Special Issue: Spotlight on the Future of Cardiovascular Engineering:Frontiers and Challenges in Cardiovascular Biomechanics

Holmes, Jeffrey W.; Wagenseil, Jessica E.

doi:10.1115/1.4034873

Cited by 4 publications

(3 citation statements)

References 49 publications

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“…For illustrative purposes, we analyzed such responses using a single layer, thin-walled description of an idealized artery, obtaining a system of nonlinear, evolved equations that yielded, precisely, the same long-term solution as the associated full constrained mixture model. Although the present mechanobiologically theory has not been extended to obtain grown and remodeled, steady-state configurations of soft tissues with more complex geometries and/or loads, we submit that it may “represent a fundamentally new capability to predict the single thing that matters most to doctors and patients: long-term outcomes” [33]. Notwithstanding these benefits, the present equilibrium formulation is not valid, in general, for the analysis of truly time-dependent responses of soft tissues, for which the full integral formulation is needed to compute the time course of the G&R.…”

Section: Discussionmentioning

confidence: 99%

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

Latorre

Humphrey

2018

Z Angew Math Mech

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Growth and remodeling of soft tissues is a dynamic process and several theoretical frameworks have been developed to analyze the time-dependent, mechanobiological and/or biomechanical responses of these tissues to changes in external loads. Importantly, general processes can often be conveniently separated into truly non-steady contributions and steady-state ones. Depending on characteristic times over which the external loads are applied, time-dependent models can sometimes be specialized to respective time-independent formulations that simplify the mathematical treatment without compromising the goodness of the particularized solutions. Very few studies have analyzed the long-term, steady-state responses of soft tissue growth and remodeling following a direct approach. Here, we derive a mechanobiologically equilibrated formulation that arises from a general constrained mixture model. We see that integral-type evolution equations that characterize these general models can be written in terms of an equivalent set of time-independent, nonlinear algebraic equations that can be solved efficiently to yield long-term outcomes of growth and remodeling processes in response to sustained external stimuli. We discuss the mathematical conditions, in terms of orders of magnitude, that yield the particularized equations and illustrate results numerically for general arterial mechano-adaptations.

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Section: Discussionmentioning

confidence: 99%

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

Latorre

Humphrey

2018

Z Angew Math Mech

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“…( 2), is equivalent to the longterm solution of its respective heredity integral model [40]. If "G&R models represent a fundamentally new capability to predict the single thing that matters most to doctors and patients: long-term outcomes" [41], a formalization of these, and others that may emerge, formulations that give rise to efficient and reliable computational methods for parameter sensitivity, uncertainty quantification, and optimization of material parameters or geometries, subject to complex loads and boundary conditions, should be pursued.…”

Section: Mechanobiological Equilibriummentioning

confidence: 99%

Modeling biological growth and remodeling: Contrasting methods, contrasting needs

Latorre

2020

Current Opinion in Biomedical Engineering

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“…The current mechanobiologically-equilibrated kinematic growth theory is able to achieve grown and remodeled, steady-state configurations of soft tissues with intricate geometries and/or loads within a finite-element framework, and its capabilities mainly rely on being able to predict long-term outcomes, which arguably matters most to medical professionals and patients [5,19].…”

Section: Discussionmentioning

confidence: 99%

A Mechanobiologically Equilibrated Kinematic Growth Model for Soft Tissues

Bezmalinovic,

Garcia-Herrera,

Celentano

et al.

Proceedings of the Seventeenth International Conference On Civil, Structural and Environmental Engineering Computing

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The concept of mechanobiological equilibrium (MBE) is incorporated into the finite kinematic growth (KG) model for growth and remodelling (G&R), in order to propose an alternative, rate-independent formulation (MBE-KG). The method proposed yields non-transient solutions to G&R problems and quasi-equilibrated evolutions when imposed perturbations are slow relative to the adaptive process. We perform a finite element implementation of the method and show its performance on some illustrative problems involving the simulation of aneurysms on a single-layered artery model.

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Special Issue: Spotlight on the Future of Cardiovascular Engineering:Frontiers and Challenges in Cardiovascular Biomechanics

Cited by 4 publications

References 49 publications

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

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

Modeling biological growth and remodeling: Contrasting methods, contrasting needs

A Mechanobiologically Equilibrated Kinematic Growth Model for Soft Tissues

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