Mechanical characterization of human brain tissue.

Experiments on brain samples under multiaxial loading have shown that human brain tissue is both extremely soft when compared to other biological tissues and characterized by a peculiar elastic response under combined shear and compression/tension: there is a significant increase in shear stress with increasing axial compression compared to a moderate increase with increasing axial tension Recent studies have revealed that many widely used constitutive models for soft biological tissues fail to capture this characteristic response Here, guided by experiments of human brain tissue, we develop a family of modeling approaches that capture the elasticity of brain tissue under varying simple shear superposed on varying axial stretch by exploiting key observations about the behavior of the nonlinear shear modulus, which can be obtained directly from the experimental data

A family of hyperelastic models for human brain tissue

Understanding the constitutive behavior of the human brain is critical to interpret the physical environment during neurodevelopment, neurosurgery, and neurodegeneration. A wide variety of constitutive models has been proposed to characterize the brain at different temporal and spatial scales. Yet, their model parameters are typically calibrated with a single loading mode and fail to predict the behavior under arbitrary loading conditions. Here we used a finite viscoelastic Ogden model with six material parameters–an elastic stiffness, two viscoelastic stiffnesses, a nonlinearity parameter, and two viscous time constants–to model the characteristic nonlinearity, conditioning, hysteresis and tension-compression asymmetry of the human brain. We calibrated the model under shear, shear relaxation, compression, compression relaxation, and tension for four different regions of the human brain, the cortex, basal ganglia, corona radiata, and corpus callosum. Strikingly, unconditioned gray matter with 0.36 kPa and white matter with 0.35 kPa were equally stiff, whereas conditioned gray matter with 0.52 kPa was three times stiffer than white matter with 0.18 kPa. While both unconditioned viscous time constants were larger in gray than in white matter, both conditioned constants were smaller. These rheological differences suggest a different porosity between both tissues and explain–at least in part–the ongoing controversy between reported stiffness differences in gray and white matter. Our unconditioned and conditioned parameter sets are readily available for finite element simulations with commercial software packages that feature Ogden type models at finite deformations. As such, our results have direct implications on improving the accuracy of human brain simulations in health and disease.

Viscoelastic parameter identification of human brain tissue.

Regional mechanical properties of human brain tissue for computational models of traumatic brain injury.

Soft structures are capable of undergoing reversible large strains and deformations when facing different types of loadings. Due to the limitations of linear elastic models, researchers have developed and employed different nonlinear elastic models capable of accurately modelling large deformations and strains. These models are significantly different in formulation and application. As hyperelastic strain energy density models provide researchers with a good fit for the mechanical behaviour of biological tissues, research studies on using these constitutive models together with different continuum-mechanics-based formulations have reached notable outcomes. With the improvements in biomechanical devices, in-vivo and in-vitro studies have increased significantly in the past few years which emphasises the importance of reviewing the latest works in this field. Besides, since soft structures are used for different mechanical and biomechanical applications such as prosthetics, soft robots, packaging, and wearing devices, the application of a proper hyperelastic strain energy density law in modelling the structure is of high importance. Therefore, in this review, a detailed classified analysis of the mechanics of hyperelastic structures is presented by focusing on the application of different hyperelastic strain energy density models. Previous studies on biological soft parts of the body (brain, artery, cartilage, liver, skeletal muscle, ligament, skin, tongue, heel pad and adipose tissue) are presented in detail and the hyperelastic strain energy models used for each biological tissue is discussed. Besides, the mechanics (deformation, buckling, inflation, etc.) of polymeric structures in different mechanical conditions is presented using previous studies in this field and the strength of hyperelastic strain energy density models in analysing their mechanics is presented. 

Hyperelastic structures: A review on the mechanics and biomechanics

Fitted hyperelastic parameters for Human brain tissue from reported tension, compression, and shear tests

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Fitted hyperelastic parameters for Human brain tissue from reported tension, compression, and shear tests