Mathematical modelling of cardiovascular fluid mechanics: physiology, pathology and clinical practice

The cardiovascular apparatus is a complex dynamical system that carries oxygen and nutrients to cells, removes carbon dioxide and wastes and performs several other tasks essential for life. The physically-based modelling of the cardiovascular system has a long history, which begins with the simple lumped Windkessel model by O. Frank in 1899. Since then, the development has been impressive and a great variety of mathematical models have been proposed. The purpose of this Thesis is to analyse and develop two different mathematical models of the cardiovascular system able to (i) shed new light into cardiovascular ageing and atrial fibrillation and to (ii) be used in clinical practice. To this aim, in-house codes have been implemented to describe a lumped model of the complete circulation and a multi-scale (1D/0D) model of the left ventricle and the arterial system. We then validate each model. The former is validated against literature data, while the latter against both literature data and numerous in-vivo non-invasive pressure measurements on a population of six healthy young subjects. Afterwards, the confirmed effectiveness of the models has been exploited. The lumped model has been used to analyse the effect of atrial fibrillation. The multi-scale one has been used to analyse the effect of ageing and to test the feasibility of clinical use by means of central-pressure blind validation of a parameter setting unambiguously defined with only non-invasive measurements on a population of 52 healthy young men. All the applications have been successful, confirming the effectiveness of this approach. Pathophysiology studies could include mathematical model in their setting, and clinical use of multi-scale mathematical model is feasible.