Structural Magnetic Resonance Imaging

Authored by: Wesley K. Thompson , Hauke Bartsch , Martin A. Lindquist

Handbook of Neuroimaging Data Analysis

Print publication date:  November  2016
Online publication date:  November  2016

Print ISBN: 9781482220971
eBook ISBN: 9781315373652
Adobe ISBN:

10.1201/9781315373652-4

 

Abstract

This chapter briefly summarizes some basic concepts related to structural magnetic resonance imaging (structural MRI). We will focus primarily on so-called T 1-weighted structural MRI, and cover image acquisition, processing, and morphometric analysis for multi-subject cross-sectional studies. Other chapters cover a diverse range of MR imaging modalities, including diffusion tensor imaging (DTI) and functional MRI (fMRI), as well as applications to longitudinal imaging studies. Hereafter, in this chapter, we generally refer to “structural MRI” as simply “MRI” for the sake of brevity. Good overviews of MRI are given in (90, 56, 66). These sources also contain more technical references regarding MRI physics and image acquisition, if the reader wishes to delve further into this topic.

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Structural Magnetic Resonance Imaging

3.1  Introduction

This chapter briefly summarizes some basic concepts related to structural magnetic resonance imaging (structural MRI). We will focus primarily on so-called T 1-weighted structural MRI, and cover image acquisition, processing, and morphometric analysis for multi-subject cross-sectional studies. Other chapters cover a diverse range of MR imaging modalities, including diffusion tensor imaging (DTI) and functional MRI (fMRI), as well as applications to longitudinal imaging studies. Hereafter, in this chapter, we generally refer to “structural MRI” as simply “MRI” for the sake of brevity. Good overviews of MRI are given in (90, 56, 66). These sources also contain more technical references regarding MRI physics and image acquisition, if the reader wishes to delve further into this topic.

The adult human brain is a complex-structured organ weighing around 1.5 kilograms and consisting of roughly 1,500 cubic centimeters of volume. Brain size varies in the population, and is correlated with age, overall body size, and gender (67, 52, 53). The two principal cell types within the brain are neurons, which process information, and glial cells, which play a variety of supporting roles. In total there are 100 billion or more neurons, and perhaps 10 times as many glial cells in the adult human brain (95). Gray matter (GM) refers to brain tissue wherein cell bodies and dendrites predominate, whereas white matter (WM) refers to brain tissue where there is a higher proportion of myelinated axons. In addition, the vasculature of the human brain is extensive and detectable via MRI (34, 96).

Macroscopically, the human brain is composed of the brain stem, the cerebellum, and the cerebrum. The cerebrum consists of two cerebral hemispheres, connected to each other by the corpus callosum. Each cerebral hemisphere is covered by a six-layered sheet of GM (the cerebral neocortex), roughly 1 to 4 mm thick, with WM in the interior. The cerebral cortices are deeply folded, and folding patterns exhibit broad-scale similarities across adult humans (29, 31). A cortical ridge is called a gyrus, while a depression is called a sulcus. It has been shown that roughly two thirds of the cerebral neocortex is hidden within sulci (36).

Each cerebral hemisphere is divided into frontal, parietal, temporal, and occipital lobes. Each lobe can be further subdivided into cortical regions, based on, for example, cytoarchitecture (17), geometrical landmarks (31), or genetic differences (17). Additionally, there are a number of GM subcortical structures lying underneath the cerebral neocortex, including structures belonging to the limbic system and the basal ganglia. Cerebral hemispheres are roughly bilaterally symmetric, though there are some systematic asymmetries in shape and function (123). In particular, most regions of the cerebrum have homologous left and right versions.

MRI is a flexible imaging modality, and different types of images can be generated to emphasize contrast related to different tissue characteristics. For example, T 1-weighted MRI provides good contrast between gray- and white- matter tissues, with GM appearing as dark gray and WM as lighter gray. Cerebrospinal fluid (CSF), a clear fluid contained within the ventricles and the subarachnoid spaces, appears as dark regions in T 1-weighted MRI. Typically, a T 1-weighted image is segmented into these three tissue types, as will be described below. They can be further subdivided into regions using expert manual tracing, or by automatic parcellation algorithms. The resulting data can then be utilized to characterize the spatial extent and distribution of different tissue types in an individual’s brain, including volumes and shapes of subcortical structures, and the volume, thickness, and surface area of cerebral cortex. Other tissue properties and aspects of brain morphometry can also be extracted from MRI signals.

Morphometric analyses of MR images have been very widely applied in the biomedical research literature over the past 20 years. The broad range of applications include the assessment of normative brain structure, e.g., development in children and adolescents (48, 49), atrophy and cognitive impairments in later life (86), the connection between brain structure and intellectual capabilities (57), personality traits (45), and so forth. Other applications focus on the impact of illness and disease on brain structure. Significant differences have been found in the morphometric properties of cases and controls in studies of psychiatric illnesses such as autism (14), schizophrenia (64), and depression (82), as well as in studies of disorders directly affecting brain structure, such as Alzheimer’s (69) and Parkinson’s disease (18). More recently, imaging genetics has focused on the relationship between genetic information and structural MRI via familial or twin (17) and genome-wide association studies (115). Another use of MRI includes the production of high-resolution anatomical references for co-localizing functional activations obtained, for example, from fMRI (109, 35). A very important clinical use for MRI, which we briefly describe below, is the detection and localization of focal and space-filling brain tumors, edema, and necrotic tissues for use in surgical planning (11).

There are several freely available software packages for preprocessing MRI data and performing morphometric analysis of the human brain. Some of the more popular packages include the Statistical Parametric Mapping package (http://www.fil.ion.ucl.ac.uk/spm/), FreeSurfer (https://surfer.nmr.mgh.harvard.edu/), the FMRIB Software Library (FSL, http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/), and AFNI (http://afni.nimh.nih.gov/). While the image processing pipelines contain broadly similar elements across each of these packages, there are some major differences. Additionally, many imaging labs create their own individualized pipelines either by extracting and adapting elements of these packages or by creating new processing scripts, depending on the particular needs of the research being performed. Statisticians involved in the analysis of MRI data are generally well served by gaining a substantial degree of familiarity about the processing pipeline and how these impact the types of possible inferences.

Note, while it is not the goal of this chapter to endorse or promote any particular processing and analysis package, we will to some extent focus on the processing and morphometric analyses originally developed within the FreeSurfer, and to a lesser extent, the SPM frameworks.

The remainder of this chapter is organized as follows. In Section 3.2 we describe the basics of structural image acquisition and preprocessing. Section 3.3 describes the steps involved in multi-subject MRI research studies, including registration and segmentation, various techniques for extracting morphometric features from structural images, and statistical analyses of the resulting data. We conclude the chapter with a brief discussion of miscellaneous issues in Section 3.4.

3.2  Image Acquisition

Nuclear magnetic resonance (NMR) imaging is one of the workhorses for non-invasive, clinical interrogation of the soft tissue structure in the brain. Since its humble origins in the 1980s, and a rebranding 1 to MR imaging (MRI), it has evolved into a multi-billion dollar industry. MRIs can be used to differentiate between brain tissue types, including normal and abnormal tissue, and therefore provides information about morphology and a diagnostic tool to detect disease.

3.2.1  MRI Physics

In order to understand the terminology used in MRI, we first take a brief look at the physics at the core of this imaging technique. MRI creates series of stacked two-dimensional (2d) images based on interactions between radiofrequency (RF) electromagnetic fields and atomic nuclei after the tissue has been placed in a strong magnetic field maintained inside an MRI scanner. Only atomic nuclei with an odd number of protons and neutrons have an angular momentum and they act as tiny magnetic dipoles that spin around their axis of rotation. The scanner is able to detect concerted changes in precession from a large number of spins. The focus is typically on the single protons found in the nuclei of hydrogen atoms within water and fat, as they are the most frequent dipoles found in the brain.

Without an external magnetic field, the spin axes are oriented randomly. Inside the scanner’s strong magnetic field, the spins align over time and eventually precess around the field’s direction. In order to measure tissue properties, MRI measures macroscopic tissue magnetization caused by the imbalance of nuclei that are orientated parallel or anti-parallel to the scanner’s magnetic field. The scanner uses an RF pulse to flip the spin orientation between the two orientations. The amplitude of the pulse determines the flip angle, and after switching off the RF pulse, the nuclei will briefly precess synchronously, resulting in measurable electromagnetic radiation picked up by the scanner’s receiver coil as an echo. 2 Due to interactions with other molecules, the spin of nuclei will quickly fall out of phase with a transversal relaxation time constant T 2. The spin axes will realign with the scanner magnetic field axis again after the longitudinal relaxation time T 1. This value depends on the rate of energy transfer of the spins with their neighbors in the tissue lattice. For example, the T 1 time is shorter in fat than in pure water, since carbon molecules in fatty acids provide more efficient energy transfer due to spin-lattice interactions. Note basic MR physics is discussed further in Chapter 6. More detailed information can be found in (56) and (66).

3.2.2  Image Reconstruction

The signal picked up by the scanner’s receiver coil contains a large signal component due to spin precession. One method for image reconstruction removes the precession by multiplication with a sine and a cosine function oscillating at, or near, the frequency of precession followed by low-pass filtering. After multiplication, both signals are combined and result in a demodulated complex signal that is interpreted as the Fourier transform of the tissue transverse magnetization. An inverse complex Fourier transform is used to assemble the series of 2d MR magnitude images, which is exported for image viewing. Phase information is usually discarded but special applications such as flow imaging use this information (83).

3.2.3  MRI Sequences

The tissue-dependent time scales for magnetic relaxation, given by T 1 and T 2, as well as the density of protons (PD) are measured by applying precisely timed combinations of RF pulses and secondary magnetic gradients. The variables that are changed between these sequences are the amplitude of the RF signal (flip angle), the time after which the echo is measured (echo time, TE) and the time interval between consecutive RF pulses (repetition time, TR). A short repetition time relative to the tissues T 1 relaxation time and a short echo time relative to the tissues T 2 time will result in predominantly T 1-weighted images. In T 1-weighted images, the fat present in WM appears bright, GM appears dark gray, and CSF appears black. In a similar manner, MRI can be used to produce predominantly T 2-and PD-weighted images. For T 2-weighted images (long TR and long TE), water present in CSF and GM appears bright, while air appears dark. PD-weighted images (long TR and short TE) provide good contrast between GM (bright) and WM (darker gray), but little contrast between brain and CSF.

Sequence development is an active field of research and can be used to probe tissue in many different ways. For example, in the time between when spins are initially aligned and measured, some might travel out of the inspected region resulting in a signal drop in T 2-weighted images, indicative of molecular motion caused by diffusion. Probing this motion in different orientations is the basis for diffusion-weighted imaging; see Chapter 4. Other sequences try to suppress the diffusion signal to better probe disease processes such as inflammation and demyelination, by increased contrast for associated changes in local water and lipid content. Similarly, T 2 *

is the combined effect of T 2 and local inhomogeneities in the magnetic field. While certain sequences attempt to eliminate the effects of these inhomogeneities, others try to emphasize them. The latter types of procedures form the basis of so-called blood-oxygen-level-dependent (BOLD functional MRI (fMRI); see Chapter 6.

3.2.4  MRI Artifacts

Discrete sampling and filtering in the Fourier domain during image reconstruction can produce a variety of different image artifacts. Artifacts can cause serious changes in image intensity and deformations in the image structure. It is therefore useful to understand some of these artifacts to guide image interpretation.

Because the signal is acquired in the Fourier domain (or k-space) with a given sampling interval, it is periodic in nature and the image repeats itself. The replication interval depends on the inverse of the sampling interval and the frequency bandwidth of the signal. If the field of view (FOV) of the image is set up improperly, this can result in overlap between adjacent replicates. Visually, this results in copies of the imaged structure appearing above and below the image. As an example, the nose of the subject might intersect the back of the brain. Another potential artifact related to the repeated structure is a ghosting artifact caused by non-matching phase shifts between the two demodulating sine and cosine signals. In this case, the copy of the object has low signal amplitude and appears shifted and superimposed on the image.

Another common image artifact is caused by the finite sampling interval in Fourier space. Any sufficiently abrupt change in image intensity will produce a ringing artifact in the reconstructed image, as an infinite number of frequencies would be required to represent an instantaneous jump in intensity. Further artifacts, which distort the image regionally, include chemical shift and magnetic susceptibility artifacts caused by non-matching RF pulse frequencies used to address spins in space. Artifacts can also be caused by patient motion during image acquisition, appearing as repeated bright features across the image. A source of intensity variation that is smoothly varying over space is a multiplicative bias field caused by interference of the RF coil signal with the imaged brain. Dependent on the scanner, the center of the brain can then appear brighter or darker compared to the periphery.

Most image artifacts caused by signal reconstruction can be controlled with appropriate acquisition sequences and filtering in Fourier space. However, most image analysis is performed long after image acquisition, and without access to the original k-space data. Manual inspection of the reconstructed images is therefore advised to identify inferior image quality, and their removal from further analysis may be necessary. Bias field correction and magnetic susceptibility artifacts are removed as a post-processing step after reconstruction. Whereas the bias field can be estimated and removed from the image due to its slowly varying characteristics, magnetic susceptibility artifacts require specialized imaging sequences in which two scans are obtained with orthogonal distortions. Using elastic registration of the two images, the mean-corrected image can be obtained.

3.3  Multi-Subject MRI

After artifact correction and transformation to Euclidean space, multi-subject MRI analyses typically require a spatial registration (or normalization) step. This entails estimating a mapping between each individual’s image and a stereotactic template (6), thus allowing the different individuals brains to be compared. The normalized image is then segmented into tissue types, including GM, WM, and CSF. Smooth intensity non-uniformity is corrected for concomitantly with registration and tissue segmentation. Atlas-based methods can further segment the images into cortical and subcortical regions of interest (ROIs) (20). The key to successful registration and segmentation is the incorporation of prior knowledge regarding the spatial topology of the brain, as well as information (e.g., a forward model) regarding MR image formation (6, 58). Morphometric measures can then be computed from individual MR images (e.g., (3)) and used as outcomes in statistical analyses, for example demonstrating association with diagnostic status (e.g., (53)). If there are many such measures, as is the case with whole-brain (voxelwise) analyses, significance levels of statistical tests need to be adjusted to account for inflation of Type-I error rates due to multiple comparisons (94).

3.3.1  Registration

The objective of registration is to map intensity images J n : ℝ3 → ℝ+, n = 1,..., N, in native space onto a template image T , where N is the number of subjects (39). Registration requires the estimation of transforms f n : ℝ3R 3, which take coordinates r = (r 1, r 2, r 3) in native space and map them to stereotactic coordinates f n ( r ) in the template space. Ideally, the transforms are (at least approximately) diffeomorphic, and are therefore smooth, continuous mappings with derivatives that are invertible while preserving the topology of the brain (23, 2, 124). The resolution of the registration should also be high enough to ensure that partial volume effects (MRI signal from voxels containing multiple tissue types) are minimized. This typically entails having roughly 1-mm isotropic voxels (3). Moreover, transforms have to leave relevant subject-level differences in the volume and shape of brain substructures as identifiable, even after correcting for global features such as the position in the scanner and overall head volume, of no, or secondary, interest. This information can be preserved by enforcing smoothness constraints that correct only for global size and shape variables (3), or by recording differences in the transformations f n across subjects (5, 2).

Note, in some registration schemes the template image is instead mapped onto each individual image (2). Ultimately, there are technical considerations that might influence the direction of the mapping. If we want to display an image in a template, or atlas space, after registration, the opposite transformation from atlas onto image space is convenient to use. This is because the sampling of the image in atlas space is done using the inverse transformation (from atlas into image space). Using the inverse transformation sampling scheme guarantees that every voxel in the atlas space has a corresponding intensity from image space using trilinear interpolation. This technique removes the requirement of computing the inverse of the image to atlas space transformation, which might be ill-defined if the transformation is not volume preserving.

3.3.1.1  Volumetric Registration

The majority of volumetric registration approaches proposed in the literature first perform a global 6- or 12-parameter transform, which can be expressed as 4 × 4 matrices in Euclidean space. The global transform is rigid (6 parameters: translation, rotation) or affine (12 parameters: rigid plus anisotropic scale and shear). These global transforms are often followed by local, non-linear transforms to match the image with the template on fine-scale structure (6, 20).

Estimation of transform parameters typically involves minimization of a cost function subject to biologically motivated constraints. Special care has to be taken if the template and mapped images are derived from different image modalities. In general, images can be aligned if their two-way histograms are in a low-entropy state. This is usually the case if brain tissue shows arbitrary, but uniform, intensities in both the template and image. If both template and image are from the same modality, a simple Euclidian distance, or correlation measure, can be used at the core of the cost function. Multi-modal registration, such as between MRI and computer tomography (CT) images, instead requires cost functions based on mutual information (104).

Several authors have proposed incorporating biologically motivated constraints using Bayesian models, and obtaining maximum a posteriori (MAP) estimates (6, 39, 40). Let θ denote the model parameters, and D the data. By Bayes’ rule we have p( θ |D) ∝ p(D| θ )p( θ ). The MAP estimate θ ^ MAP

of θ is

3.1 θ ^ MAP = argmin θ { log p ( D | θ ) log p ( θ ) } .

For example, (2) proposes a local deformation model with a velocity field consisting of a linear combination of first-degree B-splines. The coefficients θ of the splines are given a prior distribution p( θ ) consisting of a zero-mean Gaussian with a covariance structure based on membrane, bending, or linear elastic energy. The likelihood p(D| θ ) is a normal approximation based on squared differences between the transformed image and template intensities, summed across voxel mid-points. MAP estimates are obtained by minimizing the expression on the right side of Eq. 3.1 and the resulting velocity field is numerically integrated to obtain a diffeomorphic mapping.

3.3.1.2  Surface-Based Registration

Surface-based registration attempts to incorporate the topology of the cerebral cortex to construct transforms onto a template space (29, 41, 38, 76, 101). Unlike subcortical volumes, the cerebral cortex has the topology of a highly convoluted 2d sheet (29). Volumetric registration methods do not preserve this topology, as two voxels can be close neighbors in Eulidean space but lie far apart with respect to distance across the cortical surface. Moreover, cortical geography and function are best mapped following the local orientation of the cortex (121).

An exemplar surface-based registration algorithm is given by (29). After an initial voxel-based segmentation of WM, the cerebral hemispheres are cut along the corpus callosum and the pons, removing subcortical GM structures and resulting in a single mass of connected WM voxels for each hemisphere. The gray–white cortical boundary of each hemisphere is tessellated and smoothed. These tessellated surfaces are then repositioned by minimizing the intensity differences between the image and target intensity values, subject to energy functionals tangential and normal to the surface, which smooth the surface and encourage uniform spacing of vertices on the inflated cortices. These priors are built into the model via a Bayesian formulation, and the MAP estimate is obtained as described in Equation (3.1). The tessellated surfaces are given a spherical topology by “capping” the midbrain. Cortical thickness and surface area can then be computed at each vertex of the tessellation, as described below.

Unfolding of a left hemisphere cortical triangulated surface from the top left (pial surface) clock-wise to the bottom left (spherical representation). The insets show the arrangement of four triangles across the unfolding steps. Gray-scale illustrates the curvature information that is computed in the folded state and is carried over to the spherical representation.

Figure 3.1   Unfolding of a left hemisphere cortical triangulated surface from the top left (pial surface) clock-wise to the bottom left (spherical representation). The insets show the arrangement of four triangles across the unfolding steps. Gray-scale illustrates the curvature information that is computed in the folded state and is carried over to the spherical representation.

The initial steps of the mapping from subject surface to atlas surface are depicted in Figure 3.1. Correspondence between image and atlas is calculated by using the similarity between gyri and sulci patterns, measured by local Gaussian curvature. Figure 3.1 (top left) shows the folded pial surface of the left hemisphere (eyes pointing to the left) and a set of six vertices that are connected by four triangles as a close-up. The top to top-right figures show an operation that unfolds the cortex using a forced geometric approach. Gray values indicate the curvature information obtained from the initial pial surface, which is carried over (dark positive curvature in gyri, light negative curvature in sulci). The transformation is space preserving. The unfolded shape is used for visualization because the general shape is still recognizable and features in the suli can be visualized. From this unfolded state (top right) a spherical reconstruction (bottom left) creates a representation that makes the tangential surface displacement explicit (Gauss map). It can be seen in the series of insets that the surface vertices undergo a series of deformations but keep their pattern of connections. Locations in the spherical reconstruction can therefore be mapped back to the corresponding location on the unfolded pial surface.

A similar spherical representation of the atlas is used as a target for registration. Vertices of the subject brain are moved while minimizing the summed distanced between corresponding subject and atlas curvature points. This procedure stretches and shifts the pattern of surface vertices in the tangential direction of the surface to best fit the curvature observed in the atlas. Surface area expansion for each vertex can now be calculated as the change in area between the spherical representation and the original pial surface representation the procedure started with. Furthermore, after minimization, subject surface vertices get assigned the region of interest of the closest atlas vertex. Region of interest measures for thickness and surface area are computed by summing up vertex measures for all vertices that share the same label.

Automated methods have also been proposed that incorporate features of both surface-based and volumetric registration (71, 105). The goal of these registration methods is to preserve correspondences in cortical folding patterns while simultaneously aligning sub-cortical volumes, thereby providing more accurate comparisons of cortical and subcortical morphology across subjects, or more accurate co-registration of structural and functional images.

3.3.2  Segmentation

Image segmentation consists of classifying voxels into categories based on their intensities, location, and prior knowledge regarding neurobiology and MR image formation. Accurate classification depends on the fact that non-brain and brain voxels have different intensity distributions, as do voxels containing different brain tissue types. Note that MR image intensities are non-negative, because after Fourier reconstruction they are converted into magnitude images, thus placing limitations on appropriate probability distributions for voxel intensities. In particular, the distribution of noise from MR images is Rician, not Gaussian (54). Gaussian approximations can be adequate at the signal-to-noise ratio observed in MR images for gray and white matter brain tissue. However, as CSF and air can have intensities very close to zero, and distribution noise will be increasingly skewed and approach a Rayleigh distribution.

3.3.2.1  Foreground from Background Segmentation

The most basic use of classification in MRI is the separation of foreground and background based on a global intensity threshold. It is important that the classifier used for this separation is insensitive to the contrast and brightness differences common to biomedical images. A simple algorithm used for separation is based on the assumption that the general shape of the imaged object is known beforehand, so that the proportion of voxels belonging to foreground (head) and background (air) can be assumed to be approximately known. The intensity threshold for classification is then based on the cumulative distribution function (cdf) of voxel intensities. The performance of this algorithm is sufficient to provide robust and automatic brightness and contrast adjustments for image viewing on medical workstations where MRI measurements are mapped to voxel brightness using linear transfer functions. More complex histogram equalization procedures are sometimes used in research settings (15).

Intensity thresholds can also be defined if foreground and background intensities appear as a bi-modal distribution (119). This is usually the case for MRI, since brain tissue appears bright in front of the more dark-appearing air. A commonly used unsupervised clustering algorithm is Otsu’s method (97), in which the optimal threshold is defined as the one that minimizes the intra-class variance. A histogram of the image intensities is computed followed by an exhaustive search through all possible thresholds. The threshold that yields the minimal intra-class variance is then used for classification. Another unsupervised classification algorithm based on computing thresholds is the IsoData (108) algorithm, which uses an iterative procedure to compute a threshold. From an initial starting threshold the mean of both parts of the intensity histogram is computed. The threshold is then moved so it is centered between the two means and the procedure is repeated until convergence.

All global threshold procedures rely on prior image corrections for intensity inhomogeneities and sufficient signal to noise. They are useful during the initial stages of image processing because they are fast and unsupervised. They can also be applied in a hierarchical manner to compute multiple thresholds but most often they are used to provide informed initialization to more complex, model-based image segmentation algorithms. For example, in the case of segmenting objects with blurred edges in front of a high background signal, hysteresis thresholding uses an initial high threshold to define cores of regions that belong to objects of interest. Region growing from these initial seed regions using a secondary threshold results in the final object classification. Non-local threshold algorithms have also been proposed and cope with inhomogeneous intensity variations in images (93, 87). Other algorithms use derived image features such as edges for segmentation. One of the most widely used edge- or gradient-based algorithms is watershed segmentation (13). High gradient edges are interpreted as rims separating uniform low gradient areas. A flooding procedure is used to region grow, starting from the low gradient regions. As the high gradient image edges separate the different basins from each other, they are interpreted as segmentation borders separating brain from background (37).

3.3.2.2  Brain Tissue Segmentation

In addition to separating foreground and background, MR image segmentation seeks to classify voxels contained within the brain into different tissue types (GM, WM, and CSF) (3, 4, 8). Class labels can also include partial volume categories (28). Atlas-based methods further partition GM voxels into ROIs (29, 40, 20). In the simplest case, each voxel has a single label assignment. Binary labels are then used to create annotated images that share resolution and voxel size with the original image data. Both files are merged to overlay the information appropriately for visualization. Non-binary label assignments can also be used to store posterior probabilities for labels to be assigned to a particular volume. These probabilities can then be converted to binary labels by thresholding (28).

A commonly used probabilistic classifier is the Finite Gaussian Mixture Model (FGMM) (130, 40, 4, 28). Let (δn, i ∊ C denote the indicator for class membership for the ith voxel, i = 1,..., I, in the nth image, where C = {1,..., C} is the set of possible tissue classes. The probability of the entire image J n can be derived by assuming that all of the voxels are independent, and is given by

3.2 p ( J n ) = Π i = 1 I Σ c = 1 C p ( J n ( τ i ) | δ n , i = c ) p ( δ n , i = c ) = Π i = 1 I Σ c = 1 C 1 2 π σ c 2 exp { ( J n ( τ i ) μ c ) 2 2 σ c 2 } p ( δ n , i = c )

where p(δi,n = c) is the prior probability that the ith voxel is in tissue class c. In this model, prior probabilities are spatially stationary. Estimates can be obtained by pre-identifying (using prior anatomical knowledge) voxels that are highly likely to be from a given tissue type, and estimating class means and variances ( μ c , σ c 2 )

, c = 1, ..., C based on these voxels.

Equation (3.2) makes a number of unrealistic assumptions. For example, neighboring voxels are likely correlated with one another. Hence, a number of authors have incorporated a Markov Random Field (MRF) formulation (130, 28, 39), that allows the prior probabilities in Equation (3.2) to be expressed as p(δn,i = c| δ Ni ), where Ni is the set of neighbors of the ith voxel and δ Ni are their class labels. This spatial prior can be expressed as a Gibbs distribution according to the Hammersley–Clifford theorem (12). Additionally, the distributions of partial volume voxel intensities can be modeled as a function of the proportion of each tissue class contained within the voxel (110). Prior distributions can also incorporate information about local differences in MR image intensities and spatial distribution of structures (39). Non-parametric, information-theoretic approaches have also been proposed that do not rely on Gaussianity (51, 28).

The steps involved in registration and segmentation are sometimes performed sequentially (6, 3). However, several authors have proposed methods that perform registration and segmentation in a simultaneous manner (40, 4). This is beneficial because if the segmentation of each subject’s brain image were known a priori, the optimal transform to register each image to a common template would be straightforward to compute. Conversely, if the optimal transform were known for each image, segmentation would be much easier to preform (39). Other refinements to registration and segmentation of multi-subject MRI data, often tailored to specific scenarios such as longitudinal change or detection of disease states, is an ongoing and active area of research (26, 74, 77, 102, 127, 27).

3.3.3  Templates and Atlases

Registration and segmentation of multi-subject MRI depends on the use of a common template, or an intensity image to serve as a common target for registration across subjects. Templates provide a 3d stereotactic coordinate system that can be used to report results that are comparable across studies. An atlas consists of a pair of images, a template and a corresponding segmentation (labeled image) (20). Atlas-based image segmentation is essentially a registration problem, since registering an MR image to the template automatically gives a segmentation from the corresponding labeled image (39, 31, 20). This procedure works as long as the atlas is appropriate, i.e., labels represented in the atlas have a representation in the MR image. Brain tumors and surgical interventions can invalidate this assumption, as well as brain atlases that are inappropriate for the imaged subject. For example, in young children the area of the ventricles can appear partially collapsed, resulting in poor registration if one uses an atlas built using adult subjects.

An atlas may be single-subject, i.e., based on a high-resolution image of one individual. The advantage of single-subject atlases is that they allow resolution at a fine scale. The disadvantage is that a single subject is not necessarily representative of the population of interest. One of the first human brain atlases was created by Talairach and Tournoux to give a stereotactic coordinate system and labeling for brain surgeries (117, 118, 36). This is a single-subject atlas, made from drawings of slices from the brain of a 60-year-old woman. Using two landmarks easily visible on MRI images (the anterior and posterior commissure), this atlas uses a proportional grid of labeled regions. Brodmann areas, based on cytoarchitectural differences in the human cortex (17), are used for labeling of cortical structures. Talairach coordinates were first used for structural MRI in the early 1990s (36) and are still often used for reporting areas of activation in functional imaging studies (80). Another commonly used single-subject atlas is the Colin27 atlas, created from 27 high-resolution images from a single subject (63).

Alternatively, an atlas may be population-based, i.e., averaged across a number of representative individuals. These atlases retain only features that are common across the majority of subjects, at the cost of a loss of potentially informative resolution (39). Population-based atlases include those of the Montreal Neurological Institute (MNI). The first MNI atlas was based on MR images of 305 young healthy subjects, with stereotactic coordinates approximating those of Talairach and Tournoux (35). The MNI atlas has been updated several times over the years (36), including the International Consortium for Brain Mapping (ICBM152) atlas, based on 152 high-resolution MR images from a young adult population (88). Averaged templates are also often constructed using (a subset of) the subjects from the current study itself. For example, (65) used a random sample of the control subjects to construct a minimal deformation target template in an MRI study of Alzheimer’s disease and mild cognitive impairment.

In addition to volumetric atlases, there are several atlases of the human cortical surface (41, 29, 31, 122, 32). For example, (31) collected T 1 MRI data from 40 subjects: 10 young adults, 10 middle-aged adults, 10 elderly adults, and 10 patients with Alzheimer’s disease. Cerebral hemispheres were manually divided into 34 regions, based primarily on cortical (sulcal) geography. Spherical representations of the cortical surfaces were created for each of the 40 images, and were then registered together (42). Each point on the surface was then probabilistically assigned to one of the 34 regions (43).

Dozens of other atlases have been published in the literature (see (20) for a review). These atlases are often tailored to specific populations, e.g., pediatric subjects, elderly subjects, or diseased populations. Atlas labels can also be derived from biological sources other than direct anatomical or imaging information. For example, the Allen Human Brain Atlas (113) is based on gene expression data from two post-mortem adult male brains, whereas the atlas of (17) is based on genetic correlations of cortical surface area computed from an MRI study of 406 twins.

Figure 3.2 depicts an example of MRI atlas construction using the Allen Brain Atlas data. The Allen Brain Atlas project derived gene expression from small volumetric ROIs that had been cut from the original brain and analyzed using microarrays. Expression on several thousand genes is available at the center of mass of these volumetric ROIs. Coordinates in the Allen Brain Atlas are stored in MNI space, which is also used in the FreeSurfer atlas. Therefore, no explicit volume-based registration is required. The sampling density in the Allen Brain Atlas changes between cortical and sub-cortical regions. As a first approximation we can therefore assume that a vertex in the surface atlas can be linked to the closest sample region of the Allen Brain Atlas given a Euclidean distance measure. In order to improve the mapping, a subset of points can be used that represents cortical sample regions of a single hemisphere only. Figure 3.2 shows the mapping of gene expression sample regions as a color overlay on the FreeSurfer average surface. Sample regions have been generated from slabs of tissue that are visible in the bands of similar color that are an artifact of the brain preparation procedure. Using this preprocessing workflow gene expression pattern for each micro-array well can now be assigned to cortical surface vertices for subsequent statistical analysis.

3.3.4  Morphometry

3.3.4.1  Subcortical Volumes

A number of methods have been introduced to estimate volumes of subcortical GM structures. A simple approach is to run a segmentation algorithm to partition brain tissue into GM and other categories, followed by expert manual tracing of gray-matter subcortical structures based on neuroanatomy (e.g., as in (55)). Volumes are computed by counting the number of voxels falling within the tracing and multiplying by the voxel dimensions. To ensure that the manual tracings are reliable, multiple raters typically perform them, and an intra-class correlation coefficient (ICC), or some other measure of reliability, is reported. Moreover, if subcortical volumes are used as dependent measures in a statistical analysis, the manual tracing is done blinded to the independent variables of interest, such as diagnostic status. Many automated methods have also been developed for assessment of subcortical volumes (68, 9, 106, 7). These typically use atlas-based, or shape- and appearance-based, algorithms to segment subcortical structures and volumes are computed as described above.

Sample locations for gene expressions in MNI space (spheres) relative to the FreeSurfer average surface transparent (left). Surface vertices are colored according to the identifier of the closest sample regions (right).

Figure 3.2   Sample locations for gene expressions in MNI space (spheres) relative to the FreeSurfer average surface transparent (left). Surface vertices are colored according to the identifier of the closest sample regions (right).

3.3.4.2  Voxel-Based Morphometry

While volumetric analysis of pre-defined ROIs is relatively straightforward, there may be more general morphometric measures that are more highly correlated with independent variables of interest. If there are no strong a priori hypotheses regarding specific subcortical volumes, a whole-brain voxel-wise analysis may be able to discover such relationships. One such approach is termed voxel-based morphometry (VBM) (3, 53, 89). Briefly, VBM proceeds by first registering each subject MR image to a common stereotactic space. Registered images are segmented into brain tissue types and smoothed. Each voxel i of the smoothed image n is associated with a number 0 ≤ pni ≤ 1, which represents the local concentration of GM tissue. After a logistic transformation, voxel GM intensities are entered into a general linear model (GLM) to study their relationship with independent variables, while controlling for covariates of no interest. This is a massively univariate approach, i.e., a separate GLM is fit for each voxel i = 1,..., I, where I may be in the hundreds of thousands, and it is critical that multiple testing adjustments be performed to guard against inflated Type-I errors.

3.3.4.3  Deformation- and Tensor-Based Morphometry

VBM is a local measure of GM tissue intensities across individuals. In contrast, deformation-based morphometry (DBM) and tensor-based morphometry (TBM) yield more global measures of structural differences (5, 3, 24, 26, 65, 75). Both DBM and TBM utilize information from the registration-to-template transforms f n , 1 ≤ nN, to summarize morphometric differences across individuals. The advantages of these approaches is that they do not depend on strong a priori hypotheses about which ROIs are associated with the independent variables of interest, and therefore they allow for more subtle characterization of global or regional morphometric differences than simply volume or GM concentration.

The DBM approach, proposed by (5), performs an affine registration followed by a nonlinear deformation consisting of discrete cosine basis functions. The cosine basis function coefficients θ n are estimated for each image J n , resulting in K-dimensional vectors θ ^ n

, where K is large (over a thousand). Removing the effects of brain size and position, these parameters are placed in an N × K matrix A , where each row summarizes the deformation field encoding shape differences for the nth subject. A principal components analysis is then performed to reduce the dimensionality to a relatively small number of parameters per image (around 20) that capture most of the subject-to-subject variation. Finally, a Hotelling T 2 or MANCOVA can be performed on the resulting low-dimensional characterization of the deformation fields to assess associations with independent variables, possibly controlling for covariates of no interest. Note, DBM can also be used to focus on positional differences in specific ROIs (5).

TBM is similar to DBM, in that properties of the non-linear deformations f n are used to characterize shape differences among individual images. Each mapping f n can be represented as a discrete displacement vector field. A Jacobian matrix can computed by taking the gradient of the deformation at each voxel of the template image, giving rise to a tensor field that characterizes local displacements for each MR image (3). Taking the determinant of the Jacobian of f n at each voxel gives local volumetric differences across subjects relative to the template image (24, 65). Subcortical volumes can be obtained by integrating the Jacobian determinants over voxels contained within segmented substructures. As an alternative, surface-based TBM has also been proposed (26).

3.3.4.4  Surface-Based Measures

Surface-based morphometric measures include cortical surface area, thickness, and volume. In human prenatal and perinatal data, surface area is primarily related to cortical column counts whereas thickness is more closely related to neuron counts within columns (107). Surface area and cortical thickness appear to have independent genetic determinants (100). In later life, changes in both surface area and thickness may be driven by changes at the level of synapses, dendrites, and spines (116). Subject-level variation in cortical volume appears to be more closely related to surface area than to thickness, though thinning of cortices is highly prevalent in later life and probably accounts for a substantial amount of normative change with age, as well as volumetric losses caused by disorders such as Alzheimer’s disease (98, 67, 33, 116).

As described above, the FreeSurfer software implements a semi-automated approach to surface reconstruction (30, 29, 41), resulting in over 160,000 polygonal tessellation vertices for each hemisphere. Each subject’s cortical surface is mapped to a spherical atlas space using a diffeomorphic registration procedure based on folding patterns. The surface alignment method uses the entire pattern of surface curvature at every vertex across the cortex to register individual subjects to atlas space (42). Using the surface between white and gray matter (white matter surface) and the surface between gray matter and cerebral spinal fluid (pial surface), it is straightforward to calculate the cortical thickness for each pial surface vertex (38). The computation uses the assumption already implicit in the surface generation that, although convoluted due to cortical folding, both surfaces run parallel to each other with a known minimal and maximal distance. In the (inverse) direction of the pial surface normal at each vertex, a ray is calculated until it hits the white matter surface. The distance traversed by the ray is used as the cortical thickness measured at the pial surface point. Notice that this procedure is not symmetric with respect to the surface chosen for the ray-to-surface intersection and becomes noisier in regions with high surface curvature. Several other algorithms for measuring cortical thickness have been proposed in the literature (85, 76, 25).

Surface area is also computed as a vertex-based measure that reflects the size of the area of adjacent triangles (37). This, of course, depends on the number of vertices that are generated during surface tessellation and on the uniformity of the tessellation. These are both properties of the surface-generating algorithms. In order to remove this ambiguity, surfaces are matched against an atlas surface. As each surface is matched to the same atlas, changes in surface area between subjects can be compared with one another. Because this vertex measure depends on the chosen atlas, the area is referred to as the surface area expansion factor. The atlas mapping also allows for atlas-based regions of interest to be carried over to each subject’s surface. These regions are defined as collections of triangles and correspond to functional regions of the brain.

3.3.4.5  Other Morphometric Measures

There are many other ways to summarize important aspects of brain morphometry. For example, one can extract the location of the regional center of mass relative to the subject’s location or the number of disconnected regions. However, selection of appropriate measures for a particular analysis and set of subjects should be done carefully to prevent an overwhelming number of multiple comparisons.

One set of measures assesses the degree of cortical folding, or gyrification, of the cerebral cortex (84, 112, 111). For example, in (111) the outermost surface of the brain, without folds, is defined with morphological closing operations. Next, hundreds of circular and overlapping regions are defined on that outermost surface, and each region is matched with the outline of a corresponding region on the pial surface, which may be buried and/or folded underneath the outermost defined surface. Then, gyrification is calculated quantitatively as the ratio between overall buried/folded cortex (on the pial surface) to the visible cortex on the outermost surface. This measure has been studied mainly in relation to neuropsychiatric disorders (81, 99, 126, 92).

Another set of measures can be created using image analysis methods such as marching cubes to compute surface representations from segmented ROIs. These surfaces allow us to further extend the list of measures that can be calculated for a given labelled region, with the hope that some might relate to behavior, disease, or function. We can calculate the area enclosing the region or regions, and use aspect ratios as measures of elongation and sphericity, surface curvature, tortuosity, and so forth. As a specific example, we introduce a procedure that learns optimal shape measures from the given set of input shapes.

A surface can be represented as a collection of points in 3d space. Connecting each group of three points with a triangle, the surface depicts the region’s border. If the same region is segmented in another subject, a new surface can be obtained. Repeating the process for a selection of subjects, we can ask what the shape variability of that particular ROI is and how it might relate to other phenotypic measures. In particular, we can compute the mean shape and variation around the mean shape that are indicative of the shape space spanned by the input surfaces. This type of analysis provides a convenient data-driven decomposition of the observed shape variability.

In order to perform this analysis we need to represent the different shapes using the same triangulated surface topology. A point or vertex identified in one surface by a landmark has to correspond to the same landmark on all the other surfaces. Solving this problem is nontrivial, since each surface is obtained from a separate run of the marching cubes algorithm without guarantee of vertex correspondence between separate runs. We solve this problem by introducing a preprocessing stage. First, a single surface is identified as the source surface. For each subject, the source surface is now aligned and warped until it approximates the shape of the subject’s target surface. The different instantiations of the source surface can now be used as stand-ins during the subsequent analysis steps since they all share the topology of the source surface. Figure 3.3 shows a source surface warped to a subset of 774 target surfaces representing the left and right human hippocampus, a region essential for memory formation. The registration and surface warping was performed independently for the left and right homologues, but for subsequent steps, both left and right hemisphere hippocampus surfaces are combined. Calculating the cross-covariance matrix of the surface point coordinates and the eigenvalue decomposition of the matrix (principal component analysis), we decompose the shape variability into de-correlated modes sorted by variance. In Figure 3.3 the first 10 modes are displayed by varying the weight for the particular mode symmetrically around zero. The resulting two extreme surfaces are overlaid using transparency and highlight directions in which the particular mode varies.

A source surface warped to a subset of 774 target surfaces representing the left and right human hippocampus. Calculating the cross-covariance matrix of the surface point coordinates and subsequently the eigenvalue decomposition of the matrix, we decompose the shape variability into decorrelated modes sorted by variance. Here the first 10 modes are displayed by varying the weight for the particular mode symmetrically around zero. The resulting two extreme surfaces are overlaid using transparency and highlight directions in which the particular mode varies.

Figure 3.3   A source surface warped to a subset of 774 target surfaces representing the left and right human hippocampus. Calculating the cross-covariance matrix of the surface point coordinates and subsequently the eigenvalue decomposition of the matrix, we decompose the shape variability into decorrelated modes sorted by variance. Here the first 10 modes are displayed by varying the weight for the particular mode symmetrically around zero. The resulting two extreme surfaces are overlaid using transparency and highlight directions in which the particular mode varies.

Analyzing the modes of variation is instructive in itself, but we can also derive from them a compact representation of the shape of each target surface. Each target surface can be expressed in the space of shape modes by a weight vector that, when multiplied with the modes matrix and added together, approximates the target surface. Because modes are sorted by variance, we can limit the weight vector to a few entries for the modes that explain the most variance and remove weights that explain little in terms of variance. The resulting non-zero weights can be used as compact morphological measures for shape in subsequent analysis.

3.3.5  Statistical Analyses

Once a particular set of morphometric measures are produced from a collection of multi-subject MR images, these are typically entered into a statistical analysis to determine if individual differences are related to independent variables of interest. Most often this consists of performing a t-test or F-test for each morphometric measure if the independent variable is categorical, or a correlation coefficient if it is continuous. If one wants to include covariates of no interest, a general linear model (GLM) is often employed; see Chapter 9. Within this framework it is possible to perform group comparisons, and find brain correlates of various covariates such as age or disease progression.

The parametric statistical tests applied in the analysis of MRI data generally requires that the noise distribution does not depart too strongly from a Gaussian distribution. As noted above, the MR image intensities are non-negative since after Fourier reconstruction they are converted into magnitude images. This results in noise governed by a Rician distribution, which is substantially different from Gaussian only if the signal to noise of the data is small (61). Many factors affect SNR in MR images, including magnet strength and image acquisition parameters such as slice thickness, field of view, TR, TE, and flip angle (60). A correction for the intensity bias caused in regions with low signal-to-noise ratio (SNR) has been proposed in (54). In general, structural images are typically spatially smoothed, which both increases SNR and promotes a more Gaussian error distribution (3). Indeed, some authors have argued that modeling noise distributions as Rician adds considerable complexity to analyses with few tangible benefits (1).

3.3.5.1  Statistical Parametric Maps

In many instances, each MR image is summarized by a single, or at most a few, morphometric measures. Reporting the results of statistical analyses in this scenario differs little from other types of biomedical research studies. If multiple statistical tests are performed, one can control for inflation of Type I error rates via Bonferroni adjustments to p-values or by resampling-based algorithms such as those of Westfall–Young (128, 46).

In contrast, whole-brain voxel-wise approaches such as DBM, result in tens or hundreds of thousands of statistical models, one for each voxel (3). The resulting collection of statistical tests (e.g., t, chi-square, F, or Hotelling T 2 tests), after thresholding at a given critical value, is called a statistical parametric map (SPM) (30, 103). The appropriate threshold can be chosen via a number of criteria. Typically, one differentiates between methods that control the family-wise error rate (the probability of at least one false positive) or the false detection rate (the expected proportion of incorrectly rejected null hypothesis). Standard Bonferroni adjustments tend to be far too conservative, especially since the effective number of tests is typically much smaller than the number of voxels due to spatially correlated noise (16). Common multiple testing adjustments include random field theory (129, 21), permutation tests (59), and false discovery rate (47, 114). Chapter 9 covers random field theory; for additional review see (79). For additional review see (79). An alternative approach towards controlling for multiple testing in whole-brain analyses is to use multivariate statistical methods. This is what is done in the TBM analysis outlined above.

3.4  Miscellaneous Topics

3.4.1  Structural Integrity and Tumor Detection

MRI has proven to be extremely useful in detecting abnormalities in the brain. This could entail atrophy changes in the brain related to normal aging and disease progression (70), or the appearance of tumors. In fact, MRI is often able to detect many types of tumors at earlier stages of development than many other medical imaging modalities. The use of automated methods for MRI brain tumor segmentation is critical, as it provides important information for both medical diagnosis and surgical planning (73). It also offers the possibility of freeing doctors from the burdens involved in manual labeling. However, automated brain segmentation is a difficult problem due to inherent differences in the characteristics of different tumors, including their size, shape, location and intensity. For these reasons, manual tracing and delineation of tumors remains the gold standard.

More generally, MRI can be used to provide the information needed to both qualitatively and quantitatively describe the integrity of gray and white matter structures in the brain. For example, changes in the structural integrity of myelin can be measured with MRI as myelin breakdown increases the water content in white matter (10). In addition, MRI can together with diffusion weighted MRI, be used to provide a picture of white matter integrity. Also, since brain function may depend on the integrity of brain structure, it can be used together with fMRI to examine the impact of tissue loss or damage on functional responses.

3.4.2  Anatomical References for Functional Imaging

In any given functional MRI study, a number of high-resolution structural scans are collected and used for both preprocessing and presentation purposes. Typically, fMRI data is of relatively low spatial resolution (compared to structural MRI), and therefore provides relatively little anatomical detail. It is therefore useful to map the results obtained from an fMRI analysis onto a higher-resolution structural MR image for presentation purposes. This process, referred to as co-registration, is typically performed using either a rigid body or affine transformation. Because the functional and structural images are collected using different sequences and focus on different tissue properties with differences in average intensities, it is generally recommended that transformation parameters be estimated by maximizing the mutual information between the two images. Typically, a single structural image is co-registered to the first or mean functional image. Co-registration is also a necessary step for subsequent normalization of the functional data onto a template. Here the high-resolution structural image is transformed to a standard template and the same transformations are thereafter applied to the functional images that were previously co-registered to the structural scan; see Chapter 6 for more detail.

Finally, we are often interested in focusing our analysis on certain targeted regions of interest (ROI). In certain experiments with a targeted hypothesis of interest, one can pre-specify a set of anatomical regions a priori and perform statistical analysis solely on data associated with these regions. This can help minimize problems with multiple comparisons by limiting the required number of statistical tests. The structural ROIs can be defined using automated anatomical labeling of subject-specific data, allowing one to define ROIs for each subject based on their anatomy, or by using standard brain atlases.

3.4.3  Multi-Center Studies

Multi-center MRI studies are becoming an increasingly common method to answer scientific questions that would be difficult or impossible to address with a single site study (50). Multicenter studies can be especially advantageous with rare conditions, where recruiting subjects in sufficient numbers in a single geographic area would be difficult. However, the benefit from the increase in power from access to more subjects is potentially offset by differences in scanner properties that introduce substantial site effects to MRI data. If multiple sites acquire the image data, each scanner might introduce variations in the data that can hinder the detection of weak correlations or that may introduce spurious correlations. Documenting auxiliary measures such as the identity of the imaging scanner (i.e., device serial number) and the version of the software performing image reconstruction are therefore essential additional information that can lead to increased power to reject or confirm hypothesis.

A few MRI reliability studies have been performed. For example, (72) found that T 1-weighted MRI volumes produced from automated segmentation algorithms are fairly reliable as long as they are produced on the same platform and field strength. In light of recent articles critiquing the reliability of neuroscience research (19, 91), this promises to be an important area for future research.

3.4.4  Imaging Genetics

Imaging genetics is a relatively new field that attempts to associate genetic variation in a population to measures derived from structural or functional imaging (62, 120). If there are only one, or a few, genetic loci of interest, standard MRI analyses suffice. However, as with many complex phenotypes, morphometric properties of the human brain are most likely the product of many genetic loci, each with small effect (17). A genome-wide association study (GWAS) may involve millions of separate tests of association for each MR-derived outcome (120). This is a type of analysis that will clearly lead to enormous multiple testing problems.

Some authors have proposed statistical methods promoting sparse solutions for both domains simultaneously (e.g., (125)). Chen et al. (17) takes a different tack, using voxel-wise cortical surface area measures from an MRI twin study. The genetic correlation of surface area is computed for each pair of voxels, which is used to form a similarity matrix. A fuzzy clustering algorithm is applied to this similarity matrix, with the number of clusters selected via a silhouette coefficient. The end result is a probabilistic atlas of the human cortex based on genetically informed cluster assignment. Note, this approach reduces dimensionality dramatically, and reflects the fact that genetic effects are unlikely to be sparse.

3.5  Glossary of MRI Terms

Axon

A long threadlike part of a neuron, along which impulses are conducted from the cell body.

Brain Atlas

Reference brains where relevant brain structures are placed in a standardized coordinate system.

Cerebrospinal Fluid (CSF)

A watery fluid that flows in the ventricles and around the surface of the brain and spinal cord.

Dendrite

A branched extension of a neuron, along which impulses received from other cells are transmitted to the cell body.

Echo Time (TE)

The time between an excitation pulse and the start of data acquisition.

Field of View (FOV)

The extent of an image in space.

Field Strength

The strength of the static magnetic field of the MR scanner. It is typically measured in units of Tesla.

Flip Angle

The change in angle of the net magnetization immediately following excitation.

Glial Cell

A cell that surround neurons and provides them with support and nutrition.

Gray Matter (GM)

Tissue of the brain and spinal cord that consists primarily of nerve cell bodies and branching dendrites.

Image Registration

The process of transforming images into a standard coordinate system.

Image Segmentation

The process of partitioning the image according to different tissue types.

MPRAGE

Magnetization Prepared Rapid Acquisition Gradient Echo (MPRAGE) is a specialized pulse sequence defined for rapid acquisition.

Neuron

A nerve cell for processing and transmitting electrical signals.

Proton Density-Weighted Image

Images providing information about the number of protons contained within each voxel.

Pulse Sequence

The set of magnetic field gradients and oscillating magnetic fields used to create MR images.

Region of Interest (ROI)

An anatomical area of the brain of particular importance.

Repetition Time (TR)

The time between two successive excitation pulses.

Slice

The cross-section of the brain being imaged.

SPGR

Spoiled Gradient-Echo (SPGR) is a pulse sequence that destroy and remaining transverse magnetization at the end of each excitation.

Statistical Parametric Map (SPM)

An image where brain voxels are labeled according to the results of a statistical test.

T 1-Weighted Image

Images providing information about different tissues’ T 1 values.

T 2-Weighted Image

Images providing information about different tissues’ T 2 values.

Template Image

A standardized image used as the target in the process of image registration.

Voxel

A volume element. The basic unit of measurement of an MRI.

White Matter (WM)

Tissue of the brain and spinal cord that consists primarily of nerve fibers and their myelin sheaths.

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Rebranding to prevent association with ionizing radiation.

If the echo was caused by spins getting into alignment, the sequence is also called spin-echo sequence. They can also be caused by applying secondary gradients in faster gradient-echo sequences.

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