@article{pope_ellwein_zapata_novak_kelley_olufsen_2009, title={ESTIMATION AND IDENTIFICATION OF PARAMETERS IN A LUMPED CEREBROVASCULAR MODEL}, volume={6}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2009.6.93}, abstractNote={This study shows how sensitivity analysis and subset selection can be employed in a cardiovascular model to estimate total systemic resistance, cerebrovascular resistance, arterial compliance, and time for peak systolic ventricular pressure for healthy young and elderly subjects. These quantities are parameters in a simple lumped parameter model that predicts pressure and flow in the systemic circulation. The model is combined with experimental measurements of blood flow velocity from the middle cerebral artery and arterial finger blood pressure. To estimate the model parameters we use nonlinear optimization combined with sensitivity analysis and subset selection. Sensitivity analysis allows us to rank model parameters from the most to the least sensitive with respect to the output states (cerebral blood flow velocity and arterial blood pressure). Subset selection allows us to identify a set of independent candidate parameters that can be estimated given limited data. Analyses of output from both methods allow us to identify five independent sensitive parameters that can be estimated given the data. Results show that with the advance of age total systemic and cerebral resistances increase, that time for peak systolic ventricular pressure is increases, and that arterial compliance is reduced. Thus, the method discussed in this study provides a new methodology to extract clinical markers that cannot easily be assessed noninvasively.}, number={1}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Pope, Scott R. and Ellwein, Laura M. and Zapata, Cheryl L. and Novak, Vera and Kelley, C. T. and Olufsen, Mette S.}, year={2009}, month={Jan}, pages={93–115} }
 @article{devault_gremaud_novak_olufsen_vernieres_zhao_2008, title={BLOOD FLOW IN THE CIRCLE OF WILLIS: MODELING AND CALIBRATION}, volume={7}, ISSN={["1540-3467"]}, DOI={10.1137/07070231X}, abstractNote={A numerical model based on one-dimensional balance laws and ad hoc zero-dimensional boundary conditions is tested against experimental data. The study concentrates on the circle of Willis, a vital subnetwork of the cerebral vasculature. The main goal is to obtain efficient and reliable numerical tools with predictive capabilities. The flow is assumed to obey the Navier-Stokes equations, while the mechanical reactions of the arterial walls follow a viscoelastic model. Like many previous studies, a dimension reduction is performed through averaging. Unlike most previous work, the resulting model is both calibrated and validated against in vivo data, more precisely transcranial Doppler data of cerebral blood velocity. The network considered has three inflow vessels and six outflow vessels. Inflow conditions come from the data, while outflow conditions are modeled. Parameters in the outflow conditions are calibrated using a subset of the data through ensemble Kalman filtering techniques. The rest of the data is used for validation. The results demonstrate the viability of the proposed approach.}, number={2}, journal={MULTISCALE MODELING & SIMULATION}, author={Devault, Kristen and Gremaud, Pierre A. and Novak, Vera and Olufsen, Mette S. and Vernieres, Guillaume and Zhao, Peng}, year={2008}, pages={888–909} }
 @article{batzel_novak_kappel_olufsen_tran_2008, title={Introduction to the special issues: Short-term cardiovascular-respiratory control mechanisms}, volume={8}, ISSN={["1567-8822"]}, DOI={10.1007/s10558-007-9053-5}, abstractNote={This and the following issue of Cardiovascular Engineering are special issues reflecting research discussed during an interdisciplinary focused workshop entitled Short-term Cardiovascular–Respiratory Control Mechanisms. The workshop was organized by Mette Olufsen and Hien Tran at the Department of Mathematics at North Carolina State University, Jerry Batzel and Franz Kappel at the Institute for Mathematics and Scientific Computing, University of Graz, and Vera Novak at the Department of Gerontology at Harvard Medical School, and hosted by the American Institute of Mathematics (AIM), Palo Alto, California, October 9–13, 2006. The workshop was co-sponsored by AIM and the National Science Foundation.}, number={1}, journal={CARDIOVASCULAR ENGINEERING}, author={Batzel, Jerry J. and Novak, Vera and Kappel, Franz and Olufsen, Mette S. and Tran, Hien T.}, year={2008}, month={Mar}, pages={1–4} }
 @article{olufsen_alston_tran_ottesen_novak_2008, title={Modeling heart rate regulation - Part I: Sit-to-stand versus head-up tilt}, volume={8}, ISSN={["1573-6806"]}, DOI={10.1007/s10558-007-9050-8}, abstractNote={In this study we describe a model predicting heart rate regulation during postural change from sitting to standing and during head-up tilt in five healthy elderly adults. The model uses blood pressure as an input to predict baroreflex firing-rate, which in turn is used to predict efferent parasympathetic and sympathetic outflows. The model also includes the combined effects of vestibular and central command stimulation of muscle sympathetic nerve activity, which is increased at the onset of postural change. Concentrations of acetylcholine and noradrenaline, predicted as functions of sympathetic and parasympathetic outflow, are then used to estimate the heart rate response. Dynamics of the heart rate and the baroreflex firing rate are modeled using a system of coupled ordinary delay differential equations with 17 parameters. We have derived sensitivity equations and ranked sensitivities of all parameters with respect to all state variables in our model. Using this model we show that during head-up tilt, the baseline firing-rate is larger than during sit-to-stand and that the combined effect of vestibular and central command stimulation of muscle sympathetic nerve activity is less pronounced during head-up tilt than during sit-to-stand.}, number={2}, journal={CARDIOVASCULAR ENGINEERING}, author={Olufsen, Mette S. and Alston, April V. and Tran, Hien T. and Ottesen, Johnny T. and Novak, Vera}, year={2008}, month={Jun}, pages={73–87} }
 @article{ellwein_tran_zapata_novak_olufsen_2008, title={Sensitivity analysis and model assessment: Mathematical models for arterial blood flow and blood pressure}, volume={8}, ISSN={["1573-6806"]}, DOI={10.1007/s10558-007-9047-3}, abstractNote={The complexity of mathematical models describing the cardiovascular system has grown in recent years to more accurately account for physiological dynamics. To aid in model validation and design, classical deterministic sensitivity analysis is performed on the cardiovascular model first presented by Olufsen, Tran, Ottesen, Ellwein, Lipsitz and Novak (J Appl Physiol 99(4):1523-1537, 2005). This model uses 11 differential state equations with 52 parameters to predict arterial blood flow and blood pressure. The relative sensitivity solutions of the model state equations with respect to each of the parameters is calculated and a sensitivity ranking is created for each parameter. Parameters are separated into two groups: sensitive and insensitive parameters. Small changes in sensitive parameters have a large effect on the model solution while changes in insensitive parameters have a negligible effect. This analysis was successfully used to reduce the effective parameter space by more than half and the computation time by two thirds. Additionally, a simpler model was designed that retained the necessary features of the original model but with two-thirds of the state equations and half of the model parameters.}, number={2}, journal={CARDIOVASCULAR ENGINEERING}, author={Ellwein, Laura M. and Tran, Hien T. and Zapata, Cheryl and Novak, Vera and Olufsen, Mette S.}, year={2008}, month={Jun}, pages={94–108} }