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1 Department of Mathematics, North Carolina State University, Raleigh, NC, USA
2 Department of Mathematics and Physics, Roskilde University, Roskilde, MA, Denmark
3 Research and Training Institute, Hebrew SenioLife, Boston, MA, USA
4 Division of Gerontology, Beth Israel Deaconess medical Center, Boston, MA, USA; Harvard Medical School, Boston, MA, USA
* To whom correspondence should be addressed. E-mail: msolufse{at}math.ncsu.edu.
Short-term cardiovascular responses to postural change from sitting to standing involve complex interactions between the autonomic nervous system that regulates blood pressure, and cerebral Autoregulation that maintains cerebral perfusion. We present a mathematical model that can predict dynamic changes observed in beat-to-beat arterial blood pressure and middle cerebral artery blood flow velocity during postural change from sitting to standing. Our cardiovascular model utilizes 11 compartments to describe blood pressure, blood flow, compliance and resistance in the heart and systemic circulation. To include dynamics due to the pulsatile nature of blood pressure and blood flow, resistances in the large systemic arteries are modeled using nonlinear functions of pressure. A physiologically based sub-model is used to describe effects of gravity on venous blood pooling during postural change. Two types of control mechanisms are included: (i) Autonomic regulation mediated by sympathetic and parasympathetic responses that affect heart rate, cardiac contractility, resistance, and compliance. (ii) Autoregulation mediated by responses to local changes in myogenic tone, metabolic demand, and concentration of carbon dioxide (CO2) that affect cerebrovascular resistance. Finally, we formulate an inverse least squares problem for parameter estimation and to demonstrate that our mathematical model is in agreement with physiological data obtained from a young subject during postural change from sitting to standing.
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