scholarly journals A homogenized constrained mixture (and mechanical analog) model for growth and remodeling of soft tissue

2016 ◽  
Vol 15 (6) ◽  
pp. 1389-1403 ◽  
Author(s):  
C. J. Cyron ◽  
R. C. Aydin ◽  
J. D. Humphrey
Keyword(s):  
Soft Tissue ◽  
Growth And Remodeling ◽  
Analog Model ◽  
Mechanical Analog ◽  
Constrained Mixture

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 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 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.

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
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