The fiber orientation in the coronary arterial wall at physiological loading evaluated with a two-fiber constitutive model

Abstract

A patient-specific mechanical description of the coronary arterial wall is indispensable for individualized diagnosis and treatment of coronary artery disease. A way to determine the artery's mechanical properties is to fit the parameters of a constitutive model to patient-specific experimental data. Clinical data, however, essentially lack information about the stress-free geometry of an artery, which is necessary for constitutive modeling. In previous research, it has been shown that a way to circumvent this problem is to impose extra modeling constraints on the parameter estimation procedure. In this study, we propose a new modeling constraint concerning the in-situ fiber orientation (β phys ). β phys , which is a major contributor to the arterial stress-strain behavior, was determined for porcine and human coronary arteries using a mixed numerical-experimental method. The in-situ situation was mimicked using in-vitro experiments at a physiological axial pre-stretch, in which pressure-radius and pressure-axial force were measured. A single-layered, hyperelastic, thick-walled, two-fiber material model was accurately fitted to the experimental data, enabling the computation of stress, strain, and fiber orientation. β phys was found to be almost equal for all vessels measured (36.4 ± 0.3) • , which theoretically can be explained using netting analysis. In further research, this finding can be used as an extra modeling constraint in parameter estimation from clinical data.

Supersonic Shear Wave Imaging to Assess Arterial Nonlinear Behavior and Anisotropy: Proof of Principle via Ex Vivo Testing of the Horse Aorta

“…The mechanical tests clearly demonstrate hysteresis effects and thus indicate a viscoelastic component. However, axial prestretch as reported in arteries of young healthy humans or mammals and equal to ≈1.3-1.4 [43,44] could not be taken into account due to the limitations of the experimental setup (uniaxial testing). When focusing on the SSI data measured along the (presumed) tissue's circumferential direction (0 ∘ /180 ∘ ), SSI measurements varied cyclically with the same period as imposed by the uniaxial testing.…”

“…where is the shear modulus (kPa), is the elasticity modulus (kPa), is the tissue density assumed to be 1066 kg/m 3 [43], and is the group shear wave speed (m/s), which was assumed to be equal to the median SWS value derived over 15 depths for each time point.…”

Towards Patient-Specific Modeling of Coronary Hemodynamics in Healthy and Diseased State

“…In van der Horst et al [20], it was demonstrated that a model based on the two-fiber constitutive model developed by Holzapfel et al [17] was able to accurately capture the radius-pressure relations of porcine and human coronary arteries. In that model the arterial wall was modeled as a cross-ply of helically wound fibers embedded in a cylinder composed of hyperelastic material.…”

“…It was assumed that in compression no stress can be transmitted by the fibers, with τ f defined as: $\begin{array}{c}{\tau }_f=k_{\mathrm{1}}{\lambda }_f^{\mathrm{2}}\left({\lambda }_f^{\mathrm{2}}-\mathrm{1}\right)e^{k_{\mathrm{2}}{\left({\lambda }_f^{\mathrm{normal2}}-\mathrm{normal1}\right)}^{\mathrm{2}}}\hspace{1em}\text{if}\mathrm{\hspace{0.17em}\hspace{0.17em}}{\lambda }_f\ge \mathrm{1}\\ {\tau }_f=\mathrm{0}\hspace{1em}\text{if}{\mathrm{\hspace{0.17em}\hspace{0.17em}}\lambda }_f<\mathrm{1}.\end{array}$ Here, λ f is the collagen fiber stretch and k 1 and k 2 are constants determining the stress-stretch relation of the collagen fibers. For coronary arteries the value of these four parameters have been determined [20]. With removal of the outliers, the median of the four parameters are: G = 19.3 kPa, k 1 = 2.01 kPa, k 2 = 5.10, β 0 = 34.6°.…”

“…The stress-free geometry is determined by the opening angle parameter and the axial stretch λ z , which are both estimated according to optimization rules explained in van der Horst et al [20]. The first rule states that at physiological loading the circumferential stress gradients across the wall are minimal.…”