@article{clipp_steele_2012, title={An evaluation of dynamic outlet boundary conditions in a 1d fluid dynamics model}, volume={9}, number={1}, journal={Mathematical Biosciences and Engineering}, author={Clipp, R. and Steele, B.}, year={2012}, pages={61–74} }
@article{steele_valdez-jasso_haider_olufsen_2011, title={PREDICTING ARTERIAL FLOW AND PRESSURE DYNAMICS USING A 1D FLUID DYNAMICS MODEL WITH A VISCOELASTIC WALL}, volume={71}, ISSN={["1095-712X"]}, DOI={10.1137/100810186}, abstractNote={This paper combines a generalized viscoelastic model with a one-dimensional (1D) fluid dynamics model for the prediction of blood flow, pressure, and vessel area in systemic arteries. The 1D fluid dynamics model is derived from the Navier–Stokes equations for an incompressible Newtonian flow through a network of cylindrical vessels. This model predicts pressure and flow and is combined with a viscoelastic constitutive equation derived using the quasilinear viscoelasticity theory that relates pressure and vessel area. This formulation allows for inclusion of an elastic response as well as an appropriate creep function allowing for the description of the viscoelastic deformation of the arterial wall. Three constitutive models were investigated: a linear elastic model and two viscoelastic models. The Kelvin and sigmoidal viscoelastic models provide linear and nonlinear elastic responses, respectively. For the fluid domain, the model assumes that a given flow profile is prescribed at the inlet, that flow is c...}, number={4}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Steele, Brooke N. and Valdez-Jasso, Daniela and Haider, Mansoor A. and Olufsen, Mette S.}, year={2011}, pages={1123–1143} }
@article{clipp_steele_2009, title={Impedance Boundary Conditions for the Pulmonary Vasculature Including the Effects of Geometry, Compliance, and Respiration}, volume={56}, ISSN={["1558-2531"]}, DOI={10.1109/TBME.2008.2010133}, abstractNote={With few exceptions, previous models of the pulmonary vascular system have neglected the effects of respiration. This practice is acceptable for normal cardiac function; however, for compromised function, respiration may be critical. Therefore, we have initiated the steps to develop boundary conditions that incorporate the effects of respiration through the use of an impedance boundary condition derived from a bifurcating structured tree geometry. The benefit to using the geometry based method lies in that strategic changes can be made to the geometry to mimic physiologic changes in vascular impedance. In this paper, a scaling factor was used to modify the radius of resistance vessels of the structured tree to capture the maximum change in impedance caused by respiration. A large vessel geometry was established from a lung cast, the structured trees were applied at the outlets, and an experimental flow waveform was applied at the inlet. Finite-element analysis was used to compute the resulting inlet pressure waveform. An optimization minimizing the difference between measured and computed pressure waveforms was performed for two respiratory states, maximal expiration and inspiration, to determine best-fit models for the pulmonary vasculature, resulting in pressure waveforms with an rms error of 0.4224 and 0.7270 mmHg, respectively.}, number={3}, journal={IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING}, author={Clipp, Rachel B. and Steele, Brooke N.}, year={2009}, month={Mar}, pages={862–870} }