Whole brain white matter connectivity analysis using machine learning: an application to autism

Abstract

In this paper, we propose an automated white matter connectivity analysis method for machine learning classification and characterization of white matter abnormality via identification of discriminative fiber tracts. The proposed method uses diffusion MRI tractography and a data-driven approach to find fiber clusters corresponding to subdivisions of the white matter anatomy. Features extracted from each fiber cluster describe its diffusion properties and are used for machine learning. The method is demonstrated by application to a pediatric neuroimaging dataset from 149 individuals, including 70 children with autism spectrum disorder (ASD) and 79 typically developing controls (TDC). A classification accuracy of 78.33% is achieved in this cross-validation study. We investigate the discriminative diffusion features based on a two-tensor fiber tracking model. We observe that the mean fractional anisotropy from the second tensor (associated with crossing fibers) is most affected in ASD. We also find that local along-tract (central cores and endpoint regions) differences between ASD and TDC are helpful in differentiating the two groups. These altered diffusion properties in ASD are associated with multiple robustly discriminative fiber clusters, which belong to several major white matter tracts including the corpus callosum, arcuate fasciculus, uncinate fasciculus and aslant tract; and the white matter structures related to the cerebellum, brain stem, and ventral diencephalon. These discriminative fiber clusters, a small part of the whole brain tractography, represent the white matter connections that could be most affected in ASD. Our results indicate the potential of a machine learning pipeline based on white matter fiber clustering.

1. Introduction

The advent of diffusion magnetic resonance imaging (dMRI), which can infer the underlying connection structure of brain white matter in vivo via a process called tractography (Basser et al., 2000), has allowed analysis of white matter structures in a non-invasive way. Models of brain white matter connectivity have been shown to be valuable for understanding neurological function, development and disease (Assaf and Pasternak, 2008; Horsfield and Jones, 2002; Ciccarelli et al., 2008). Traditional statistical analyses of tractography usually investigate a predetermined hypothesis that certain fiber tracts of interest are affected in one group (Catani et al., 2008; Pugliese et al., 2009; Hong et al., 2011). However, there is increased interest in developing statistical and machine learning methods that can assess potential combined effects from multiple fiber tracts (Gong et al., 2009; Robinson et al., 2010; Wang et al., 2016; Ratnarajah et al., 2013; O’Donnell et al., 2013; Meskaldji et al., 2013).

In this study, we investigate computational methods to analyze whole brain connectivity patterns at multiple coarse-to-fine scales of white matter parcellation. We propose a machine learning methodology to learn underlying whole brain white matter connectivity patterns using dMRI and to provide insights into white matter structures that are discriminative between groups. The proposed computational method provides a novel whole white matter global tract assessment and end-to-end classification framework to study alterations in brain white matter connectivity. The method includes a study-specific data-driven tractography parcellation and a high-dimensional multivariate machine-learning-based group classification, which allows identification of tracts that may be most affected by pathology in the whole brain. Results are interpreted and visualized in terms of tracts with known cortical terminations.

We demonstrate our method with an application of classification between autism spectrum disorder (ASD) and typically developing control (TDC). While the current diagnosis of ASD is based on behavioral assessment (Lord et al., 1994, 2000; Association, 2000), there has been high interest in investigating dMRI-based white matter analysis for classification of ASD (Lange et al., 2010; Ingalhalikar et al., 2011; Mostapha et al., 2015). The literature has suggested broad white matter impairments in ASD compared to TDC, and altered white matter connectivity has been hypothesized to associate with symptoms of core and comorbid conditions across the autism spectrum, as described in recent review papers (Travers et al., 2012; Hoppenbrouwers et al., 2014; Ameis and Catani, 2015). Therefore, we hypothesized that a whole brain tractography analysis could predict ASD by inferring global white matter abnormality patterns.

To the best of our knowledge, this work represents the first investigation of machine-learning-based whole brain fiber clustering analysis for group classification. This investigation extends our preliminary work (Zhang et al., 2016) to employ a multi-fiber tractography model that is more sensitive in tracking through regions of crossing fibers, a hemisphere-based cluster separation to observe potentially lateralized white matter abnormalities, and a multiple feature selection to assess the most discriminative clusters that present abnormalities in different diffusion properties such as anisotropy and diffusivity.

2. Methods and Materials

Here we first give a brief overview of our proposed method, followed by more detailed descriptions of the computational processing methods. Then, we introduce the dataset and the multi-fiber tractography method and experimental evaluations employed in this work.

2.1. Method Overview

Our approach had two main steps: data-driven fiber clustering white matter parcellation and high-dimensional multivariate diffusion feature classification.

Figure 1 illustrates the fiber clustering pipeline (Section 2.2), including a groupwise tractography registration, a groupwise fiber cluster atlas generation, a subject-specific fiber clustering, and a hemisphere-based cluster separation. Overall, these steps enabled parcellation of corresponding fiber clusters in the whole brain of all subjects. We note that the whole pipeline worked in an automated data-driven fashion. A recently released implementation of these steps provides a publicly available software package for groupwise fiber-clustering-based white matter parcellation in the whitematteranalysis⁵ package. Our recent work has shown successful applications of the pipeline (Zhang et al., 2016; O’Donnell et al., 2017; Zhang et al., 2017a,c).

Figure 1.

Outline of the fiber clustering white matter parcellation. (a) Groupwise whole brain tractography registration for simultaneous joint alignment of tractography across all subjects. Overlap of all subjects’ tractography before and after registration is displayed, with fibers from different subjects colored differently. (b) Atlas generation using spectral clustering to discover common white matter structures in the population. Fiber colors are automatically generated from the spectral embedding, where each fiber cluster has a unique color, and similar clusters have similar colors. Example individual atlas clusters are displayed. (c) Subject-specific fiber clustering based on the obtained atlas. Fibers are colored accordingly to the atlas. Example subject-specific clusters corresponding to those in (b) are shown. (d) Hemisphere-based subject cluster separation to divide each subject cluster into hemispheric or commissural clusters.

Figure 2 gives an overview of the machine-learning-based classification (Section 2.3). It included a standard machine learning classification procedure, consisting of feature extraction, feature ranking and selection, classifier training, new data classification, and performance evaluation in a cross-validation. We extracted multiple diffusion features (see Section 2.3.1) from each fiber cluster per subject and conducted the classification using these features separately to investigate their individual discriminative ability between two groups (TDC vs ASD in this application). Fiber clusters that were robustly discriminative across the multiple features were identified as the output discriminative white matter regions between the groups.

Figure 2.

Overview of the machine-learning-based classification. (a) Diagram of the classification steps using an individual feature. Feature ranking and selection were conducted using the signal-to-noise (s2n) ratio coefficient. Support vector machine (SVM) was used as the classifier. A leave-subjects-out cross-validation was performed for performance evaluation. (b) Feature-specific discriminative clusters, which obtained the highest classification accuracy for each individual feature, were identified in the cross-validation. (c) Discriminative clusters that were robustly retained across multiple features were identified as the robustly discriminative clusters. (d) The anatomical connectivity of each robustly discriminative cluster was assessed by comparing its fiber endpoints to a brain parcellation into multiple cortical/subcortical regions (red: left postcentral gyrus; magenta: brain stem).

The proposed method was demonstrated by application to a pediatric neuroimaging dataset from 149 individuals, including 70 children with autism spectrum disorder (ASD) and 79 typically developing controls (TDC) (see Section 2.6 for details of the dataset). The study was conducted based on open source software, including fiber tracking ukftractography, fiber clustering whitematter-analysis, feature extraction and tractography visualization in 3D Slicer¹ via SlicerDMRI (Norton et al., 2017)².

2.2. Fiber Clustering White Matter Parcellation

This section illustrates the applications of the groupwise tractography registration (Section 2.2.1) and the data-driven fiber clustering (Sections 2.2.2 and 2.2.3).

2.2.1. Groupwise Tractography Registration

We first computed an unbiased groupwise whole brain tractography registration (Figure 1(a)) to align all subjects’ tractography into a common space (the atlas space), where the fiber clustering was performed. The method performed an entropy-based registration in a multiscale manner based on the pairwise fiber trajectory similarity (mean closest point distance) across all subjects. We first applied an affine transform (O’Donnell et al., 2012). Then, a recently implemented b-spline transform was conducted in a coarse-to-fine fashion following the affine transform. This enabled nonrigid deformations of the fibers for improvements of parcellation consistency across subjects. The transforms were conducted in a symmetric registration manner, which registered all subjects including midsagittal plane reflected copies of the subjects. In this way, the registration can effectively perform tractography alignment across the midsagittal plane. This could benefit the bilateral clustering for atlas generation (Section 2.2.2) and also enabled the hemisphere-based subject cluster separation (Section 2.2.3).

Detailed parameter settings used in our experiments were as follows. The groupwise tractography registration employed 20,000 fibers randomly sampled from each subject (a total of 149 subjects) for a total of about 3 million fibers. The affine registration was conducted with multiscale sigmas from 20mm down to 5mm, applied to the pairwise fiber similarity via Gaussian transform. Then, the coarse-to-fine nonrigid b-spline registration was calculated with the sigmas from 5mm to 2mm and b-spline grid sizes from 4 × 4 × 4 to 8 × 8 × 8. Each subject’s full tractography was transformed accordingly to the affine and nonrigid registrations. All parameters (also for the fiber clustering in Sections 2.2.2 and 2.2.3) were chosen for reasonable performance, computational time and memory usages. Other parameters were left as default values in the whitematteranalysis⁵ package, which have been tuned for optimal performance in general. The computations were conducted using a 48 core machine in a high performance computing (HPC) Linux Cluster.

2.2.2. Groupwise Fiber Cluster Atlas Generation

After the registration, spectral embedding was conducted on the pairwise fiber affinity to convert each fiber to a point in a high-dimensional spectral embedding space (O’Donnell and Westin, 2007). In this space, fibers were interpreted with respect to their similarities to all others, where neighborhoods in general grouped similar fibers. We applied the mean closest point distance, a popular fiber distance measure used in fiber clustering (Ding et al., 2003; Moberts et al., 2005; Garyfallidis et al., 2012; O’Donnell and Westin, 2007; Wang et al., 2016). The fiber distance was converted to a fiber affinity using a Gaussian-like kernel with sigma of 60 mm as in (O’Donnell and Westin, 2007; O’Donnell et al., 2017; Zhang et al., 2017a,b,c). We used the Nystrom sampling method to represent the embedding space compactly and to reduce the computations considering the large number of fiber pairs across subjects. K-means clustering was then performed to create the cluster atlas in a data-driven way (Figure 1(b)). Each atlas fiber cluster was obtained across subjects, representing common white matter structures in the population. Bilateral clustering that simultaneously clustered fibers in both hemispheres was applied to improve clustering robustness (O’Donnell and Westin, 2007). The total number of bilateral clusters in the atlas was defined as K_b.

We further incorporated an outlier removal to remove the spurious fibers for cluster consistency in the atlas. For each cluster, we excluded the fibers that were present in only few subjects to reject uncommon tractography errors. Specifically, we considered a fiber as an outlier if it was distant from other fibers within its cluster. To quantitatively decide the outliers, we define a probability for each fiber based on the pairwise fiber distances (the mean closest point distance) mapped through a Gaussian kernel with sigma 20 (O’Donnell et al., 2017). The probability of each fiber given its cluster was computed using the fibers from all other subjects in this cluster. The fibers whose probability was more than two standard deviations away from the cluster mean probability were regarded as outliers and rejected. The threshold of two standard deviations was chosen as a good value to remove uncommon tractography errors (spurious fibers), based on our recent works (O’Donnell et al., 2017; Zhang et al., 2017a,b,c). The fiber clustering and outlier removal were performed iteratively to get a final fiber cluster atlas.

In the experiments, all 149 subjects were used for atlas generation, with 5,000 fibers randomly sampled from each subject for a total of 745,000 fibers. 3500 fibers were sampled for the Nystrom method and two rounds of outlier rejection with a Gaussian kernel of σ=20mm were applied to create a final atlas. We generated multiple cluster atlases given different numbers of bilateral clusters, i.e., K_b from 400 to 4000 which provided reasonable parcellation with respect to the white matter anatomy, to explore the influence of white matter parcellations at different scales.

2.2.3. Fiber Clustering of Subjects

We then applied the obtained fiber cluster atlas to each individual subject for a subject-specific tractography parcellation (Figure 1(c)) using spectral embedding (O’Donnell and Westin, 2007). In details, affinity values for a new fiber (already affine and nonrigid transformed) were calculated by comparison to each fiber stored in the atlas (the stored Nystrom sample of 3500 fibers), using the same fiber affinity computation as in the atlas generation (Section 2.2.2). Spectral embedding was then used to embed each new fiber in the same atlas embedding space in which the fiber clustering was performed originally. The subject-specific fiber clusters were then obtained by assigning the fibers to their closest atlas cluster (O’Donnell and Westin, 2007). We note that each subject’s fibers were clustered individually according to the atlas, thus any individual fiber tract property, e.g. the fractional anisotropy or the fiber count, was preserved. We then applied an outlier removal process for each subject cluster, similar to that in the atlas creation. Any outlier fiber whose probability/affinity given its atlas cluster was over two standard deviations from the cluster’s mean fiber probability was removed.

A hemisphere-based cluster separation was then conducted to obtain intra-an inter-hemispheric clusters (Figure 1(d)). Given the bilateral clustering of the atlas, the subject clusters were detected bilaterally, which presented white matter tracts in both hemispheres. Considering the potentially lateralized asymmetry of white matter microstructure in ASD (Herbert et al., 2005; Lange et al., 2010), we divided the bilateral clusters into left-hemispheric (L), right-hemispheric (R) and commissural (C) clusters according to the brain midsagittal plane. We obtained a total of K_s = 3 × K_b clusters per subject after the separation, in which some presented empty tracts. For example, a before-separation cluster of commissural tracts would produce a C cluster but empty L/R clusters.

After the bilateral cluster separation, valid L/R/C clusters were identified as those that passed a nonparametric one-tailed sign test (Bonferroni corrected at a significance level of 0.05) in the population. This method has been applied in multiple studies to identify valid white matter connections (Gong et al., 2009; Ratnarajah et al., 2013). Specifically, for each L/R/C cluster, the sign test was performed across all the subjects to determine the existence of the cluster. The sign test was used to find the ones most consistently present across subjects and resulted in a total number of clusters, K, retained for each subject to conduct ASD/TDC classification.

2.3. Machine Learning Classification

After the fiber clustering white matter parcellation, multiple diffusion features were extracted from each valid fiber cluster (Section 2.3.1) and used separately to inspect their individual discriminative ability in ASD classification. For each feature, we performed a 10-fold cross-validation (Section 2.4), i.e., the feature ranking, the feature selection (Section 2.3.2) and the SVM model training (Section 2.3.3) were conducted using all subjects from all but the left-out subjects, as illustrated in Figure 2(a).

2.3.1. Diffusion Feature Extraction

Diffusion feature extraction was then conducted to quantitatively describe the K valid fiber clusters for each subject. Studies in the literature (Travers et al., 2012; Hoppenbrouwers et al., 2014; Ameis and Catani, 2015) have observed diffusion anisotropy and diffusivity differences, which are generally described by fractional anisotropy (FA) and mean diffusivity (MD) measures, in ASD relative to normal controls. Therefore, in this study we focused on these two measures. In addition to the typical mean FA and MD features along fiber tracts that have been studied in ASD (Catani et al., 2008; Pugliese et al., 2009; Ge et al., 2010; Hong et al., 2011; Langen et al., 2012), we also measured extreme values (minimum and maximum) of FA and MD for each fiber cluster. As recent studies of autism have found local along-tract diffusion differences between ASD and TDC (Johnson et al., 2014; Libero et al., 2015), we extracted these extreme features for the potential to detect local along-tract diffusion changes.

Specifically, for each fiber cluster, FA and MD were computed at each point for both tensors (T1 and T2), and the minimum, mean and maximum values for each measure were calculated. Thus, given the statistics s ∈ {min, mean, max} of the measure m ∈ {FA, MD} of the tensor t ∈ {T1, T2}, a total of 12 features, $f=m_t^s$, were extracted from each cluster. Then, for each feature, each subject was associated with a feature vector that involved K fiber clusters, F_K. Anextension to the 3D Slicer module FiberTractScalarMeasurements was implemented to compute these features.

2.3.2. Feature Ranking and Selection

Selection of a compact discriminatory subset of features is one important step, in particular for high-dimensional data, in machine learning classification tasks for accuracy improvement and better data understanding (Guyon and Elisseeff, 2003) (i.e., which white matter structures were more discriminative in ASD). Therefore, for our machine learning pipeline, we started with a feature ranking and selection to eliminate potential feature redundancy.

Specifically, we employed the signal-to-noise (s2n) ratio coefficient (Golub et al., 1999) for the feature ranking and selection. The s2n ratio has been widely applied in machine learning tasks to improve classification performance, e.g., between genes (Golub et al., 1999; Mishra and Sahu, 2011). It has also been employed and proven efficient in finding discriminative features for ASD classification (Ingalhalikar et al., 2011). Therefore, in our work, we applied s2n to rank each fiber cluster according to its feature values (as introduced in Section 2.3.1) between the TDC and ASD groups and hypothesized that the top ranked clusters could be more discriminative to improve the group classification. Given a certain feature, the s2n ratio was computed for each cluster based on a set of training subjects annotated with ASD (class label 0) or TDC (class label 1). Specifically, for a feature $f=m_t^s$, the s2n ranked the cluster k based on the ratio of the absolute difference of the class means over the average class standard deviation, as:

$$s2n(k)=|\frac{{\mu }_0^k(m_t^s)-{\mu }_1^k(m_t^s)}{{\sigma }_0^k{\left(m_t^s\right)}^2+{\sigma }_1^k{\left(m_t^s\right)}^2}|$$ (1)

where ${\mu }_0^k(m_t^s)$ and ${\sigma }_0^k{\left(m_t^s\right)}^2$ are the mean and variance of the feature across the subjects annotated with ASD (label 0), similarly to ${\mu }_1^k(m_t^s)$ and ${\sigma }_1^k{\left(m_t^s\right)}^2$ for TDC (label 1). It is noted that there can be clusters where some subjects had empty tracts due to tractography noise and/or individual anatomical variability. To avoid any ranking bias towards these empty clusters, the features were set to the mean from the non-empty corresponding tracts across all subjects before computing the s2n ratio.

Feature selection was then conducted by retaining the top ranked clusters that were considered most discriminative between the groups. Assuming R is the number of the selected clusters, each subject was represented as a new feature vector that involved R fiber clusters, F_R. The new feature vectors were then used for the classification. In our experiments, the optimal R was defined as the number that generated the highest classification in a 10-fold cross-validation as discussed in Section 2.4.

2.3.3. Classification with SVM

After the feature selection that retained a small number of clusters (R), we used support vector machine (SVM) to conduct the ASD classification. SVM is one of the most widely used machine learning techniques to classify high-dimensional-feature data in neuroimage analysis (Plant et al., 2010; Dyrba et al., 2013) and has effectively captured the multivariate relationships among anatomical regions in ASD (Lange et al., 2010; Ingalhalikar et al., 2011; Desh-pande et al., 2013; Goch et al., 2014; Mostapha et al., 2015). Briefly, SVM is a supervised classification method and treats each feature vector as a point in a high dimensional space. It classifies the input data into different groups (ASD vs TDC) by identifying a separating hyperplane or decision boundary in the feature space. Here, given the feature vector $F_R^{\mathit{train}}$ and its class label (0 for ASD, 1 for TDC) of each subject in the training set, a SVM model was first trained. The feature vector of a new subject (each left-out subject) $F_R^{\mathit{new}}$ was then fed into the model to predict its class. In our experiments, we used the nu-SVC SVM with polynomial kernel and default parameters (gamma = 1/number of features, coef0 = 0, degree = 3 and cost = 1) from the LIBSVM (Chang and Lin, 2011) toolbox³.

2.4. Cross-validation and Classification Performance Evaluation

We conducted 10-fold cross-validation, which has been suggested as a good cross-validation strategy for accuracy estimation and model selection (Kohavi, 1995; Krstajic et al., 2014), for performance evaluation (Figure 2(a)). In each trial, subgroups (1/10 of the total subjects) of the ASD and TDC subjects were randomly pulled out as a test set, while the remaining were used as a training set for ranking and selecting features and learning the SVM model. The classifier was evaluated based on the predicted label of the left-out test subjects. By repeatedly leaving subjects out for testing and averaging the accuracies over all cross-validation trails, we obtained an average classification accuracy.

To determine an optimal R, we performed the cross-validation for each possible R ∈ [1, K] and obtained an accuracy curve given all R values. The threshold to select the optimal R was the value that generated the highest averaged accuracy in the cross-validation, which corresponded to the smallest cross-validation error (Guyon and Elisseeff, 2003). This analysis has been successfully applied in previous studies (Ingalhalikar et al., 2011; Zhang et al., 2016). Specifically, given a feature $f=m_t^s$, in each cross-validation trial feature ranking and selection was conducted to keep the top R ranked clusters. An SVM model was then trained given these clusters on the training subjects and was used for predicting the test subjects using the corresponding clusters. We then obtained an average accuracy, acc, across all cross-validation trials for this particular R. Repeating the above process given different R values, we obtained an average accuracy curve C = {acc(R)|R ∈ [1, K. The R′ leading to the highest average accuracy on the curve was set to as the optimal setting, and the highest average accuracy was defined as the classification accuracy obtained by the feature f, i.e., acc′.

2.5. Robustly Discriminative Clusters via Multiple Feature Selection

We conducted a multiple-feature-based analysis to assess which fiber clusters were robustly discriminative for classification. The feature ranking and selection (Section 2.3.2) was performed on each individual feature, which retained R′ feature-specific discriminative clusters (for best classification) given the cross-validation process (Figure 2(b)). Here, we selected the clusters that were robustly retained across the features (Figure 2(c)). In detail, for an individual feature $f=m_t^s$, as the retained clusters may slightly vary between the cross-validation trials, we considered the ones that appeared in all cross-validation trials as feature-specific discriminative clusters. Following this, the clusters that were retained for most of the features were selected as robustly discriminative clusters. In the experiments, we selected the clusters that were retained in at least 8 features, which generated a reasonable number (21) of robustly discriminative clusters (Section 3.3 and Figure 8).

Figure 8.

Visual presentation of the robustly discriminative fiber clusters.

For each robustly discriminative cluster, we assessed which brain anatomical regions it may connect to, by comparing its fiber endpoints to a Freesurfer brain parcellation into multiple cortical/subcortical gray matter regions (Fischl, 2012) (Figure 2(d)). We developed a 3D Slicer module FiberEndPointFromLabelMap to calculate the percentage of endpoints per cluster touching the Freesurfer regions. We considered that a cluster was connected to a segmented gray matter region if at least 20% of its endpoints touched it, as the fiber tracking may end in the white matter region near the gray matter parcels. In our experiments, we identified the top two connected gray matter regions across all subjects for most of the robustly discriminative clusters. However, considering there were clusters touching different segmented regions, for several discriminative clusters we also included the third and fourth connected gray matter regions (see Section 3.3 and Table 4).

Table 4.

List of the Freesurfer regions to which the robustly discriminative clusters (Figure 8) connect. The endpoints of the clusters that mostly ended in white matter regions were displayed as empty.

	Color	Region A	Region B
(a)	P	L-SupFron	R-SupFron
	B	L-SupFron	R-SupFron
	Y	L-FronPol	R-FronPol
	R	L-ParsOrb, L-SupFron	R-ParsOrb, R-SupFron
	C†	L-RosMidFron	–
	G	–	R-RosMidFron
(b)	P†	L-PCN	R-PCN
	Y†	L-SupPari	R-SupPari
	G	L-SupPari	R-SupPari
	B	L-PCN, L-SupTemp	R-PCN, R-SupTemp
(c)	Y†	L-RosMidFron, L-ParsOrb	L-SupFron
	R†	L-RosMidFron, L-ParsOrb	L-SM
	P†	L-RosMidFron, L-ParsOrb	L-LatOcci
(d)	G	BS	L-PosCen
	P	BS	L-CAU
	R	BS	L-CAU
(e)	P	L-CBLM	L-PreCen
	Y	L-CBLM	L-CAU
	G†	L-CBLM	L-CAU
(f)	G	R-VDC	R-InfPari
	R	R-VDC	R-RosMidFron

^†indicates the clusters retained in at least 9 features.

Abbreviations: hemispheres, L - left; R - right. Freesurfer regions, BS - brain stem; CAU - caudate; CBLM -cerebellum; FronPol - frontal pole; LatOcci - lateral occipital gyrus; ParsOrb - pars orbitalis; PCN - precuneus; SupPari - superior parietal gyrus; PreCen - precentral gyrus; RosMidFron - rostral middle frontal gyrus; SM - supramarginal gyrus; SupFron - superior frontal gyrus; SupTemp - superior temporal gyrus; VDC - ventral diencephalon.

2.6. Data Acquisition and Tractography

We demonstrate the proposed method using a diffusion weighted imaging (DWI) dataset from 149 pediatric male children (70 ASD, age: 11.0±2.6 and 79 TDC, age: 11.1±2.7). Detailed population demographics are listed in Table 1. This data was acquired at the Center for Autism Research, Children’s Hospital of Philadelphia, with approval of the local ethics board. The diagnoses were made with gold standard research procedures, by consensus by two experienced clinicians. Age distributions did not differ between groups. Overall general conceptual ability (GCA) IQ scores (ASD: 106.1±20.1 and TDC: 110.4±14.9) were not significantly different between the two groups. DWI data were acquired using a Siemens 3T Verio™ scanner with a 32 channel head coil. A monopolar Stejskal-Tanner diffusion weighted spin-echo was used to perform high angular resolution diffusion imaging (HARDI) acquisition (TR/TE = 14.8s/110ms, b = 3000s/mm², 2mm isotropic resolution, and 64 gradient directions). The DWI images were processed using a joint linear minimum mean squared error filter for Rician noise removal. Eddy current correction was performed by registering each DWI volume to the baseline image.

Table 1.

Demographic and neuropsychological variables of the ASD and TDC groups

	ASD	TDC	p-valued
Number of subjects	70 (Male)	79 (Male)	–
Agea	11.0 ± 2.6	11.1 ± 2.7	0.982
GCAb	106.1 ± 20.1	110.4± 14.9	0.140
SRSc	76.9 ± 10.8	41.9 ± 7.0	<0.001

^aAge ranges of the two groups were matched, where the ASD group was from 6.1 to 17.9 years and the TDC group was from 6.3 to 17.7 years.

^bGeneral conceptual ability (GCA) score evaluates the reasoning and conceptual abilities and gives an overall score for IQ (Kotz et al., 2008).

^cSocial responsiveness scale (SRS) score is a standard socio-psychological biomarker indicating social impairments (Constantino et al., 2003).

^dA two sample Student’s t-test was used to derive the p-value.

We conducted whole brain tractography using a two-tensor unscented Kalman filter (UKF) method (Malcolm et al., 2010), as implemented in the ukftractography⁴ package. The UKF method fits a mixture model of two tensors to the diffusion data while tracking fibers, in a recursive estimation fashion (the current tracking estimate is guided by the previous one). The mixture model assumes there are two distinct tract directions within voxels, in which the first one represents the principal direction and the other one is from the second tract. The two-tensor UKF model was shown to be more sensitive than standard single-tensor tractography, in particular in the presence of crossing fibers (Baumgartner et al., 2012; Chen et al., 2015, 2016). In our experiments, tractography was seeded with 10 seeds per voxel (for a more thorough tracking result as suggested in the software), in all voxels within the brain mask where FA was greater than 0.18 (default). Tracking stopped where the FA value fell below 0.22 or the generalized anisotropy (GA) (a normalized variance of the tensor diffusivities in all gradient directions) fell below 0.13. These two stopping thresholds were set slightly above the default values, which were defined for more traditional datasets with a b-value of 1000, while we used DWI data with a higher b-value of 3000. Other parameters were left as default values. This generated about 350,000 fibers for each subject. Visual and quantitative quality control of the tractography was performed using the whitematteranalysis⁵ package.

3. Experimental Results

3.1. White Matter Parcellation Consistency

Figure 3 shows the mean intra- and inter-cluster fiber pair distances (i.e. the mean closest point distance) given the different white matter parcellation atlases (K_b from 400 to 4000). Both intra- and inter-cluster distances were highly similar across the multiple atlases, with lower intra-cluster distances (around 20 mm) compared to the inter-cluster distances (around 70 mm). Under the statistical criterion of the sign test (p < 0.05, corrected), Table 2 shows the numbers of valid clusters (K) per white matter parcellation. About 67% of the clusters were retained after the sign test across all the parcellations. We note that, as expected, most of the excluded clusters were produced by the hemisphere-based separation. Figure 4 shows the percentage of the K valid clusters given the numbers of subjects presenting them. The retained fiber clusters were highly consistent across the subjects. 86.5% of the clusters were detected in at least 140 subjects, and only a small percentage were detected in 109 or fewer subjects. Figure 5 displays some example fiber clusters across subjects. The fiber clustering subdivided the thalamus-to-superior-frontal-gyrus connections into several smaller tracts. The subject-specific clusters were highly similar across subjects indicating a corresponding division of the white matter anatomy.

Figure 3.

The mean intra- and inter-cluster fiber pair distances across the different white matter parcellation atlases under study. The fiber clustering method identified fiber clusters within which the fibers had similar geometric trajectories (i.e. similar white matter anatomy), thus a fiber cluster was considered as anatomically coherent if its intra-cluster fiber distances were low. Across the multiple atlases, the similar mean intra-cluster fiber pair distances suggested that the fiber clustering method could identify highly anatomically coherent white matter subdivisions at different parcellation scales.

Table 2.

The numbers of valid clusters of the different white matter parcellations under study.

Kb	400	800	1200	1600	2000	2400	2800	3200	3600	4000
Ks	1200	2400	3600	4800	6000	7200	8400	9600	10800	12000
K	837	1666	2413	3161	3927	4697	5468	6233	6974	7718

K_b is the number of bilateral clusters; K_s is the number of clusters obtained after hemisphere-based separation; K is the number of valid clusters that were retained after the sign test.

Figure 4.

White matter parcellation consistency of the valid clusters across the population. 86.5% of the valid clusters were detected in at least 140 subjects, while only fewer than 1% were detected in 109 or fewer subjects. The displayed percentage per pie slice is the average value across the multiple parcellations under the different K values.

Figure 5.

Visual presentation of the fiber clusters connecting the thalamus and the superior frontal gyri in a Freesurfer parcellation across multiple subjects. (a) shows the top six clusters connecting the two regions from the white matter parcellation under K=4697, according to the anatomical region assessment process introduced in Section 3.3. (b) shows the corresponding subject-specific clusters across multiple subjects.

3.2. Classification Accuracy

Table 3 displays the classification accuracy given the fiber clustering white matter parcellations at different scales. For each parcellation, we performed ASD classification separately using each of the 12 features and thus obtained 12 classification accuracies (acc′). The average $ac{c}_A^{{ }^{\prime }}$ (across all features) and highest $ac{c}_H^{{ }^{\prime }}$ (feature-specific) accuracies were reported for each K. The best classification performance was obtained when K = 4697, with the average and highest accuracies of 70.64% and 78.33%. Other classification performance measurements, corresponding to the best classification accuracy, were computed, as sensitivity = 84.81%, specificity = 72.86%, positive predictive value = 77.91% and negative predictive value = 80.95%. Please see the video included in the supplementary material for a visualization of each individual fiber cluster within this atlas (K = 4697).

Table 3.

Classification accuracies given the white matter parcellations at different scales.

K	837	1666	2413	3161	3927	4697	5468	6233	6974	7718
$ac{c}_A^{{ }^{\prime }}$	66.70±4.58	68.02±4.00	68.89±4.39	69.39±4.62	70.03±4.50	70.64±4.23	69.68±5.26	69.80±4.74	69.67±4.98	67.26±5.29
$ac{c}_H^{{ }^{\prime }}$	74.74	75.21	75.88	76.50	77.02	78.33	77.54	76.40	76.50	75.52

Average $ac{c}_A^{{ }^{\prime }}$ (± standard deviation) (across all features) and highest $ac{c}_H^{{ }^{\prime }}$ (feature-specific) accuracies are shown. The number of valid clusters K corresponds to that displayed in Table 2.

The K values from 3927 to 5468 were considered better given the different parcellations under study. Dividing the whole brain tractography into more or fewer clusters tended to decrease the classification performance. Outlier removal was employed in creating the atlas for the purpose of improving cluster consistency by removing any anatomically incoherent fibers. Experiments demonstrated insensitivity of the machine learning to the fiber outlier removal (under 2% change in average classification accuracy across the multiple parcellations under study).

Figure 6 shows the classification accuracies obtained from the multiple features. $F{A}_{T2}^{\mathit{mean}}$ generated overall best classification results, with the highest mean and a relatively small standard deviation. The accuracy from $F{A}_{T2}^{\mathit{max}}$ was the second best, which was close to that from $F{A}_{T2}^{\mathit{mean}}$. In addition, higher accuracies were obtained using the extreme features from FA_T1, MD_T1 and MD_T2 when compared to their corresponding mean feature.

Figure 6.

Classification accuracies given the different features. The bar and error bar indicate the mean and standard deviation across the different K values.

3.3. Robustly Discriminative Clusters

To identify the most discriminative fiber clusters given the multiple feature selection, we used the white matter parcellation of K=4697, which generated the best accuracies (Table 3). Figure 7 gives the average accuracy curve C of the multiple features for this parcellation. For each feature, the feature-specific discriminative clusters were the top R′ ones that generated the highest average cross-validation accuracy acc′ (annotated in blue). To measure the feature weight stability, we computed the number of clusters that were consistently selected as the top ranked R clusters per feature across the 10-fold trials. For example, for the $F{A}_{T1}^{\mathit{min}}$, 654 clusters (91.7%) of the top R′= 713 clusters across the 10-fold trials were consistently selected. Across all the diffusion features, the average percentage of the clusters that were consistently identified was 92.6%, showing a high stability of the s2n feature weighting across the validation runs. We selected the clusters that were retained in at least 8 (out of the 12) features as the most discriminative ones. We chose the threshold of 8 to produce a reasonable number of robustly discriminative clusters, i.e., a total of 21 clusters as displayed in Figure 8. Table 4 lists the Freesurfer cortical/subcortical regions to which the clusters connect. A lower threshold of the number of features retained a larger number of fiber clusters. For example, the number of retained clusters in at least 7 features was 116. On the other hand, a higher threshold value led to only a small number of retained clusters. As shown in Figure 7, several features, such as $F{A}_{T1}^{\mathit{min}}$ and $F{A}_{T2}^{\mathit{min}}$, have relatively small optimal R′ values, which reduced the total possible retained clusters across features. We found only 7 retained clusters in at least 9 features (annotated in Table 4) and did not obtain any clusters that were retained in 10 or more features.

Figure 7.

Average classification accuracy given the number of selected clusters R. The blue circle indicates the highest average cross-validation accuracy that was obtained using the optimal number of clusters R′.

To evaluate which features from the robustly discriminative clusters were most informative between the two groups, we identified the 8 features for each cluster that were used to retain this cluster. Across the 21 clusters, the most widely used features (i.e. the most informative features) included $F{A}_{T1}^{\mathit{max}}$, $M{D}_{T2}^{\mathit{min}}$, $F{A}_{T2}^{\mathit{mean}}$, $M{D}_{T2}^{\mathit{max}}$ and $F{A}_{T2}^{\mathit{max}}$ that were used by 16, 16, 14, 12 and 11 clusters respectively. These features in general corresponded to the ones that had the best classification accuracies (Figure 6).

Among the 21 robustly discriminative fiber clusters, nearly half (10/21) belonged to the corpus callosum, which were mainly from the anterior (Figure 8(a)) and posterior (Figure 8(b)) regions. Three clusters that were potentially from the uncinate fasciculus (Figure 8(c), purple), the aslant tract (Figure 8(c), yellow) and the arcuate fasciculus/superior longitudinal fasciculus (Figure 8(c), red) were identified. We also found clusters related to the brain stem (Figure 8(d)) and the cerebellum (Figure 8(e)). There were also two clusters connecting to the ventral diencephalon (Figure 8(f)).

4. Discussion

In this paper, we presented a machine learning method based on groupwise data-driven fiber clustering to differentiate whole brain white matter connectivity patterns. We demonstrated the method’s performance with an application of ASD/TDC classification. We have several overall observations about the results. We observed that fine white matter parcellations (K from 3927 to 5468) tended to provide higher classification accuracy, likely due to the fact that the extracted diffusion features could be more specific to smaller scale subdivisions of the white matter anatomy. For example, we found one discriminative cluster (Figure 8(d), green) that comprised only a small portion of the whole corticospinal-tract pathway. We also observed that the 12 measured diffusion features performed differently for the ASD classification. We found that the mean FA feature from the second tensor ( $F{A}_{T2}^{\mathit{mean}}$) was the most effective in classifying the two groups. The two-tensor UKF model enables tracking through crossing fiber regions, where the crossing fibers are mainly represented by the second tensor (Malcolm et al., 2010). Thus the highest classification accuracy from $F{A}_{T2}^{\mathit{mean}}$ could suggest that the diffusion anisotropy in crossing fiber regions was affected in ASD. Furthermore, analyzing the extracted fiber clusters we noticed that the maximum FA and minimum MD features normally corresponded to a more middle/core fiber tract region, while the minimum FA and maximum MD features were more likely to appear at the endpoint regions of the fibers. This was in accordance with the relatively well-known along-tract FA and MD patterns (Colby et al., 2012; O’Donnell et al., 2009). Among these extreme features, $F{A}_{T1}^{\mathit{min},\mathit{max}}$, $M{D}_{T1}^{\mathit{min},\mathit{max}}$ and $M{D}_{T2}^{\mathit{min},\mathit{max}}$ obtained higher accuracies when compared to their corresponding mean features. Thus our results suggest potential alterations in diffusion not only in the overall fiber mean features, but also in the central cores of the fiber tracts and at the white matter/gray matter interface.

Most of the robustly discriminative clusters found here correspond to fiber tracts that have been previously implicated in ASD, such as fiber tracts related to corpus callosum (Alexander et al., 2007; Hong et al., 2011), cerebellum (Catani et al., 2008), brain stem (Travers et al., 2015a), uncinate fasciculus (Pardini et al., 2012), arcuate fasciculus (Fletcher et al., 2010), superior longitudinal fasciculus (Nagae et al., 2012) and aslant tract (Lo et al., 2016). We note that the discriminative clusters may include or connect to only part of these structures, and that clusters can potentially combine fibers from more than one anatomical structure. For example the red colored cluster in Figure 8(c) may include parts of arcuate fasciculus and superior longitudinal fasciculus, and thus may not be specific to either structure. Additional related findings in ASD can be found in (Travers et al., 2012; Hoppenbrouwers et al., 2014; Ameis and Catani, 2015). We also found two discriminative clusters related to the ventral diencephalon (Figure 8(f)). A larger volume of diencephalon (including thalamus and ventral diencephalon) was reported in ASD when compared to controls (Herbert et al., 2003). However, we were not able to find any previous work on white matter fiber tracts related to the ventral diencephalon.

These white matter tracts were obtained using the multi-fiber UKF tractography, which has been shown to be more sensitive in tracking through the regions in the presence of crossing fibers (Baumgartner et al., 2012; Chen et al., 2015, 2016). This could reduce the well-known tractography problem of missing fiber error and enable investigation of more white matter connections. For example, we found discriminative corpus callosum clusters following the lateral paths to the pars orbitalis gyri (Figure 8(a)) and to the temporal lobe (Figure 8(b)); however, these white matter tracts can hardly be tracked in a basic single-tensor streamline method (Malcolm et al., 2010). Given the diffusion features extracted from the multi-fiber tractography, we compared the average feature value across the identified discriminative clusters between the two groups. Feature change directions of the discriminative clusters in mean and maximum FA, as well as mean and minimum MD, were in line with the general findings of decreased anisotropy and increased diffusivity in many ASD studies using dMRI (Travers et al., 2012; Hoppenbrouwers et al., 2014; Ameis and Catani, 2015). On the other hand, higher minimum FA and lower maximum MD of the discriminate clusters suggested potentially increased anisotropy and decreased diffusivity at fiber endpoint regions in ASD.

The aforementioned discriminative clusters may imply potential altered brain functions in ASD. With reference to a 7-region corpus callosum subdivision (CC1 to CC7) (Makris et al., 1999), among the 6 anterior corpus callosum clusters, we found one from the anterior half of the body of the callosal commissure (CC3) while the others were from the rostrum (CC1) and genu (CC2). The CC3 cluster connected to the supplementary motor area that is related to planning and initialization of movement activities. In addition, we observed more left hemisphere lateralized white matter alterations in ASD. There were discriminative clusters connecting to the left precentral and postcentral gyri, which suggest potential motor and somatosensory function alteration in ASD. We also found several discriminative clusters connecting to the left pars orbitalis region that potentially indicate language processing abnormality in ASD. These potential altered functions in ASD have been reported in previous studies (Hong et al., 2011; D’Mello and Stoodley, 2015; Travers et al., 2015a; Herbert et al., 2005; Nagae et al., 2012; Pardini et al., 2012; Fletcher et al., 2010). Our results were consistent with these research outputs, but we demonstrated these clusters using a whole brain analysis, which suggested their related functions could be more affected than other altered white matter connections.

In related work, multiple methods have been applied to study dMRI in ASD. The first category has focused on identifying group differences between ASD and TDC groups using statistical analysis. Traditional hypothesis-driven studies of dMRI have been conducted based on region-of-interest (ROI) methods to identify regional white matter structural abnormalities in ASD (Brito et al., 2009; Alexander et al., 2007; Pardini et al., 2012; Travers et al., 2015b). Other studies have applied voxel-based approaches, such as voxel-based morphometry (VBM) (Cheung et al., 2009; Keller et al., 2007) and tract-based spatial statistics (TBSS) (Billeci et al., 2012; Cheon et al., 2011), for whole brain white matter analysis. Tractography-based analysis has enabled measurement of macrostructural white matter tract properties for a more detailed investigation of specific subpopulations of fibers. Tract-of-interest studies (Catani et al., 2008; Pugliese et al., 2009; Ge et al., 2010; Hong et al., 2011; Langen et al., 2012; Wolff et al., 2012) using tractography have identified atypical white matter structures in ASD.

Another category of dMRI-based studies, to which our proposed method belongs, has focused on applying machine learning methodology to classify ASD/TDC for diagnostic prediction. Unlike the statistical analysis methods that aim to find white matter structures with statistical group difference, the machine-learning-based methods aim to offer predictive diagnostic relevance. Multiple approaches have been proposed to address this challenging problem. Several groups have employed a priori knowledge of affected regions specific to autism pathology to define white matter regions of interest for classification (Adluru et al., 2009; Lange et al., 2010; Deshpande et al., 2013), while other work has used volumetric regions of interest located throughout the whole white matter (Ingalhalikar et al., 2011). Additional whole white matter approaches have studied fiber tracts by employing cortical-parcellation-based (CPB) segmentation of tractography. This has enabled measurement of graph theoretic measures derived from connectome matrices, e.g. average node degree that describes the number of tracts connecting cortex parcels (Goch et al., 2014), as well as extraction of diffusion features for description of the whole brain white matter connectivity (Mostapha et al., 2015). To characterize white matter connections for analysis, the most common method has adopted mean diffusion features within fiber tracts for an overall description. For example, mean FA and/or MD were applied (Lange et al., 2010; Mostapha et al., 2015) to perform ASD classification. In contrast to the above approaches, our method has extracted multiple FA and MD features in a multi-fiber model, and we employed a study-specific fiber clustering tractography segmentation of the whole white matter, which has been suggested to be more consistent in finding corresponding white matter parcels across subjects compared to the CPB method (Zhang et al., 2017b). Our previous research work has also shown the fiber clustering method’s high repeatability performance in terms of spectral embedding stability (O’Donnell and Westin, 2007), fiber cluster reproducibility at different parcellation scales (O’Donnell, 2006) and segmentation consistency across multiple populations (O’Donnell et al., 2017; Zhang et al., 2017b). In addition, our proposed multiple feature analysis provides a way to identify potential local along-tract abnormalities, such as in the central cores of fiber tracts and at the white matter/gray matter interface.

One benefit of the data-driven fiber clustering method is that it allows a white matter parcellation into a large number of fiber clusters. Fine scale brain parcellations have been suggested to provide better description of locally specific brain regions compared to coarse-grained parcellations (Hagmann et al., 2008; van den Heuvel et al., 2008; Liu et al., 2017). One goal of this study is to determine an optimal white matter parcellation (i.e. an optimal number of fiber clusters K) based on a certain real-world problem. Choosing the optimal K for anatomical fiber clustering is a challenge, because many white matter structures are relatively continuous with no clear boundaries, while different structures have different size scales. Optimal white matter subdivision thus depends on the desired application (such as visualization, which can benefit from fewer clusters, or quantitative measurement, which can benefit from finer subdivisions thus more clusters). Our previous work has determined a reasonable value (K ≥ 200) by testing clustering and embedding reproducibility in single-tensor tractography (O’Donnell and Westin, 2007) and by empirically determining a value (K ≥ 800) that could separate structures considered to be anatomically different according to expert judgment using sensitive multi-fiber tractography (O’Donnell et al., 2017). Many spectral clustering techniques have been proposed for automatic determination of an optimal K by analyzing eigenvectors of the embedding matrix (Sanguinetti et al., 2005; Zelnik-Manor and Perona, 2005). However, without including prior knowledge about brain anatomical subdivisions of interest, such an automated decision could potentially prevent a finer parcellation into more locally specific subdivisions. In this work, we investigated multiple parcellations at different scales and determined an optimal K value in a machine learning pipeline by identifying local white matter differences that could differentiate the two groups to the largest extent.

Potential future directions and limitations of the current work are as follows. First, we applied the feature statistics of minimum, mean and maximum to approximately locate along-tract abnormality. Advanced feature descriptions, which can characterize along-tract feature distributions and locate exact abnormality position, will potentially increase the discriminative ability of a fiber cluster in differentiating different populations. For example, our and other research groups have utilized features, such as percentile feature along fiber tract (Zhang et al., 2016), return-to-the-origin probability (RTOP) feature from multiple-shell-dMRI-based tractography (Zhang et al., 2017c), and along-tract diffusion distribution feature (Colby et al., 2012), to study between-group white matter alterations. Also, the number of fibers within fiber tracts has been used to measure structural connectivity differences between ASD and other developmental disorders (Conti et al., 2017). These features and many others provide diffusion property descriptions from different perspectives, thus are expected to extend and improve the proposed method to study other neurological diseases/disorders. In addition, the study ASD and TDC populations were matched on age, gender and IQ so that the two groups did not differ on these factors. Therefore, we did not conduct feature control on these variables that could be mediated by brain connectivity. However, controlling features could reduce their influence to focus on the neuropathology of autism to a greater extent. For example, diffusion parameters change rapidly during childhood and adolescence and such age-related changes could provide important longitudinal information to study brain white matter. Third, in this study, we created one fiber clustering atlas from the whole population so that the same atlas was used in all cross-validation runs (which enabled identification of discriminative clusters in the population). A future investigation could include building an atlas from a separate cohort or applying a leave-testing-subjects-out atlas creation approach to further cross-validate the machine-learning-based classification. However, for our current study, we believe that the usage of the whole-population-based atlas should have effects that were too minimal to generate any subject biases during the cross-validation, given the facts that the atlas was created from a large population (evenly distributed groups with matched ages and same genders), and the atlas only used the geometric information from a small subset of the tractography per subject (5,000 fibers per subject or on average 1.5% of the fibers from each subject). Fourth, to investigate focal diffusion measurements corresponding to small parcels of the white matter, we created fine scale white matter parcellations therefore higher dimensional features (e.g. K = 4697). These feature dimensions were relatively higher than the sample size (n = 149) thus potentially introduced model overfitting or subject bias. In our current study, we applied a 10-fold cross-validation approach with a feature selection process to reduce any potential overfitting or subject bias effects from the high feature dimensions. However, a further study could include an investigation of the method using a larger cohort. Fifth, the more sensitive UKF tracking method may introduce more false positive or anatomically incorrect errors compared to a standard fiber tracking method. While it is commonly considered impossible to assess the existence of such errors without ground truth, we believe our outlier removals have ameliorated the false positive fibers to a certain extent. The groupwise fiber trajectory-based computation can naturally enable the rejection of the fibers that were improbable (trajectory-dissimilar) in the cluster. However, this method cannot remove apparent tractography errors that are present in all subjects while being inconsistent with expected anatomy. For instance, in Figure 8(e) we found fiber clusters connecting the cortex and cerebellum in the same hemisphere.

5. Conclusion

In this paper, we have demonstrated a fiber-clustering-based whole brain white matter connectivity analysis with the application of automated ASD classification. Our results indicate the potential of a machine learning pipeline based on white matter fiber clustering. The method enables high white matter parcellation consistency across the population and assessment of alterations in multiple diffusion features. The proposed method may provide a general framework for observing white matter connectivity alterations between disordered and control groups. In addition, the method works in data-driven manner to identify tracts that may be most affected by pathology in whole-brain tractography. This allows further hypothesis-driven research on certain white matter structures from the whole brain. We note the related software is publicly available, enabling its future application to other diffusion MRI datasets.