Cardiovascular dynamics during head-up tilt assessed via pulsatile and non-pulsatile models

• Published in: Journal of mathematical biology Vol. 79; no. 3; pp. 987 - 1014
• Main Authors: Williams, Nakeya D., Brady, Renee, Gilmore, Steven, Gremaud, Pierre, Tran, Hien T., Ottesen, Johnny T., Mehlsen, Jesper, Olufsen, Mette S.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2019; Springer Nature B.V
• Subjects: Adult; Applications of Mathematics; Autonomic nervous system; Blood flow; Blood Pressure; Cardiac output; Cardiac Output - physiology; Cardiovascular system; Compliance; Computer simulation; Heart; Heart Rate; Hemodynamics; Homeostasis; Humans; Male; Mathematical and Computational Biology; Mathematical models; Mathematics; Mathematics and Statistics; Models, Cardiovascular; Muscle contraction; Parameter estimation; Parameter identification; Predictions; Pressure head; Pulsatile Flow; Splines; Supine Position; Tilt-Table Test; Vascular Resistance - physiology; Ventricle; 76Z05; Parameter estimation; 92C42; Head-up tilt; Cardiovascular dynamics modeling; 92C35; Pulsatile versus non-pulsatile modeling; Orthostatic intolerance; 92C30; 92C50
• ISSN: 0303-6812; 1432-1416; 1432-1416
• DOI: 10.1007/s00285-019-01386-9

This study develops non-pulsatile and pulsatile models for the prediction of blood flow and pressure during head-up tilt. This test is used to diagnose potential pathologies within the autonomic control system, which acts to keep the cardiovascular system at homeostasis. We show that mathematical modeling can be used to predict changes in cardiac contractility, vascular resistance, and arterial compliance, quantities that cannot be measured but are useful to assess the system’s state. These quantities are predicted as time-varying parameters modeled using piecewise linear splines. Having models with various levels of complexity formulated with a common set of parameters, allows us to combine long-term non-pulsatile simulations with pulsatile simulations on a shorter time-scale. We illustrate results for a representative subject tilted head-up from a supine position to a 60 ∘ angle. The tilt is maintained for 5 min before the subject is tilted back down. Results show that if volume data is available for all vascular compartments three parameters can be identified, cardiovascular resistance, vascular compliance, and ventricular contractility, whereas if model predictions are made against arterial pressure and cardiac output data alone, only two parameters can be estimated either resistance and contractility or resistance and compliance.