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4-year Interval

2 weeks

Figure 5.4. Growth patterns in the developing human brain. A young normal subject was scanned at the age of 7 and again four years later, at the age of 11, with the same protocol (data from Thompson et al., 1998a). Scan histograms were matched and 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 anatomical change but is a precursor to more complex tensor models of structural change (see the main text and Figures 5.5 and 5.6), which not only map local patterns of differences or change in three dimensions, but also allow calculations of rates of dilation, contraction, shearing, and torsion (Toga et al., 1996; Thompson et al., 1998a). (See Color Plate 3.)

Figure 5.4. Growth patterns in the developing human brain. A young normal subject was scanned at the age of 7 and again four years later, at the age of 11, with the same protocol (data from Thompson et al., 1998a). Scan histograms were matched and 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 anatomical change but is a precursor to more complex tensor models of structural change (see the main text and Figures 5.5 and 5.6), which not only map local patterns of differences or change in three dimensions, but also allow calculations of rates of dilation, contraction, shearing, and torsion (Toga et al., 1996; Thompson et al., 1998a). (See Color Plate 3.)

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.

Three-dimensional (2562 x 124 resolution) 71-weighted fast SPGR (spoiled GRASS) MRI volumes were acquired from young normal subjects (mean age: 8.6 + 3.1 years) at intervals ranging from 2 weeks to 4 years. 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 frequency bias field correction algorithm, and rigidly registered using automated image registration software (Woods, Mazziotta, and Cherry, 1993). Registered scans were then histogram-matched, and a preliminary map of differences in MR signal intensities between the two scans was constructed (Figure 5.4). While difference maps help to determine whether structural change has occurred in such diseases as dementia (Freeborough, Woods, and Fox, 1996), these maps do not localize change, nor do they provide three-dimensional measures of dilation, contraction, or shearing of anatomical regions. To address this, parametric mesh models (Thompson et al., 1996a, 1996b, 1997, 1998a) were created to represent a comprehensive set of deep sulcal, callosal, caudate, and ventricular surfaces at each time point. Surface models based on manually digitized data were averaged across multiple trials (N = 6) to minimize error. The deformation field that is required to match the surface anatomy of one scan with the other was extended to the full volume using a continuum-mechanical model based on the Cauchy-Navier operator of linear elasticity (Thompson and Toga, 1998). Deformation processes recovered by the warping algorithm were then analyzed using vector field operators to produce a variety of tensor maps (Figures 5.5 and 5.6). 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.

Tensor Maps of Growth In contrast to the near-zero maps of change recovered at short time intervals (2 weeks), tensor maps of growth spanning large time in

Figure 5.5. Tensor maps of callosal growth. A complex pattern of growth is detected in the corpus callosum of a young normal subject (upper panel). This map illustrates structural change occurring in the 4-year period from 7 to 11 years of age. The effects of the transformation are shown on a regular along in the transformation that matches it with the target. Despite minimal changes in overall cerebral volume, callosal growth is dramatic, with peak values occurring at the isthmus. The pattern of growth contrasts with the near-zero maps of change observed between scans acquired over a 2-week inter-

Figure 5.5. Tensor maps of callosal growth. A complex pattern of growth is detected in the corpus callosum of a young normal subject (upper panel). This map illustrates structural change occurring in the 4-year period from 7 to 11 years of age. The effects of the transformation are shown on a regular along in the transformation that matches it with the target. Despite minimal changes in overall cerebral volume, callosal growth is dramatic, with peak values occurring at the isthmus. The pattern of growth contrasts with the near-zero maps of change observed between scans acquired over a 2-week inter-

grid ruled over the reference anatomy and passively carried val (lower panel).

tervals (4 years) showed complex and heterogeneous patterns of change. In one subject who was scanned at ages 7, 9, and 11, comparative stability of lobar and thalamic anatomy and negligible changes at the cortex were accompanied by pronounced focal growth of the callosal isthmus (Figure 5.5), ventricular enlargement, and loss of caudate tissue.

Growth in Callosal Anatomy To further characterize the growth process at the callosum (Figure 5.5), derived properties of the deformation fields were examined (Figure 5.6), including local expansion, contraction, or shearing effects recovered by the warping transformation. As was noted earlier, the Jacobian of the deformation field has been used as a local index of gender-specific shape differences in the corpus callosum (Davatzikos, 1996), while here it is used to indicate its growth. Other local vector field operators, including the gradient and divergence (Vu(x), Vr¬Ľu(x); see Thompson et al., 1998a) and the specialized norm x divergence operator (\\u(x)\\.'T*u(x); see Thirion and Calmon, 1997) can be applied to deformation fields. These operators are specifically designed to reveal and emphasize different aspects of growth or pathological processes, including their local magnitude and directional biases.

Regional Topography of Callosal Growth Figure 5.6 shows the complex patterns of growth detected in a young normal subject during the 4-year period from 7 to 11 years of age. Despite minimal changes in overall

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