Deciphering mysteries of the structure-function relationship in cortical folding has emerged as the cynosure of recent research on brain. Understanding the mechanism of convolution patterns can provide useful insight into the normal and pathological brain function. However, despite decades of speculation and endeavors the underlying mechanism of the brain folding process remains poorly understood. This paper focuses on the three-dimensional morphological patterns of a developing brain under different tissue specification assumptions via theoretical analyses, computational modeling, and experiment verifications. The living human brain is modeled with a soft structure having outer cortex and inner core to investigate the brain development. Analytical interpretations of differential growth of the brain model provide preliminary insight into the critical growth ratio for instability and crease formation of the developing brain followed by computational modeling as a way to offer clues for brain's postbuckling morphology. Especially, tissue geometry, growth ratio, and material properties of the cortex are explored as the most determinant parameters to control the morphogenesis of a growing brain model. As indicated in results, compressive residual stresses caused by the sufficient growth trigger instability and the brain forms highly convoluted patterns wherein its gyrification degree is specified with the cortex thickness. Morphological patterns of the developing brain predicted from the computational modeling are consistent with our neuroimaging observations, thereby clarifying, in part, the reason of some classical malformation in a developing brain.

Electrospun fibrous mats, characterized by their large surface-to-volume ratios, have unique and beneficial properties for various applications. The micro or nanoscale architectures of these structures significantly affects the mechanical properties of the material. The lack of knowledge for predicting the mechanical behavior of electrospun fibrous mats may prevent applications utilizing the se mats from reaching their full potential. In this paper, we propose a new computational model to predict the mechanical behavior of an electrospun fibrous mat by considering its microstructure and the percentage of the cross-points that are bonded. The model of the electrospun mat with randomly distributed fibers is considered in uniaxial and biaxial tension. Three cases are studied: (1) no interaction in cross-points of intersecting fibers, (2) half of the cross-points are bonded, (3) all of the cross-points are bonded. The results show that along with the mechanical properties of individual fibers, the fusion bonding of fibers is a critical parameter for tuning the mechanical properties of the bulk material. In a predefined porosity, the interfiber fusion enhanced the stiffness of the mat by 60%, which is independent of the loading mode and the mechanical property of individual fibers. For all ranges of porosities, bonding increases the stiffness of the mat; however, the bonding is more effective at stiffening when the porosity of the mat is low.

Cortical folding pattern analysis is very important to understand brain organization and development. Since previous studies mostly focus on human brain cortex, the regularity and variability of cortical folding patterns across primate brains (macaques, chimpanzees and human) remain largely unknown. This paper presents a novel computational framework to identify common or unique gyral folding patterns in macaque, chimpanzee and human brains using magnetic resonance imaging (MRI) data. We quantitatively characterize gyral folding patterns via hinge numbers with cortical surfaces constructed from MRI data, and identify 6 common three-hinge gyral folds that exhibit consistent anatomical locations across these three species as well as 2 unique three hinges in macaque, 6 ones in chimpanzee and 14 ones in human. A novel morphology descriptor is then applied to classify three-hinge gyral folds, and the increasing complexity is identified among the species analyzed. This study may provide novel insights into the regularity and variability of the cerebral cortex from developmental perspective and may potentially facilitate novel neuroimage analyses such as cortical parcellation with correspondences across species in the future.

As a significant type of cerebral cortical convolution pattern, the gyrus is widely preserved across species. Although many hypotheses have been proposed to study the underlying mechanisms of gyrus formation, it is currently still far from clear which factors contribute to the regulation of consistent gyrus formation. In this paper, we employ a joint analysis scheme of experimental data and computational modeling to investigate the fundamental mechanism of gyrus formation. Experimental data on mature human brains and fetal brains show that thicker cortices are consistently found in gyral regions and gyral cortices have higher growth rates. We hypothesize that gyral convolution patterns might stem from heterogeneous regional growth in the cortex. Our computational simulations show that gyral convex patterns may occur in locations where the cortical plate grows faster than the cortex of the brain. Global differential growth can only produce a random gyrification pattern, but it cannot guarantee gyrus formation at certain locations. Based on extensive computational modeling and simulations, it is suggested that a special area in the cerebral cortex with a relatively faster growth speed could consistently engender gyri.

Recent studies have shown that quantitative description of gyral shape patterns offers a novel window to examine the relationship between brain structure and function. Along this research line, this paper examines a unique and interesting type of cortical gyral region where 3 different gyral crests meet, termed 3-hinge gyral region. We extracted 3-hinge gyral regions in macaque/chimpanzee/human brains, quantified and compared the relevant DTI-derived fiber densities in 3-hinge and 2-hinge gyral regions. Our observations consistently showed that DTI-derived fiber densities in 3-hinge regions are much higher than those in 2-hinge regions. Therefore, we hypothesize that besides the cortical expansion, denser fiber connections can induce the formation of 3-hinge gyri. To examine the biomechanical basis of this hypothesis, we constructed a series of 3-dimensional finite element soft tissue models based on continuum growth theory to investigate fundamental biomechanical mechanisms of consistent 3-hinge gyri formation. Our computational simulation results consistently showed that during gyrification gyral regions with higher concentrations of growing axonal fibers tend to form 3-hinge gyri. Our integrative approach combining neuroimaging data analysis and computational modeling appears effective in probing a plausible theory of 3-hinge gyri formation and providing new insights into structural and functional cortical architectures and their relationship.