A mathematical model of pressure and flow waveforms in the aortic root.

The differences in the pressure and flow waveforms in the aortic root have not been explained so far in a satisfactory mathematical way. It is a generally accepted idea that the existence of the reflected wave causes the differences in shapes of pressure and flow. In this paper, a mathematical model is proposed that explains the blood pressure and flow waveforms based on changes in left ventricular volume during blood ejection into the aorta. According to the model, a change in volume of the left ventricle during contraction can be mathematically presented with solutions of differential equations that describe the behavior of a second-order system. The proposed mathematical equations of pressure and flow waveforms are derived from left ventricular volume change and basic equations of fluid dynamics. The position of the reflected wave depends on the age and elasticity of arteries, and has an effect on the flow and pressure waveforms. The model is in acceptable agreement with the experimental data available.