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118  Chapter 4 Data-driven reduction of cardiac models




                                         sure values as produced by state-of-the-art physiological mod-
                                         els of blood flow. To enhance its performance and generalization
                                         properties, the deep learning model is trained on an extensive
                                         database of synthetically generated anatomical models of the hu-
                                         man coronary tree, spanning the geometric variability of a refer-
                                         ence human population.
                                            Atrial fibrillation is an increasing socio-economic burden.
                                         Patient-specific modeling of atrial electrophysiology has the po-
                                         tential to help understanding the disease but also devise effective
                                         treatments. Unfortunately, these models are often computation-
                                         ally demanding, controlled by a large number of parameters, and
                                         therefore not directly applicable within a clinical workflow. Sec-
                                         tion 4.2 describes the definition of a surrogate model of cellular
                                         electrical activity to speed up atrial electrophysiology simulation.
                                         The time pattern of the cellular action potential as expressed by
                                         state-of-the-art computational models is estimated using regres-
                                         sion from the model parameters. The estimated action potential
                                         is then used in combination with standard computational models
                                         of organ-level electrophysiology to replace the explicit computa-
                                         tion of the cellular electrical potential dynamics, enabling drastic
                                         speed-up while accurately reproducing key features of the action
                                         potential morphology.
                                            Finally, the prediction of heart motion and its mechanical char-
                                         acterization can provide valuable information on the state and
                                         function of the organ, as well as insights on the effect of differ-
                                         ent therapy options for the specific patient. As detailed in sec-
                                         tion 4.3, a model can be trained using deep learning to predict
                                         myocardium acceleration from the kinematic and dynamic state
                                         of the system. The predicted acceleration is used in an explicit
                                         time advancing scheme for the solution of the elastodynamics
                                         of structures with mechanical properties compatible with those
                                         of biological tissue. Compared with a state-of-the-art numerical
                                         solver for the computation of soft tissue deformations, this ap-
                                         proach allows the use of time steps one order of magnitude larger,
                                         relaxing the stability condition of the numerical scheme and po-
                                         tentially allowing significant speed-up.


                                         4.1 Deep-learning model for real-time,
                                              non-invasive fractional flow reserve

                                         4.1.1 Introduction
                                            Hemodynamically significant coronary lesions are treated typ-
                                         ically through Percutaneous Coronary Intervention (PCI). Clinical
                                         decision making is often based on anatomical features, like the
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