scholarly journals A mechanobiologically equilibrated constrained mixture model for growth and remodeling of soft tissues

2018 ◽  
Vol 98 (12) ◽  
pp. 2048-2071 ◽  
Author(s):  
Marcos Latorre ◽  
Jay D. Humphrey
Keyword(s):  
Mixture Model ◽  
Soft Tissues ◽  
Growth And Remodeling ◽  
Constrained Mixture

A 3-D Constrained Mixture Model for Vascular Growth and Remodeling

2009 ◽  
Author(s):  
William Wan ◽  
Laura Hansen ◽  
Rudolph L. Gleason
Keyword(s):  
Mechanical Properties ◽  
Blood Vessels ◽  
Mixture Model ◽  
Coronary Thrombosis ◽  
Coronary Bypass ◽  
Mechanical Tests ◽  
Loading Conditions ◽  
Growth And Remodeling ◽  
Constrained Mixture ◽  
Coronary Bypass Grafts

It is known that arteries adapt and remodel to changes in their loading conditions. Evolution of mechanical properties of blood vessels is associated with numerous chronic and acute conditions such as hypertension and coronary thrombosis. In addition, treatments such as bypass surgery create loading conditions not seen in normal arteries. Blood vessels used in coronary bypass grafts experience abnormal loading conditions in both circumferential and axial directions. Blood vessels remodel by altering structural components to restore homeostatic values of stress. Such changes may include smooth muscle cell proliferation, migration and collagen synthesis, degradation, and remodeling. While biaxial mechanical tests and organ culture experiments provide values for global variables such as mean stresses and total thickness, mathematical models can help describe local mechanical properties at locations throughout the vessel wall. Experimental observations suggest that constituents of arteries turnover at different rates; thus, it is important that models are able to track individual constituents of the artery separately. Here, we present a 3D constrained mixture model for growth and remodeling of arteries exposed to large changes in flow, pressure, and axial stretch -induced.

scholarly journals Parameter Sensitivity Study of a Constrained Mixture Model of Arterial Growth and Remodeling

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
A. Valentín ◽  
J. D. Humphrey
Keyword(s):  
Shear Stress ◽  
Smooth Muscle ◽  
Wall Shear Stress ◽  
Mixture Model ◽  
Rapid Change ◽  
Parameter Sensitivity ◽  
Growth And Remodeling ◽  
Constrained Mixture ◽  
Wall Shear ◽  
Parameter Values

Computational models of arterial growth and remodeling promise to increase our understanding of basic biological processes, such as development, tissue maintenance, and aging, the biomechanics of functional adaptation, the progression and treatment of disease, responses to injuries, and even the design of improved replacement vessels and implanted medical devices. Ensuring reliability of and confidence in such models requires appropriate attention to verification and validation, including parameter sensitivity studies. In this paper, we classify different types of parameters within a constrained mixture model of arterial growth and remodeling; we then evaluate the sensitivity of model predictions to parameter values that are not known directly from experiments for cases of modest sustained alterations in blood flow and pressure as well as increased axial extension. Particular attention is directed toward complementary roles of smooth muscle vasoactivity and matrix turnover, with an emphasis on mechanosensitive changes in the rates of turnover of intramural fibrillar collagen and smooth muscle in maturity. It is shown that vasoactive changes influence the rapid change in caliber that is needed to maintain wall shear stress near its homeostatic level and the longer term changes in wall thickness that are needed to maintain circumferential wall stress near its homeostatic target. Moreover, it is shown that competing effects of intramural and wall shear stress-regulated rates of turnover can develop complex coupled responses. Finally, results demonstrate that the sensitivity to parameter values depends upon the type of perturbation from normalcy, with changes in axial stretch being most sensitive consistent with empirical reports.

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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