Development of cortical shape in the human brain from 6 to 24 months of age via a novel measure of shape complexity
Introduction
Many quantitative brain morphometric measurements, such as regional volumes (Holland et al., 2014, Koran et al., 2014, Lange et al., 2015, Marcus Jenkins et al., 2013, Sowell et al., 2002), cortical thickness, and surface area (Hudziak et al., 2014, Sowell et al., 2004, Storsve et al., 2014, Zielinski et al., 2014) have been used to analyze for brain development, clinical differences, and diagnostic guidelines. These measurements allow for analyses of the global or local developmental trajectory over age, differential anatomical changes, and the relationship between anatomical changes and brain functions or environment factors. As the human cerebral cortex is a highly folded, convoluted object composed of sulci and gyri, the maturation patterns of sulcal and gyral folding have increasingly been studied.
Historically, older studies of cortical folding have focused on global measurements that encompass whole hemispheres, particularly the global gyrification index (GI) measurement, which is defined as the area ratio between the outer cortical surface, such as cerebral hull surface, and the cortical gray matter surface (Armstrong et al., 1995). While global GI measurements have the strong advantage of scale invariance, they generally cannot yield localized measures of complexity. Another global cortical folding measure is the fractal dimension (FD) (Free et al., 1996), which provides information about the inherent scale of the folding in such a complex structure. It has the advantage of being free of a reference smooth surface, such as the cerebral hull for GI, but it has shown to be very sensitive to noise in the surface reconstruction (Free et al., 1996).
More recently, local measurements have been emerging due to developing computing technology. The traditional FD analysis used a box-counting approach, but that has to assure the subject alignment and normalize of brain size. The spherical harmonic reconstruction reduced the effect of alignment error and brain size variant (Yotter et al., 2011). Also, the cortical surface's local intrinsic or extrinsic curvatures at each location were proposed as surrogate measures of cortical folding (Gaser et al., 2006, Li et al., 2010, Li et al., 2014). Both intrinsic (called Gaussian curvature) and extrinsic curvatures (called mean curvature) are fundamental measurements of local surface shape. Intrinsic curvature captures the tangential expansion of the local surface and quantifies the amount of excessive local area compared to the projected area in a tangential plane with the sign capturing whether the local setting is cup-like or saddle-like (Ronan et al., 2012, Ronan et al., 2014). Similarly, local sulcal depth (Dierker et al., 2015, Meng et al., 2014, Rettmann et al., 2006) and sulcal length (Kochunov et al., 2010) measures have been suggested for analysis as sulcal depth captures a coarse, simplified measure of folding distance to the cerebral hull in the child and fetal cerebral cortex of primates.
However, the definition of kernel size or window would be an issue in performing the local analysis. The local measures of GI have been proposed using a larger sized kernel defined by Euclidean distance (Su et al., 2013) or a quasi-geodesic N-ring neighborhood (Li et al., 2014, Schaer et al., 2008). The Euclidean spherical kernel was defined using intersecting locations between the outer surface and a sphere of fixed radius. For the local GI analysis to be sensible, an adaptive kernel size needs to encompass at least one sulcal or gyral region. Larger sizes were usually chosen, typically larger than 20 mm–25 mm, which leads to local GI measures that encompass several gyri and sulci within the same kernel. None of the local curvature-based studies known to the authors take into account the overall brain surface size, which affects the density of the cortical surface sampling. Thus, larger brains would generally encompass larger local areas for averaging the curvature within a certain kernel size than smaller brain would. Local GI studies often correct for overall brain size differences. However, the local change of surface area has not been taken into account in longitudinal studies of brain development (Li et al., 2014).
Sulcal or gyral patterns analyzed via the above measures may reflect morphological development and pathological functioning associated with neuropsychiatric disorders, such as autism and schizophrenia (Lui et al., 2011). The development of morphological folding is apparent from approximately 16 weeks of gestational age and develops into an increasingly complex folding pattern into the early childhood period (Armstrong et al., 1995, Wright et al., 2014, Zilles et al., 1988). While the predominant view is one of consistent increase in cortical folding complexity, with considerable variability of the exact pattern across different studies, Rettmann et al. (2006) have reported a decrease in local cortex curvature in the central, cingulate, and parieto-occipital sulcal regions over the first 4-years of human development. The observed diversity of reported results in cortical folding studies may arise from multiple factors, mainly the selection of the measure, as well as the choice of scale. Studies of sulcal depth and local curvature yield measures at a very fine scale, measured just within the immediate neighborhood of a cortical location, whereas studies of local GI yield relatively large scale measures, capturing regions across multiple sulci and gyri, combining regions that may be functionally quite divergent.
In this work, we propose an alternative scale that quantifies the cortical folding via a local complexity metric computed within an intermediate neighborhood size that does not span across multiple gyri or sulci. This novel measure complements the existing set of cortical folding measures and provides a novel viewpoint to the study of cortical complexity that is relevant for understanding and investigating underlying mechanisms of development in the early postnatal period. This measure is able to distinguish whether a sulcal or gyral region undergoes a widening or deepening process, which would be undistinguishable via local GI measures. Also, we aim with the measure to capture the emergence and development of secondary and tertiary sulci with enhanced localization as compared to GI due to the smaller kernel size. It is furthermore noteworthy that the discussion of the kernel size is often treated with limited consideration. Like intrinsic curvature and GI measures, the novel measure we propose here is susceptible to the choice of the kernel size, which we aim to address via the kernel size normalization. This normalization of the kernel size allows the proposed surface complexity index (SCI) to have invariant results in terms of brain size and also takes into account expected surface area changes in longitudinal studies. In addition, the SCI is directly measureable on surface points without the need of reference surfaces, such as the smoothed or inflated/simplified brain surface needed for the computation of GI. Finally, in a reliability study, we demonstrate the robustness and stability of the SCI measure.
Section snippets
Participants
We studied 202 brain MR images from typically developing subjects with no family history of autism spectrum disorder assessed at 6, 12 and 24 months of age as part of a National Institutes of Health-funded, multi-site, Autism Centers of Excellence (ACE) Network study: the Infant Brain Imaging Study (IBIS). The MRI scans were acquired at 4 different sites (University of North Carolina at Chapel Hill, University of Washington at Seattle, Washington University at Saint Louis and Children's Hospital
Local complexity example
Fig. 3 shows two examples of the local SCI measure alongside the local SI histogram distribution and the idealized histogram of its corresponding best fitting basic geometry setting. In this particular example, the selected gyral region, which is close to a gyral top, is more complex than the selected sulcal region as indicated by the higher EMD score (Fig. 3a). The deep sulcal fundus regions, sulcal wall in deep sulcal regions or wide gyral regions tend to have simpler complexity, as expected,
Local shape complexity index (SCI)
This paper introduces a novel method called shape complexity index for the quantification of local cortical shape. The SCI maps show that wide sulcal fundal regions display the lowest levels of local complexity, whereas several gyral walls and narrow gyral ridges display a high level of complexity. Gyral saddle regions and wider gyral ridges display intermediate complexity levels. As concave cup and convex dome regions are located at the opposite extremes of the SI scale, these cortical
Conclusion
In this paper, we propose a novel method to calculate local cortical surface shape complexity that does not require a reference simplified surface model. The measure captures local shape changes mainly within a single sulcal or gyral region, which allows us to discriminate the widening (reduced SCI) versus deepening (non-reduced SCI) of regions, as well as to identify regions with developing secondary and tertiary sulci. The proposed SCI does not aim to capture any particular cortical region
Funding
IBIS Network: The Infant Brain Imaging Study (IBIS) Network is an NIH funded Autism Center of Excellence project and consists of a consortium of 8 universities in the U.S. and Canada. Clinical Sites: University of North Carolina: J. Piven (IBIS Network PI), H.C. Hazlett, C. Chappell; University of Washington: S. Dager, A. Estes, D. Shaw; Washington University: K. Botteron, R. McKinstry, J. Constantino, J. Pruett; Children's Hospital of Philadelphia: R. Schultz, S. Paterson; University of
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