Poynting effect of brain matter in torsion

Programmable nonreciprocal Poynting effect enabled by lattice metamaterials

Shear nonreciprocity, implying unequal shear forces in opposite shear directions, can be achieved by arranging structures asymmetrically. However, the nonreciprocal Poynting effect, i.e., unequal normal stresses induced by the same shear displacements to the left and right, has not been fully explored. We discover the nonreciprocal Poynting effect using a generalized directional truss model. Inspired by this discovery, the cylindrical lattice metamaterials constructed from antisymmetric curled microstructures are used as a case study to generate the nonreciprocal Poynting effect. We develop a design framework that integrates digital generation, finite deformation theory, finite element modeling, and three-dimensional printing to program the nonreciprocal Poynting effect. Applications such as bionic Poynting effect matching, wave energy converter, and unidirectional motion limitation are demonstrated. This framework allows the one-to-one mapping between the torque and normal forces, paving the way for designing soft devices with precise force transmission capabilities.

An Ogden hyperelastic 3D micromechanical model to depict Poynting effect in brain white matter

Shear and torsional load on soft solids such as brain white matter purportedly exhibits the Poynting Effect. It is a typical nonlinear phenomenon associated with soft materials whereby they tend to elongate (positive Poynting effect) or contract (negative Poynting effect) in a direction perpendicular to the shearing or twisting plane. In this research, a novel 3D micromechanical Finite Element Model (FEM) has been formulated to describe the Poynting effect in bi-phasic modeled brain white matter (BWM) representative volume element (RVE) with axons tracts embedded in surrounding extracellular matrix (ECM) for simulating brain matter's response to pure and simple shear. In the presented BWM 3D FEM, nonlinear Ogden hyper-elastic material model is deployed to interpret axons and ECM material phases. The modeled bi-phasic RVEs have axons tied to the surrounding ECM. In this proof-of-concept (POC) FEM, three simple shear loading configurations and a pure shear case were analyzed. Root mean square deviation (RMSD) was calculated for stress and deformation response plots to understand the effect of axon-ECM orientations and loading conditions on the degree of Poynting behavior. Variations in normal stresses (S11, S22, or S33) perpendicular to the shear plane underscored the significance of axonal fiber-matrix interactions. From the simulated ensemble of cases, a transitional dominance trend was noticed, as simple sheared axons showed pronounced Poynting behavior, but shear deformation build-up in the purely sheared brain model exhibited the highest Poynting behavior at higher strain % limits. At lower strain limits, simple shear imparted across and perpendicular to axonal tract directions emerged as the dominant Poynting effect configurations. At high strains, the stress-strain% plots manifested mild strain stiffening effects and bending stresses in purely sheared axons, substantiated the strong non-linearity in brain tissues' response.

Brain tissue mechanics is governed by microscale relations of the tissue constituents

Local mechanical tissue properties are a critical regulator of cell function in the central nervous system (CNS) during development and disorder. However, we still don't fully understand how the mechanical properties of individual tissue constituents, such as cell nuclei or myelin, determine tissue mechanics. Here we developed a model predicting local tissue mechanics, which induces non-affine deformations of the tissue components. Using the mouse hippocampus and cerebellum as model systems, we show that considering individual tissue components alone, as identified by immunohistochemistry, is not sufficient to reproduce the local mechanical properties of CNS tissue. Our results suggest that brain tissue shows a universal response to applied forces that depends not only on the amount and stiffness of the individual tissue constituents but also on the way how they assemble. Our model may unify current incongruences between the mechanics of soft biological tissues and the underlying constituents and facilitate the design of better biomedical materials and engineered tissues. To this end, we provide a freely-available platform to predict local tissue elasticity upon providing immunohistochemistry images and stiffness values for the constituents of the tissue.

Canceling the elastic Poynting effect with geometry

The Poynting effect is a paragon of nonlinear soft matter mechanics. It is the tendency (found in all incompressible, isotropic, hyperelastic solids) exhibited by a soft block to expand vertically when sheared horizontally. It can be observed whenever the length of the cuboid is at least four times its thickness. Here we show that the Poynting effect can be easily reversed and the cuboid can shrink vertically, simply by reducing this aspect ratio. In principle, this discovery means that for a given solid, say one used as a seismic wave absorber under a building, an optimal ratio exists where vertical displacements and vibrations can be completely eliminated. Here we first recall the classical theoretical treatment of the positive Poynting effect, and then show experimentally how it can be reversed. Using finite-element simulations, we then investigate how the effect can be suppressed. We find that cubes always provide a reverse Poynting effect, irrespective of their material properties (in the third-order theory of weakly nonlinear elasticity).

Automated model discovery for human brain using Constitutive Artificial Neural Networks

The brain is our softest and most vulnerable organ, and understanding its physics is a challenging but significant task. Throughout the past decade, numerous competing models have emerged to characterize its response to mechanical loading. However, selecting the best constitutive model remains a heuristic process that strongly depends on user experience and personal preference. Here we challenge the conventional wisdom to first select a constitutive model and then fit its parameters to data. Instead, we propose a new strategy that simultaneously discovers both model and parameters. We integrate more than a century of knowledge in thermodynamics and state-of-the-art machine learning to build a Constitutive Artificial Neural Network that enables automated model discovery. Our design paradigm is to reverse engineer the network from a set of functional building blocks that are, by design, a generalization of popular constitutive models, including the neo Hookean, Blatz Ko, Mooney Rivlin, Demiray, Gent, and Holzapfel models. By constraining input, output, activation functions, and architecture, our network a priori satisfies thermodynamic consistency, objectivity, symmetry, and polyconvexity. We demonstrate that-out of more than 4000 models-our network autonomously discovers the model and parameters that best characterize the behavior of human gray and white matter under tension, compression, and shear. Importantly, our network weights translate naturally into physically meaningful parameters, such as shear moduli of 1.82kPa, 0.88kPa, 0.94kPa, and 0.54kPa for the cortex, basal ganglia, corona radiata, and corpus callosum. Our results suggest that Constitutive Artificial Neural Networks have the potential to induce a paradigm shift in soft tissue modeling, from user-defined model selection to automated model discovery. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN. STATEMENT OF SIGNIFICANCE: Human brain is ultrasoft, difficult to test, and challenging to model. Numerous competing constitutive models exist, but selecting the best model remains a matter of personal preference. Here we automate the process of model selection. We formulate the problem of autonomous model discovery as a neural network and capitalize on the powerful optimizers in deep learning. However, rather than using a conventional neural network, we reverse engineer our own Constitutive Artificial Neural Network from a set of modular building blocks, which we rationalize from common constitutive models. When trained with tension, compression, and shear experiments of gray and white matter, our network simultaneously discovers both model and parameters that describes the data better than any existing invariant-based model. Our network could induce a paradigm shift from user-defined model selection to automated model discovery.

Modelling brain tissue elasticity with the Ogden model and an alternative family of constitutive models†

The Ogden model is often considered as a standard model in the literature for application to the deformation of brain tissue. Here, we show that, in some of those applications, the use of the Ogden model leads to the non-convexity of the strain-energy function and mis-prediction of the correct concavity of the experimental stress-stretch curves over a range of the deformation domain. By contrast, we propose a family of models which provides a favourable fit to the considered datasets while remaining free from the highlighted shortcomings of the Ogden model. While, as we discuss, those shortcomings might be due to the artefacts of the testing protocols, the proposed family of models proves impervious to such artefacts. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

Brain structure analysis of different age groups of Diannan small-ear pigs

The objective of the study is to investigate the brain development and atrophy of Diannan small-ear pigs in different ages using magnetic resonance imaging (MRI). A total of 12 Diannan small-ear pigs were included and divided into the young group, adult group, and middle-and-old age (M&O) group according to their age. The brain structure of pigs was scanned using MRI, and the brain data obtained were statistically analyzed by signal conversion and image reconstruction. Compared with the young group, the signals of most brain structures in the adult group and M&O group were significantly decreased (p < 0.05). Compared with the adult group, the signal intensity of the right caudate nucleus and the right lateral ventricle in the M&O group was significantly increased, while the signal intensity of other regions was almost significantly decreased (p < 0.05). Compared with the young group, both adult and M&O groups had some degree of brain atrophy. Brain atrophy in the precuneus and the inferior temporal gyrus was more predominant in the M&O group in comparison with the adult group. The present study demonstrated that the brain signal of Diannan small-ear pigs gradually diminished with age, while the degree of brain atrophy was the opposite, providing the basic data on the brain of Diannan small-ear pigs.

Coupling solid and fluid stresses with brain tumour growth and white matter tract deformations in a neuroimaging-informed model

Brain tumours are among the deadliest types of cancer, since they display a strong ability to invade the surrounding tissues and an extensive resistance to common therapeutic treatments. It is therefore important to reproduce the heterogeneity of brain microstructure through mathematical and computational models, that can provide powerful instruments to investigate cancer progression. However, only a few models include a proper mechanical and constitutive description of brain tissue, which instead may be relevant to predict the progression of the pathology and to analyse the reorganization of healthy tissues occurring during tumour growth and, possibly, after surgical resection. Motivated by the need to enrich the description of brain cancer growth through mechanics, in this paper we present a mathematical multiphase model that explicitly includes brain hyperelasticity. We find that our mechanical description allows to evaluate the impact of the growing tumour mass on the surrounding healthy tissue, quantifying the displacements, deformations, and stresses induced by its proliferation. At the same time, the knowledge of the mechanical variables may be used to model the stress-induced inhibition of growth, as well as to properly modify the preferential directions of white matter tracts as a consequence of deformations caused by the tumour. Finally, the simulations of our model are implemented in a personalized framework, which allows to incorporate the realistic brain geometry, the patient-specific diffusion and permeability tensors reconstructed from imaging data and to modify them as a consequence of the mechanical deformation due to cancer growth.

Normal cerebral blood vessels under ultrasound in SD rats of different ages

The objective of this study was to examine whether ultrasound can examine the development of cerebral vascular structure and cerebral blood flow in Sprague-Dawley (SD) rats by ultrasound in a noninvasive manner, which provides a reference for ultrasound research of SD rats. Thirty-nine SD rats (7-16 days old) were divided into seven groups according to age, and the number of SD rats in each group was, respectively, 7, 17, 1, 3, 2, 8, and 1. Ultrasound was used to detect cerebral blood vessels, cerebrovascular flow velocity, and heart rate in SD rats in the sagittal and coronal positions, and images were obtained in B-mode ultrasound. The cerebral vascular structure of 39 SD rats (7-16 days) was dynamically observed under B-ultrasound. We found that the cerebral vascular structure of the rats aged 7-10 days was clear and detectable. Rats aged 11-16 days of cerebral vascular structures became thinner and undetectable. Quantitative analysis of cerebrovascular flow rate and heart rate in rats found that there was no significant difference in cerebrovascular blood flow rate and heart rate between 7 and 8 days. Ultrasound can also be used in rat animal studies, that is, the cerebral blood flow in rats of different ages can be monitored in real-time by ultrasound in a noninvasive way.

Tissue-Scale Biomechanical Testing of Brain Tissue for the Calibration of Nonlinear Material Models

Brain tissue is one of the most complex and softest tissues in the human body. Due to its ultrasoft and biphasic nature, it is difficult to control the deformation state during biomechanical testing and to quantify the highly nonlinear, time-dependent tissue response. In numerous experimental studies that have investigated the mechanical properties of brain tissue over the last decades, stiffness values have varied significantly. One reason for the observed discrepancies is the lack of standardized testing protocols and corresponding data analyses. The tissue properties have been tested on different length and time scales depending on the testing technique, and the corresponding data have been analyzed based on simplifying assumptions. In this review, we highlight the advantage of using nonlinear continuum mechanics based modeling and finite element simulations to carefully design experimental setups and protocols as well as to comprehensively analyze the corresponding experimental data. We review testing techniques and protocols that have been used to calibrate material model parameters and discuss artifacts that might falsify the measured properties. The aim of this work is to provide standardized procedures to reliably quantify the mechanical properties of brain tissue and to more accurately calibrate appropriate constitutive models for computational simulations of brain development, injury and disease. Computational models can not only be used to predictively understand brain tissue behavior, but can also serve as valuable tools to assist diagnosis and treatment of diseases or to plan neurosurgical procedures. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC.

Characterizing viscoelastic properties of synthetic and natural fibers and their coatings with a torsional pendulum

Characterizing and understanding the viscoelastic mechanical properties of natural and synthetic fibers is of great importance in many biological and industrial applications. Microscopic techniques such as micro/nano indentation have been successfully employed in such efforts, yet these tests are often challenging to perform on fibers and come with certain limitations in the interpretation of the obtained results within the context of the macroscopic viscoelasticity in the fiber. Here we instead explore the properties of a series of natural and synthetic fibers, using a freely-oscillating torsional pendulum. The torsional oscillation of the damped mass-fiber system is precisely recorded with a simple HD video-camera and an image processing algorithm is used to analyze the resulting videos. Analysis of the processed images show a viscoelastic damped oscillatory response and a simple mechanical model describes the amplitude decay of the oscillation data very well. The natural frequency of the oscillation and the corresponding damping ratio can be extracted using a logarithmic decrement method and directly connected to the bulk viscoelastic properties of the fiber. We further study the sensitivity of these measurements to changes in the chemo-mechanical properties of the outer coating layers on one of the synthetic fibers. To quantify the accuracy of our measurements with the torsional pendulum, a complementary series of tests are also performed on a strain-controlled rheometer in both torsional and tensile deformation modes.

The effect of fiber-matrix interaction on the Poynting effect for torsion of fibrous soft biomaterials

The response of fibrous soft tissues undergoing torsional deformations is a topic of considerable current interest. Such deformations are common in ligaments and tendons and are also of particular interest in cardiac mechanics. A well-known context where such issues arise is in understanding the mechanical response of papillary muscles of the heart. Thus the classical torsion problem for solid or hollow cylinders composed of rubber-like materials has received renewed recent attention in the context of anisotropic materials. Here we consider the torsion of a solid circular cylinder composed of a transversely isotropic incompressible fiber-reinforced hyperelastic material. The focus of the work is on examining the effect of fiber-matrix interaction on the axial stress response with emphasis on the Poynting effect. The classic Poynting effect for isotropic rubber-like materials where torsion induces elongation of the cylinder is shown to be significantly different for the transversely isotropic models considered here. For sufficiently small total angles of twist, well within the range of physiological response, a reverse-Poynting effect is shown to hold where the cylinder tends to shorten on twisting while for larger angles of twist, the usual positive Poynting effect occurs. It is shown that the influence of the fiber-matrix interaction is to enhance the reverse Poynting effect. The results are illustrated using experimental data of other authors for skeletal muscles and for brain white matter.

Experimental study of the Poynting effect in a soft unidirectional fiber-reinforced material under simple shear

The aim of this work was to investigate the shear and lateral normal responses of a soft unidirectional fiber-reinforced material subjected to simple shear. The Poynting effect was also investigated. Soft composites were manufactured from a flexible adhesive reinforced by a single family of parallel and continuous fibers of nylon. Specimens with fibers oriented at an angle (-45°, 0°, 45° and 90°) with respect to the applied shear force were tested. A simple shear test apparatus was developed to measure shear and normal forces simultaneously. A standard reinforcing model based on strain-energy density function was used to verify the mechanical behavior of the soft composite with different fiber orientation. Results showed that the initial stiffness of the composite with fibers oriented at -45° and 45° was approximately the same and was higher than those at 0° and 90°. Also, there was no significant difference between values of initial stiffness for angles of 0° and 90° and the neat matrix. The effect of the stretching resistance of the fibers was more pronounced for fibers oriented at 45° and 90°. There was no Poynting effect for the neat matrix or for the composite with fibers at 0° while positive and negative Poynting effects were observed for fibers oriented at -45° and 45° (and 90°), respectively. The standard reinforcing model was only verified for a limited range of amount of shear due to composite failure. Fiber debonding and fiber buckling were observed in the composites with fibers oriented at 45° (and 90°) and -45°, respectively, at large deformations.