A Constitutive Model for Soft Tissue and its Application to a Boundary Value Problem

2013 ◽  
Author(s):  
P. Mythravaruni ◽  
Parag Ravindran
Keyword(s):  
Soft Tissue ◽  
Mixture Theory ◽  
Axial Loading ◽  
Tissue Growth ◽  
Theory Approach ◽  
Growth And Remodeling ◽  
Constrained Mixture ◽  
Set Up ◽  
And Function ◽  
Turn Over

Mechanical loading induces changes in the structure and function of soft tissue. Growth and remodeling results from the production and removal of constituents. We consider a tissue constituted of elastin and collagen. The collagen turns over at a much higher rate than elastin. In this work we propose a two-constituent, constrained mixture model for this soft tissue. One constituent is modeled as a viscoelastic material and the other as an elastic material. It is assumed that the collagen turns over depending on the stress applied and the elastin does not turn over. The standard mixture theory approach is followed and the balance equations are set-up. The model is studied in simple uni-axial loading to test its efficacy.

scholarly journals Fast, Rate-Independent, Finite Element Implementation of a 3D Constrained Mixture Model of Soft Tissue Growth and Remodeling

2020 ◽  
Author(s):  
Marcos Latorre ◽  
Jay D. Humphrey
Keyword(s):  
Finite Element ◽  
Soft Tissue ◽  
Mixture Models ◽  
Tissue Growth ◽  
Aortic Aneurysms ◽  
Growth And Remodeling ◽  
Adaptive Process ◽  
Finite Element Implementation ◽  
Constrained Mixture ◽  
Diseased Segment

AbstractConstrained mixture models of soft tissue growth and remodeling can simulate many evolving conditions in health as well as in disease and its treatment, but they can be computationally expensive. In this paper, we derive a new fast, robust finite element implementation based on a concept of mechanobiological equilibrium that yields fully resolved solutions and allows computation of quasi-equilibrated evolutions when imposed perturbations are slow relative to the adaptive process. We demonstrate quadratic convergence and verify the model via comparisons with semi-analytical solutions for arterial mechanics. We further examine the enlargement of aortic aneurysms for which we identify new mechanobiological insights into factors that affect the nearby non-aneurysmal segment as it responds to the changing mechanics within the diseased segment. Because this new 3D approach can be implemented within many existing finite element solvers, constrained mixture models of growth and remodeling can now be used more widely.

A CONSTRAINED MIXTURE MODEL FOR GROWTH AND REMODELING OF SOFT TISSUES

2002 ◽  
Vol 12 (03) ◽  
pp. 407-430 ◽  
Author(s):  
J. D. HUMPHREY ◽  
K. R. RAJAGOPAL
Keyword(s):  
Soft Tissues ◽  
Constitutive Relations ◽  
Viscoelastic Behavior ◽  
Mixture Theory ◽  
Theory Model ◽  
Structure And Function ◽  
Material Point ◽  
Growth And Remodeling ◽  
Constrained Mixture ◽  
And Function

Not long ago it was thought that the most important characteristics of the mechanics of soft tissues were their complex mechanical properties: they often exhibit nonlinear, anisotropic, nearly incompressible, viscoelastic behavior over finite strains. Indeed, these properties endow soft tissues with unique structural capabilities that continue to be extremely challenging to quantify via constitutive relations. More recently, however, we have come to appreciate an even more important characteristic of soft tissues, their homeostatic tendency to adapt in response to changes in their mechanical environment. Thus, to understand well the biomechanical properties of a soft tissue, we must not only quantify their structure and function at a given time, we must also quantify how their structure and function change in response to altered stimuli. In this paper, we introduce a new constrained mixture theory model for studying growth and remodeling of soft tissues. The model melds ideas from classical mixture and homogenization theories so as to exploit advantages of each while avoiding particular difficulties. Salient features include the kinetics of the production and removal of individual constituents and recognition that the neighborhood of a material point of each constituent can have a different, evolving natural (i.e. stress-free) configuration.

scholarly journals Critical roles of time-scales in soft tissue growth and remodeling

2018 ◽  
Vol 2 (2) ◽  
pp. 026108 ◽  
Author(s):  
Marcos Latorre ◽  
Jay D. Humphrey
Keyword(s):  
Soft Tissue ◽  
Time Scales ◽  
Tissue Growth ◽  
Growth And Remodeling

scholarly journals A Constrained Mixture Theory Model to Study Autoregulation in the Coronary Circulation

2020 ◽  
Author(s):  
Hamidreza Gharahi ◽  
Daniel A. Beard ◽  
C. Alberto Figueroa ◽  
Seungik Baek
Keyword(s):  
Coronary Circulation ◽  
Mixture Theory ◽  
Extensive Literature ◽  
Optimization Approach ◽  
List Type ◽  
Growth And Remodeling ◽  
Constrained Mixture Theory ◽  
Constrained Mixture ◽  
Wide Range

AbstractCoronary autoregulation is a short-term response manifested by a relatively constant flow over a wide range of perfusion pressures for a given metabolic state. This phenomenon is thought to be facilitated through a combination of mechanisms, including myogenic, shear dependent, and metabolic controls. The study of coronary autoregulation is challenging due to the coupled nature of the mechanisms and their differential effects through the coronary tree. In this paper, we developed a novel framework to study coronary autoregulation based on the constrained mixture theory. This structurally-motivated autoregulation model required calibration of anatomical and structural parameters of coronary trees via a homeostatic optimization approach using extensive literature data. Autoregulation was then simulated for two different coronary trees: subepicardial and subendocardial. The structurally calibrated model reproduced available baseline hemodynamics and autoregulation data for each coronary tree. The autoregulation analysis showed that the diameter of the intermediate and small arterioles varies the most in response to changes in perfusion pressure. Finally, we demonstrated the utility of the model in two application examples: 1) response to drops in epicardial pressure, and 2) response to drug infusion in the coronary arteries. The proposed structurally-motivated model could be extended to study long-term growth and remodeling in the coronary circulation in response to hypertension, atherosclerosis, etc.Key pointsCoronary autoregulation is defined as the capability of the coronary circulation to maintain the blood supply to the heart over a range of perfusion pressures. This phenomenon is facilitated through intrinsic mechanisms that control the vascular resistance by regulating the mechanical function of smooth muscle cells. Understanding the mechanisms involved in coronary autoregulation is one of the most fundamental questions in coronary physiology.This paper presents a structurally-motivated coronary autoregulation model that uses a nonlinear continuum mechanics approach to account for the morphometry and vessel wall composition in two coronary trees in the subepicardial and subendocardial layers.The model is calibrated against diverse experimental data from literature and is used to study heterogeneous autoregulatory response in the coronary trees. This model drastically differs from previous models, which relied on lumped parameter model formulations, and is suited to the study of long-term pathophysiological growth and remodeling phenomena in coronary vessels.

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