Analysis Framework

The goal of both studies is the identification of population level differences in WM orga- nization. This is facilitated through two analyses paradigms. The first strives to identify differences in the local WM architecture, while the second, utilizes network models of brain connectivity to identify differences in structural connectivity patterns and topology. Each of these approaches is described below, as is the model fitting procedure that serves as the starting point for both paradigms.

6.2.1. Imaging Datasets

The imaging dataset used in the SCZ study consists of a 64 direction, b = 1000 s/mm2, DW-MRI acquisition acquired on 66 patients (37 Males/29 Females) diagnosed with SCZ as well 66 (37 Males/29 Females) age-matched control subjects. While the low b-value is not ideal for HARDI modeling, this approach provides a unique ability to compare and contrast the ability of each model for identify group differences in-vivo.

The ASD dataset consists of two DW-MRI acquisitions acquired on 39 subjects diagnosed with ASD (30 Males/9 Females) as well as 27 (14 Males/13 Females) age-matched typ- ically developing children (TDC). The first acquisition, an optimized 30 direction, b = 1000 s/mm2, DTI acquisition was acquired enabling the computation of DTI images for each subject. The second was a 64 direction, b = 3000 s/mm2 acquisition, facilitating the computation of the FOD in a more optimal setting. Structural MP-RAGE acquisitions were also performed on each subject, in both studies, facilitating tissue segmentation. Please see Sections A.1.1and A.1.2for complete descriptions of the two datasets.

6.2.2. Model Fitting & Registration

Images from each subject underwent the preprocessing and model fitting procedures, dis- cussed in SectionA.2. Briefly, this process consisted of Rician and eddy current correction performed on each DWI dataset, followed by DT and FOD model fitting. In the case of the SCZ dataset both models were fit to theb= 1000 s/mm2 set of DWIs, whereas in the ASD study, the FOD was fit to the set of b = 3000 s/mm2 DWIs. Structural images were first corrected for field inhomogeneity and segmented into WM, GM and CSF. The resulting images were rigidly registered to the FOD space, yielding co-registered, DT, FOD image and tissue segmentation images for each subject.

A single subject from each study was chosen to act as that study’s template. A 37 year old male subject was chosen to act the registration template for the SCZ study and a 10 year old male was chosen for the ASD study. The FOD-Demons registration method described in Chapter3was used to align the FOD images of both populations while the DTI-DROID [88] registration algorithm was used to align the DT images.

6.2.3. Regional WM Architecture

From the registered DTI and FOD images of each subject, a number of scalar measures can be computed and used to represent the local WM architecture at each location. From the FOD images, we compute the spectral power of each of the five orders (l levels) of the RSH expansion of the FOD, using equation B.3, yielding five scalar images, P0, P2, P4, P6 and P8, corresponding to the even RSH orders. Additionally the generalized fractional anisotropy (GFA) [172] of the FOD at each voxel, x, is computed as:

GF A(x) = std(f) rms(f) = s nPn i=1(f(ui)−f¯)2 (n−1)Pn i=1f(ui)2 (6.1)

where{ui} are a set of (n= 1000) sampling directions,f(ui) and ¯f, are the FOD values in theuith direction and the average value off. This yields six scalar images computed from each subject’s FOD images.

ASD Atlas _{SCZ Atlas}

Figure 6.1: Population atlases generated from the control populations of the ASD and SCZ studies. Different parameters were used to compute the voxel similarities (equation 4.2) to control for difference characteristics of the population averaged FOD images. The ASD atlas was generated using σf = 0.08 and σs = 6 mm, while the SCZ atlas used σf = 0.12 and σs= 6 mm.

To serve as a comparison, two common DTI-based scalars were also computed:

F A(x) = s 3 2 (λ1−¯λ)2+ (λ2−¯λ)2+ (λ3−¯λ)2 λ2 1+λ22+λ23 T R(x) = 3ADC(x) = 3 ¯λ=λ1+λ2+λ3

whereλ1,λ2 and λ3 are the eigenvalues of the DT at voxel x.

WM Atlas Generation

For both control populations, average FOD images were computed and parcellated using the method described in Chapter 4. The process generated two atlases, each consisting of 500 ROIs. The generation of both atlases usedσs= 6 mm to control the spatial component of the similarity kernel (Equation4.2). However different values ofσf were chosen to account for the different characteristics, due to the difference in b-value, of the population average FOD images. The SCZ atlas usedσf = 0.12, while the ASD atlas usedσf = 0.08. Representative slices of each can be seen in Figure 6.1. For each ROI defined, regional averages of the above computed scalars were collected into a feature vector used to represent the particular

ROI. This process reduces the dimensionality of each subject’s representation from 8 scalar images of roughly 80,000 voxels to 500 feature vectors, each vector representing a single ROI.

6.2.4. Structural Connectivity

Structural connectivity networks are computed by first defining, in the template space, the GM regions that will serve as network nodes. This was accomplished by segmenting each study’s template structural image, into GM, WM, CSF, using Freesurfer [55] software package. This process also segments the cortical and sub-cortical GM into regions defined in the Desikan atlas [50]. Connectivity networks, using these 86 regions as nodes, were then generated using the methods developed in Chapter5.

From these networks, five global scalars are computed1 and used to capture the topological properties of the structural connectivity networks:

1. The characteristic path length is the average shortest path length between all pairs of nodes and is commonly used as a measure of network integration.

2. Global efficiency is defined as the average inverse shortest path length. Like the characteristic path length, global efficiency is a measure of network integration. It is, however, more heavily influenced by shorter paths than the characteristic path length which is heavily influenced by long paths.

3. Network Density is the ratio of number of present connections to possible connections and is a measure of the overall degree of connectivity in the network.

4. Modularity quantifies the degree to which the network can be subdivided into clearly delineated non-overlapping groups. This approach seeks to define modules that max- imize the number of intra-module edges and minimize inter-module edges.

1

Topological features are computed from their weighted undirected definitions, using the brain- connectivity- toolbox [141]

5. Transitivity is a simpler approach to quantitate the modularity of a network. It is based on the average number of triangles, occurring when a node’s connected neighbors are also connected to one another.

6.2.5. Processing Summary

These two processing approaches allow the connectivity of each subject to be investigated at a number of levels. At the voxel and regional level, the WM architecture can be investigated using the five spectral powers of the FOD and the GFA. At a global or systems level, the network connectivity structure can be investigated based on the topological properties or on the basis of individual network connections.