A Hypertension Blood Flow Model in Arteries

Higher blood pressure, known as hypertension, refers to a condition where the normal force of blood against the artery walls is above the standard range. Elevated blood pressure levels increase the likelihood of experiencing several health issues, including cardiac disease, heart attack, and stroke. This study presents a mathematical model that captures the blood pressure waveform and characterizes the motion of blood flow within the arterial network. The proposed approach combines the conventional Windkessel modeling of aortic flow with the solution of Womersley pulsatile flow equations to achieve greater accuracy. The derivation setup comprises two compartments, namely proximal and distal, designed in a Windkessel-type fashion. These compartments are interconnected by a tube, simulating the aorta. The blood flow within the aorta is characterized using the Womersley solution, an approach to the simplified Navier-Stokes equations. The model results show the ability to: (i) describe the arterial input impedance; (ii) to mimic changes in the aortic root pressure profile and wave reflections in large arteries; and (iii) to predict physiological frictional and inertial pressure drops in large arteries is presented. The results have been verified using in-vivo data on aortic pressure and flow rate from patients diagnosed with hypertension.