Numerical analysis of the hemodynamic response to orthostatic stress

The main function of the cardiovascular system is to transport blood to the tissue and thereby provide it with sufficient oxygen. The total blood flow and its distribution over the circulation can be regulated in response to a change in oxygen demand or to external stress factors. Orthostatic stress, i.e. gravitational stress in the upright position, induces a blood volume shift from the head towards the feet. This results in decreased cerebral perfusion, which increases oxidative stress, and increased transmural pressure in the lower extremity. To minimize these stresses a complex system of protection mechanisms is activated, which includes amongst others: (1) the presence of venous valves, ensuring unidirectional flow, (2) the muscle pump effect, which squeezes the embedded deep veins upon calf muscle contraction, and (3) the baroreflex, aiming to maintain systemic pressure by regulating heart rate, contractility and peripheral resistance. Many experimental studies confirmed the importance of the above mentioned mechanisms in compensating for the gravity-induced blood volume shift in the upright position. However, a causal dependency and thereby full mechanistic insight in the physiology is often missing. In the past, mathematical models based on physical laws and physiological mechanisms have proven to increase the understanding of the cardiovascular (patho-)physiology. Therefore, in the current thesis a numerical approach is presented to gain more insight in the mechanisms compensating for the gravity-induced blood volume shift towards the lower body. In the current PhD project, mathematical models have been developed in order to examine three major mechanisms reducing the gravity-induced blood volume shift: the muscle pump effect, venous valves and regulation of vascular tone. To reveal their individual importance the included number of mechanisms is increased stepby-step. First, to capture the dynamics involved with the muscle pump effect, an existing 1D arterial pulse wave propagation model is extended to include venous collapsibility, venous valves and gravitational stress. The simulations reveal the importance of the venous valves for increasing effective venous return as well as shielding the hydrostatic pressure. Furthermore, adding the superficial venous system results in a fastening of venous refilling. However, the small increase in simulated arterial flow after muscle contraction in comparison to in vivo, implies that the model does not yet contain all relevant mechanisms. Second, a global sensitivity analysis of the venous valve dynamics under head up tilt is performed to gain insight in the importance of the various model parameters and their interactions. From this, it is concluded that improved assessment of venous radius and pressure drop at valve opening can reduce model uncertainty. Third, inclusion of a regulation model accounting for the metabolic, myogenic and baroreflex regulation, results in good agreement between the simulated and in vivo flow response. From the regulatory activation it is concluded that the metabolic activation induces the flow increase after muscle contraction and that myogenic and baroreflex activation result in a decreased baseline flow in the tilted position. Finally, a full circulation model is presented including a new micro-circulation element to account for the blood volume and its distribution. This model can serve as a backbone for future models in which all physiological mechanisms activated upon orthostatic stress are integrated. Such a model allows examination of the global response of local phenomena and their mutual interaction. In summary, the developed models provide an important step towards full understanding of the hemodynamic response to orthostatic stress. Furthermore, they provide many opportunities for further research into the physiological mechanisms protecting the cardiovascular system against the gravity-induced stresses