Abstract
Elastography is a noninvasive imaging technique that provides information on soft tissue stiffness. Young's modulus is typically used to characterize soft tissues' response to the applied force, as soft tissues are often considered linear elastic, isotropic, and quasi-incompressible materials. This approximation is reasonable for small strains, but soft tissues undergo large deformations also for small values of force and exhibit nonlinear elastic behavior. Outside the linear regime, the elastic modulus is dependent on the strain level and is different for any kind of tissue. The aim of this study was to characterize, ex vivo, the mechanical response of two different mice muscles to an external force. A system for transverse force-controlled uniaxial compression enabled obtaining the stress-strain (σ-ε) curve of the samples. The strain-dependent Young's modulus (SYM) model was adopted to reproduce muscle compression behavior and to predict the elastic modulus for large deformations. After that, a recursive linear model was employed to identify the initial linear region of the σ-ε curve. Results showed that both muscle types exhibited a strain hardening effect and that the SYM model provided good fitting of the entire σ-ε curves. The application of the recursive linear model allowed capturing the initial linear region in which the approximation of these tissues as linear elastic materials is reasonable. The residual analysis displayed that even if the SYM model better summarizes the muscle behavior on the entire region, the linear model is more precise when considering only the initial part of the σ-ε curve.
Highlights
Measuring and Modelling Nonlinear Elasticity of Ex Vivo Mouse MusclesElastography is a noninvasive imaging technique that provides information on soft tissue stiffness
Noninvasive measurement of soft biological tissues’ mechanical properties is of significant clinical interest as pathologies are generally correlated with changes in tissue stiffness
Even though soft biological tissues exhibit a nonlinear σ-ε behavior, they are typically assumed to be linear elastic if a significant linear region of the σ-ε curve exists in the limit of small deformation to the applied stress [32], and elastography is generally based on this approximation [3, 6, 26]
Summary
Elastography is a noninvasive imaging technique that provides information on soft tissue stiffness. Is approximation is reasonable for small strains, but soft tissues undergo large deformations for small values of force and exhibit nonlinear elastic behavior. E strain-dependent Young’s modulus (SYM) model was adopted to reproduce muscle compression behavior and to predict the elastic modulus for large deformations. A recursive linear model was employed to identify the initial linear region of the σ-ε curve. Results showed that both muscle types exhibited a strain hardening effect and that the SYM model provided good fitting of the entire σ-ε curves. E residual analysis displayed that even if the SYM model better summarizes the muscle behavior on the entire region, the linear model is more precise when considering only the initial part of the σ-ε curve Results showed that both muscle types exhibited a strain hardening effect and that the SYM model provided good fitting of the entire σ-ε curves. e application of the recursive linear model allowed capturing the initial linear region in which the approximation of these tissues as linear elastic materials is reasonable. e residual analysis displayed that even if the SYM model better summarizes the muscle behavior on the entire region, the linear model is more precise when considering only the initial part of the σ-ε curve
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