Modeling of the blood flow in the lower extremities for dynamic diffuse optical tomography of peripheral artery disease

Peripheral Arterial Disease (PAD) is caused by a reduction of the internal diameters of the arteries in the upper or lower extremities mainly due to atherosclerosis. If not treated, its worsening may led to a complete occlusion, causing the death of the cells lacking proper blood supply, followed by gangrene that may require chirurgical amputation. We have recently performed a clinical study in which good sensitivities and specificities were achieved with dynamic diffuse optical tomography. To gain a better understanding of the physiological foundations of many of the observed effects, we started to develop a mathematical model for PAD. The model presented in this work is based on a multi-compartment Windkessel model, where the vasculature in the leg and foot is represented by resistors and capacitors, the blood pressure with a voltage drop, and the blood flow with a current. Unlike existing models, the dynamics induced by a thigh-pressure-cuff inflation and deflation during the measurements are taken into consideration. This is achieved by dynamically varying the resistances of the large veins and arteries. By including the effects of the thigh-pressure cuff, we were able to explain many of the effects observed during our dynamic DOT measurements, including the hemodynamics of oxy- and deoxy-hemoglobin concentration changes. The model was implemented in MATLAB and the simulations were normalized and compared with the blood perfusion obtained from healthy, PAD and diabetic patients. Our preliminary results show that in unhealthy patients the total system resistance is sensibly higher than in healthy patients.