Abstract
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.
Highlights
We implement a nonlinear rotation-free shell formulation capable of handling large deformations for applications in vascular biomechanics
The Coupled Momentum Method (CMM)9 utilizes this simplification by employing a 2D representation of the vessel wall for modeling blood flow in compliant arteries
The CMM employs a linear membrane formulation, resulting in minimal additional computational costs compared to methods with rigid wall approximation
Summary
We implement a nonlinear rotation-free shell formulation capable of handling large deformations for applications in vascular biomechanics. To model blood flow in compliant arteries, various fluid-structure interaction (FSI) techniques including Arbitrary Lagrangian-Eulerian and immersed methods have emerged6–8 Modeling both the fluid and solid domain using three-dimensional elements has resulted in high computational costs for complex, patient-specific geometries, posing a significant challenge to achieve results in a clinically relevant time-frame, limiting broad adoption in clinical practices. Various isogeometric shell models with inherent high continuity in basis functions have been proposed to satisfy the C1 continuity requirement in Kirchhoff-Love theory for thin s hells16,24–26 Another promising approach is to express the curvature field in terms of the displacement of nodes of neighboring elements, thereby avoiding the need for rotational degrees of freedom. A rotation-free nonlinear shell formulation for vascular biomechanics will allow vessel wall nonlinearities to be incorporated in biomechanical analyses of complex subject-specific geometries and future extensions to FSI problems via an adaption of the CMM to large displacements
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