Blood pressure and blood flow variation during postural change from sitting to standing: model development and validation

1 Department of Mathematics, North Carolina State University, Raleigh, North Carolina; 2 Department of Mathematics and Physics, Roskilde University, Roskilde, Denmark; and 3 Hebrew SeniorLife, Research and Training Institute, and 4 Division of Gerontology, Beth Israel Deaconess Medical Center and Harvard Medical School, Boston, Massachusetts Submitted 14 February 2005 ; accepted in final form 26 April 2005 Short-term cardiovascular responses to postural change from sitting to standing involve complex interactions between the autonomic nervous system, which regulates blood pressure, and cerebral autoregulation, which maintains cerebral perfusion. We present a mathematical model that can predict dynamic changes 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 submodel is used to describe effects of gravity on venous blood pooling during postural change. Two types of control mechanisms are included: 1 ) autonomic regulation mediated by sympathetic and parasympathetic responses, which affect heart rate, cardiac contractility, resistance, and compliance, and 2 ) autoregulation mediated by responses to local changes in myogenic tone, metabolic demand, and CO 2 concentration, which affect cerebrovascular resistance. Finally, we formulate an inverse least-squares problem to estimate parameters and demonstrate that our mathematical model is in agreement with physiological data from a young subject during postural change from sitting to standing. cardiovascular system; mathematical modeling; cerebral blood flow; gravitational effect; autonomic regulation; cerebral autoregulation Address for reprint requests and other correspondence: M. S. Olufsen, Dept. of Mathematics, North Carolina State Univ., Raleigh, NC 27695 (E-mail: msolufse{at}math.ncsu.edu )