Dynamic Brain Atlases

11.1 4D Coordinate Systems

Atlasing of developmental brain data presents unique challenges. Imposition of standardized coordinate systems is difficult, and their relationship to anatomic nomenclature is hard to define, when potentially drastic morphological differences exist among data sets. In Yoon et al. [136], a photographic atlas of the human embryo was created, based on detailed observations in utero from the 4th to the 7th week after ovulation (Carnegie Stages 10-18). In Chong et al. [13], 26 normal formalin-fixed fetal specimens with a gestational age of 9 to 24 weeks were examined with high-resolution MRI using a conventional clinical magnet and pulse sequences, and MR findings were correlated with histologic atlas data. Although templates of normal development helped to identify expected developmental features, it was noted that direct correlation of fetal MR images with anatomic atlases might result in a mistaken diagnosis of delayed development, because of a time lag in the detection of structures on MR images.

Current atlases of fetal development [29,73] use collections of labeled data from multiple imaging modalities to characterize specific developmental stages. The first comprehensive MRI atlas of pediatric cranial anatomy [86] incorporates 180 MRI scans acquired parallel to the orbito-meatal anatomical plane, and 360 explanatory diagrams depicting functional neuroanatomy from birth through 16 years of age. In this collection, 3D horizontal and sagittal images facilitate identification of sulci and gyri. However, stereotaxic coordinate systems were not applied to the atlas data because of difficulties in using them to reference embryonic and pediatric data. In the spirit of the deformable atlas methods described earlier, extreme deformations could be imposed to fit all stages of development into a standardized atlas, but this would hardly meet the primary requirement of atlasing, which is to provide a natural coordinate framework in which to localize and classify structures present in developing brains. Alternatively, different atlases and coordinate systems for several discrete stages of development might be used. Numerous anatomic features, because of their emergence and disappearance during development, could be used to place individual brains into an appropriate atlas in the set. Warping approaches could then be applied to the atlas coordinate systems as a basis to compare and quantitate development [112,113, 120].

In many ways, static representations of brain structure are ill suited to analyzing dynamic processes of brain development and disease. Dramatic changes in brain geometry in brain development and disease mandate the design of mathematical systems to track anatomical changes over time, and map dynamic patterns of growth or degeneration.

11.2 Temporal Maps of Brain Structure

Current structural brain imaging investigations typically focus on the analysis of 3D models of brain structure, derived from volumetric images acquired at a single time point from each subject in the study. However, serial scanning of human subjects, when combined with warping and analysis algorithms, can enable disease and growth processes to be tracked in their full spatial and temporal complexity. Maps of anatomical change can be generated by warping scans acquired from the same subject over time [105,112]. Serial scanning of human subjects [34,37,112] or experimental animals [54] in a dynamic state of disease or development offers the potential to create 4D models of brain structure. These models incorporate dynamic descriptors of how the brain changes during maturation or disease.

In our initial human studies [113] we developed several algorithms to create 4D quantitative maps of growth patterns in the developing human brain. Time series of high-resolution pediatric MRI scans were analyzed. The resulting tensor maps of growth provided spatially detailed information on local growth patterns, quantifying rates of tissue maturation, atrophy, shearing, and dilation in the dynamically changing brain architecture. Pairs of scans were selected to determine patterns of structural change across the interval between the two scans. These scan pairs were preprocessed with a radio-

FIGURE 7 Growth patterns in the developing human brain. A young normal subject was scanned at the age of 7, and again four years later, aged 11, with the same protocol (data from [112]). Scan histograms were matched, rigidly registered, and a voxel-by-voxel map of intensity differences (left) reveals global growth. In a control experiment, identical procedures were applied to two scans from a 7-year-old subject acquired just 2 weeks apart, to detect possible artifactual change due to mechanical effects, and due to tissue hydration or CSF pressure differences in the young subject between the scans. These artifacts were minimal, as shown by the difference image, which, as expected, is largely noise. Rigid registration of the scans does not localize anatomic change, but is a precursor to more complex tensor models of structural change (see main text). Tensor maps of growth [112] not only map local patterns of differences or change in three dimensions, but also allow calculations of rates of dilation, contraction, shearing, and torsion [112, 120]. See also Plate 110.

FIGURE 8 Tensor maps of growth. (Top panel) A complex pattern of growth is detected in the corpus callosum of a young normal male subject in the 4-year period from 7 to 11 years of age. Vector field operators emphasize patterns of contractions and dilations, emphasizing their regional character. The color code shows values of the local Jacobian of the warping field, which indicates local volume loss or gain. The effects of the transformation are shown on a regular grid ruled over the reference anatomy and passively carried along in the transformation that matches it with the later anatomy. Despite minimal changes in overall cerebral volume, callosal growth is dramatic, with peak values occurring throughout the posterior midbody. Pronounced neuroanatomical growth in the 4-year interval (top panel) contrasts sharply with the negligible change detected over a 2-week time-span (middlepanel). Rapid heterogeneous growth, with a strikingly similar topographic pattern, is also observed in a young normal female (bottom panel), during a 4-year period spanning puberty, from 9 to 13 years of age. See also Plate 111.

frequency bias field correction algorithm, and rigidly registered using automated image registration software [132]. Registered scans were then histogram-matched and a preliminary map of differences in MR signal intensities between the two scans was constructed (Fig. 7). Parameterized cortical surface models were automatically extracted from each of the mutually registered histogram-matched scans. Deformation processes recovered by the warping algorithm were then analyzed using vector field operators to produce a variety of tensor maps (Figs 8, 9). These maps were designed to reflect the magnitude and principal directions of dilation or contraction, the rate of strain, and the local curl, divergence, and gradient of flow fields representing the growth processes recovered by the transformation.

It is to be hoped that in the near future we will be able to create 4D atlases that map growth and degeneration in their full spatial and temporal complexity. In spite of logistic and technical challenges, these mapping approaches hold tremendous promise for representing, analyzing, and understanding

FIGURE 9 3D patterns of deep nuclear tissue loss. (a) 3D displacement vector maps show the deformation required to match the caudate head in the earlier scan (at 7 yrs) with its counterpart in the later scan (11 yrs). (b) Stability of the caudate tail (blue colors) contrasts sharply with dorsolateral regression of the caudate head and ventromedial progression of the internal capsule. These surface deformations are used to derive a volumetric deformation field (vectors, (b)), from which local measures of three-dimensional tissue dilation or contraction can be quantified (c). In a smaller region selected for detailed analysis (green square, inset, (d)), a local 50% tissue loss was detected at the caudate head, as well as a 20-30% growth of the internal capsule and a 5-10% dilation of the superior ventricular horn. Visualization (d) of these maps in a graphical format indicates the anatomical context and regional complexity of the growth and regressive processes detected during the period spanned by the two scans. See also Plate 112.

FIGURE 9 3D patterns of deep nuclear tissue loss. (a) 3D displacement vector maps show the deformation required to match the caudate head in the earlier scan (at 7 yrs) with its counterpart in the later scan (11 yrs). (b) Stability of the caudate tail (blue colors) contrasts sharply with dorsolateral regression of the caudate head and ventromedial progression of the internal capsule. These surface deformations are used to derive a volumetric deformation field (vectors, (b)), from which local measures of three-dimensional tissue dilation or contraction can be quantified (c). In a smaller region selected for detailed analysis (green square, inset, (d)), a local 50% tissue loss was detected at the caudate head, as well as a 20-30% growth of the internal capsule and a 5-10% dilation of the superior ventricular horn. Visualization (d) of these maps in a graphical format indicates the anatomical context and regional complexity of the growth and regressive processes detected during the period spanned by the two scans. See also Plate 112.

the extremely complex dynamic processes that affect regional anatomy in the healthy and diseased brain.

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