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

在包括美国在内的工业化国家，心脏病仍然是主要的死亡原因，在美国，心脏病导致的死亡占总死亡人数的三分之一。正常情况下，心脏收缩是对通过心肌传播的电波的反应；然而，当这些电波产生干扰并导致心脏不规则收缩时，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之外)，不仅可以理解这些病理，而且还可以设计设备和优化治疗方法。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电导和其他参数值是至关重要的。不幸的是，对于这些参数没有共同的共识，围绕它们的值的不确定性影响了定量分析的可靠性。在这个项目中，我们使用数学方法、计算技术和实验相结合的方法来准确地估计这些参数，以正确地对正常和病变组织中的心脏组织动力学进行数值模拟。这项研究有可能通过为模拟提供量化的试验台来阐明心律失常的机制和开发治疗方法。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通过TheVirtualHeart.org在线向公众和其他研究人员公布。心电学的双域模型是公认的数学形式，用于模拟包括细胞内和细胞外成分时心脏动作电位的跨组织传播。心脏组织中电传播的数值模拟对用于电导率的值非常敏感，电导率由空间中每个点的3D对称张量来描述。从数学和生物学的角度来看，对张量条目的精确量化在实践中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一个变分反问题。电导率被视为控制变量，用于最小化计算的激活时间与从电势测量中恢复的激活时间之间的失配。本提案涉及的两个挑战是：(1)开发和分析解决逆问题的具体计算方法，包括在真实情况下解决问题的适当模型简化技术；(2)在实验环境中对心脏内不同组织，如右、左心室和心房，以及不同哺乳动物组织，广泛验证这些方法。提出的研究将为反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的心脏组织中波传播的理解。它将进一步允许在实际应用中使用数学模型和方法，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.