Efficient computational modelling of smooth muscle orientation and function in the aorta

Abstract

Understanding the mechanical effects of smooth muscle cell (SMC) contraction on the initiation and the propagation of cardiovascular diseases such as aortic dissection is critical. Framed by elastic lamellar sheets in the lamellar unit, there are SMCs in the media with a distinct radial tilt, which indicates their contribution to the radial strength. However, the mechanical effects of this type of anisotropy have not been fully discussed. Therefore, in this study, we propose a constitutive framework that models the passive and active mechanics of the aorta, taking into account the dispersed nature of the aortic constituents by applying the discrete fibre dispersion method. We suggest an isoparametric approach by evaluating various numerical integration methods and introducing a non-uniform discretization of the unit hemisphere to increase its computational efficiency. Finally, the constitutive parameters are fitted to layer-specific experimental data and initial computational results are briefly presented. The radial tilt of SMCs is also analysed, which has a noticeable influence on the mechanical behaviour of the aorta. In the absence of sufficient experimental data, the results indicate that the active contribution of SMCs has a remarkable impact on the mechanics of the healthy aorta.

Stochastic Modeling of Inhomogeneities in the Aortic Wall and Uncertainty Quantification using a Bayesian Encoder-Decoder Surrogate

“…At this point, the discrete character of the applied DFD method must be discussed with regard to the uncertainties of the model. As emphasized in previous studies [47,104], the exclusion of degraded elastic fibers strongly depends on the number of discrete elements on the unit hemisphere.…”

On the role of tissue mechanics in fluid–structure interaction simulations of patient‐specific aortic dissection

“…To fully exploit the model complexity when postprocessing the stresses, the anisotropic material properties were taken into account in tissue stress measures. Related works are based on the von Mises stress 20,21 or the maximum principal stress, 34,80 but none of these works relate the Cauchy stress directly to the microstructure orientation of the vessel. In this work, we investigated the spatio-temporal distribution of the latter stress measure, but also included the normal and tangential traction components of the tissue.…”

“…We found values of 𝜎 I within the range reported in. 34,80 Differences between tissue layers and models are illustrated in Figure 17. The E90 model provided an order of magnitude higher values, but also provided displacements of the dissection flap displacement comparable to the hyperelastic models, see Figure 7.…”

“…Note that Equation ( 2) is only valid for homogeneous isotropic linear elastic materials, but yields high penalty values 𝜅 b → ∞ that approach full incompressibility as 𝜈 s → 1∕2. For all tissue layers we consider k 1 = 1.4 kPa, k 2 = 22.1, while the remaining fiber parameters for the dissection flap and the media are based on Weisbecker et al 33 and Rolf-Pissarczyk et al 34 The mean out-of-plane fiber orientation is controlled with Θ = 0 • , yielding the classical helical pattern.…”

“…Note that Equation (2) is only valid for homogeneous isotropic linear elastic materials, but yields high penalty values $$$ {\kappa}_b\to \infty $$$ that approach full incompressibility as $$$ {\nu}_s\to 1/2 $$$. For all tissue layers we consider $$$ {k}_1=1.4\kern0.3em \mathrm{kPa} $$$, $$$ {k}_2=22.1 $$$, while the remaining fiber parameters for the dissection flap and the media are $$$ {a}_1={a}_2=3.62 $$$, $$$ {b}_1={b}_2=34.30 $$$ and $$$ {\Phi}_1={\Phi}_2=\pm 27.4{7}^{\circ } $$$, for the adventitia, we set $$$ a=3.08 $$$, $$$ b=33.20 $$$, and $$$ {\Phi}_1={\Phi}_2=\pm 52.8{8}^{\circ } $$$, based on Weisbecker et al 33 and Rolf‐Pissarczyk et al 34 The mean out‐of‐plane fiber orientation is controlled with $$…”