Most arteries and veins are characterized by a low wall thickness to radius ratio and can therefore be modeled as a thin structure. In comparison to standard 3D solid formulations, thin structure formulations offer not only significant computational savings but also circumvent difficulties associated with various locking phenomena and meshing. This work presented a nonlinear rotation-free shell formulation that is 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 formulation allows incorporation of general 3D constitutive material models and includes both a prestress algorithm and an external tissue support boundary condition to facilitate biomechanical analyses in complex, patient-specific anatomies. The lack of rotational degrees of freedom and the ability to handle non-structured meshes for complex, subject-specific geometries makes this formulation ideally-suited for incorporation in fluid-structure interaction (FSI) frameworks for cardiovascular applications. This formulation serves as the structural foundation for realizing our overall vision of developing a strongly coupled, monolithic, computationally efficient, nonlinear FSI framework for vascular biomechanics within the open-source hemodynamic modeling environment, CRIMSON.
Recently, we collaborated with Prof. Alberto Figueroa and Prof. Nicholas Burris at University of Michigan to combine this framework with medical image-based assessments of aortic growth for improved assessment of the relationship of aortic wall abnormalities in aortic dissection with underlying biomechanical metrics (transmural/shear stresses etc.).
References:
- N. Nama, M. Aguirre, J. D. Humphrey, and C. A. Figueroa, A nonlinear rotation-free shell formulation with prestressing for vascular biomechanics, Scientific Reports, Vol. 10, pp. 17528, 2020.
- CRIMSON software. http://www.crimson.software/
- I. B. Houben*, N. Nama*, F. L. Moll, J. A. van Herwaarden, D. A. Nordsletten, D. M. Williams, H. J. Patel, C. A. Figueroa, and N. S. Burris, Mapping pre-dissection aortic wall abnormalities: a multiparametric assessment, European Journal of Cardio-Thoracic Surgery, Vol. 57(6), pp. 1061-1067, 2020. (* denotes equal contributions)