The origin of compression influences geometric instabilities in bilayers

Geometric instabilities in bilayered structures control the surface morphology in a wide range of biological and technical systems. Depending on the application, different mechanisms induce compressive stresses in the bilayer. However, the impact of the chosen origin of compression on the critical conditions, post-buckling evolution and higher-order pattern selection remains insufficiently understood. Here, we conduct a numerical study on a finite-element set-up and systematically vary well-known factors contributing to pattern selection under the four main origins of compression: film growth, substrate shrinkage and whole-domain compression with and without pre-stretch. We find that the origin of compression determines the substrate stretch state at the primary instability point and thus significantly affects the critical buckling conditions. Similarly, it leads to different post-buckling evolutions and secondary instability patterns when the load further increases. Our results emphasize that future phase diagrams of geometric instabilities should incorporate not only the film thickness but also the origin of compression. Thoroughly understanding the influence of the origin of compression on geometric instabilities is crucial to solving real-life problems such as the engineering of smart surfaces or the diagnosis of neuronal disorders, which typically involve temporally or spatially combined origins of compression

On the influence of inhomogeneous stiffness and growth on mechanical instabilities in the developing brain

The characteristic surface morphology of the mammalian brain is closely correlated with brain function and dysfunction. During development, the initially smooth surface evolves into an elaborately convoluted pattern. Growing evidence suggests that mechanical instabilities emerging from differential growth between a faster growing outer gray matter and a slower growing inner white matter play a major role in brain morphogenesis. Previous studies assume uniform growth and stiffness; yet, recent experiments indicate that the properties of brain tissue are highly inhomogeneous. Here, we hypothesize that regionally varying developmental pathways across the brain result in nonuniform material properties at the onset of cortical folding. We establish a computational model of brain growth to explore the effects of stiffness and growth variations in gray and white matter tissue to mimic cellular processes and evolving tissue microstructure. We present an effective approach to determine critical growth values from geometrical data and systematically study the effect of inhomogeneous material properties on growth-induced primary and secondary instabilities. Our results reveal that critical growth and wavelength strongly depend on the stiffness distribution in the developing brain. Regional variations in cortical growth affect secondary instabilities and evoke highly irregular folding patterns, but characteristic wavelength and critical growth remain relatively stable. The interplay of different influential factors including cortical thickness, brain geometry, stiffness, and growth explains how primary folds are highly preserved across individuals, whereas secondary and tertiary folds vary significantly. Our findings are directly applicable to imaging data of fetal brains and ultimately enable early diagnostics of cortical malformations to improve treatment of neurodevelopmental disorders including epilepsy, autism, spectrum disorders, and schizophrenia

The role of mechanics during brain development

Convolutions are a classical hallmark of most mammalian brains. Brain surface morphology is often associated with intelligence and closely correlated with neurological dysfunction. Yet, we know surprisingly little about the underlying mechanisms of cortical folding. Here we identify the role of the key anatomic players during the folding process: cortical thickness, stiffness, and growth. To establish estimates for the critical time, pressure, and the wavelength at the onset of folding, we derive an analytical model using the Föppl–von Kármán theory. Analytical modeling provides a quick first insight into the critical conditions at the onset of folding, yet it fails to predict the evolution of complex instability patterns in the post-critical regime. To predict realistic surface morphologies, we establish a computational model using the continuum theory of finite growth. Computational modeling not only confirms our analytical estimates, but is also capable of predicting the formation of complex surface morphologies with asymmetric patterns and secondary folds. Taken together, our analytical and computational models explain why larger mammalian brains tend to be more convoluted than smaller brains. Both models provide mechanistic interpretations of the classical malformations of lissencephaly and polymicrogyria. Understanding the process of cortical folding in the mammalian brain has direct implications on the diagnostics of neurological disorders including severe retardation, epilepsy, schizophrenia, and autism

Physical biology of human brain development

Neurodevelopment is a complex, dynamic process that involves a precisely orchestrated sequence of genetic, environmental, biochemical, and physical events. Developmental biology and genetics have shaped our understanding of the molecular and cellular mechanisms during neurodevelopment. Recent studies suggest that physical forces play a central role in translating these cellular mechanisms into the complex surface morphology of the human brain. However, the precise impact of neuronal differentiation, migration, and connection on the physical forces during cortical folding remains unknown. Here we review the cellular mechanisms of neurodevelopment with a view toward surface morphogenesis, pattern selection, and evolution of shape. We revisit cortical folding as the instability problem of constrained differential growth in a multi-layered system. To identify the contributing factors of differential growth, we map out the timeline of neurodevelopment in humans and highlight the cellular events associated with extreme radial and tangential expansion. We demonstrate how computational modeling of differential growth can bridge the scales-from phenomena on the cellular level toward form and function on the organ level-to make quantitative, personalized predictions. Physics-based models can quantify cortical stresses, identify critical folding conditions, rationalize pattern selection, and predict gyral wavelengths and gyrification indices. We illustrate that physical forces can explain cortical malformations as emergent properties of developmental disorders. Combining biology and physics holds promise to advance our understanding of human brain development and enable early diagnostics of cortical malformations with the ultimate goal to improve treatment of neurodevelopmental disorders including epilepsy, autism spectrum disorders, and schizophrenia

Simulating the mechanical stimulation of cells on a porous hydrogel scaffold using an FSI model to predict cell differentiation

3D-structured hydrogel scaffolds are frequently used in tissue engineering applications as they can provide a supportive and biocompatible environment for the growth and regeneration of new tissue. Hydrogel scaffolds seeded with human mesenchymal stem cells (MSCs) can be mechanically stimulated in bioreactors to promote the formation of cartilage or bone tissue. Although in vitro and in vivo experiments are necessary to understand the biological response of cells and tissues to mechanical stimulation, in silico methods are cost-effective and powerful approaches that can support these experimental investigations. In this study, we simulated the fluid-structure interaction (FSI) to predict cell differentiation on the entire surface of a 3D-structured hydrogel scaffold seeded with cells due to dynamic compressive load stimulation. The computational FSI model made it possible to simultaneously investigate the influence of both mechanical deformation and flow of the culture medium on the cells on the scaffold surface during stimulation. The transient one-way FSI model thus opens up significantly more possibilities for predicting cell differentiation in mechanically stimulated scaffolds than previous static microscale computational approaches used in mechanobiology. In a first parameter study, the impact of the amplitude of a sinusoidal compression ranging from 1% to 10% on the phenotype of cells seeded on a porous hydrogel scaffold was analyzed. The simulation results show that the number of cells differentiating into bone tissue gradually decreases with increasing compression amplitude, while differentiation into cartilage cells initially multiplied with increasing compression amplitude in the range of 2% up to 7% and then decreased. Fibrous cell differentiation was predicted from a compression of 5% and increased moderately up to a compression of 10%. At high compression amplitudes of 9% and 10%, negligible areas on the scaffold surface experienced high stimuli where no cell differentiation could occur. In summary, this study shows that simulation of the FSI system is a versatile approach in computational mechanobiology that can be used to study the effects of, for example, different scaffold designs and stimulation parameters on cell differentiation in mechanically stimulated 3D-structured scaffolds

Automated discovery of interpretable hyperelastic material models for human brain tissue with EUCLID

We propose an automated computational algorithm for simultaneous model selection and parameter identification for the hyperelastic mechanical characterization of human brain tissue. Following the motive of the recently proposed computational framework EUCLID (Efficient Unsupervised Constitutive Law Identitication and Discovery) and in contrast to conventional parameter calibration methods, we construct an extensive set of candidate hyperelastic models, i.e., a model library including popular models known from the literature, and develop a computational strategy for automatically selecting a model from the library that conforms to the available experimental data while being represented as an interpretable symbolic mathematical expression. This computational strategy comprises sparse regression, i.e., a regression problem that is regularized by a sparsity promoting penalty term that filters out irrelevant models from the model library, and a clustering method for grouping together highly correlated and thus redundant features in the model library. The model selection procedure is driven by labelled data pairs stemming from mechanical tests under different deformation modes, i.e., uniaxial compression/tension and simple torsion, and can thus be interpreted as a supervised counterpart to the originally proposed EUCLID that is informed by full-field displacement data and global reaction forces. The proposed method is verified on synthetical data with artificial noise and validated on experimental data acquired through mechanical tests of human brain specimens, proving that the method is capable of discovering hyperelastic models that exhibit both high fitting accuracy to the data as well as concise and thus interpretable mathematical representations

Poro-viscoelastic material parameter identification of brain tissue-mimicking hydrogels

Understanding and characterizing the mechanical and structural properties of brain tissue is essential for developing and calibrating reliable material models. Based on the Theory of Porous Media, a novel nonlinear poro-viscoelastic computational model was recently proposed to describe the mechanical response of the tissue under different loading conditions. The model contains parameters related to the time-dependent behavior arising from both the viscoelastic relaxation of the solid matrix and its interaction with the fluid phase. This study focuses on the characterization of these parameters through indentation experiments on a tailor-made polyvinyl alcohol-based hydrogel mimicking brain tissue. The material behavior is adjusted to ex vivo porcine brain tissue. An inverse parameter identification scheme using a trust region reflective algorithm is introduced and applied to match experimental data obtained from the indentation with the proposed computational model. By minimizing the error between experimental values and finite element simulation results, the optimal constitutive model parameters of the brain tissue-mimicking hydrogel are extracted. Finally, the model is validated using the derived material parameters in a finite element simulation

Exploring human brain mechanics by combining experiments, modeling, and simulation

Brain tissue is not only one of the most important but also the arguably most complex and compliant tissue in the human body. While long underestimated, increasing evidence confirms that mechanics plays a critical role in modulating brain function and dysfunction. Computational models based on nonlinear continuum mechanics can help understand the basic processes in the brain, e.g., during development, injury, and disease, and facilitate prevention, early diagnosis, and treatment of neurological disorders. By closely integrating biomechanical experiments on human brain tissue, microstructural analyses, continuum mechanics modeling, and finite element simulations, we develop computational models that capture both biological processes at the cell scale and macroscopic loading and pathologies at the tissue or organ scale. To model the former, we introduce the cell density as an additional field controlling the local tissue stiffness and brain growth during development. We demonstrate that our models are capable of capturing the evolution of cell density and cortical folding in the developing brain as well as regional variations in tissue properties in the adult brain. In the future, those models could help provide deeper insights into the behavior of the human brain under physiological and pathological conditions, and tackle clinically relevant problems

Size and curvature regulate pattern selection in the mammalian brain

Mammalian brains display a wide variety of shapes and surface morphologies. Their characteristically folded surface is closely correlated to neuronal activity and serves as a clinical indicator for physiological and pathological conditions. Yet, the regulators of pattern formation in evolution and development remain poorly understood. Here we show how brain size and curvature affect the folding pattern in the developing mammalian brain. We model cortical folding as the instability problem of a bilayered system subjected to growth-induced compression. Using analytical estimates and continuum models for finite growth, we systematically explore the effects of geometric factors on the evolution of surface shape. We demonstrate that extrinsic geometric features–including brain size, cortical thickness, and cortical curvature–tightly regulate pattern selection: The mammalian brain is extremely soft and even small environmental changes can create extremely large alterations in its surface morphology. Our simulations explain why gyrification increases with brain size and why longer brains tend to fold more longitudinally than radially. Our results suggest that brain folding is driven, at least in part, by extreme mechanics, rather than by phylogeny alone