A finite element implementation of a growth and remodeling model for soft biological tissues: Verification and application to abdominal aortic aneurysms

Horvat, Nino; Virag, Lana; Holzapfel, Gerhard; Sorić, Jurica; Karšaj, Igor

doi:10.1016/j.cma.2019.04.041

Cited by 38 publications

(29 citation statements)

References 45 publications

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“…In contrast, endothelial dysfunction could manifest within the enlarged aneurysmal region, where disturbed flows exist and smooth muscle cell dropout is prevalent as well. These model predictions during quasi-static mechanobiologically equilibrated evolutions, complemented with others in [30] that show a dynamic stabilization of the expansion of abdominal aortic aneurysms afforded by similar effects of flow-induced shear stresses [4], thus motivate the need for new regional-specific assessments of cell functionality in these lesions.…”

Section: Discussionsupporting

confidence: 55%

“…Figure 2(b) shows associated in vivo volumetric Cauchy pre-stresses σ vo = (1/3) tr σ o . This discretization is consistent with the one for displacements adopted in [30], where twelve mixed elements, linear in displacements and constant in pressure, were used to discretize three layers through the wall. As we explain below, volumetric locking is not expected during our quasi-static computations of mechanobiologically equilibrated G&R during Stage II, hence, mixed formulations with additional interpolations of pressure at the element level were not needed here.…”

Section: Computation Of the Original Homeostatic State (Stage I)mentioning

confidence: 94%

“…(49) and (50). Lastly, because mechanobiologically equilibrated G&R typically implies a local change in volume, or, at least, it is not constrained (recall Remark 1), no special formulations were needed to prevent volumetric locking during these computations, a numerical issue characteristic of nearly incompressible elastic or distortional elastoplastic responses [31], but also transient elastic responses during G&R [30]. In this respect, all solution variables changed gradually between adjacent elements and agreed well with analytical results, including global geometric outputs (e.g., inner radius and thickness).…”

Section: Equilibrated Gandr Response (Stagementioning

confidence: 99%

“…Indeed, given the computational efficiency, we considered full arterial segment geometries in all of the analyses, with up to 38400 elements, even though by obvious symmetry considerations partial sectors of the specimen could have been analyzed equivalently. Importantly, a recent FE implementation of the original heredity-integral constrained mixture G&R formulation reported 30 hours, on average, to complete a simulation for a 2 o cylindrical sector of an axisymmetric fusiform aneurysm meshed with 1200 elements [30]. Thus, the computational time reduces drastically when one employs a rate-independent counterpart of that formulation, which, with 40 times more elements, and running 180 times faster, roughly represents a 3-to 4-fold enhancement in computational efficiency.…”

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

confidence: 99%

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

Latorre¹,

Humphrey

2020

Preprint

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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.

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Section: Discussionsupporting

confidence: 55%

Section: Computation Of the Original Homeostatic State (Stage I)mentioning

confidence: 94%

Section: Equilibrated Gandr Response (Stagementioning

confidence: 99%

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

confidence: 99%

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

Latorre¹,

Humphrey

2020

Preprint

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show abstract

“…The relationship between tissue strength and microstructure, however, needs to be fully investigated. Furthermore, growth and remodeling (G&R) biomechanical models are also emerging [ 97 , 98 ]. In the context of AAA, G&R models aim at predicting both the geometrical grow of the aneurysm as well as the accompanying tissue remodeling, with the dual goal of better understanding the progression of AAA and assessing patient risks.…”

Section: Studies and Limitationsmentioning

confidence: 99%

Predictors of Abdominal Aortic Aneurysm Risks

2020

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Computational biomechanics via finite element analysis (FEA) has long promised a means of assessing patient-specific abdominal aortic aneurysm (AAA) rupture risk with greater efficacy than current clinically used size-based criteria. The pursuit stems from the notion that AAA rupture occurs when wall stress exceeds wall strength. Quantification of peak (maximum) wall stress (PWS) has been at the cornerstone of this research, with numerous studies having demonstrated that PWS better differentiates ruptured AAAs from non-ruptured AAAs. In contrast to wall stress models, which have become progressively more sophisticated, there has been relatively little progress in estimating patient-specific wall strength. This is because wall strength cannot be inferred non-invasively, and measurements from excised patient tissues show a large spectrum of wall strength values. In this review, we highlight studies that investigated the relationship between biomechanics and AAA rupture risk. We conclude that combining wall stress and wall strength approximations should provide better estimations of AAA rupture risk. However, before personalized biomechanical AAA risk assessment can become a reality, better methods for estimating patient-specific wall properties or surrogate markers of aortic wall degradation are needed. Artificial intelligence methods can be key in stratifying patients, leading to personalized AAA risk assessment.

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The risk of rupture and abdominal aortic aneurysm morphology: A computational study

Živić

Virag

Horvat

et al. 2021

Numer Methods Biomed Eng

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Prediction of rupture and optimal timing for abdominal aortic aneurysm (AAA) surgical intervention remain wanting even after decades of clinical, histological, and numerical research. Although studies estimating rupture from AAA geometrical features from CT imaging showed some promising results, they are still not being used in practice. Patient‐specific numerical stress analysis introduced too many assumptions about wall structure for the related rupture potential index (RPI) to be considered reliable. Growth and remodeling (G&R) numerical models eliminate some of these assumptions and thus might have the most potential to calculate mural stresses and RPI and increase our understanding of rupture. To recognize numerical models as trustworthy, it is necessary to validate the computed results with results derived from imaging. Elastin degradation function is one of the main factors that determine idealized aneurysm sac shape. Using a hundred different combinations of variables defining AAA geometry or influences AAA stability (elastin degradation function parameters, collagen mechanics, and initial healthy aortic diameters), we investigated the relationship between AAA morphology and RPI and compared numerical results with clinical findings. Good agreement of numerical results with clinical expectations from the literature gives us confidence in the validity of the numerical model. We show that aneurysm morphology significantly influences the stability of aneurysms. Additionally, we propose new parameters, geometrical rupture potential index (GRPI) and normalized aneurysm length (NAL), that might predict rupture of aneurysms without thrombus better than currently used criteria (i.e., maximum diameter and growth rate). These parameters can be computed quickly, without the tedious processing of CT images.

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A finite element implementation of a growth and remodeling model for soft biological tissues: Verification and application to abdominal aortic aneurysms

Cited by 38 publications

References 45 publications

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

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

Predictors of Abdominal Aortic Aneurysm Risks

The risk of rupture and abdominal aortic aneurysm morphology: A computational study

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