Maps of local growth rates (Figs 1–4) revealed the complexity and regional heterogeneity of the tissue growth, pruning and maturation processes of late brain development. In subjects aged 6–15 years, the highest growth rates were consistently attained in temporo-parietal systems which are functionally specialized for language, and for understanding spatial relations (Fig. 2). In contrast to the near-zero maps of change recovered at short time intervals ('Two-week interval' in Fig. 2), growth maps spanning large time intervals showed complex and heterogeneous patterns of change. Between ages 7 and 11 years (Fig. 2), comparative stability of the splenial and rostral fibre systems of the corpus callosum contrasted sharply with rapid focal growth at the callosal isthmus (up to 80%). Although global measurements indicated an overall 22.4% increase in mid-sagittal callosal area during the four-year time span (from 527.6 mm² to 645.6 mm ²), these global values disguise the complexity of local growth patterns. Local growth is as high as 80% (Fig. 2), a feature which may not be apparent with conventional volumetric descriptors.

Figure 1 Growth patterns in the developing human brain detected at ages 3–15 years.   Full legend   High resolution image and legend (43k)

Figure 2 Mapping dynamic patterns of brain development: four-dimensional growth maps.   Full legend   High resolution image and legend (177k)

Although some individual variation was expected, this focus of extreme growth at the callosal isthmus was detected consistently in all subjects tracked between 6 and 15 years (Fig. 2), suggesting that cortico-cortical networks supporting rapid associative relay and language functions may myelinate more extensively³ and over longer periods than rostral fibre systems. In a girl scanned twice exactly one year apart at ages 6 and 7 years, extreme growth (up to 85%) at the callosal isthmus contrasted with a comparatively quiescent region in the more rostral systems that innervate frontal and pre-frontal cortices. When a four-year growth map was generated for a slightly older child (11–15 years, Fig. 2), growth rates were correspondingly reduced in every region. Nonetheless, growth patterns at the isthmus and splenium (commonly defined as the posterior fifth of the callosum) were still more rapid (20–25% locally) than in the more anterior rostrum and genu (near-zero change). In an analysis of grey matter at the cortex⁴, we recently observed a localized grey matter loss in frontal cortex that persists in normal subjects throughout adolescence even into adulthood. The gradual quiescence of growth at the rostral callosum around puberty may therefore be a precursor to a prolonged regressive process of grey matter loss through adolescence into adulthood in the frontal circuits it innervates.

Several near-zero maps of change were recovered at short time intervals. Figure 2 shows a typical map from a subject scanned at age 8 years, exactly four years later at age 12 years, and again two weeks later. Negligible change at short time intervals ('Two-week interval' in Fig. 2) contrasted with a highly heterogeneous map of growth across the four-year time span. Growth rates again achieved their highest rates in the associative and linguistic networks that cross at the callosal isthmus.

A subject scanned at ages 3 and 6 years exhibited a focus of peak growth rates (60–80% locally) throughout the anterior corpus callosum, in frontal circuits that help to sustain a vigilant mental state and regulate the organization and planning of new actions. The extremely rapid rates of local growth are consistent with metabolic studies using positron emission tomography⁵, which show an extraordinary doubling of the rates of glucose metabolism in the frontal cortex between ages 2 and 4 years, with frontal metabolic rates remaining at 199% of their adult values throughout the age range of 3–8 years. Between ages 3 and 6 years, when language function and associative thinking are not yet fully developed, growth rates at the isthmus were more quiescent (Fig. 2; 0–20% growth). Later growth foci in the isthmus, found consistently in all subjects aged 6–15 years, may reflect fine tuning of language functions known to occur late in childhood.

Regressive processes (tissue loss) were also detected at the same time as rapid growth. In the 7–11 and 9–13 year old subjects (Fig. 3), maps of lobar growth revealed pronounced (2–6 mm) temporo-parietal and pre-frontal enlargement. Somatosensory, motor and occipital brain regions were comparatively stable, with near-zero change in all brain regions at short time intervals (Fig. 3b). Up to 50% loss of tissue volume was detected at the caudate head ( Fig. 4e and f). This tissue loss was highly localized, and contrasted with a 20–30% growth of the adjacent internal capsule (for which a separate surface model was made) and a 5–10% dilation of the superior ventricular horn (Fig. 4a). Gross volumetric measures confirmed an overall 60 mm³ tissue loss at the caudate head, although these global measures disguise the regional complexity of the change. This example helps illustrate how tensor maps distinguish local growth patterns (Fig. 4e) from bulk shifts, such as global displacements of the adjacent cerebral ventricles ( Fig. 4a and b). Three-dimensional vector displacement maps (Fig. 4b and d) emphasize that both global and local displacements are required to match modelled anatomical elements across time. The three-dimensional deformation field, however, encodes the patterns of local anatomical dilation and contraction, and its values are unaffected by global displacements. Maps of local three-dimensional growth are therefore not critically dependent on how well scans are initially aligned, and can define growth at arbitrary three-dimensional points in the local anatomy (Fig. 4e). Figure 4f indicates the anatomical context and regional complexity of these growth and regressive processes. The foci of tissue loss corroborate the hypothesis that pruning processes occur during this developmental stage², suggesting that these processes can be tracked in an individual child.

Figure 3 Patterns of cerebral growth.   Full legend   High resolution image and legend (77k)

Figure 4 Detecting three-dimensional patterns of deep nuclear tissue loss.   Full legend   High resolution image and legend (52k)

We detected striking, spatially complex patterns of growth and tissue loss in the developing human brain. A rostro-caudal wave of peak growth rates (Fig. 1) was identified in the corpus callosum. Fibre systems that mediate language function and associative thinking grew more rapidly than surrounding regions across time spans before and during puberty (6–13 years), with growth attenuated shortly afterwards (11–15 years). This temporal pattern coincides with the ending of a well-known critical period for learning language, consistently noted in studies of second-language acquisition, including sign language, and in isolated children not exposed to language during early development⁶. The ability to learn new languages declines rapidly after the age of 12 years, as does the ability to recover language function if linguistic areas in one brain hemisphere are surgically resected. Peak growth rates in linguistic callosal regions, as well as their attenuation around puberty, may reflect the conclusion of the critical period for learning language and for accelerating signal transduction in networks that support both associative reasoning and language function. We recently found that the same temporo-parietal fibre system, crossing at the callosal isthmus, degenerates fastest in early Alzheimer's disease⁷, when progressive neuronal loss and perfusion deficits begin to occur in temporo-parietal association cortices and their commissural projection systems. The sensitivity of the approach may therefore offer advantages in tracking fine-scale effects of therapeutic interventions in dementia and oncology, mapping the local complexities of disease processes using dynamic rather than static criteria.

Methods
Magnetic resonance imaging and pre-processing Three-dimensional (256² x 124 x 0.97 mm x 0.97 mm x 1.5 mm resolution) T₁-weighted fast SPGR (spoiled GRASS (gradient-recalled acquisition in the steady state)) MRI volumes were acquired from young normal subjects (mean age 8.6 +/- 3.1 years) at intervals ranging from two weeks to four years. For each scan pair, a radio-frequency bias field correction algorithm8 was applied to both scans to eliminate intensity drifts caused by scanner field inhomogeneity. The initial scan was then rigidly registered to the target using automated image registration software⁹ and resampled using chirp-Z (in-plane) and linear (out-of-plane) interpolation. Registered scans were histogram-matched (that is, their intensity distributions were equalized) and a preliminary map of differences in MRI signal intensities between the two scans was constructed^{1, 10}. Tensor models of structural change were then used to calculate rates of tissue dilation, contraction and shearing, mapping local patterns of change in three dimensions.

Image analysis A high-resolution surface model of the cortex was automatically extracted¹¹ from each scan pair, and three-dimensional digital anatomical models, based on parametric surface meshes^{12, 13}, were generated to represent a comprehensive set of deep sulcal, callosal, caudate and ventricular surfaces at each time point¹⁴. Surface models based on manually digitized data were averaged across multiple trials (N = 6) to minimize error¹⁵. These model surfaces provided anatomic constraints for an elastic image registration algorithm^{12, 14}. For each subject, this algorithm calculated a three-dimensional elastic deformation vector field, with 384² x 256 x 3, or approximately 0.1 billion degrees of freedom, reconfiguring the anatomy at the earlier time point into the shape of the anatomy of the later scan. Surface deformations were used to derive a volumetric deformation field from which local measures of three-dimensional tissue dilation or contraction were quantified. Landmark points, surfaces, and curved anatomic interfaces were matched up in the pair of three-dimensional image sets, and the biological validity of the resulting anatomical transformation was guaranteed by forcing a large system of anatomical surface boundaries to match exactly. These included multiple structural, functional, and tissue type boundaries in three dimensions, including the callosum, caudate, cortex and ventricles. The deformation field driving the earlier onto the later anatomy was extended to the full volume using a continuum-mechanical model based on the Cauchy–Navier operator of linear elasticity^{14, 16-18}. The resulting system of 0.1 billion second-order elliptic partial differential equations was solved by successive over-relaxation methods, with multi-grid acceleration^{12, 14}, on a standard radiologic workstation. Potential artefactual differences due to differences in how surfaces were parametrized in each scan were compensated for, using a field of Christoffel symbols to modify the surface differential operators during the anatomical transformation¹⁴.

Tensor map computation From this transformation, local rates of tissue dilation, contraction and shearing were calculated. Deformation processes recovered by the image-matching algorithm were analysed mathematically with vector field operators¹⁴ to produce a variety of tensor maps. These maps reflect the magnitude and principal directions of tissue dilation or contraction, and the local rates, divergence and gradients of the growth processes detected in the dynamically changing brain.