# American Institute of Mathematical Sciences

2009, 6(1): 93-115. doi: 10.3934/mbe.2009.6.93

## Estimation and identification of parameters in a lumped cerebrovascular model

 1 Department of Mathematics, North Carolina State University, Campus Box 8205, Raleigh, NC 27695, United States, United States, United States 2 Olin Engineering Center, Marquette University, 1515 West Wisconsin Ave, Room 206, Milwaukee, WI 53233, United States 3 Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, UT 84112, United States 4 Harvard Medical School and Beth Israel Deaconess Medical Center Division of Gerontology, 110 Francis Street LM0B Suite 1b, Boston, MA 02215, United States

Received  July 2008 Revised  September 2008 Published  December 2008

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.
Citation: Scott R. Pope, Laura M. Ellwein, Cheryl L. Zapata, Vera Novak, C. T. Kelley, Mette S. Olufsen. Estimation and identification of parameters in a lumped cerebrovascular model. Mathematical Biosciences & Engineering, 2009, 6 (1) : 93-115. doi: 10.3934/mbe.2009.6.93
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