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.
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%.
A microrheological model of aggregating dispersions is proposed in which the shear stress is estimated as the sum of hydrodynamic and structural parts. The former is attributed to the hydrodynamic cores of fractal aggregates, which behave as a suspension of impermeable spheres. The latter accounts for the forces transmitted by chains of particles linking neighboring aggregates into a transient network. To calculate the structural part the concept of fractal aggregation is incorporated into a transient network theory, to account for the creation and breakup of chains of colloidal particles connecting the aggregates. Rigid and soft chains are distinguished. The former have multiply connected backbones which deform as contorted elastic rods, while the latter have at least one soft junction and deform without elastic resistance until fully loaded. The contribution of the soft chains to the stress tensor is neglected. The calculations treat two different mechanisms for the evolution of rigid chains: a purely mechanical one, which corresponds to a shear-controlled structure built up in flow, and a thermal mechanism, which pertains to a quasiequilibrium structure undisturbed by shear. We calculate steady-shear viscosities in the former case and viscoelastic functions in the latter. The model can be fitted satisfactorily to the experimental results for a well-characterized polystyrene latex dispersion with physically acceptable parameters.
Modeling the mechanical response of the brain has become increasingly important over the past decades. Although mechanical stimuli to the brain are small under physiological conditions, mechanics plays a significant role under pathological conditions including brain development, brain injury, and brain surgery. Well calibrated and validated constitutive models for brain tissue are essential to accurately simulate these phenomena. A variety of constitutive models have been proposed over the past three decades, but no general consensus on these models exists. Here, we provide a comprehensive and structured overview of state-of-the-art modeling of the brain tissue. We categorize the different features of existing models into time-independent, time-dependent, and history-dependent contributions. To model the time-independent, elastic behavior of the brain tissue, most existing models adopt a hyperelastic approach. To model the time-dependent response, most models either use a convolution integral approach or a multiplicative decomposition of the deformation gradient. We evaluate existing constitutive models by their physical motivation and their practical relevance. Our comparison suggests that the classical Ogden model is a well-suited phenomenological model to characterize the time-independent behavior of the brain tissue. However, no consensus exists for mechanistic, physics-based models, neither for the time-independent nor for the time-dependent response. We anticipate that this review will provide useful guidelines for selecting the appropriate constitutive model for a specific application and for refining, calibrating, and validating future models that will help us to better understand the mechanical behavior of the human brain.
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