A stress driven growth model for soft tissue considering biological availability

Imbalance of stress/strain microenvironment can lead to adverse remodelling and pathogenesis in various soft tissues, tumour included. Therefore, there is a critical need for accurate quantification of the biomechanical homeostasis in soft tissue through mathematical modelling, which is critically dependent on constitutive models, the mathematical descriptions that approximate the mechanical behaviours of material under specific conditions by considering information from subcellular, cellular and tissue levels. In most soft biological tissue, collagen is the major component of the extracellular matrix, its architecture largely determines the material property (stiffness). In this work, we will use myocardium as an example to show how we can develop a constitutive law from various ex vivo experiments within the continuum mechanics framework, and demonstrate the applications to real patient data. We will further focus on parameter calibrations from ex/in vivo measurements. We believe this approach of constitutive modelling and calibration can be applied to various soft biological tissues and shed light on physiological and pathological mechanobiology.

Efficient Time-Stepping for the Evolution Equations of Damage-Induced Growth and Remodelling in Soft Biological Tissues

A computational multilayer model to simulate hollow needle insertion into biological porcine liver tissue

Logarithmic rate based elasto-viscoplastic cyclic constitutive model for soft biological tissues

Finite element implementation of a stochastic three dimensional finite-strain damage model for fibrous soft tissue

Development of a crop growth model for the energy analysis of controlled agriculture environment spaces

A continuum mechanics framework and a constitutive model for remodelling of collagen gels and collagenous tissues

A new mechanistic theory was developed for soft tissues growth and remodeling (G&R). The theory considers tissues with unidirectional fibers. It is based on the loading-dependent local turnover events of each constituent and on the resulting evolution of the tissue micro-structure, the tissue dimensions and its mechanical properties. The theory incorporates the specific mechanical properties and turnover kinetics of each constituent, thereby establishing a general framework which can serve for future integration of additional mechanisms involved in G&R. The feasibility of the theory was examined by considering a specific realization of tissues with one fibrous constituent (collagen fibers), assuming a specific loading-dependent first-order fiber's turnover kinetics and the fiber's deposition characteristics. The tissue was subjected to a continuous constant rate growth. Model parameters were adopted from available data. The resulting predictions show qualitative agreement with a number of well-known features of tissues including the fibers' non-uniform recruitment density distribution, the associated tissue convex nonlinear stress-stretch relationship, and the development of tissue pre-stretch and pre-stress states. These results show that mechanistic micro-structural modeling of soft tissue G&R based on first principles can successfully capture the evolution of observed tissues' structure and size, and of their associated mechanical properties.

In this contribution a coupled material framework is presented, which considers the effects of damage and growth in soft biological tissues. The tissue is described as a porous medium by taking into account a solid and a fluid phase. The fluid phase is assumed to carry nutrients supplying growth of the solid phase. The latter one is described as a fiber‐reinforced material, where a damage variable is introduced for the fiber part of the associated free energy function. The performance of the proposed model is demonstrated in a finite element analysis of a simplified human heart model. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

In spite of impressive progress in developing general constitutive laws for soft tissues, there exists still no comprehensive model valid for any general deformation scheme. The present study focuses on the uniaxial response of the skin as a model for other multifibrous soft tissues. While the skin's nonlinear viscoelastic constitutive response has been extensively studied and modeled, the phenomena associated with mechanical preconditioning have so far not been dealt with. Yet preconditioning is an inherent response feature in the skin, both in vitro and in vivo. It is hypothesized that by considering the structure of the elastic and collagen fibers and their individual rheological properties, it is possible to develop a reliable general constitutive law for the skin's uniaxial response. A stochastic hybrid constitutive model was developed based on the collagen and elastic fiber morphologies and their rheological properties. The multiple protocol uniaxial data of Eshel and Lanir ("Effects of Strain Level and Proteoglycan Depletion on Preconditioning and Viscoelastic Responses of Rat Dorsal Skin," 2001, Ann. Biomed. Eng., 29, pp. 164-172) served to estimate the model's parameters and to validate its reliability. Parametric investigation was then used to test model parsimony (minimal form) and to elucidate the roles of response mechanism and the relative contribution of each constituent. The model predictions show a very close fit to the data and good predictive capability. The results are consistent with the quasilinear viscoelastic response of both elastic and collagen fibers and are likewise consistent with the notion (supported by published experimental observations) that preconditioning in collagen is probably due to an increase in the fiber reference length and is due to strain softening (Mullins effect) in elastic fibers. The predictions also agree with the observed predominance of elastic fibers at low strains and suggest that as strain increases, collagen becomes predominant, but the effect of elastic fibers is still significant. The parsimony analysis of the 22 model parameters (18 are nonlinear in the model) points to the predominant role of viscoelasticity and preconditioning in both fibers, followed in order of importance by collagen waviness and elastic fiber nonlinearity. A reliable and comprehensive uniaxial constitutive law for the rat skin was developed based on the tissue microstructure and on its constituents' rheological properties.

Basic research into the aetiology of pressure ulcers suggests that the concentration of mechanical strain in biological soft tissues is critical to their development. Direct measurement of in vivo strain is not compatible with clinical routine. To overcome this problem, several finite element models (FEM) have been proposed by the biomechanical community to estimate strain from imaging data. However, no direct experimental validation of the underlying relationships between mechanical loading and soft tissue strain distribution predicted by the model has been performed, and such validation evidence must be obtained prior to any clinical evaluation. Building on the experimental results obtained in N=10 healthy volunteers (Zappalá et al., 2024), the relevance of the modelling hypotheses of the finite element model proposed in this study, which is based on a simplified geometric representation of the ischial region (Macron et al., 2020), was investigated. A methodology was proposed to estimate the different parameters needed to construct the model from the available MRI masks. The FEM was then used to estimate in vivo compressive and shear strains. The resulting strains were then compared with experimental data. The results show that the model assumptions lead to an overall overestimation of the compressive and shear strains in the muscle tissue, especially directly under the ischial tuberosity. Similarly, the model underestimates the strain in adipose tissue (mean error in shear strain of -0.2). This study highlights the fact that the assumptions usually made for the geometric modelling of muscle tissue (homogeneous soft tissue layer) lead to an incorrect estimation of peak strain localisation. Further work should be done to improve the representation of muscle tissue.

Growth and remodeling of soft tissues is a dynamic process and several theoretical frameworks have been developed to analyze the time-dependent, mechanobiological and/or biomechanical responses of these tissues to changes in external loads. Importantly, general processes can often be conveniently separated into truly non-steady contributions and steady-state ones. Depending on characteristic times over which the external loads are applied, time-dependent models can sometimes be specialized to respective time-independent formulations that simplify the mathematical treatment without compromising the goodness of the particularized solutions. Very few studies have analyzed the long-term, steady-state responses of soft tissue growth and remodeling following a direct approach. Here, we derive a mechanobiologically equilibrated formulation that arises from a general constrained mixture model. We see that integral-type evolution equations that characterize these general models can be written in terms of an equivalent set of time-independent, nonlinear algebraic equations that can be solved efficiently to yield long-term outcomes of growth and remodeling processes in response to sustained external stimuli. We discuss the mathematical conditions, in terms of orders of magnitude, that yield the particularized equations and illustrate results numerically for general arterial mechano-adaptations.

Specific features of photon density normalized maximum movement in soft biological tissue under the influence of deforming force are described. Soft biological tissue is simulated as a turbid and linear isotropic pseudo-incompressible medium. It has been shown that the deforming effects do not influence the direction of photon density normalized maximum (PDNM) movement, but affect the speed of its movement. The decay of diffuse transmittance intensity is 8 to 10% faster in undeformed state than in those with deformations. The established features can be useful for the generation of an initial approximation to the spatial distributions of optical parameters during solution of the diffuse optical tomography (DOT) inverse problem.

Soft materials such as polymers and biological tissues have several engineering and biomechanical applications. These materials exhibit complex mechanical behavior, characterized by large strains, hysteresis, rate sensitivity, stress softening (Mullins effect), and deviatoric and volumetric plasticity. The need to accurately predict the behavior of such materials has been a tremendous challenge for scientists and engineers. This thesis presents a seamless, fully variational constitutive model capable of capturing all of the above complex characteristics. Also, this work describes a fitting procedure based on the use of Genetic Algorithms, which proves to be necessary for the multi-modal, non-convex optimization required to identify fitting material parameters. The capabilities of the presented model are demonstrated via several fits of experimental tests on a wide range of materials. These tests involve monotonic and cyclic loading of polyurea, high-density polyethylene, and brain tissue, and also involve cyclic hysteresis, softening, rate effects, shear, and cavitation plasticity. Application to ballistic impact on a polyurea retrofitted DH36 steel plate is simulated and validated, utilizing the soft material model presented in this thesis for the polymer and a porous plasticity model for the metal. Localization elements are also included in this application to capture adiabatic shear bands. Moreover, computational capability for assessing the blast performance of metal/elastomer composite shells utilizing the soft material model for the elastomer is also presented. Another implemented application is in the area of traumatic brain injuries under impact/acceleration loading. Clinically observed brain damage is reproduced utilizing the model presented in this work and a predictive capability of the distribution, intensity, and reversibility/irreversibility of brain tissue damage is demonstrated.

This paper addresses evaluation and visualization of stress and strain on soft biological tissues in contact given three-dimensional models of reconstructed organs from magnetic resonance images (MRI), we use an anatomy-based kinematical model combined with a soft tissues model to represent their shape and behavior. Then, we compute resulting distribution of stress and strain on deforming surface when motion is simulated. The computed stress and strain are then effectively visualized using an interactive animation framework. Experimental results are illustrated in the case of the hip joint cartilage.