Predictive capabilities of various constitutive models for arterial tissue

Schroeder, Friedrich Christian; Polzer, Stanislav; Slažanský, Martin; Man, Vojtěch; Skácel, Pavel

doi:10.1016/j.jmbbm.2017.11.035

Cited by 49 publications

(32 citation statements)

References 47 publications

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“…In 2007, Hu et al (55) showed that adding longitudinal and circumferential collagen fiber families improves fitting, also when taking into account the additional parameters required using the Akaike information criterion. Schroeder et al (109) recently compared several constitutive models and concluded that the four-fiber family model best predicted biaxial arterial behavior from uniaxial testing data. Zulliger et al (160) proposed the use of a two-fiber family collagen model but formulated the mechanical behavior of the individual families differently by explicitly modeling engagement.…”

Section: H702mentioning

confidence: 99%

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Constitutive interpretation of arterial stiffness in clinical studies: a methodological review

Reesink

Spronck

2019

American Journal of Physiology-Heart and Circulatory Physiology

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Clinical assessment of arterial stiffness relies on noninvasive measurements of regional pulse wave velocity or local distensibility. However, arterial stiffness measures do not discriminate underlying changes in arterial wall constituent properties (e.g., in collagen, elastin, or smooth muscle), which is highly relevant for development and monitoring of treatment. In arterial stiffness in recent clinical-epidemiological studies, we systematically review clinical-epidemiological studies (2012–) that interpreted arterial stiffness changes in terms of changes in arterial wall constituent properties (63 studies included of 514 studies found). Most studies that did so were association studies (52 of 63 studies) providing limited causal evidence. Intervention studies (11 of 63 studies) addressed changes in arterial stiffness through the modulation of extracellular matrix integrity (5 of 11 studies) or smooth muscle tone (6 of 11 studies). A handful of studies (3 of 63 studies) used mathematical modeling to discriminate between extracellular matrix components. Overall, there exists a notable gap in the mechanistic interpretation of stiffness findings. In constitutive model-based interpretation, we first introduce constitutive-based modeling and use it to illustrate the relationship between constituent properties and stiffness measurements (“forward” approach). We then review all literature on modeling approaches for the constitutive interpretation of clinical arterial stiffness data (“inverse” approach), which are aimed at estimation of constitutive properties from arterial stiffness measurements to benefit treatment development and monitoring. Importantly, any modeling approach requires a tradeoff between model complexity and measurable data. Therefore, the feasibility of changing in vivo the biaxial mechanics and/or vascular smooth muscle tone should be explored. The effectiveness of modeling approaches should be confirmed using uncertainty quantification and sensitivity analysis. Taken together, constitutive modeling can significantly improve clinical interpretation of arterial stiffness findings.

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Section: H702mentioning

confidence: 99%

“…2) (150). Although a four-fiber family description of collagen has been shown to be superior over a two-fiber using laboratory ex vivo data (55,109), it does require more parameters to be estimated. Therefore, we recommend starting using a two-fiber collagen description and ideally compare it in the in vivo setting to the four-fiber description.…”

Section: H702mentioning

confidence: 99%

Constitutive interpretation of arterial stiffness in clinical studies: a methodological review

Reesink

Spronck

2019

American Journal of Physiology-Heart and Circulatory Physiology

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“…Regardless, some investigators infer stiffness from plots of stress versus stretch or strain (yielding so-called tangent moduli), but stiffness depends on the full multiaxial deformation and is best computed from an appropriate constitutive relation as noted above for the referential stiffness (

). Given the complex microstructure of the vascular wall, most investigators now prefer the so-called fiber-family constitutive models [ 35 – 37 ] to characterize multiaxial data, though the Fung exponential provides good fits to data in many cases (recall that Appendix B reviews a general orthotropic Fung relation). Best-fit values of material parameters for any appropriate constitutive relation can be determined via nonlinear regression of pressure-diameter and axial force-length data, with data from multiple biaxial protocols typically combined to improve the parameter estimation, again via (nonlinear) least squares regression.…”

Section: Approachesmentioning

confidence: 99%

Arterial Stiffness: Different Metrics, Different Meanings

Spronck

Humphrey

2019

Journal of Biomechanical Engineering

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Findings from basic science and clinical studies agree that arterial stiffness is fundamental to both the mechanobiology and the biomechanics that dictate vascular health and disease. There is, therefore, an appropriately growing literature on arterial stiffness. Perusal of the literature reveals, however, that many different methods and metrics are used to quantify arterial stiffness, and reported values often differ by orders of magnitude and have different meanings. Without clear definitions and an understanding of possible inter-relations therein, it is increasingly difficult to integrate results from the literature to glean true understanding. In this paper, we briefly review methods that are used to infer values of arterial stiffness that span studies on isolated cells, excised intact vessels, and clinical assessments. We highlight similarities and differences and identify a single theoretical approach that can be used across scales and applications and thus could help to unify future results. We conclude by emphasizing the need to move toward a synthesis of many disparate reports, for only in this way will we be able to move from our current fragmented understanding to a true appreciation of how vascular cells maintain, remodel, or repair the arteries that are fundamental to cardiovascular properties and function.

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“…The weak form of linear momentum balance can be expressed as with where ρ 0 is the mass density, ü = ∂ 2 u ∂t 2 the acceleration, f the external force, δu the virtual displacement, δE m the variation of Green-Lagrange strain tensor, δχ the variation of the curvature, and N , M are the force and bending stress resultants with their components given by Eqs. (45) and (46).…”

Section: Methodsmentioning

confidence: 99%

A nonlinear rotation-free shell formulation with prestressing for vascular biomechanics

Nama

Aguirre

Humphrey

et al. 2020

Sci Rep

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We implement a nonlinear rotation-free shell formulation capable of handling large deformations for applications in vascular biomechanics. The formulation employs a previously reported shell element that calculates both the membrane and bending behavior via displacement degrees of freedom for a triangular element. The thickness stretch is statically condensed to enforce vessel wall incompressibility via a plane stress condition. Consequently, the formulation allows incorporation of appropriate 3D constitutive material models. We also incorporate external tissue support conditions to model the effect of surrounding tissue. We present theoretical and variational details of the formulation and verify our implementation against axisymmetric results and literature data. We also adapt a previously reported prestress methodology to identify the unloaded configuration corresponding to the medically imaged in vivo vessel geometry. We verify the prestress methodology in an idealized bifurcation model and demonstrate the significance of including prestress. Lastly, we demonstrate the robustness of our formulation via its application to mouse-specific models of arterial mechanics using an experimentally informed four-fiber constitutive model.

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Predictive capabilities of various constitutive models for arterial tissue

Cited by 49 publications

References 47 publications

Constitutive interpretation of arterial stiffness in clinical studies: a methodological review

Constitutive interpretation of arterial stiffness in clinical studies: a methodological review

Arterial Stiffness: Different Metrics, Different Meanings

A nonlinear rotation-free shell formulation with prestressing for vascular biomechanics

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