@article{cousins_gremaud_tartakovsky_2013, title={A NEW PHYSIOLOGICAL BOUNDARY CONDITION FOR HEMODYNAMICS}, volume={73}, ISSN={["1095-712X"]}, DOI={10.1137/120895470}, abstractNote={We propose a new physiologically-based outflow boundary condition for hemodynamics under general transient regimes. This is in contrast to previous studies that impose restrictions of temporal periodicity. The new condition is analyzed and its numerical implementation is discussed in detail. We show that existing impedance boundary conditions can be viewed as numerical approximations of the new condition. Our study provides a partial justification for using some of these existing conditions beyond the periodic problems for which they were designed. Moreover, the new condition has better stability properties. The theoretical results are illustrated by numerical experiments pertaining to cerebral blood flow.}, number={3}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Cousins, Will and Gremaud, Pierre A. and Tartakovsky, Daniel M.}, year={2013}, pages={1203–1223} }
 @article{cousins_gremaud_2012, title={Boundary conditions for hemodynamics: The structured tree revisited}, volume={231}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2012.04.038}, abstractNote={The structured tree boundary condition is a physiologically-based outflow boundary condition used in hemodynamics. We propose an alternative derivation that is considerably simpler than the original one and yields similar, but not identical, results. We analyze the sensitivity of this boundary condition to its parameters and discuss its domain of validity. Several implementation issues are discussed and tested in the case of arterial flow in the Circle of Willis. Additionally, we compare results obtained from the structured tree boundary condition to the Windkessel boundary condition and measured data.}, number={18}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Cousins, W. and Gremaud, P. A.}, year={2012}, month={Jul}, pages={6086–6096} }