Investigating the passive mechanical behaviour of skeletal muscle fibres: Micromechanical experiments and Bayesian hierarchical modelling

Böl, Markus; Kumar, Rahul Iyer; Dittmann, Johannes; Garcés-Schröder, Mayra

doi:10.1016/j.actbio.2019.05.015

Cited by 19 publications

(12 citation statements)

References 101 publications

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“…Some studies have been able to measure properties of isolated muscle fibres. However, tensile data are only available for the longitudinal direction of the muscle fibres [40], which may not necessarily represent the response in the transverse direction. Ideally, data for the cellular component of the base material would be tensile data for fibre and other cellular components measured transverse to the fibre orientation.…”

Section: Plos Onementioning

confidence: 99%

Modelling extracellular matrix and cellular contributions to whole muscle mechanics

2021

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Skeletal muscle tissue has a highly complex and heterogeneous structure comprising several physical length scales. In the simplest model of muscle tissue, it can be represented as a one dimensional nonlinear spring in the direction of muscle fibres. However, at the finest level, muscle tissue includes a complex network of collagen fibres, actin and myosin proteins, and other cellular materials. This study shall derive an intermediate physical model which encapsulates the major contributions of the muscle components to the elastic response apart from activation-related along-fibre responses. The micro-mechanical factors in skeletal muscle tissue (eg. connective tissue, fluid, and fibres) can be homogenized into one material aggregate that will capture the behaviour of the combination of material components. In order to do this, the corresponding volume fractions for each type of material need to be determined by comparing the stress-strain relationship for a volume containing each material. This results in a model that accounts for the micro-mechanical features found in muscle and can therefore be used to analyze effects of neuro-muscular diseases such as cerebral palsy or muscular dystrophies. The purpose of this study is to construct a model of muscle tissue that, through choosing the correct material parameters based on experimental data, will accurately capture the mechanical behaviour of whole muscle. This model is then used to look at the impacts of the bulk modulus and material parameters on muscle deformation and strain energy-density distributions.

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Section: Plos Onementioning

confidence: 99%

Modelling extracellular matrix and cellular contributions to whole muscle mechanics

2021

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“…Following calibration, UC and CC slow- A second set of UC and CC finite element models with the same constitutive formulation were calibrated using only the UC fast compression data. This is to reflect the approach of assuming near-incompressibility with a single-parameter bulk hyperelastic term, as is most common in finite element models of skeletal muscle [23], [25], [33], [49], [50]. The volumetric parameters ( ) were assumed to be three, four, and five orders of magnitude larger than the isochoric parameters ( 0 ) to reflect a range of assumptions.…”

Section: Finite Element Modellingmentioning

confidence: 99%

“…Blemker et al used a decoupled strain energy formulation to model the biceps branchii in which the volumetric or bulk parameter is assumed to be five orders of magnitude larger than the isochoric or shear parameters [33]. Similarly, Calvo et al and Grasa et al take the only volumetric parameter to be between two and three orders of magnitude larger than the isochoric parameters [25], [66]. In this study we collect volumetric compression data (CC) and span the assumptions made by Blemker et al and Calvo et al to predict the CC data.…”

Section: Model Findingsmentioning

confidence: 99%

An experimental and computational investigation of the effects of volumetric boundary conditions on the compressive mechanics of passive skeletal muscle

Vaidya

Wheatley

2020

Journal of the Mechanical Behavior of Biomedical Materials

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Computational modeling, such as finite element analysis, is employed in a range of biomechanics specialties, including impact biomechanics and surgical planning. These models rely on accurate material properties for skeletal muscle, which comprises roughly 40% of the human body. Due to surrounding tissues, compressed skeletal muscle in vivo likely experiences a semi-confined state. Nearly all previous studies investigating passively compressed muscle at the tissue level have focused on muscle in unconfined compression. The goals of this study were to (1) examine the stiffness and time-dependent material properties of skeletal muscle subjected to both confined and unconfined compression (2) develop a model that captures passive muscle mechanics under both conditions and (3) determine the extent to which different assumptions of volumetric behavior affect model results. Muscle in confined compression exhibited stiffer behavior, agreeing with previous assumptions of near-incompressibility. Stress relaxation was found to be faster under unconfined compression, suggesting there may be different mechanisms that support load these two conditions. Finite element calibration was achieved through nonlinear optimization (normalized root mean square error <6%) and model validation was strong (normalized root mean square error <17%). Comparisons to commonly employed assumptions of bulk behavior showed that a simple one parameter approach does not accurately simulate confined compression. We thus recommend the use of a properly calibrated, nonlinear bulk constitutive model for modeling of skeletal muscle in vivo. Future work to determine mechanisms of passive muscle stiffness would enhance the efforts presented here.

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“…In Reference 22, random field models for anisotropic nonlinear elastic material functions, with applications to vascular mechanics, have been presented. One of the authors of the present paper has applied Bayesian inference to analyze the behavior of skeletal muscle fibers under uncertainty 23 …”

Section: Introductionmentioning

confidence: 99%

“…One of the authors of the present paper has applied Bayesian inference to analyze the behavior of skeletal muscle fibers under uncertainty. 23 In the present work, we consider uncertainty quantification in the context of calibration and computational prediction with isotropic and hyperelastic biomechanical models. We present a comprehensive computational approach, summarized in Figure 1, which allows us to approximate the functional relation between force-displacement responses and isotropic hyperelastic material parameters with a surrogate model and hence, to efficiently calibrate the material model.…”

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confidence: 99%

Surrogate‐based Bayesian calibration of biomechanical models with isotropic material behavior

Liu

Böl

2022

Numer Methods Biomed Eng

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This work introduces a computational methodology to calibrate material models in biomechanical applications under uncertainty. We adopt a Bayesian approach, which estimates the probability distributions of hyperelastic material parameters, based on force‐strain measurements. We approximate the parametric biomechanical model by combining a reduced order representation of the force response with a Polynomial Chaos expansion. The surrogate model allows to employ sampling‐intensive Markov chain Monte Carlo methods and provides an efficient way to estimate (generalized) Sobol coefficients. We use a Sobol sensitivity analysis to assess the influence of material parameters and present an iterative procedure to quantify the accuracy of the surrogate model as additional uncertainty during Bayesian updating. The methodology is illustrated with three cases, tensile experiments on heat‐induced whey protein gel, indentation experiments for oocytes and a manufactured example. Real experimental data are used for the calibration.

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Investigating the passive mechanical behaviour of skeletal muscle fibres: Micromechanical experiments and Bayesian hierarchical modelling

Cited by 19 publications

References 101 publications

Modelling extracellular matrix and cellular contributions to whole muscle mechanics

Modelling extracellular matrix and cellular contributions to whole muscle mechanics

An experimental and computational investigation of the effects of volumetric boundary conditions on the compressive mechanics of passive skeletal muscle

Surrogate‐based Bayesian calibration of biomechanical models with isotropic material behavior

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