Mathematical Modelling and Simulation of Coronary Blood Flow

As in vivo observations and measurements of flow conditions in the coronary circulation are extremely difficult and clinically almost infeasible, the use of mathematical models and the performance of simulation studies are the only practical way for a good understanding of coronary haemodynamics. As the range of clinical applicability of known models in this field is rather limited, we developed a detailed lumped parameter model of the coronary haemodynamics. From the beginning we aimed at its use as an aid for interventional cardiologists and heart surgeons. At this stage of development, our lumped parameter model can already be of some help to physicians, when appraising the adverse effects of stenoses on myocardial blood supply and assessing the attainable improvement of the supply by therapy. The crude approximations inherent in lumped parameter modelling restrict the applicability of this unsophisticated approach to an imprecise global assessment of the blood supply to the myocardium and its detoriation in the case of coronary artery disease. However, to be able to assess other specific pathophysiological processes, such as thrombus development and stenoses growth, for instance, we need precise knowledge of the local three-dimensional flow pattern in a stenosed section of the coronary artery tree, especially around the apex of the stenosis. We present simulation studies of the three-dimensional flow in stenosed sections of the coronary arteries, based on a distributed parameter modelling approach. In these studies, the governing partial differential equations are solved with the finite element method. Particular attention is given to the acquisition of patient-specific data, especially of data describing the geometry of the patient’s epicardial arteries, derived from medical images. These data are required not only for the patient-specific adaptation of our lumped parameter model but also, in the case of our three-dimensional flow simulations, for the generation of a finite element mesh in the flow domain under investigation. However, we deal with the mesh generation issues only very briefly.