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4  Chapter 1 Multi-scale models of the heart for patient-specific simulations




                                         and ventricles, as well as a left (systemic) and right (pulmonary)
                                         side. The oxygen-poor blood enters first the right atrium, then the
                                         right ventricle through the tricuspid valve. The right ventricle then
                                         ejects the blood into the lungs through the pulmonary valve. The
                                         blood gets oxygenated by the lungs and then goes back to the heart
                                         in the left atrium chamber, from where it reaches the left ventricle
                                         through the mitral valve. Finally, the left ventricle ejects the blood
                                         through the aortic valve into the circulatory system. The muscle,
                                         called myocardium, of the atria is much thinner than ventricular
                                         myocardium as they only need to transfer the blood to the ventri-
                                         cles. The ventricles have to provide a more significant amount of
                                         work to push blood in the peripheral circulation. The heart is en-
                                         closed into a relatively stiff bag called pericardium, which is fixed
                                         in the thoracic cavity. A thin layer of pericardial fluid between the
                                         pericardium and the external layer of the myocardium (called epi-
                                         cardium) ensures frictionless motion of the heart inside the peri-
                                         cardial bag.





















                                         Figure 1.1. Diagram of heart anatomy and blood flow. (Source: Wikipedia.)

                                            Depending on the application, various anatomical models
                                         have been used by researchers. Regarding the ventricles, the
                                         most common model for physiology and disease understanding
                                         is surely based on analytical formulations. The left ventricle is
                                         modeled using a prolate spheroidal model [43,44], which approx-
                                         imates relatively well its healthy shape. In these models, the other
                                         chambers are ignored. Generic bi-ventricular models have also
                                         been created to investigate inter-ventricular interactions and ob-
                                         tain more realistic results [45](Fig. 1.2, left panel). As detailed 3D
                                         imaging became possible, researchers quickly moved to more re-
                                         alistic, and sometimes also pathological geometries. First, cardiac
                                         anatomies extracted from 3D scans of animals were used [46], and
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