Time-Dependent Outflow Boundary Conditions for Blood Flow in the Arterial System
We present time-dependent outflow boundary conditions for blood flow simulations in the arterial system. The new method allows for embedding clinically obtained patient-specific data into the patient-specific geometric models of the circulation system. Bl
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Abstract We present time-dependent outflow boundary conditions for blood flow simulations in the arterial system. The new method allows for embedding clinically obtained patient-specific data into the patient-specific geometric models of the circulation system. Blood rheology is accounted for by shear-rate dependent models for blood. Our recently developed stabilized finite element method for nonNewtonian fluid models is extended to include downstream effects by incorporating clinically measured downstream resistance via a novel functional form for the outflow boundary conditions. Patient-specific flow-rate and pressure profiles measured clinically (e.g., ultrasound device, CT, or MRI) are used to determine timedependent resistance functions. For verification of the new method, we compare the clinically measured time-dependent resistance outflow boundary conditions to the constant pressure, constant resistance, and the impedance outflow boundary conditions. Numerical tests verify that the time-dependent outflow boundary conditions proposed in this work impose the most accurate downstream effects that are caused by the non-Newtonian behavior of blood as well as the geometrical complexity of the branching arteries. Our numerical tests show that the reduced geometry with the proposed outflow boundary conditions results in an order of magnitude reduction in computational cost as compared to that of the full arterial geometry model.
J. Kwack • S. Kang • A. Masud () University of Illinois at Urbana-Champaign, Urbana, IL, USA e-mail: [email protected] G. Bhat Advocate Christ Medical Center, Oak Lawn, IL, USA © Springer International Publishing Switzerland 2016 Y. Bazilevs, K. Takizawa (eds.), Advances in Computational Fluid-Structure Interaction and Flow Simulation, Modeling and Simulation in Science, Engineering and Technology, DOI 10.1007/978-3-319-40827-9_28
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1 Introduction Blood is composed of various cell types (i.e., red blood cells, white blood cells, and platelets) that are suspended in blood plasma (i.e., water, dissipated proteins, glucose, mineral ions, hormones, and carbon dioxide). The complex rheological response of blood is a function of a variety of interactions between cells and plasma, that manifest themselves via shear-rate dependent viscous stress and viscoelastic stress [1–5]. A literature review shows that several mathematical models have been developed for the non-Newtonian behavior of fluids [6–11]. Masud and Kwack have developed variational multi-scale (VMS)-based stabilized methods for viscoelastic [12, 13] and shear-rate dependent [14–16] non-Newtonian fluids wherein a variety of convergent finite elements are presented. Blood flow simulations in the human cardiovascular system that account for the complexity of the patient-specific geometries, transition to turbulence in arteries, and blood–artery interactions have also been reported in the literature [17–23]. The cardiovascular system is comprised of the heart and blood vessels that form a closed network. Develo
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