Collaborative Research: Novel Data Assimilation Techniques in Mathematical Cardiology-Development, Analysis and Validation

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Heart disease remains the leading cause of death in industrialized countries, including the US, where it causes 1/3 of all total deaths. Normally, the heart contracts in response to electrical waves that propagate through cardiac muscle; however, deadly arrhythmias can result when disturbances arise in these electrical waves occur and lead to irregular heart contractions. Scientific computing applied to cardiovascular problems is becoming a formidable tool (in addition to in vitro and in vivo studies) not only to understand these pathologies but also to design devices and optimize therapies. For computing simulations to be reliable and accurate in clinical settings, it is crucial that cardiac conductivities and other parameter values utilized in mathematical models are estimated carefully. Unfortunately, there is no common agreement for these parameters, and the uncertainty surrounding their values affects the reliability of quantitative analysis. In this project, we use a combined approach of mathematical methods, computing techniques and experiments to estimate accurately these parameters necessary to perform numerical simulations of cardiac tissue dynamics in normal and diseased tissue correctly. This research has the potential to elucidate arrhythmia mechanisms and to develop therapies by providing a quantified testbed for simulations. It is a truly interdisciplinary project that connects biology, physiology, physics and computation through a mathematical methodology and an integrative approach between theory, simulations and experiments. Results will be made available the public and other researchers via publications and online via TheVirtualHeart.org.The bidomain model for electrocardiology is the accepted mathematical formalism for modeling the propagation of cardiac action potentials across tissue when including intra- and extracellular components. Numerical simulations of electrical propagation in heart tissue are extremely sensitive to the values used for the conductivity, which is described by a 3D symmetric tensor for each point in space. A precise quantification of the entries of this tensor in practice is still an open and challenging problem from both the mathematical and biological points of view. We formulate the problem of conductivity quantification as a variational inverse problem. The conductivities are regarded as the control variable for the minimization of the mismatch between the activation time computed and the one retrieved from potential measurements. The two challenges addressed by the present proposal are (i) development and analysis of specific computational methods for the solution of the inverse problem including appropriate model reduction techniques to solve the problem in real cases and (ii) extensive validation of the methods in experimental settings for different tissues within the heart, such as right and left ventricles and atria, and for different mammalian tissues. The proposed research will develop new mathematical methods and techniques for inverse problems and will advance our understanding of wave propagation in cardiac tissue for normal and diseased states. It will further allow the use of mathematical models and methods for real applications, particularly when addressing clinical problems.