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

心脏病仍然是包括美国在内的工业化国家的主要死亡原因，占总死亡人数的1/3。 正常情况下，心脏收缩响应于通过心肌传播的电波;然而，当这些电波发生干扰并导致不规则的心脏收缩时，可能会导致致命的心律失常。应用于心血管问题的科学计算正在成为一个强大的工具（除了体外和体内研究），不仅可以了解这些病理，而且可以设计设备和优化治疗。为了在临床环境中可靠和准确地计算模拟，仔细估计数学模型中使用的心脏传导率和其他参数值至关重要。不幸的是，这些参数没有共同的协议，其值的不确定性影响定量分析的可靠性。在这个项目中，我们使用的数学方法，计算技术和实验相结合的方法来准确地估计这些参数进行正常和病变组织的心脏组织动力学的数值模拟正确。这项研究有可能通过提供量化的模拟测试平台来阐明心律失常机制并开发治疗方法。这是一个真正的跨学科项目，通过数学方法和理论，模拟和实验之间的综合方法将生物学，生理学，物理学和计算联系起来。结果将通过出版物和TheVirtualHeart.org在线提供给公众和其他研究人员。心电学的bidomain模型是公认的数学形式主义，用于模拟心脏动作电位在组织中的传播，包括细胞内和细胞外成分。心脏组织中的电传播的数值模拟对用于电导率的值极其敏感，电导率由空间中每个点的3D对称张量描述。从数学和生物学的角度来看，这个张量的条目在实践中的精确量化仍然是一个开放的和具有挑战性的问题。我们将电导率量化问题表述为变分反问题。的电导率被视为控制变量之间的不匹配的激活时间计算和检索从潜在的测量。本提案解决的两个挑战是（i）开发和分析用于解决逆问题的特定计算方法，包括适当的模型简化技术以解决真实的情况下的问题，以及（ii）在心脏内的不同组织（例如，右心室和左心室以及心房）以及不同哺乳动物组织的实验设置中对方法进行广泛验证。这项研究将为逆问题开发新的数学方法和技术，并将促进我们对正常和疾病状态下心脏组织中波传播的理解。它将进一步允许将数学模型和方法用于真实的应用，特别是在解决临床问题时。

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.