Mathematical Modeling of Cardiovascular Dynamics During Head-up Tilt.

摘要

Short-term cardiovascular responses during head-up tilt (HUT) involve complex regulation in order to maintain blood pressure at homeostatic levels. Patient specific pulsatile and non-pulsatile models that use heart rate as an input to predict dynamic changes in arterial blood pressure during HUT are presented in this dissertation. This study shows how mathematical modeling can be used to extract features of the system that cannot be measured experimentally. More specifically, it is shown that it is possible to develop mathematical models that can predict changes in cardiac contractility and vascular resistance, quantities that cannot be measured invasively, but which are useful to assess the state of the system. The cardiovascular system is pulsatile, yet predicting the control in response to head-up tilt for the complete system is computationally challenging, and limits the applicability of the model. Therefore, a simpler non-pulsatile model is developed that can be interchanged with the pulsatile model, which is significantly easier to compute, yet it still is able to predict internal variables. The pulsatile and non-pulsatile models contain five compartments representing arteries and veins in the upper and lower body of the systemic circulation, as well as the left ventricle. A physiologically based sub-model describes gravitational pooling of blood into the lower extremities during HUT. For both the pulsatile and non-pulsatile models, cardiovascular regulation models adjust cardiac contractility and vascular resistance to the blood pressure changes during HUT. In addition, an optimal control approach involving a direct transcription method, is explored to predict changes in cardiac contractility and vascular resistance during HUT and head-down tilt (HDT). Head-down tilt for our purposes is defined as tilting the patient back to supine position after head-up tilt.;The model is rendered patient specific via the use of parameter estimation techniques. This process involves sensitivity analysis, prediction of a subset of identifiable parameters, and nonlinear optimization. The approach proposed here was applied to analysis of carotid blood pressure (carotid and aortic for the pulsatile model) and heart rate HUT data from healthy young subjects. Results showed that it is possible to identify a subset of model parameters that can be estimated allowing the models to predict changes in arterial blood pressure observed at the level of the carotid bifurcation. It is also shown that a simpler non-pulsatile model can be used in conjunction with other physiological models, yet still portray the same dynamics as the pulsatile model. We also show that an optimal control approach is useful for controlling quantities that effect the cardiovascular system during HUT in comparison to numerical optimization with piece-wise linear splines. Moreover, the model estimates physiologically reasonable values for arterial and venous blood pressures, blood volumes, and cardiac output for which data are not available.