Brain morphometry

This article uses direct referencing.

As a subfield of both morphometry and the brain sciences, brain morphometry (or neuromorphometry, particularly in the earlier literature, e.g. Haug 1986) is concerned with the quantification of anatomical features in the brain, and changes thereof, particularly from ontogenetic and phylogenetic perspectives. These features include whole-brain properties like shape, mass, volume, encephalization quotient, the distribution of grey matter and white matter as well as cerebrospinal fluid but also derived parameters like gyrification and cortical thickness or quantitative aspects of substructures of the brain, e.g. the volume of the hippocampus, the relative size of the primary versus secondary visual cortex, the amount of neurons in the optic tectum or of Dopamine D1 receptors in neurons in the mouse basal ganglia.

There are two major prerequisites for brain morphometry: First, the brain features of interest must be measurable, and second, statistical methods have to be in place to compare the measurements quantitatively. Shape feature comparisons form the basis of Linnaean taxonomy, and even in cases of convergent evolution or brain disorders, they still provide a wealth of information about the nature of the processes involved. Shape comparisons have long been constrained to simple and mainly volume- or slice-based measures but profited enormously from the digital revolution, as now all sorts of shapes in any number of dimensions can be handled numerically.

In addition, though the extraction of morphometric parameters like brain mass or liquor volume may be relatively straightforward in post mortem samples, most studies in living subjects will by necessity have to use an indirect approach: A spatial representation of the brain or its components is obtained by some appropriate neuroimaging technique, and the parameters of interest can then be analysed on that basis. Such a structural representation of the brain is also a prerequisite for the interpretation of functional neuroimaging data (e.g. Anticevic et al., 2008).

Biological background

The morphology and function of a complex organ like the brain are the result of numerous biochemical and biophysical processes interacting in a highly complex manner across multiple scales in space and time (Vallender et al., 2008). Most of the genes known to control these processes during brain development, maturation and aging are highly conserved (Holland, 2003), though some show polymorphisms (cf. Meda et al., 2008), and pronounced differences at the cognitive level abound even amongst closely related species, or between individuals within a species (Roth and Dicke, 2005).

In contrast, variations in macroscopic brain anatomy (i.e. at a level of detail still discernable by the naked human eye) are sufficiently conserved to allow for comparative analyses, yet diverse enough to reflect variations within and between individuals and species: As morphological analyses that compare brains at different ontogenetic or pathogenetic stages can reveal important information about the progression of normal or abnormal development within a given species, cross-species comparative studies have a similar potential to reveal evolutionary trends and phylogenetic relationships, though the concept of progression has to be used with caution here, especially when considering contemporary species.

Study design

The design of a brain morphometric study depends on multiple factors that can be roughly categorized as follows: First, depending on whether ontogenetic, pathological or phylogenetic issues are targeted, the study can be designed as longitudinal (within the same brain, measured at different times), cross-sectional (across brains). Second, brain image data can be acquired using different neuroimaging modalities. Third, brain properties can be analyzed at different scales (e.g. in the whole brain, regions of interest, cortical or subcortical structures). Fourth, the data can be subjected to different kinds of processing and analysis steps. Brain morphometry as a discipline is mainly concerned with the development of tools addressing this fourth point and integration with the previous ones.

Methodologies

With the exception of the usually slice-based histology of the brain, neuroimaging data are generally stored as matrices of voxels. The most popular morphometric method, thus, is known as Voxel-based morphometry (VBM; cf. Wright et al., 1995; Ashburner and Friston, 2000). Yet as an imaging voxel is not a biologically meaningful unit, other approaches have been developed that potentially bear a closer correspondence to biological structures: Deformation-based morphometry (DBM), surface-based morphometry (SBM) and fiber tracking based on diffusion-weighted imaging (DTI or DSI). All four are usually performed based on Magnetic Resonance (MR) imaging data, with the former three commonly using T1-weighted and sometimes T2-weighted pulse sequences, and DTI/DSI diffusion-weighted ones.

T1-weighted MR-based brain morphometry

Preprocessing

MR images are generated by a complex interaction between static and dynamic electromagnetic fields and the tissue of interest, namely the brain that is encapsulated in the head of the subject. Hence, the raw images contain noise from various sources -- namely head movements (a scan suitable for morphometry typically takes on the order of 10 min) that can hardly be corrected or modeled, and bias fields (neither of the electromagnetic fields involved is homogeneous across the whole head nor brain) which can be modeled.

In the following, the image is segmented into non-brain and brain tissue, with the latter usually being sub-segmented into at least gray matter (GM), white matter (WM) and cerebrospinal fluid. Since image voxels near the class boundaries do not generally contain just one kind of tissue, partial volume effects ensue that can be corrected for.

For comparisons across different scans (within or across subjects), differences in brain size and shape are eliminated by spatially normalizing (i.e. registering) the individual images to a the stereotactic space of a template brain. Registration can be performed using low-resolution (i.e. rigid-body or affine transformations) or high-resolution (i.e. highly non-linear) methods, and templates can be generated from the study's pool of brains, from a brain atlas or a derived template generator.

Both the registered images and the deformation fields generated upon registration can be used for morphometric analyses, thereby providing the basis for Voxel-Based Morphometry (VBM) and Deformation-Based Morphometry (DBM). Images segmented into tissue classes can also be used to convert segmentation boundaries into parametric surfaces, the analysis of which is the focus of Surface-Based Morphometry (SBM).

Voxel-based morphometry

After the individual images were segmented, they are registered to the template. Each voxel then contains a measure of the probability, according to which it belongs to a specific segmentation class. For gray matter, this quantity is usually referred to as gray matter density (GMD) or gray matter concentration (GMC), or gray matter probability (GMP).

In order to correct for the volume changes due to the registration, the gray matter volume (GMV) in the original brain can be calculated by multiplying the GMD with the Jacobian determinants of the deformations used to register the brain to the template. Class-specific volumes for WM and CSF are defined analogously.

The local differences in the density or volume of the different segmentation classes can then be statistically analyzed across scans and interpreted in anatomical terms (e.g. as gray matter atrophy). Since VBM is available for many of the major neuroimaging software packages (e.g. FSL and SPM), it provides an efficient tool to test or generate specific hypotheses about brain changes over time.

Deformation-based morphometry

In DBM, highly non-linear registration algorithms are used, and the statistical analyses are not performed on the registered voxels but on the deformation fields used to register them (which requires multivariate approaches) or derived scalar properties thereof, which allows for univariate approaches. One common variant -- sometimes referred to as Tensor-based morphometry (TBM) -- is based on the Jacobian determinant of the deformation matrix.

Of course, multiple solutions exist for such non-linear warping procedures, and to balance appropriately between the potentially opposing requirements for global and local shape fit, ever more sophisticated registration algorithms are being developed. Most of these, however, are computationally expensive if applied with a high-resolution grid. The biggest advantage of DBM with respect to VBM is its ability to detect subtle changes in longitudinal studies. However, due to the vast variety of registration algorithms, no widely accepted standard for DBM exists, which also prevented its incorporation into major neuroimaging software packages.

Surface-based morphometry

Surface-based morphometry (SBM) involves the creation of a surface representation (i.e. parametric meshes) of structural boundaries defined by or on the basis of the segmentation of a brain. This does not require registering the individual brain images to a template brain, though comparisons across brains demand a reference surface that belongs to the same topological genus (i.e. 0) and is normalized in size. The brains are thus mapped to a unit sphere on which their original properties can be compared with each other, and results are mapped back to a reference brain surface.

The surfaces most appropriate for cortical analyses are the boundaries between WM and GM or between GM and CSF (the latter is also often referred to as pial surface, since the pia mater is not commonly segmented into a class of its own) but various representations of the so-called central surface (roughly corresponding to the anatomical lamina IV) are also in use. For some subcortical structures (e.g. the hippocampus or basal ganglia), appropriate surfaces can be defined in a similar way, while lateral delineation of the corpus callosum, for instance, is difficult.

Statistical analyses in SBM are based on properties of the individual mesh elements and aggregations thereof. These latter ones include, foremostly, some measure of the distance between different surfaces-- typically the cortical thickness-- or sulcal depth but also some local or global measures of area, curvature (e.g. gyrification) or overall shape (e.g. via spherical wavelets, spherical harmonics or Laplace-Beltrami spectra).

Diffusion-weighted MR-based brain morphometry

Fiber-tracking techniques

Nerve fiber-tracking techniques are the latest offspring of this suite of MR-based morphological approaches. They determine the tract of nerve fibers within the brain by means of diffusion-tensor imaging or diffusion-spectrum imaging (e.g. Douaud et al., 2007 and O'Donnell et al., 2009).

Applications

Currently, most applications of brain morphometry have a clinical focus, i.e. they serve to diagnose and monitor neuropsychiatric disorders, in particular neurodevelopmental disorders (like schizophrenia) or neurodegenerative diseases (like Alzheimer), but brain development and aging as well as learning and brain evolution can also be studied this way.

Confounds

Given that the imaging modalities commonly employed for brain morphometric investigations are essentially of a molecular or even sub-atomic nature, a number of factors may interfere with derived quantification of brain structures. These include all of the parameters mentioned in "Applications" but also the state of hydration, hormonal status, medication and substance abuse.