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. Blood rheology is accounted for by shear-rate dependent models for blood. Our recently developed stabilized finite element method for non-Newtonian 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.