Global sensitivity analysis of a model for venous valve dynamics.

Chronic venous disease is defined as dysfunction of the venous system caused by incompetent venous valves with or without a proximal venous obstruction. Assessing the severity of the disease is challenging, since venous function is determined by various interacting hemodynamic factors. Mathematical models can relate these factors using physical laws and can thereby aid understanding of venous (patho-)physiology. To eventually use a mathematical model to support clinical decision making, first the model sensitivity needs to be determined. Therefore, the aim of this study is to assess the sensitivity of the venous valve model outputs to the relevant input parameters. Using a 1D pulse wave propagation model of the tibial vein including a venous valve, valve dynamics under head up tilt are simulated. A variance-based sensitivity analysis is performed based on generalized polynomial chaos expansion. Taking a global approach, individual parameter importance on the valve dynamics as well as importance of their interactions is determined. For the output related to opening state of the valve, the opening/closing pressure drop (dpvalve,0) is found to be the most important parameter. The venous radius (rvein,0) is related to venous filling volume and is consequently most important for the output describing venous filling time. Finally, it is concluded that improved assessment of rvein,0 and dpvalve,0 is most rewarding when simulating valve dynamics, as this results in the largest reduction in output uncertainty. In practice, this could be achieved using ultrasound imaging of the veins and fluid structure interaction simulations to characterize detailed valve dynamics, respectively.

A 1D pulse wave propagation model of the hemodynamics of calf muscle pump function.

The calf muscle pump is a mechanism which increases venous return and thereby compensates for the fluid shift towards the lower body during standing. During a muscle contraction, the embedded deep veins collapse and venous return increases. In the subsequent relaxation phase, muscle perfusion increases due to increased perfusion pressure, as the proximal venous valves temporarily reduce the distal venous pressure (shielding). The superficial and deep veins are connected via perforators, which contain valves allowing flow in the superficial-to-deep direction. The aim of this study is to investigate and quantify the physiological mechanisms of the calf muscle pump, including the effect of venous valves, hydrostatic pressure, and the superficial venous system. Using a one-dimensional pulse wave propagation model, a muscle contraction is simulated by increasing the extravascular pressure in the deep venous segments. The hemodynamics are studied in three different configurations: a single artery-vein configuration with and without valves and a more detailed configuration including a superficial vein. Proximal venous valves increase effective venous return by 53% by preventing reflux. Furthermore, the proximal valves shielding function increases perfusion following contraction. Finally, the superficial system aids in maintaining the perfusion during the contraction phase and reduces the refilling time by 37%.