Homogenized constrained mixture models for anisotropic volumetric growth and remodeling

2016 ◽  
Vol 16 (3) ◽  
pp. 889-906 ◽  
Author(s):  
F. A. Braeu ◽  
A. Seitz ◽  
R. C. Aydin ◽  
C. J. Cyron
Keyword(s):  
Mixture Models ◽  
Growth And Remodeling ◽  
Volumetric Growth ◽  
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.

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.

Relevant subtask learning by constrained mixture models

2010 ◽  
Vol 14 (6) ◽  
pp. 641-662 ◽  
Author(s):  
Jaakko Peltonen ◽  
Yusuf Yaslan ◽  
Samuel Kaski
Keyword(s):  
Mixture Models ◽  
Constrained Mixture

Development of a Finite Element Model Framework for Studying Growth of Cartilage Anlage

2009 ◽  
Author(s):  
Roza Mahmoodian ◽  
Sorin Siegler ◽  
Franco Capaldi
Keyword(s):  
Deformation Gradient ◽  
Newborn Infants ◽  
Element Model ◽  
Driving Mechanism ◽  
Elastic Tissue ◽  
Growth And Remodeling ◽  
Volumetric Growth ◽  
Model Framework ◽  
Important Research Topic ◽  
As Stress

Growth and remodeling are fundamental processes in the development of tissues in normal and pathological conditions. Mechanical quantities such as stress, strain or strain energy in the tissue can modulate its growth and remodeling; however, it is not clear yet which mechanical quantity takes this role. Experimental data can be found to support both. Furthermore, the driving-mechanism may be tissue-dependent and therefore, a universal growth law may not exist [7,8]. This field has been an important research topic in biomechanics over the recent decades. The review articles by Humphrey [4] and Taber [8] contain numerous related references. An important contribution was made by Rodriguez et al. [7] to the area of volumetric growth of soft elastic tissue which allowed for the coupling between stress and finite growth through multiplicative decomposition of the deformation gradient into elastic and growth parts. This theory has been followed in our study. Our goal is to model growth of the hind foot cartilage anlagen in newborn infants, and explore effect of congenital anomalies on the otherwise normal development.

Lip Posture Estimation using Kinematically Constrained Mixture Models

1998 ◽  
Author(s):  
P. H. Kelly ◽  
E. A. Hunter ◽  
K. Kreutz-Delgado ◽  
R. Jain
Keyword(s):  
Mixture Models ◽  
Constrained Mixture ◽  
Posture Estimation
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