Investigation of the Compressive Viscoelastic Properties of Brain Tissue Under Time and Frequency Dependent Loading Conditions

Abstract

The mechanical characterization of brain tissue has been generally analyzed in the frequency and time domain. It is crucial to understand the mechanics of the brain under realistic, dynamic conditions and convert it to enable mathematical modelling in a time domain. In this study, the compressive viscoelastic properties of brain tissue were investigated under time and frequency domains with the same physical conditions and the theory of viscoelasticity was applied to estimate the prediction of viscoelastic response in the time domain based on frequency-dependent mechanical moduli through Finite Element models. Storage and loss modulus were obtained from white and grey matter, of bovine brains, using dynamic mechanical analysis and time domain material functions were derived based on a Prony series representation. The material models were evaluated using brain testing data from stress relaxation and hysteresis in the time dependent analysis. The Finite Element models were able to represent the trend of viscoelastic characterization of brain tissue under both testing domains. The outcomes of this study contribute to a better understanding of brain tissue mechanical behaviour and demonstrate the feasibility of deriving time-domain viscoelastic parameters from frequency-dependent compressive data for biological tissue, as validated by comparing experimental tests with computational simulations.

The alteration of the structure and macroscopic mechanical response of porcine patellar tendon by elastase digestion

“…Since the theory of this model is linear viscosity hypothesis, it cannot fully describe the nonlinear viscoelastic behavior of various biological soft tissues ( Shetye et al, 2014 ). However, Prony series is widely used and proved to be a constitutive equation that can effectively express the viscoelasticity of materials ( Grega et al, 2020 ; Shearer et al, 2020 ; Li et al, 2021 ; Morrison et al, 2023 ). In this study, R 2 and NRMSE obtained by fitting the experimental data of stress relaxation of patellar tendon before and after treatment showed that Prony series had a good fitting effect and was suitable for this study.…”

A genetic algorithm optimization framework for the characterization of hyper-viscoelastic materials: application to human articular cartilage

“…Part of what could have been hindering the algorithm in some instances is the variation that was seen in the initial dataset that more points for the machine learning algorithm to use in its prediction of the parameters increasing the likelihood of a reduced error comparison to the tissue experimental data. Prony series have been shown to be useful for characterizing biological tissues in the time domain, so as to predict frequency-domain mechanics [25,46]. However, a challenge with Prony series is that there is not one single set of parameters which may represent a dataset.…”

“…where μ|t is the time-dependent relaxation modulus, G∞ is the equilibrium modulus and gi and true0ti′ are the spring relaxation modulus and relaxation time of the Prony series for N spring–dashpot pairs or frequency delays. The relaxation modulus μ|t can be expressed as a discrete set of exponential decays [25] and the complex modulus u* is defined as…”

“…Applying such data to FEA simulations in a time domain, though challenging, is feasible via the characterization of a Prony series. For instance, a Prony series has been characterized by frequency-dependent storage and loss moduli for white and grey brain matter [ 25 ].…”

Review of the Brain’s Behaviour after Injury and Disease for Its Application in an Agent-Based Model (ABM)

“…From a purely mechanical perspective, brain tissue exhibits nonlinear mechanical responses—its stress–strain curve is approximately exponential. Additionally, considering the aforementioned strain rate dependency (and thus, time dependency), viscoelastic models [ 398 , 399 ] or a combination [ 400 ] are preferred over solely hyperelastic ones [ 117 , 401 ]. These kinds of models can be useful when evaluating the consequences of physical brain trauma—brain injury, that is—and setting the mechanical limits to avoid, as well as providing a model for damage evaluation and treatment follow-up.…”