediction of X ( t ) without the information of x s , will be estimated. The estimationprocesses is identical to the previous one, with the only difference being that we have to remove the augmentedtime-series x s and its corresponding column in the PCA coefficient matrix W .The computation of a lsXGC index is based on comparing the variance of the prediction errors obtained withand without consideration of x s . The lsXGC index f x s −→ x t , which indicates the influence of x s on x t , can becalculated by the following equation: f x s −→ x t = log var( e s )var( e \ s ) , (3)where e \ s is the error in predicting x t when x s was not considered, and e s is the error, when x s was used. Inthis study, we set p = 8 and m = 1. Brain connections served as features for classification in this study and were estimated by two methods, namelylsXGC and cross-correlation. Before using high-dimensional connectivity feature vectors as input to a classifier,feature selection was carried out to reduce input features’ dimension. .2.1 Feature selection
In order to lessen the number of features, feature selection was performed on each training data set with k-foldcross-validation using
Kendall’s Tau rank correlation coefficient [75] and 10% −
90% of test-to-train split ratio.This approach quantifies each feature’s relevance to the task of classification and assigns ranks by testing forindependence between different classes for each feature [75].
To cross-validate the classification performance in 100 iterations, the data set was divided into two groups: atraining data set (90%) and a test data set (10%) that the percentage of samples for each class was preserved.Also, this was repeated with different numbers of features ranging from 5 to 175. A Support Vector Machine(SVM) [76] was used for classification between healthy subjects and schizophrenia patients. All procedures wereperformed using MATLAB 9.8 (MathWorks Inc., Natick, MA, 2020a), and Python 3.8.
4. RESULTS
Mean connectivity matrices, which were extracted using lsXGC and cross-correlation, are shown in Fig. 1 forschizophrenia patient and healthy control cohorts. Distinct patterns are visible to the naked eye for both meth-ods. In the following, we quantitatively investigate the difference between the two patient cohorts’ connectivitypatterns using an MVPA approach.Classification results were evaluated using the Area Under the Receiver Operator Characteristic Curve (AUC)and accuracy. An AUC = 1 indicates a perfect classification, AUC = 0.5 indicates random class assignment. Inthis study, we chose eight as the number of the retained components of PCA in the lsXGC algorithm and modelorder of 1 for the multivariate vector autoregression function based on preliminary analyses. The plots of accuracyand AUC results in Fig. 2, clearly demonstrate that lsXGC outperforms cross-correlation for diversified numbersof features. Across the wide range of examined numbers of features, the performance of lsXGC is consistentlyhigher with its mean AUC within [0.861, 0.983] and its mean accuracy within [0.767, 0.940]. On the other hand,cross-correlation performs quite poorly compared to lsXGC with its mean AUC within [0.744, 0.860] and itsmean accuracy within [0.721, 0.751].
5. CONCLUSIONS
In this research, we use a recently developed method for brain connectivity analysis, large-scale Extended GrangerCausality (lsXGC), and apply it to a subset of the COBRE data repository to classify individuals with schizophre-nia from typical controls by estimating a measure of directed causal relations among regional brain activities ealthy controls using lsXGC Schizophrenia patients using lsXGCHealthy controls using correlation Schizophrenia patients using correlation
Figure 1: Mean connectivity matrices: top left: mean connectivity of healthy control subjects using lsXGC,top right: mean connectivity matrix of schizophrenia patients using lsXGC, bottom left: mean connectivitymatrix of healthy control subjects using cross-correlation, bottom right: employing cross-correlation to obtainmean connectivity matrix of schizophrenia patients. Remarkably different methods appear to extract differentconnectivity features, and that they appear to be slight differences in connectivity patterns between the healthysubject and the schizophrenia patients.
15 25 50 75 100 125 150 175Number of Features0.50.60.70.80.91.0 M e a n A U C lsXGCCorrelation (a) Mean AUC M e a n A cc u r a c y lsXGCCorrelation (b) Mean accuracy Figure 2: Plots are comparing the performance of cross-correlation and the proposed large-scale extended Grangercausality (lsXGC). The shaded areas represent the 95% confidence interval. It demonstrates that lsXGC outper-forms cross-correlation for most numbers of selected features.recorded in resting-state fMRI. Following the construction of connectivity matrices as characterizing featuresfor brain network analysis, we use Kendall’s tau rank correlation coefficient to select a significant feature and asupport vector machine to classify. We demonstrate that our method (lsXGC) favorably compares to standardanalysis using cross-correlation, as shown by the significantly enhancing accuracy and AUC values. The effec-tiveness of lsXGC as a potent biomarker for identifying schizophrenia in prospective clinical trials is yet to bevalidated. Nevertheless, our results suggest that our approach outperforms the current clinical standard, namelycross-correlation, at revealing meaningful information from functional MRI data.
ACKNOWLEDGMENTS
This research was funded by Ernest J. Del Monte Institute for Neuroscience Award from the Harry T. MangurianJr. Foundation. This work was conducted as a Practice Quality Improvement (PQI) project related to AmericanBoard of Radiology (ABR) Maintenance of Certificate (MOC) for Prof. Dr. Axel Wism¨uller. This work is notbeing and has not been submitted for publication or presentation elsewhere.
REFERENCES [1] Li, A., Zalesky, A., Yue, W., Howes, O., Yan, H., Liu, Y., Fan, L., Whitaker, K. J., Xu, K., Rao, G., et al., “Aneuroimaging biomarker for striatal dysfunction in schizophrenia,”
Nature Medicine (4), 558–565 (2020).[2] Calhoun, V. D., Sui, J., Kiehl, K., Turner, J. A., Allen, E. A., and Pearlson, G., “Exploring the psychosisfunctional connectome: aberrant intrinsic networks in schizophrenia and bipolar disorder,” Frontiers inpsychiatry , 75 (2012).3] Norman, K. A., Polyn, S. M., Detre, G. J., and Haxby, J. V., “Beyond mind-reading: multi-voxel patternanalysis of fMRI data,” Trends in cognitive sciences (9), 424–430 (2006).[4] Cheng, H., Newman, S., Go˜ni, J., Kent, J. S., Howell, J., Bolbecker, A., Puce, A., O’Donnell, B. F., andHetrick, W. P., “Nodal centrality of functional network in the differentiation of schizophrenia,” Schizophreniaresearch (1-2), 345–352 (2015).[5] Schreiber, T., “Measuring information transfer,”
Physical review letters (2), 461 (2000).[6] Kraskov, A., St¨ogbauer, H., and Grassberger, P., “Estimating mutual information,” Physical review E (6),066138 (2004).[7] Mozaffari, M. and Yilmaz, Y., “Online multivariate anomaly detection and localization for high-dimensionalsettings,” arXiv preprint arXiv:1905.07107 (2019).[8] Mozaffari, M. and Yilmaz, Y., “Online anomaly detection in multivariate settings,” in [ ], 1–6, IEEE (2019).[9] Barnett, L., Barrett, A. B., and Seth, A. K., “Granger causality and transfer entropy are equivalent forGaussian variables,” Physical review letters (23), 238701 (2009).[10] Vosoughi, M. A. and Wism¨uller, A., “Large-scale kernelized Granger causality to infer topology of directedgraphs with applications to brain networks,” arXiv preprint arXiv:2011.08261 (2020).[11] Wism¨uller, A., DSouza, A. M., Abidin, A. Z., and Vosoughi, M. A., “Large-scale nonlinear Granger causality:A data-driven, multivariate approach to recovering directed networks from short time-series data,” arXivpreprint arXiv:2009.04681 (2020).[12] Vosoughi, M. A. and Wism¨uller, A., “Large-scale extended Granger causality for classification of marijuanausers from functional MRI,” arXiv preprint arXiv:2101.01832 (2021).[13] Nattkemper, T. W. and Wism¨uller, A., “Tumor feature visualization with unsupervised learning,”
MedicalImage Analysis (4), 344–351 (2005).[14] Bunte, K., Hammer, B., Wism¨uller, A., and Biehl, M., “Adaptive local dissimilarity measures for discrimi-native dimension reduction of labeled data,” Neurocomputing (7-9), 1074–1092 (2010).[15] Wism¨uller, A., Vietze, F., and Dersch, D. R., “Segmentation with neural networks,” in [ Handbook of medicalimaging ], 107–126, Academic Press, Inc. (2000).[16] Leinsinger, G., Schlossbauer, T., Scherr, M., Lange, O., Reiser, M., and Wism¨uller, A., “Cluster analysis ofsignal-intensity time course in dynamic breast MRI: does unsupervised vector quantization help to evaluatesmall mammographic lesions?,”
European radiology (5), 1138–1146 (2006).17] Wism¨uller, A., Vietze, F., Behrends, J., Meyer-Baese, A., Reiser, M., and Ritter, H., “Fully automatedbiomedical image segmentation by self-organized model adaptation,” Neural Networks (8-9), 1327–1344(2004).[18] Hoole, P., Wism¨uller, A., Leinsinger, G., Kroos, C., Geumann, A., and Inoue, M., “Analysis of tongueconfiguration in multi-speaker, multi-volume MRI data,” (2000).[19] Wism¨uller, A., “Exploratory morphogenesis (XOM): a novel computational framework for self-organization,” Ph. D. thesis, Technical University of Munich, Department of Electrical and Computer Engineering (2006).[20] Wism¨uller, A., Dersch, D. R., Lipinski, B., Hahn, K., and Auer, D., “A neural network approach to func-tional MRI pattern analysis—clustering of time-series by hierarchical vector quantization,” in [
InternationalConference on Artificial Neural Networks ], 857–862, Springer (1998).[21] Wism¨uller, A., Vietze, F., Dersch, D. R., Behrends, J., Hahn, K., and Ritter, H., “The deformable featuremap-a novel neurocomputing algorithm for adaptive plasticity in pattern analysis,”
Neurocomputing (1-4),107–139 (2002).[22] Behrends, J., Hoole, P., Leinsinger, G. L., Tillmann, H. G., Hahn, K., Reiser, M., and Wism¨uller, A., “Asegmentation and analysis method for MRI data of the human vocal tract,” in [ Bildverarbeitung f¨ur dieMedizin 2003 ], 186–190, Springer (2003).[23] Wism¨uller, A., “Neural network computation in biomedical research: chances for conceptual cross-fertilization,”
Theory in Biosciences (1997).[24] Bunte, K., Hammer, B., Villmann, T., Biehl, M., and Wism¨uller, A., “Exploratory observation machine(XOM) with Kullback-Leibler divergence for dimensionality reduction and visualization.,” in [
ESANN ], ,87–92 (2010).[25] Wism¨uller, A., Vietze, F., Dersch, D. R., Hahn, K., and Ritter, H., “The deformable feature map—adaptiveplasticity for function approximation,” in [ International Conference on Artificial Neural Networks ], 123–128,Springer (1998).[26] Wism¨uller, A., “The exploration machine–a novel method for data visualization,” in [
International Work-shop on Self-Organizing Maps ], 344–352, Springer (2009).[27] Wism¨uller, A., “Method, data processing device and computer program product for processing data,”(July 28 2009). US Patent 7,567,889.[28] Huber, M. B., Nagarajan, M., Leinsinger, G., Ray, L. A., and Wism¨uller, A., “Classification of intersti-tial lung disease patterns with topological texture features,” in [
Medical Imaging 2010: Computer-AidedDiagnosis ], , 762410, International Society for Optics and Photonics (2010).29] Wism¨uller, A., “The exploration machine: a novel method for analyzing high-dimensional data in computer-aided diagnosis,” in [ Medical Imaging 2009: Computer-Aided Diagnosis ], , 72600G, International So-ciety for Optics and Photonics (2009).[30] Bunte, K., Hammer, B., Villmann, T., Biehl, M., and Wism¨uller, A., “Neighbor embedding XOM fordimension reduction and visualization,” Neurocomputing (9), 1340–1350 (2011).[31] Meyer-B¨ase, A., Lange, O., Wism¨uller, A., and Ritter, H., “Model-free functional MRI analysis usingtopographic independent component analysis,” International journal of neural systems (04), 217–228(2004).[32] Wism¨uller, A., “A computational framework for nonlinear dimensionality reduction and clustering,” in[ International Workshop on Self-Organizing Maps ], 334–343, Springer (2009).[33] Meyer-Base, A., Auer, D., and Wism¨uller, A., “Topographic independent component analysis for fMRIsignal detection,” in [
Proceedings of the International Joint Conference on Neural Networks, 2003. ], ,601–605, IEEE (2003).[34] Meyer-Baese, A., Schlossbauer, T., Lange, O., and Wism¨uller, A., “Small lesions evaluation based onunsupervised cluster analysis of signal-intensity time courses in dynamic breast MRI,” International journalof biomedical imaging (2009).[35] Wism¨uller, A., Lange, O., Auer, D., and Leinsinger, G., “Model-free functional MRI analysis for detectinglow-frequency functional connectivity in the human brain,” in [
Medical Imaging 2010: Computer-AidedDiagnosis ], , 76241M, International Society for Optics and Photonics (2010).[36] Meyer-B¨ase, A., Saalbach, A., Lange, O., and Wism¨uller, A., “Unsupervised clustering of fMRI and MRItime series,” Biomedical Signal Processing and Control (4), 295–310 (2007).[37] Huber, M. B., Nagarajan, M. B., Leinsinger, G., Eibel, R., Ray, L. A., and Wism¨uller, A., “Performanceof topological texture features to classify fibrotic interstitial lung disease patterns,” Medical Physics (4),2035–2044 (2011).[38] Wism¨uller, A., Verleysen, M., Aupetit, M., and Lee, J. A., “Recent advances in nonlinear dimensionalityreduction, manifold and topological learning.,” in [ ESANN ], (2010).[39] Meyer-Baese, A., Lange, O., Wism¨uller, A., and Hurdal, M. K., “Analysis of dynamic susceptibility contrastMRI time series based on unsupervised clustering methods,”
IEEE Transactions on Information Technologyin Biomedicine (5), 563–573 (2007).[40] Wism¨uller, A., Behrends, J., Hoole, P., Leinsinger, G. L., Reiser, M. F., and Westesson, P.-L., “Human vocaltract analysis by in vivo 3d MRI during phonation: a complete system for imaging, quantitative modeling,nd speech synthesis,” in [ International Conference on Medical Image Computing and Computer-AssistedIntervention ], 306–312, Springer (2008).[41] Wism¨uller, A., “Method and device for representing multichannel image data,” (Nov. 17 2015). US Patent9,189,846.[42] Huber, M. B., Bunte, K., Nagarajan, M. B., Biehl, M., Ray, L. A., and Wism¨uller, A., “Texture fea-ture ranking with relevance learning to classify interstitial lung disease patterns,”
Artificial intelligence inmedicine (2), 91–97 (2012).[43] Wism¨uller, A., Meyer-Baese, A., Lange, O., Reiser, M. F., and Leinsinger, G., “Cluster analysis of dynamiccerebral contrast-enhanced perfusion MRI time-series,” IEEE transactions on medical imaging (1), 62–73(2005).[44] Twellmann, T., Saalbach, A., Muller, C., Nattkemper, T. W., and Wism¨uller, A., “Detection of suspiciouslesions in dynamic contrast enhanced MRI data,” in [ The 26th Annual International Conference of the IEEEEngineering in Medicine and Biology Society ], , 454–457, IEEE (2004).[45] Otto, T. D., Meyer-Baese, A., Hurdal, M., Sumners, D., Auer, D., and Wism¨uller, A., “Model-free functionalMRI analysis using cluster-based methods,” in [ Intelligent Computing: Theory and Applications ], , 17–24, International Society for Optics and Photonics (2003).[46] Varini, C., Nattkemper, T. W., Degenhard, A., and Wism¨uller, A., “Breast MRI data analysis by lle,” in[ ], , 2449–2454, IEEE (2004).[47] Huber, M. B., Lancianese, S. L., Nagarajan, M. B., Ikpot, I. Z., Lerner, A. L., and Wism¨uller, A., “Predictionof biomechanical properties of trabecular bone in mr images with geometric features and support vectorregression,” IEEE Transactions on Biomedical Engineering (6), 1820–1826 (2011).[48] Meyer-Base, A., Pilyugin, S. S., and Wism¨uller, A., “Stability analysis of a self-organizing neural networkwith feedforward and feedback dynamics,” in [ ], , 1505–1509, IEEE (2004).[49] Meyer-Baese, A., Lange, O., Schlossbauer, T., and Wism¨uller, A., “Computer-aided diagnosis and visu-alization based on clustering and independent component analysis for breast MRI,” in [ ], 3000–3003, IEEE (2008).[50] Wism¨uller, A., Meyer-B¨ase, A., Lange, O., Schlossbauer, T., Kallergi, M., Reiser, M., and Leinsinger, G.,“Segmentation and classification of dynamic breast magnetic resonance image data,” Journal of ElectronicImaging (1), 013020 (2006).51] Bhole, C., Pal, C., Rim, D., and Wism¨uller, A., “3d segmentation of abdominal ct imagery with graphicalmodels, conditional random fields and learning,” Machine vision and applications (2), 301–325 (2014).[52] Nagarajan, M. B., Coan, P., Huber, M. B., Diemoz, P. C., Glaser, C., and Wism¨uller, A., “Computer-aideddiagnosis in phase contrast imaging x-ray computed tomography for quantitative characterization of ex vivohuman patellar cartilage,” IEEE Transactions on Biomedical Engineering (10), 2896–2903 (2013).[53] Wism¨uller, A., Meyer-B¨ase, A., Lange, O., Auer, D., Reiser, M. F., and Sumners, D., “Model-free functionalMRI analysis based on unsupervised clustering,” Journal of Biomedical Informatics (1), 10–18 (2004).[54] Meyer-Baese, A., Wism¨uller, A., Lange, O., and Leinsinger, G., “Computer-aided diagnosis in breast MRIbased on unsupervised clustering techniques,” in [ Intelligent Computing: Theory and Applications II ], ,29–37, International Society for Optics and Photonics (2004).[55] Nagarajan, M. B., Coan, P., Huber, M. B., Diemoz, P. C., Glaser, C., and Wism¨uller, A., “Computer-aideddiagnosis for phase-contrast x-ray computed tomography: quantitative characterization of human patellarcartilage with high-dimensional geometric features,” Journal of digital imaging (1), 98–107 (2014).[56] Nagarajan, M. B., Huber, M. B., Schlossbauer, T., Leinsinger, G., Krol, A., and Wism¨uller, A., “Classifica-tion of small lesions on dynamic breast MRI: Integrating dimension reduction and out-of-sample extensioninto cadx methodology,” Artificial intelligence in medicine (1), 65–77 (2014).[57] Yang, C.-C., Nagarajan, M. B., Huber, M. B., Carballido-Gamio, J., Bauer, J. S., Baum, T. H., Eckstein,F., Lochm¨uller, E.-M., Majumdar, S., Link, T. M., et al., “Improving bone strength prediction in humanproximal femur specimens through geometrical characterization of trabecular bone microarchitecture andsupport vector regression,” Journal of electronic imaging (1), 013013 (2014).[58] Wism¨uller, A., Nagarajan, M. B., Witte, H., Pester, B., and Leistritz, L., “Pair-wise clustering of largescale Granger causality index matrices for revealing communities,” in [ Medical Imaging 2014: BiomedicalApplications in Molecular, Structural, and Functional Imaging ], , 90381R, International Society forOptics and Photonics (2014).[59] Wism¨uller, A., Wang, X., DSouza, A. M., and Nagarajan, M. B., “A framework for exploring non-linearfunctional connectivity and causality in the human brain: mutual connectivity analysis (mca) of resting-statefunctional MRI with convergent cross-mapping and non-metric clustering,” arXiv preprint arXiv:1407.3809 (2014).[60] Schmidt, C., Pester, B., Nagarajan, M., Witte, H., Leistritz, L., and Wism¨uller, A., “Impact of multivariateGranger causality analyses with embedded dimension reduction on network modules,” in [ ], 2797–2800, IEEE(2014).61] Wism¨uller, A., Abidin, A. Z., D’Souza, A. M., Wang, X., Hobbs, S. K., Leistritz, L., and Nagarajan, M. B.,“Nonlinear functional connectivity network recovery in the human brain with mutual connectivity analysis(MCA): convergent cross-mapping and non-metric clustering,” in [ Medical Imaging 2015: Biomedical Appli-cations in Molecular, Structural, and Functional Imaging ], , 94170M, International Society for Opticsand Photonics (2015).[62] Wism¨uller, A., Abidin, A. Z., DSouza, A. M., and Nagarajan, M. B., “Mutual connectivity analysis (MCA)for nonlinear functional connectivity network recovery in the human brain using convergent cross-mappingand non-metric clustering,” in [ Advances in Self-Organizing Maps and Learning Vector Quantization ], 217–226, Springer (2016).[63] Schmidt, C., Pester, B., Schmid-Hertel, N., Witte, H., Wism¨uller, A., and Leistritz, L., “A multivariateGranger causality concept towards full brain functional connectivity,”
PloS one (4) (2016).[64] Abidin, A. Z., Chockanathan, U., DSouza, A. M., Inglese, M., and Wism¨uller, A., “Using large-scaleGranger causality to study changes in brain network properties in the clinically isolated syndrome (CIS)stage of multiple sclerosis,” in [ Medical Imaging 2017: Biomedical Applications in Molecular, Structural,and Functional Imaging ], , 101371B, International Society for Optics and Photonics (2017).[65] DSouza, A. M., Abidin, A. Z., Leistritz, L., and Wism¨uller, A., “Exploring connectivity with large-scaleGranger causality on resting-state functional MRI,” Journal of neuroscience methods , 68–79 (2017).[66] Chen, L., Wu, Y., DSouza, A. M., Abidin, A. Z., Wism¨uller, A., and Xu, C., “MRI tumor segmentation withdensely connected 3d cnn,” in [
Medical Imaging 2018: Image Processing ], , 105741F, InternationalSociety for Optics and Photonics (2018).[67] Abidin, A. Z., DSouza, A. M., Nagarajan, M. B., Wang, L., Qiu, X., Schifitto, G., and Wism¨uller, A., “Alter-ation of brain network topology in HIV-associated neurocognitive disorder: A novel functional connectivityperspective,” NeuroImage: Clinical , 768–777 (2018).[68] Abidin, A. Z., Deng, B., DSouza, A. M., Nagarajan, M. B., Coan, P., and Wism¨uller, A., “Deep transferlearning for characterizing chondrocyte patterns in phase contrast x-ray computed tomography images ofthe human patellar cartilage,” Computers in biology and medicine , 24–33 (2018).[69] DSouza, A. M., Abidin, A. Z., Chockanathan, U., Schifitto, G., and Wism¨uller, A., “Mutual connectivityanalysis of resting-state functional MRI data with local models,” NeuroImage , 210–223 (2018).[70] Chockanathan, U., DSouza, A. M., Abidin, A. Z., Schifitto, G., and Wism¨uller, A., “Automated diagno-sis of HIV-associated neurocognitive disorders using large-scale Granger causality analysis of resting-statefunctional MRI,”
Computers in Biology and Medicine , 24–30 (2019).[71] Bellec, P., “COBRE preprocessed with NIAK 0.17 - lightweight release,” (2016).72] Abraham, A., Pedregosa, F., Eickenberg, M., Gervais, P., Mueller, A., Kossaifi, J., Gramfort, A., Thirion, B.,and Varoquaux, G., “Machine learning for neuroimaging with scikit-learn,”
Frontiers in neuroinformatics ,14 (2014).[73] NIAK-pipeline, “http://niak.simexp-lab.org/,” (2019). Last accessed 19 August 2020.[74] Bellec, P., “Mining the hierarchy of resting-state brain networks: selection of representative clusters in amultiscale structure,” in [ ], 54–57,IEEE (2013).[75] Kendall, M. G., “The treatment of ties in ranking problems,” Biometrika (3), 239–251 (1945).[76] Suykens, J. A. and Vandewalle, J., “Least squares support vector machine classifiers,” Neural processingletters9