Reduced order models for the simulation of pathological heart valves

Numerical modeling of the human cardiovascular system (CVS) represents an active branch of research which allows the medical specialists to advance in understanding of underlined processes of blood circulation and the heart work at any scale, moreover, it helps to analyze the potential problems which can arise in the CVS by modifying the parameters inside the mathematical models. Due to inability to capture in details the pressure and flow parameters without invasion into heart chambers, the process of diagnosing heart diseases can become very complicated, the limited data on atrial pressure and cardiogram results can give only overall representation of the heart condition and the exactness of the diagnosis is based mainly on experience of the doctor. Nevertheless, the development of numerical models of CVS helps to get better understanding on processes which can cause particular disease (reverse flow leakage in heart chambers, improper contraction of heart muscles due to infarction of tissue). Mathematical model allows the analysis of all physical values of the system during the heart beat as well as possibility to adjust individual parameters specific to each patient. Therefore, it becomes an efficient tool for doctors to diagnose properly the heart disease, to assign the necessary treatment and surgery, and to predict the effect of implanting cardiac-assist devices.