Temperature-dependent elastic properties of brain tissues measured with the shear wave elastography method

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.

An atlas of the heterogeneous viscoelastic brain with local power-law attenuation synthesised using Prony-series

This review addresses the acute need to acknowledge the mechanical heterogeneity of brain matter and to accurately calibrate its local viscoelastic material properties accordingly. Specifically, it is important to compile the existing and disparate literature on attenuation power-laws and dispersion to make progress in wave physics of brain matter, a field of research that has the potential to explain the mechanisms at play in diffuse axonal injury and mild traumatic brain injury in general. Currently, viscous effects in the brain are modelled using Prony-series, i.e., a sum of decaying exponentials at different relaxation times. Here we collect and synthesise the Prony-series coefficients appearing in the literature for twelve regions: brainstem, basal ganglia, cerebellum, corona radiata, corpus callosum, cortex, dentate gyrus, hippocampus, thalamus, grey matter, white matter, homogeneous brain, and for eight different mammals: pig, rat, human, mouse, cow, sheep, monkey and dog. Using this data, we compute the fractional-exponent attenuation power-laws for different tissues of the brain, the corresponding dispersion laws resulting from causality, and the averaged Prony-series coefficients. STATEMENT OF SIGNIFICANCE: Traumatic brain injuries are considered a silent epidemic and finite element methods (FEMs) are used in modelling brain deformation, requiring access to viscoelastic properties of brain. To the best of our knowledge, this work presents 1) the first multi-frequency viscoelastic atlas of the heterogeneous brain, 2) the first review focusing on viscoelastic modelling in both FEMs and experimental works, 3) the first attempt to conglomerate the disparate existing literature on the viscoelastic modelling of the brain and 4) the largest collection of viscoelastic parameters for the brain (212 different Prony-series spanning 12 different tissues and 8 different animal surrogates). Furthermore, this work presents the first brain atlas of attenuation power-laws essential for modelling shear waves in brain.

Mechanical behavior of the hippocampus and corpus callosum: An attempt to reconcile ex vivo with in vivo and micro with macro properties

Mechanical properties of brain tissue are very complex and vary with the species, region, method, and dynamic range, and between in vivo and ex vivo measurements. To reconcile this variability, we investigated in vivo and ex vivo stiffness properties of two distinct regions in the human and mouse brain - the hippocampus (HP) and the corpus callosum (CC) - using different methods. Under quasi-static conditions, we examined ex vivo murine HP and CC by atomic force microscopy (AFM). Between 16 and 40Hz, we investigated the in vivo brains of healthy volunteers by magnetic resonance elastography (MRE) in a 3-T clinical scanner. At high-frequency stimulation between 1000 and 1400Hz, we investigated the murine HP and CC ex vivo and in vivo with MRE in a 7-T preclinical system. HP and CC showed pronounced stiffness dispersion, as reflected by a factor of 32-36 increase in shear modulus from AFM to low-frequency human MRE and a 25-fold higher shear wave velocity in murine MRE than in human MRE. At low frequencies, HP was softer than CC, in both ex vivo mouse specimens (p < 0.05) and in vivo human brains (p < 0.01) while, at high frequencies, CC was softer than HP under in vivo (p < 0.01) and ex vivo (p < 0.05) conditions. The standard linear solid model comprising three elements reproduced the observed HP and CC stiffness dispersions, while other two- and three-element models failed. Our results indicate a remarkable consistency of brain stiffness across species, ex vivo and in vivo states, and different measurement techniques when marked viscoelastic dispersion properties combining equilibrium and non-equilibrium mechanical elements are considered.

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.

The effects of electric fields on the mechanical properties and microstructure of ex vivo porcine brain tissues

As a popular tool for regulating the physiological conditions of the brain and treating brain diseases, electrotherapy has become increasingly mature in clinical applications. However, the mechanical properties and microstructure of the brain that change with weak electric fields are often overlooked. Thus, the mechanical behaviors of the brain tissue, which play a critical role in modulating the brain form and brain function, need to be taken into account. Herein, the direct current electric fields were combined with a customized indentation device and simultaneously focused on the changes in the mechanical properties and microstructure of ex vivo porcine brain tissues under electric fields. The experimental results showed that the electric fields reduced the shear modulus and viscosity and increased the relaxation rate of ex vivo porcine brain tissues. Moreover, electric fields polarized the cell bodies and reduced proteoglycan content in the cortex. The TEM observation confirmed that the electric fields deepened the degree of endoplasmic reticulum expansion and decreased the structural integrity of the cell membrane and myelin sheath. This study confirmed the effect of electric fields on ex vivo brain tissues; concurrently, it created comparable space in microscopic structure/compositions and mechanical parameters for future deeper brain experiments under stress-electric field coupling.

Sensitivity analysis of effective transverse shear viscoelastic and diffusional properties of myelinated white matter

Motivated by the need to interpret the results from a combined use of in vivo brain Magnetic Resonance Elastography (MRE) and Diffusion Tensor Imaging (DTI), we developed a computational framework to study the sensitivity of single-frequency MRE and DTI metrics to white matter microstructure and cell-level mechanical and diffusional properties. White matter was modeled as a triphasic unidirectional composite, consisting of parallel cylindrical inclusions (axons) surrounded by sheaths (myelin), and embedded in a matrix (glial cells plus extracellular matrix). Only 2D mechanics and diffusion in the transverse plane (perpendicular to the axon direction) was considered, and homogenized (effective) properties were derived for a periodic domain containing a single axon. The numerical solutions of the MRE problem were performed with ABAQUS and by employing a sophisticated boundary-conforming grid generation scheme. Based on the linear viscoelastic response to harmonic shear excitation and steady-state diffusion in the transverse plane, a systematic sensitivity analysis of MRE metrics (effective transverse shear storage and loss moduli) and DTI metric (effective radial diffusivity) was performed for a wide range of microstructural and intrinsic (phase-based) physical properties. The microstructural properties considered were fiber volume fraction, and the myelin sheath/axon diameter ratio. The MRE and DTI metrics are very sensitive to the fiber volume fraction, and the intrinsic viscoelastic moduli of the glial phase. The MRE metrics are nonlinear functions of the fiber volume fraction, but the effective diffusion coefficient varies linearly with it. Finally, the transverse metrics of both MRE and DTI are insensitive to the axon diameter in steady state. Our results are consistent with the limited anisotropic MRE and co-registered DTI measurements, mainly in the corpus callosum, available in the literature. We conclude that isotropic MRE and DTI constitutive models are good approximations for myelinated white matter in the transverse plane. The unidirectional composite model presented here is used for the first time to model harmonic shear stress under MRE-relevant frequency on the cell level. This model can be extended to 3D in order to inform the solution of the inverse problem in MRE, establish the biological basis of MRE metrics, and integrate MRE/DTI with other modalities towards increasing the specificity of neuroimaging.

A knowledge map analysis of brain biomechanics: Current evidence and future directions

Although brain, one of the most complex organs in the mammalian body, has been subjected to many studies from physiological and pathological points of view, there remain significant gaps in the available knowledge regarding its biomechanics. This article reviews the research trends in brain biomechanics with a focus on injury. We used published scientific articles indexed by Web of Science database over the past 40 years and tried to address the gaps that still exist in this field. We analyzed the data using VOSviewer, which is a software tool designed for scientometric studies. The results of this study showed that the response of brain tissue to external forces has been one of the significant research topics among biomechanicians. These studies have addressed the effects of mechanical forces on the brain and mechanisms of traumatic brain injury, as well as characterized changes in tissue behavior under trauma and other neurological diseases to provide new diagnostic and monitoring methods. In this study, some challenges in the field of brain injury biomechanics have been identified and new directions toward understanding the gaps in this field are suggested.

Non-invasive Quantitative Assessment of Muscle Force Based on Ultrasonic Shear Wave Elastography

The objective of this study was to investigate the feasibility of using shear wave elastography (SWE) to indirectly measure passive muscle force and to examine the effects of muscle mass and scan angle. We measured the Young's moduli of 24 specimens from six muscles of four swine at different passive muscle loads under different scan angles (0°, 30°, 60° and 90°) using SWE. Highly linear relationships between Young's modulus E and passive muscle force F were found for all 24 muscle specimens at 0^o scan angle with coefficients of determination R² ranging from 0.984 to 0.999. The results indicate that the muscle mass has no significant effect on the muscle E-F relationship, whereas E-F linearity decreases disproportionately with increased scan angle. These findings suggest that SWE, when carefully applied, can provide a highly reliable tool to measure muscle Young's modulus, and could be used to assess the muscle force quantitatively.

Indentation response in porcine brain under electric fields

Electric fields in the environment can have profound effects on brain function and behavior. In clinical practice, some noninvasive/microinvasive therapies with electrical fields such as transcranial electrical stimulation (tES), deep brain stimulation (DBS), and electroconvulsive therapy (ECT) have emerged as powerful tools for the treatment of neuropsychiatric disorders and neuromodulation. Nonetheless, currently, most studies focus on the mechanisms and effects of therapies and do not to address the mechanical properties of brain tissue under electric fields. Thus, the mechanical behavior of brain tissue, which plays an important role in modulating both brain form and brain function, should be given attention. The present study addresses this paucity by presenting, for the first time, the mechanical properties of brain tissue under various intensities of direct current electric field (0, 2, 5, 10, 20, and 50 V) using a custom-designed indentation device. Prior to brain indentation, validation tests were performed in different hydrogels to ensure that there was no interference in the electric fields from the indentation device. Subsequently, the load trace data obtained from the indentation-relaxation tests was fitted to both linear elastic and viscoelastic models to characterize the sensitivity of the mechanical behavior of the brain tissue to the electric fields. The brain tissue was found to be softened at a higher electric field level and less viscous, and substantially responded more quickly with an increase in electric field. The explanations for the above behaviors were further discussed based on the analysis of the resistance and thermal responses during the testing process. Understanding the effect of electric fields on brain tissue at the mechanical level can provide a better understanding of the mechanisms of some therapies, which may be beneficial to guide therapy protocols.

Temperature dependent of viscoelasticity measurement on fat emulsion phantom using acoustic radiation force elasticity imaging method

During the past two decades, tissue elasticity has been extensively studied and has been used in clinical disease diagnosis. But biological soft tissues are viscoelastic in nature. Therefore, they should be simultaneously characterized in terms of elasticity and viscosity. In addition, the mechanical properties of soft tissues are temperature dependent. However, how the temperature influences the shear wave dispersion and the viscoelasticity of soft tissue are still unclear. The aim of this study is to compare viscoelasticity of fat emulsion phantom with different temperature using acoustic radiation force elasticity imaging method. In our experiment, we produced four proportions of ultrasonic phantom by adding fat emulsion gelatin. Through adjusting the component of the fat emulsion, we change the viscoelasticity of the ultrasonic phantom. We used verasonics system to gather data and voigt model to fit the elasticity and viscosity value of the ultrasonic phantom we made. The influence of temperature to the ultrasonic phantom also measured in our study. The results show that the addition of fat emulsion to the phantom can increase the viscosity of the phantom, and the shear wave phase velocity decreases gradually at each frequency with the temperature increases, which provides a new material for the production of viscoelastic phantom.