Analysing the pattern of pulse waves in arterial networks: a time-domain study

Abstract

The mechanisms underlying the shape of pulse waves in the systemic arterial network are studied using the time-domain, one-dimensional (1-D) equations of blood flow in compliant vessels. The pulse waveform at an arbitrary location in the network is initially separated into a peripheral component that depends on the cardiac output, total compliance and total peripheral resistance of the network, and a conduit component governed by reflections at the junctions of the large conduit arteries and at the aortic valve. The dynamics of the conduit component are then analysed using a new algorithm that describes all the waves generated in the linear 1-D model network by a single wavefront starting at the root. This algorithm allows one to systematically follow all the waves arriving at the measuring site and identify all the reflection sites that these waves have visited. Application of this method to the pulse waves simulated using a 1-D model of the largest 55 systemic arteries in the human demonstrates that peripheral components make a larger contribution to aortic pressure waveforms than do the conduit components. Conduit components are closely related to the outflow from the left ventricle in early systole. Later in the cardiac cycle, they are the result of reflections at the arterial junctions and aortic valve. The number of reflected waves increases approximately as 3^m, with m being the number of reflection sites encountered. The pressure changes associated with these waves can be positive or negative but their absolute values tend to decrease exponentially. As a result, wave activity is minimal during late diastole, when the peripheral components of pressure and the flow are dominant, and aortic pressures tend to a space-independent value determined by the cardiac output, total compliance and total peripheral resistance. The results also suggest that pulse-wave propagation is the mechanism by which the arterial system reaches the mean pressure dictated by the cardiac output and total resistance that is required to perfuse the microcirculation. The total compliance determines the rate at which this pressure is restored when the system has departed from its equilibrium state of steady oscillation. This study provides valuable information on identifying and measuring the parameters and pathways of the arterial network that have the largest effect on the simulated pulse waveforms.