Simulating the pulse wave in the human pulmonary circulation

This thesis deals with the development and application of an existing [169] non-linear, one-dimensional mathematical and computational model of pulse wave propagation in the human pulmonary circulation with an aim to improve our ability to predict blood pressure and flow in the pulmonary arteries and veins and enhance our understanding of haemodynamic changes occurring during health and disease. The existing model by Vaughan [169] is developed in two ways, firstly by improving the descriptions of venous geometry, values of physiological parameters, inflow and outflow boundary conditions, and then by extending the model to predict pressure drop across the pulmonary vascular beds. The arteries and veins are treated as thin, homogeneous elastic tubes, and blood as a viscous, homogeneous and incompressible fluid. The non-linear effects of pulse wave propagation are predicted in the large arteries and veins, solving the governing equations by means of two-step Lax-Wendroff scheme. For an accurate haemodynamic prediction, the effects of downstream vasculature are incorporated through dynamic structured-tree matching conditions by linking the arterial and venous pressures and flows. For each blood vessel in the structured trees, linearised governing equations are solved analytically. The modelling capability is enhanced by imposing four out flow conditions at the orifices of four large veins opening in the left atrium. Considering the fundamental differences between pulmonary and systemic compliance behaviour, a revised compliance parameter value is used to obtain improved predictions of the pulmonary pressure pulse. The model is applied to various hypotheses of pulmonary hypertension to analyse the haemodynamic disorders linked with the causes of the pulmonary hypertension. The prescribed flow-rate boundary condition at the system inlet limits the occurrence of any changes in the flow patterns due to the hypertension, so a new pressure boundary condition, simulating remodelling of the heart or ventricular dysfunction, is imposed to study the effects of the hypertension on the volume flow-rate. To better understand the microcirculatory characteristic in the pulmonary circulation, under normal and diseased conditions, the model is further extended to predict the mean pressure drop across the pulmonary arterioles and venules by treating the connected structure trees not only as boundary conditions but also an active fluid dynamical part of the model. A more insightful interpretation of the results is provided by separating the pulse waveforms into incident and reflected components using Wave Intensity Analysis. Finally, the model is applied to assess the effectiveness of commonly used techniques to estimate local pulse wave velocity in the pulmonary arteries. This thesis is a step forward in understanding the performance of the pulmonary circulation and its behaviour in response to various anatomical and physiological changes in health and disease. Moreover, despite having room for further developments and validation, the model has the ability to simulate physiologically relevant pulse waveforms at a reasonable computational cost and therefore has a prospect of clinical application in the long run.