Modelling the period-average transport of species within pulsatile blood flow

Abstract

Time-averaging is a technique that is often applied in models of the cardiovascular system to filter out temporal variations. In the context of modelling pulsatile blood flow, it is used to derive the time-invariant state, about which the flow periodically oscillates. It is known from past studies, that blood flow oscillations can interact to produce disturbances that directly influence the period-average of their local flow field. In this study, it is shown that the transport of blood-borne species also inherits disturbances that can influence its period-average. Over the course of a period of oscillation, the influence of disturbances can aggregate and cause the period-average to substantially differ from its equivalent steady-state. This poses a problem for models of physiological processes that rely on the long-term transport of blood-borne species, such as of atherosclerosis and thrombosis growth. This is because an explicit resolution of all periods of oscillation can be computationally expensive to resolve, significantly more so than the equivalent steady-state. To overcome this problem, the Reynolds Period-Average (RPA) species transport model is developed in this study, to model the period-average of pulsatile species transport. In the present form of the RPA model, the influence of flow disturbances is integrated, whereas species transport disturbances are assumed to be relatively negligible. This simplification is observed to hold well for conditions of low to moderate flow pulsatility, such as within human coronary arteries. Under these conditions, the present form of the RPA model is shown to well approximate the period-average transport of species, such as low density lipoprotein, with relatively little computational expense.