Pulsatile Aortic Pressure-Flow Analysis using Fractional Calculus for Minimally-invasive Applications

Abstract

Time-dependent pulsatile pressure and flow waveforms in the aorta carry with them considerable information regarding the underlying dynamic behavior of the cardiovascular system. The aortic pressure-flow relationship has traditionally been described using integer calculus. As such, periodicity and linear system assumptions are necessarily imposed to extract hemodynamic information. We introduce the use of fractional calculus (FC) to relate minimally-invasive measurements, of the velocity of aortic blood flow with an esophageal Doppler monitor, to the derived aortic pressure. The basis for this research is a Taylor series model of the velocity of aortic blood flow with subsequent term-by-term fractional integration as well as fractional differentiation. These results demonstrate that this FC approach could potentially generate the aortic pressure waveform throughout systole. Further studies of its first derivative, or the time rate of pressure change,