Growth and remodeling in the pulmonary autograft: computational evaluation using kinematic growth models and constrained mixture theory

2021 ◽  
Author(s):  
Julie Vastmans ◽  
Lauranne Maes ◽  
Mathias Peirlinck ◽  
Emma Vanderveken ◽  
Filip Rega ◽  
...  
Keyword(s):  
Growth Models ◽  
Mixture Theory ◽  
Growth And Remodeling ◽  
Pulmonary Autograft ◽  
Computational Evaluation ◽  
Constrained Mixture Theory ◽  
Constrained Mixture

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.

scholarly journals VASCULAR MECHANICS, MECHANOBIOLOGY, AND REMODELING

2009 ◽  
Vol 09 (02) ◽  
pp. 243-257 ◽  
Author(s):  
J. D. HUMPHREY
Keyword(s):  
Constitutive Relations ◽  
Mixture Theory ◽  
Clinical Treatment ◽  
Vascular Mechanics ◽  
Growth And Remodeling ◽  
Theoretical Frameworks ◽  
Future Directions ◽  
Constrained Mixture Theory ◽  
Constrained Mixture ◽  
Recent Developments

Arteries exhibit a remarkable ability to adapt in response to sustained alterations in hemodynamic loading as well as to disease, injury, and clinical treatment. A better understanding of such adaptations will be aided greatly by formulating, testing, and refining appropriate theoretical frameworks for modeling the biomechanics and associated mechanobiology. The goal of this brief review is to highlight some recent developments in the use of a constrained mixture theory of arterial growth and remodeling, with particular attention to the requisite constitutive relations, and to highlight future directions of needed research.

scholarly journals A Two-Dimensional Model of Hypertension-Induced Arterial Remodeling With Account for Stress Interaction Between Elastin and Collagen

2019 ◽  
Vol 142 (4) ◽  
Author(s):  
Alexander Rachev ◽  
Tarek Shazly
Keyword(s):  
Mixture Theory ◽  
Natural State ◽  
Arterial Remodeling ◽  
Two Dimensional ◽  
Structural Reorganization ◽  
Constrained Mixture Theory ◽  
Novel Structure ◽  
Constrained Mixture ◽  
Arterial Tissue ◽  
The Individual

Abstract We propose a novel structure-based two-dimensional (2D) mathematical model of hypertension-induced arterial remodeling. The model is built in the framework of the constrained mixture theory and global growth approach, utilizing a recently proposed structure-based constitutive model of arterial tissue that accounts for the individual natural configurations of and stress interaction between elastin and collagen. The basic novel predictive result is that provided remodeling causes a change in the elastin/collagen mass fraction ratio, it leads to a structural reorganization of collagen that manifests as an altered fiber undulation and a change in direction of the helically oriented fibers in the tissue natural state. Results obtained from the illustrative simulations for a porcine renal artery show that when remodeling is complete the collagen reorganization might have significant effects on the initial arterial geometry and mechanical properties of the arterial tissue. The proposed model has potential to describe and advance mechanistic understanding of adaptive arterial remodeling, promote the continual refinement of mathematical models of arterial remodeling, and provide motivation for new avenues of experimental investigation.

scholarly journals A constituent-based model of age-related changes in conduit arteries

2011 ◽  
Vol 301 (4) ◽  
pp. H1286-H1301 ◽  
Author(s):  
Alkiviadis Tsamis ◽  
Alexander Rachev ◽  
Nikos Stergiopulos
Keyword(s):  
Mechanical Properties ◽  
Time Course ◽  
Present Report ◽  
Finite Elasticity ◽  
Mixture Theory ◽  
Constrained Mixture Theory ◽  
Age Related ◽  
Constrained Mixture ◽  
Arterial Tissue ◽  
Age Related Changes

In the present report, a constituent-based theoretical model of age-related changes in geometry and mechanical properties of conduit arteries is proposed. The model was based on the premise that given the time course of the load on an artery and the accumulation of advanced glycation end-products in the arterial tissue, the initial geometric dimensions and properties of the arterial tissue can be predicted by a solution of a boundary value problem for the governing equations that follow from finite elasticity, structure-based constitutive modeling within the constrained mixture theory, continuum damage theory, and global growth approach for stress-induced structure-based remodeling. An illustrative example of the age-related changes in geometry, structure, composition, and mechanical properties of a human thoracic aorta is considered. Model predictions were in good qualitative agreement with available experimental data in the literature. Limitations and perspectives for refining the model are discussed.

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.

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 Global Sensitivity Analysis of a Homogenized Constrained Mixture Model of Arterial Growth and Remodeling

2021 ◽  
Author(s):  
Sebastian Brandstaeter ◽  
Sebastian L. Fuchs ◽  
Jonas Biehler ◽  
Roland C. Aydin ◽  
Wolfgang A. Wall ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Model Parameters ◽  
Computational Studies ◽  
Growth And Remodeling ◽  
Global Sensitivity ◽  
Output Variability ◽  
Constrained Mixture ◽  
The One ◽  
Influential Parameters

AbstractGrowth and remodeling in arterial tissue have attracted considerable attention over the last decade. Mathematical models have been proposed, and computational studies with these have helped to understand the role of the different model parameters. So far it remains, however, poorly understood how much of the model output variability can be attributed to the individual input parameters and their interactions. To clarify this, we propose herein a global sensitivity analysis, based on Sobol indices, for a homogenized constrained mixture model of aortic growth and remodeling. In two representative examples, we found that 54–80% of the long term output variability resulted from only three model parameters. In our study, the two most influential parameters were the one characterizing the ability of the tissue to increase collagen production under increased stress and the one characterizing the collagen half-life time. The third most influential parameter was the one characterizing the strain-stiffening of collagen under large deformation. Our results suggest that in future computational studies it may - at least in scenarios similar to the ones studied herein - suffice to use population average values for the other parameters. Moreover, our results suggest that developing methods to measure the said three most influential parameters may be an important step towards reliable patient-specific predictions of the enlargement of abdominal aortic aneurysms in clinical practice.

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