Modeling biological growth and remodeling: Contrasting methods, contrasting needs

2020

Preprint

Self Cite

Constrained mixture models of soft tissue growth and remodeling enable one to simulate many evolving conditions in health, disease, and its treatment, but they tend to be computationally expensive. In this paper, we derive a new fast, robust finite element implementation based on a concept of mechanobiological equilibrium which allows computation of fully resolved long-term solutions as well as quasi-equilibrated evolutions for which 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 more complex situations, including the enlargement of aneurysms, and identify new mechanobiological insights into factors that affect the nearby non-aneurysmal segment as it responds to the changing mechanics within the diseased segment. Since this new 3D approach can be implemented within many existing finite element solvers, we submit that constrained mixture models of growth and remodeling can now be used more widely.

Section: Discussionmentioning

confidence: 99%

Section: Non-uniform Equilibrated Gandr Response (Stage Ii) To Localizementioning

confidence: 99%

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

Latorre¹,

2020

Preprint

Self Cite

“…We have previously presented finite element implementations of our constrained mixture model (e.g., [ 34 , 35 ]), but herein we use a fast, efficient 3-D implementation [ 36 ] that is based on the underlying assumption that each G&R state is mechanobiologically equilibrated [ 27 ], which holds for cases wherein the characteristic timescale of the remodeling process is shorter than the timescale for the driving stimulus, that is, for fully quasi-static G&R [ 37 , 38 ].…”

Section: Methodsmentioning

confidence: 99%

Numerical knockouts–In silico assessment of factors predisposing to thoracic aortic aneurysms

Latorre

2020

PLoS Comput Biol

Self Cite

Myriad risk factors–including uncontrolled hypertension, aging, and diverse genetic mutations–contribute to the development and enlargement of thoracic aortic aneurysms. Detailed analyses of clinical data and longitudinal studies of murine models continue to provide insight into the natural history of these potentially lethal conditions. Yet, because of the co-existence of multiple risk factors in most cases, it has been difficult to isolate individual effects of the many different factors or to understand how they act in combination. In this paper, we use a data-informed computational model of the initiation and progression of thoracic aortic aneurysms to contrast key predisposing risk factors both in isolation and in combination; these factors include localized losses of elastic fiber integrity, aberrant collagen remodeling, reduced smooth muscle contractility, and dysfunctional mechanosensing or mechanoregulation of extracellular matrix along with superimposed hypertension and aortic aging. In most cases, mild-to-severe localized losses in cellular function or matrix integrity give rise to varying degrees of local dilatations of the thoracic aorta, with enlargement typically exacerbated in cases wherein predisposing risk factors co-exist. The simulations suggest, for the first time, that effects of compromised smooth muscle contractility are more important in terms of dysfunctional mechanosensing and mechanoregulation of matrix than in vessel-level control of diameter and, furthermore, that dysfunctional mechanobiological control can yield lesions comparable to those in cases of compromised elastic fiber integrity. Particularly concerning, therefore, is that loss of constituents such as fibrillin-1, as in Marfan syndrome, can compromise both elastic fiber integrity and mechanosensing.

“…Importantly, Eqs. ( 6) and ( 7) also approximate G&R processes wherein the characteristic rate for adaptation is faster than the rate of change of the stimulation, thus yielding mechanobiologically quasi-equilibrated G&R evolutions [10,11].…”

Section: Mechanobiological Equilibriummentioning

confidence: 99%

Fast, rate-independent, finite element implementation of a 3D constrained mixture model of soft tissue growth and remodeling

Latorre

Computer Methods in Applied Mechanics and Engineering

2020

Self Cite

Constrained 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.