Mir Jalil Razavi

Cortical Folding Pattern and its Consistency Induced by Biological Growth

Cortical folding, characterized by convex gyri and concave sulci, has an intrinsic relationship to the brain’s functional organization. Understanding the mechanism of the brain’s convoluted patterns can provide useful clues into normal and pathological brain function. In this paper, the cortical folding phenomenon is interpreted both analytically and computationally, and, in some cases, the findings are validated with experimental observations. The living human brain is modeled as a soft structure with a growing outer cortex and inner core to investigate its developmental mechanism. Analytical interpretations of differential growth of the brain model provide preliminary insight into critical growth ratios for instability and crease formation of the developing brain. Since the analytical approach cannot predict the evolution of cortical complex convolution after instability, non-linear finite element models are employed to study the crease formation and secondary morphological folds of the developing brain. Results demonstrate that the growth ratio of the cortex to core of the brain, the initial thickness, and material properties of both cortex and core have great impacts on the morphological patterns of the developing brain. Lastly, we discuss why cortical folding is highly correlated and consistent by presenting an intriguing gyri-sulci formation comparison.

Role of mechanical factors in cortical folding development.

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 brains 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.

Nanoscale Surface Creasing Induced by Post-polymerization Modification.

Creasing in soft polymeric films is a result of substantial compressive stresses that trigger instability beyond a critical strain and have been directly related to failure mechanisms in different materials. However, it has been shown that programming these instabilities into soft materials can lead to new applications, such as particle sorting, deformable capillaries, and stimuli-responsive interfaces. In this work, we present a method for fabricating reproducible nanoscale surface instabilities using reactive microcontacting printing (μCP) on activated ester polymer brush layers of poly(pentafluorophenyl acrylate). The sizes and structures of the nanoscale creases can be modulated by varying the grafting density of the brush substrate and pressure applied during μCP. Stress is generated in the film under confinement due to the molecular weight increase of the side chains during post-polymerization modification, which results in substantial in-plane growth in the film and leads to the observed nanoscale creases.

Morphological patterns of a growing biological tube in a confined environment with contacting boundary

Growing soft tissue with a confined boundary is accompanied by a large strain and stress which lead to instability and the formation of surface wrinkling, folding or creasing. This paper presents the morphological evolution of the growth of a biological tube composed of a neo-Hookean hyperelastic material within a confined environment. Critical growth ratios for the triggering of creases or detachment from the contacting boundary have been investigated both analytically and numerically. Results show that compressive residual stresses induced by confined growth of the tubular tissue can lead to a variety of surface folding patterns which strongly depend on the thickness of the tube. In a thick tube creases begin to form at the inner surface of the tube and in a thin tube the structure detaches from the confining wall. Between these two extremes there is a transitional area wherein the tube starts to crease at first and then detaches from the confining wall. Further modeling reveals that a gap between the tube and the confinement can tune the shape evolution of the growing biological tube. These findings may provide some fundamental understanding to growth modeling of complicated biological phenomena such as cortical folding of the brain and the growth of solid tumors.

Commonly preserved and species-specific gyral folding patterns across primate brains.

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.

Surface and interfacial creases in a bilayer tubular soft tissue.

Surface and interfacial creases induced by biological growth are common types of instability in soft biological tissues. This study focuses on the criteria for the onset of surface and interfacial creases as well as their morphological evolution in a growing bilayer soft tube within a confined environment. Critical growth ratios for triggering surface and interfacial creases are investigated both analytically and numerically. Analytical interpretations provide preliminary insights into critical stretches and growth ratios for the onset of instability and formation of both surface and interfacial creases. However, the analytical approach cannot predict the evolution pattern of the model after instability; therefore nonlinear finite element simulations are carried out to replicate the poststability morphological patterns of the structure. Analytical and computational simulation results demonstrate that the initial geometry, growth ratio, and shear modulus ratio of the layers are the most influential factors to control surface and interfacial crease formation in this soft tubular bilayer. The competition between the stretch ratios in the free and interfacial surfaces is one of the key driving factors to determine the location of the first crease initiation. These findings may provide some fundamental understanding in the growth modeling of tubular biological tissues such as esophagi and airways as well as offering useful clues into normal and pathological functions of these tissues.

Mechanisms of circumferential gyral convolution in primate brains

Mammalian cerebral cortices are characterized by elaborate convolutions. Radial convolutions exhibit homology across primate species and generally are easily identified in individuals of the same species. In contrast, circumferential convolutions vary across species as well as individuals of the same species. However, systematic study of circumferential convolution patterns is lacking. To address this issue, we utilized structural MRI (sMRI) and diffusion MRI (dMRI) data from primate brains. We quantified cortical thickness and circumferential convolutions on gyral banks in relation to axonal pathways and density along the gray matter/white matter boundaries. Based on these observations, we performed a series of computational simulations. Results demonstrated that the interplay of heterogeneous cortex growth and mechanical forces along axons plays a vital role in the regulation of circumferential convolutions. In contrast, gyral geometry controls the complexity of circumferential convolutions. These findings offer insight into the mystery of circumferential convolutions in primate brains.

Mechanism of Consistent Gyrus Formation: an Experimental and Computational Study.

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.

4D Origami by Smart Embroidery

There exist many methods for processing of materials: extrusion, injection molding, fibers spinning, 3D printing, to name a few. In most cases, materials with a static, fixed shape are produced. However, numerous advanced applications require customized elements with reconfigurable shape. The few available techniques capable of overcoming this problem are expensive and/or time-consuming. Here, the use of one of the most ancient technologies for structuring, embroidering, is proposed to generate sophisticated patterns of active materials, and, in this way, to achieve complex actuation. By combining experiments and computational modeling, the fundamental rules that can predict the folding behavior of sheets with a variety of stitch-patterns are elucidated. It is demonstrated that theoretical mechanics analysis is only suitable to predict the behavior of the simplest experimental setups, whereas computer modeling gives better predictions for more complex cases. Finally, the applicability of the rules by designing basic origami structures and wrinkling substrates with controlled thermal insulation properties is shown.

Erratum: Corrigendum: Mechanism of Consistent Gyrus Formation: an Experimental and Computational Study

Scientific Reports 6: Article number: 37272; published online: 17 November 2016; updated: 07 March 2017. In the methods section, under the subheading ‘Human Fetal Brain Atlas Dataset’ “Generally, this dataset includes T2 templates and tissue probability maps (for the brain mask, cortex, hemispheres,cerebrospinal fluid [CSF], and ventricles) for ages between 23–37 weeks of gestation.