Tools for multiple granularity analysis of brain MRI data for individualized image analysis

Highlights

• We develop a new approach for analyzing neuroanatomical images.

• Our approach uses a multiple-atlas algorithm to automatically parcellate the brain.

• Our approach utilizes ontology-based hierarchical structural relationships.

• Our approach examines the brain anatomy from multiple granularity levels.

• Our approach is suitable for phenotype analysis of individual patients.

Abstract

Voxel-based analysis is widely used for quantitative analysis of brain MRI. While this type of analysis provides the highest granularity level of spatial information (i.e., each voxel), the sheer number of voxels and noisy information from each voxel often lead to low sensitivity for detection of abnormalities. To ameliorate this issue, granularity reduction is commonly performed by applying isotropic spatial filtering. This study proposes a systematic reduction of the spatial information using ontology-based hierarchical structural relationships. The 254 brain structures were first defined in multiple (n = 29) geriatric atlases. The multiple atlases were then applied to T1-weighted MR images of each subject's data for automated brain parcellation and five levels of ontological relationships were established, which further reduced the spatial dimension to as few as 11 structures. At each ontology level, the amount of atrophy was evaluated, providing a unique view of low-granularity analysis. This reduction of spatial information allowed us to investigate the anatomical features of each patient, demonstrated in an Alzheimer's disease group.

Introduction

Analysis of images from multiple subjects necessitates that, first and foremost, anatomically corresponding structures are identified across the subjects. The region-of-interest (ROI) approach, in which specific target structures, such as the hippocampus, are manually defined, is the most widely used approach and is considered to be the gold standard in the field of quantitative neuroanatomy. This approach however, is time-consuming and is applicable only to a small portion of anatomical structures. For example, with a 1 mm isotropic spatial resolution, a brain with a 1.2 L volume would have 1.2 million voxels. The hippocampus volume is typically about 4000 voxels (4 ml), meaning only 0.3% of the voxels are evaluated. An alternative approach is voxel-based analysis (VBA), in which correspondence is established automatically across all 1.2 million voxels between the two brains (see e.g., Ashburner and Friston, 2000). Suppose we have 50 control and 50 patient images. The entire dataset can be expressed as two matrices of [(50 subjects) × (1.2 million voxels)]_{Control, Patient}. This voxel-vector (of 1.2 million voxels) needs to be re-ordered, such that any arbitrary vector element, say, the i^th voxel of the 1.2 million-element vector, identifies the same anatomical location across the 100 subjects. Then, we can contract the 50-element population dimension to the average and the standard deviations; the two matrices are now [(average, standard deviation) × (1.2 million voxels)]. The actual measurements could be voxel intensity (e.g., T2, fractional anisotropy, mean diffusivity) or morphometric parameters representing local atrophy or hypertrophy (e.g., Jacobian). This contraction now enables us to perform a t-test at each voxel, identifying voxels with significantly different values between the two populations.

Voxel-based analysis is powerful because it retains the maximum amount of location information until the final statistical analysis; the entire brain is examined at the highest granularity level, i.e., 1.2 million voxels. However, the limitations of this approach are also widely recognized (see e.g., Davatzikos, 2004). First of all, the information each voxel carries is noisy. This issue is magnified by that fact that there are 1.2 million intricately dependent observations. Second, the accuracy of voxel-based registration is not guaranteed (the 1.2 million voxel-vectors may not be well-aligned across subjects). This lack of accuracy can be attributed to two sources: 1) lack of contrast—the voxel-to-voxel mapping between two corresponding regions is not accurate if the regions lack contrast; and 2) anatomical heterogeneity—excessive anatomical variability in certain areas, such as cortical folding, could prevent us from accurately identifying corresponding voxels between two brains in such areas. To ameliorate the issue of noise, we typically reduce the level of granularity by applying a uniform spatial filter, effectively reducing the image resolution through voxel averaging (Fig. 1).

In this study, we provide tools to analyze the 50 × 1,200,000 matrices using an alternative approach. In many clinical studies, even if the patient population is as homogenized as possible by stringent clinical criteria, a considerable amount of anatomical and, potentially, pathological heterogeneity remains. Our primary interest is, therefore, to characterize the anatomical heterogeneity within a patient group. Different patients may have abnormalities in different locations. If so, our interest is the first subject dimension (e.g., n = 50) of the matrices, and the group-aggregated statistics (reduction of the average and standard deviation) at each location are no longer appropriate for analysis. This naturally leads us to an alternative concept, which is the reduction of the second dimension (n = 1,200,000). In VBA, this is achieved by spatial filtering. While this is an effective approach, the level of granularity remains high (2300) even with an 8³ reduction of voxel size, and considerable amount of anatomical information is lost. To address these issues, we used an alternative approach, in which voxels are not grouped uniformly according to spatial proximity, but rather, according to pre-defined anatomical criteria called atlases.

This anatomy-specific filtering based on a pre-defined atlas, however, has several issues. First, the number of defined structures is limited by available image contrasts. T1-based contrast could define up to several hundred structures. If there are 300 defined structures, each structure has, on average 4000 voxels. Compared to VBA, the level of granularity is substantially low, potentially making the measurement insensitive to highly localized abnormalities. Second, there are multiple criteria by which to define structures, and, depending on pathology, different criteria may be used. For example, for vascular diseases, brain parcellation based on the vascular territories may make more sense than classical ontology-based brain parcellation. Third, the accuracy issues of VBA due to the lack of the contrasts and cross-subject variability still exist for the structure-based analysis, although they may influence the results in different ways. Once the voxels are grouped to define a structure, the location information of each voxel inside the structure degenerates and there is no longer a voxel-wise accuracy issue. Instead, it manifests as the accuracy of the boundary definition.

In this study, we developed a tool that can flexibly change the granularity level based on the hierarchical relationships of 254 structures defined in our atlas. We tested this tool within the framework of a multiple-atlas brain parcellation algorithm (Aljabar et al., 2009, Artaechevarria et al., 2009, Heckemann et al., 2006, Langerak et al., 2010, Lotjonen et al., 2010, Rohlfing et al., 2004, Warfield et al., 2004). Using 29 pre-parcellated atlases, test data were automatically parcellated into the smallest structural units (254 structures). Then, these structures were dynamically combined at five different hierarchical levels, down to 11 structures (Mai et al., 2007, Puelles et al., 2013). This provides a flexible view to evaluate brain anatomy at multiple granularity levels. This tool was first applied to a control group to measure test–retest reproducibility and normal range of anatomical variability. Then, we analyzed Alzheimer's disease (AD) patients for demonstration purposes.