Nonlinear viscoelastic constitutive model for bovine liver tissue

Capilnasiu, Adela; Bilston, Lynne E.; Sinkus, Ralph; Nordsletten, David

doi:10.1007/s10237-020-01297-5

Cited by 27 publications

(17 citation statements)

References 51 publications

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“…From the results obtained for our building block models, the overall lower range of fractional orders obtained for all linear/nonlinear models is 0.17-0.3, indicating a predominantly elastic yet highly anomalous behavior with smaller decay rates at long times, i.e., the presence of far-from-equilibrium dynamics. A similar parametric range was obtained in other anomalous systems such as arterial wall relaxation [2], aortic valve tissue [51], 1D and 3D brain artery walls under fluid-structure interactions [70,71], canine and bovine liver tissue [72,73], and lung tissue [4]. As suggested by Doehring et al [51], small α-values can be indications of strong fractality in bio-tissue microstructure such as collagen fibers, which are vastly present in the UB, and particularly with a larger network in the trigone region.…”

Section: Discussionsupporting

confidence: 72%

A Data-Driven Memory-Dependent Modeling Framework for Anomalous Rheology: Application to Urinary Bladder Tissue

et al. 2021

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We introduce a data-driven fractional modeling framework for complex materials, and particularly bio-tissues. From multi-step relaxation experiments of distinct anatomical locations of porcine urinary bladder, we identify an anomalous relaxation character, with two power-law-like behaviors for short/long long times, and nonlinearity for strains greater than 25%. The first component of our framework is an existence study, to determine admissible fractional viscoelastic models that qualitatively describe linear relaxation. After the linear viscoelastic model is selected, the second stage adds large-strain effects to the framework through a fractional quasi-linear viscoelastic approach for the nonlinear elastic response of the bio-tissue of interest. From single-step relaxation data of the urinary bladder, a fractional Maxwell model captures both short/long-term behaviors with two fractional orders, being the most suitable model for small strains at the first stage. For the second stage, multi-step relaxation data under large strains were employed to calibrate a four-parameter fractional quasi-linear viscoelastic model, that combines a Scott-Blair relaxation function and an exponential instantaneous stress response, to describe the elastin/collagen phases of bladder rheology. Our obtained results demonstrate that the employed fractional quasi-linear model, with a single fractional order in the range α = 0.25–0.30, is suitable for the porcine urinary bladder, producing errors below 2% without need for recalibration over subsequent applied strains. We conclude that fractional models are attractive tools to capture the bladder tissue behavior under small-to-large strains and multiple time scales, therefore being potential alternatives to describe multiple stages of bladder functionality.

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Section: Discussionsupporting

confidence: 72%

A Data-Driven Memory-Dependent Modeling Framework for Anomalous Rheology: Application to Urinary Bladder Tissue

et al. 2021

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“…The first term denotes the deviatoric component of the stress depending on the fractional derivative of S v which follows a similar form to a typical hyperelastic material model of the right Cauchy-Green strain (see Following the parameterization process in [9], parameters α = 0.2, b = 1.5 and δ = 126.4Pa were observed to provide the best fit to the data (see Fig. 9).…”

Section: Fe Approximation Of Fractional Differential Equationsmentioning

confidence: 92%

An efficient and accurate method for modeling nonlinear fractional viscoelastic biomaterials

Zhang

Capilnasiu

Sommer

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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Computational biomechanics plays an important role in biomedical engineering: using modeling to understand pathophysiology, treatment and device design. While experimental evidence indicates that the mechanical response of most tissues is viscoelasticity, current biomechanical models in the computation community often assume only hyperelasticity. Fractional viscoelastic constitutive models have been successfully used in literature to capture the material response. However, the translation of these models into computational platforms remains limited. Many experimentally derived viscoelastic constitutive models are not suitable for three-dimensional simulations. Furthermore, the use of fractional derivatives can be computationally prohibitive, with a number of current numerical approximations having a computational cost that is O(N 2 T ) and a storage cost that is O(N T ) (N T denotes the number of time steps). In this paper, we present a novel numerical approximation to the Caputo derivative which exploits a recurrence relation similar to those used to discretize classic temporal derivatives, giving a computational cost that is O(N ) and a storage cost that is fixed over time. The approximation is optimized for numerical applications, and the error estimate is presented to demonstrate efficacy of the method. The method is shown to be unconditionally stable in the linear viscoelastic case. It was then integrated into a computational biomechanical framework, with several numerical examples verifying accuracy and computational efficiency of the method, including in an analytic test, in an analytic fractional differential equation, as well as in a computational biomechanical model problem. Fractional Derivatives and their Approximations Caputo fractional derivativeThe concept of fractional calculus started with questions about about the generalization of integral and differential operators by L'Hospital and Leibniz [68] from the set of integers to the set of real numbers.Subsequently, many prominent mathematicians focused on fractional calculus (for reviews, see, Ross [68] and Machado [51]). Within the field, many different definitions for fractional differential and integral operators of arbitrary order have been introduced [64]. In this work, we focus on the Caputo definition where the fractional derivative, D α t (with α > 0), of a n-times differentiable function f can be written as,

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“…This type of analysis and the process of model fitting results in the determination of simplified constitutive models that contain the key ingredients required to accurately represent the aforementioned characteristics of the liver subjected to both combinatory deformation and a variety of frequencies. Specifically, this is apparently among the first liver investigations to examine combined large uniaxial and shear stresses at multiple frequencies, and suggests a 3D nonlinear viscoelastic model with the ability to account for the large-amplitude oscillatory response over a wide array of preloads and frequencies ( Capilnasiu et al, 2020 ).…”

Section: Viscoelasticity Of Cells Varies Due To Disease State and Pro...mentioning

confidence: 95%

“…These are the polynomial model (a modified type of the Mooney–Rivlin model, which is referred to as vMR*), which is the simplest model, the viscoelastic Ogden (vOG) model, which is based on the strain-energy function, and the viscoelastic exponential (vEXP) model, which is the isotropic exponential Fung-type model based on the strain energy function. The latter two models are similarly appropriate, as the two models are better at accounting for the nonlinear tendencies ( Capilnasiu et al, 2020 ).…”

Section: Viscoelasticity Of Cells Varies Due To Disease State and Pro...mentioning

confidence: 99%

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Mierke

2022

Front. Cell Dev. Biol.

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Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells’ migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

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Nonlinear viscoelastic constitutive model for bovine liver tissue

Cited by 27 publications

References 51 publications

A Data-Driven Memory-Dependent Modeling Framework for Anomalous Rheology: Application to Urinary Bladder Tissue

A Data-Driven Memory-Dependent Modeling Framework for Anomalous Rheology: Application to Urinary Bladder Tissue

An efficient and accurate method for modeling nonlinear fractional viscoelastic biomaterials

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

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