Identifying a Minimal Rheological Configuration: A Tool for Effective and Efficient Constitutive Modeling of Soft Tissues

Abstract

We describe a modeling methodology intended as a preliminary step in the identification of appropriate constitutive frameworks for the time-dependent response of biological tissues. The modeling approach comprises a customizable rheological network of viscous and elastic elements governed by user-defined 1D constitutive relationships. The model parameters are identified by iterative nonlinear optimization, minimizing the error between experimental and model-predicted structural (load-displacement) tissue response under a specific mode of deformation. We demonstrate the use of this methodology by determining the minimal rheological arrangement, constitutive relationships, and model parameters for the structural response of various soft tissues, including ex-vivo perfused porcine liver in indentation, ex-vivo porcine brain cortical tissue in indentation, and ex-vivo human cervical tissue in unconfined compression. Our results indicate that the identified rheological configurations provide good agreement with experimental data, including multiple constant strain-rate load/unload tests and stress-relaxation tests. Our experience suggests that the described modeling framework is an efficient tool for exploring a wide array of constitutive relationships and rheological arrangements, which can subsequently serve as a basis for 3D constitutive model development and finite-element implementations. The proposed approach can also be employed as a self-contained tool to obtain simplified 1D phenomenological models of the structural response of biological tissue to single-axis manipulations for applications in haptic technologies.

Nonlinear viscoelastic constitutive model for bovine liver tissue

“…Both oscillatory shear and uniaxial deformation tests show that, at low strains, the liver exhibits quasi-linearity, with the nonlinear behaviour being exposed at higher strains (Liu and Bilston 2000;Gao et al 2010;Tan et al 2013). Additionally, loading-unloading tests reveal that hysteresis effects are taking place (Jordan et al 2011), with the response being rate dependent (Liu and Bilston 2000;Miller 2000). Multifrequency soft tissue measurements of the shear modulus G * indicate a fractional-order dependence on the angular frequency in the form of G * ∝ (Holm and Sinkus 2010), with ∈ [0.2, 0.35] [e.g.…”

One-period stability analysis of polygonal sweeping processes with application to an elastoplastic model

“…Aiming to design materials with better properties, there has been a great deal of work lately where a discrete structure comes from a certain microstructure formulated through a lattice of elastic springs [13] (metals), [15] (polymers), [6] (titanium alloys), [10] (biological materials). At the same time, recent findings show [4] that a pivotal role in the performance of heterogeneous materials under cyclic loading is played by micro-plasticity.…”

A Mathematical Model for Analyzing the Elasticity, Viscosity, and Failure of Soft Tissue: Comparison of Native and Decellularized Porcine Cardiac Extracellular Matrix for Tissue Engineering

“…Such combinations of several modes and/or regions are not only common in many experiments, but also better resemble the physiological conditions in which these biomaterials are believed to operate. 41,42 Much like multiple relaxation time (MRT) models, SRT models are expected to correlate to a large extent with empirical data and may provide better assessments of viscoelastic properties than the Young's modulus alone, [43][44][45] with an advantage of avoiding the information redundancy commonly incurred by MRT models. SRT models may also facilitate the analysis of soft biomaterials, not as monolithic solids, but as a bundle of strings, each having the same elastic moduli and viscosity, but with different failure points, thereby enabling the modeling of such solids beyond their apparent linear viscoelastic region and into their failure region.…”