Computational Mechanics & Numerical Mathematics University of Groningen

1. The carotid bifurcation wall as a linear elastic membrane Carotid bifurcation Fluid dynamics Global cardiovascular circulation wall motion pressure Wall dynamics R u G Multi-scale modeling of the carotid artery Gerk Rozema, Natasha Maurits, Arthur Veldman Wall elasticity model Introduction Atherosclerosis is a disease in which gradual thickening of the vessel wall occurs due to the accumulation of fatty plaques. Atherosclerosis of the carotid arteries is a major cause of ischemic strokes. Therefore the department of Neurology (UMCG) hopes to be able to use CFD models in the future to predict atherosclerotic risk profiles. The vessel wall is modeled as a linear elastic membrane: circumferential and longitudinal stress and strain are calculated using the generalized Hooke’s law for isotropic materials. The model can be seen as a new implementation of the well established Navier equations. Carotidbifurcation Circulation model To reflect the dependence on the rest of the cardiovascular system, an electric network model for the global circulation is coupled to the 3D model of the carotid artery. This allows (pathological) characteristics of individual patients to be taken into account. Multi-scale computational model The computational model consists of several submodels: The fluid and wall submodels are combined using a strong coupling method: the equations are solved in an iterative manner within one time step. This method is stable for arbitrary fluid-structure mass ratios. • A model for the blood flow in the carotid bifurcation • A model for the wall elasticity in the carotid bifurcation Carotid bifurcation • A model for the global cardiovascular circulation heart Results & Future Ultrasound measurements were used to scan the carotid artery of a human volunteer. Preliminary comparison between measured and calculated flow wave forms shows that elasticity and peripheral resistance must both be taken into account [1]. The latter will be improved upon by the above circulation model. CFD model of carotid bifurcation The blood flow in the carotid bifurcation is modeled with the CFD program ComFlo. It employs a finite-volume discretization of the Navier-Stokes equations on a rectilinear Cartesian grid. The boundary of the domain (the vessel wall) is described using the Cartesian Cut Cells method: the vessel wall is allowed to cut computational cells, i.e. it does not necessarily need to coincide with the grid lines, hereby avoiding frequent regridding. CFD calculation Ultrasound measurement 1. N.M. Maurits, E. Loots, A.E.P. Veldman. J. Biomech. 40 (2007) 427-436. Computational Mechanics & Numerical Mathematics University of Groningen P.O. Box 800, 9700 AV Groningen University Medical Center GroningenDepartment of NeurologyP.O. Box 30.001, 9700 RB Groningen