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The mammalian brain is composed of an outer layer of gray matter, consisting of cell bodies, dendrites, and unmyelinated axons, and an inner core of white matter, consisting primarily of myelinated axons. Recent evidence suggests that microstructural differences between gray and white matter play an important role during neurodevelopment. While brain tissue as a whole is rheologically well characterized, the individual features of gray and white matter remain poorly understood. Here we quantify the mechanical properties of gray and white matter using a robust, reliable, and repeatable method, flat-punch indentation. To systematically characterize gray and white matter moduli for varying indenter diameters, loading rates, holding times, post-mortem times, and locations we performed a series of n=192 indentation tests. We found that indenting thick, intact coronal slices eliminates the common challenges associated with small specimens: it naturally minimizes boundary effects, dehydration, swelling, and structural degradation. When kept intact and hydrated, brain slices maintained their mechanical characteristics with standard deviations as low as 5% throughout the entire testing period of five days post mortem. White matter, with an average modulus of 1.895kPa±0.592kPa, was on average 39% stiffer than gray matter, p<0.01, with an average modulus of 1.389kPa±0.289kPa, and displayed larger regional variations. It was also more viscous than gray matter and responded less rapidly to mechanical loading. Understanding the rheological differences between gray and white matter may have direct implications on diagnosing and understanding the mechanical environment in neurodevelopment and neurological disorders.

Brain tissue is not only one of the most important but also the 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 simulations-based on the field equations of nonlinear continuum mechanics-can provide important insights into the underlying mechanisms of brain injury and disease that go beyond the possibilities of traditional diagnostic tools. Realistic numerical predictions, however, require mechanical models that are capable of capturing the complex and unique characteristics of this ultrasoft, heterogeneous, and active tissue. In recent years, contradictory experimental results have caused confusion and hindered rapid progress. In this review, we carefully assess the challenges associated with brain tissue testing and modeling, and work out the most important characteristics of brain tissue behavior on different length and time scales. Depending on the application of interest, we propose appropriate mechanical modeling approaches that are as complex as necessary but as simple as possible. This comprehensive review will, on the one hand, stimulate the design of new experiments and, on the other hand, guide the selection of appropriate constitutive models for specific applications. Mechanical models that capture the complex behavior of nervous tissues and are accurately calibrated with reliable and comprehensive experimental data are key to performing reliable predictive simulations. Ultimately, mathematical modeling and computational simulations of the brain are useful for both biomedical and clinical communities, and cover a wide range of applications ranging from predicting disease progression and estimating injury risk to planning surgical procedures.

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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.

SUMMARYThis paper describes a new beam ÿnite element formulation based upon the geometrically exact beam theory. In contrast to many previously proposed beam ÿnite element formulations the present discretization approach retains the frame-indi erence (or objectivity) of the underlying beam theory. The space interpolation of rotational degrees-of-freedom is circumvented by the introduction of a reparameterization of the weak form corresponding to the equations of motion of the geometrically exact beam theory.

Increasing evidence suggests that the mechanical environment of the brain plays an important role in neuronal development and disease. Reported stiffness values vary significantly, but the origin of these variations remains unknown. Here we show that stiffness of our brain is correlated to the underlying tissue microstructure and directly proportional to the local myelin content. Myelin has been discovered in 1854 as an insulating layer around nerve cells to improve electric signal propagation. Our study now shows that it also plays an important mechanical role: Using a combined mechanical characterization and histological characterization, we found that the white matter stiffness increases linearly with increasing myelin content, from 0.5kPa at a myelin content of 63-2.5kPa at 92%.

SUMMARYThe numerical modelling of non-linear electroelasticity is presented in this work. Based on well-established basic equations of non-linear electroelasticity a variational formulation is built and the finite element method is employed to solve the non-linear electro-mechanical coupling problem. Numerical examples are presented to show the accuracy of the implemented formulation.