MATHEMATICAL MODELING AND SIMULATION

该子项目是利用 由NIH/NCRR资助的中心赠款提供的资源。子项目和 研究者（PI）可能从另一个NIH来源获得主要资金， 因此可以在其他CRISP条目中表示。列出的机构是 中心，不一定是研究者的机构。 数学建模与仿真 子项目说明 作为一个中心，我们已经建立了生物电场模拟领域的专业知识，在当前的资助期内建立了这种专业知识，并建议继续使这种形式的模拟成为我们未来研究活动的核心。在该中心成立之初，我们的重点是躯干和头部的被动电特性及其对内源性生物电源（心脏和大脑）的响应;我们解决了基于已知来源的正向问题以及逆问题，其中我们试图从体表（或体表外）的测量中识别和定位生物电源。 近年来，我们也开始模拟生物电活动本身，从而研究生物电源的性质;这些电源是高度动态的，增加对它们行为的了解将有助于提高我们预测其功能和疾病功能障碍后果的能力。我们建议继续这项研究，重点是模拟心肌缺血和除颤对心脏和癫痫的影响以及大脑中的深部脑刺激。为了将中心内的发现和计算发展转化为更广泛的生物医学用户社区，我们将继续开发，出版，发布和支持软件，这些软件将包含动态生物电源模型以及创建相关正向和反向问题的有效解决方案的工具。 生物电活动的模拟的一个应用是在心肌组织的微观模型中的激励的传播的计算。 本研究的目的是解决长期存在的差距，在多尺度建模的心脏电生理学之间的非常进化和良好的表征行为的心脏细胞膜和模拟的电活动在整个心脏。 心脏模拟的发展主要是因为在每个有意义的尺度上都存在模型，从离子通道的随机模型到整个心脏和躯干。 然而，需要在尺度的每个转变处进行简化，因此需要在一个尺度处的结果在下一个尺度处找到相关联的表达式。 例如，组织模型必须能够纳入细胞行为变化的影响，以模拟或预测药理学机制的病理生理学。 同样重要的是，直到最近，在这种跨尺度的翻译中，微观结构的变化在组织水平模型中得到表达，这是一个重大的遗漏。 我们已经解决了这一遗漏。 我们已经开发的方法，我们已经命名为“微域”建模，是为了将结构信息在微观尺度上，然后一般的参数，饲料到组织水平的模拟框架称为“bidomain”的方法。 我们建立的每个微区模型都包含适度数量（30- 150）的心肌细胞，这些心肌细胞被离散的细胞外空间包围，这也是模型的一个明确部分。 这些模型的信息来自显微镜和组织学，以及电解质的基本电导率和连接肌细胞的差距连接。 通过将微域镶嵌成数百万个有限元，可以计算细胞内和细胞外各向异性电导率的体积值，这些电导率是bidomain中的等效参数。 生物蛋白质是均质化过程的产物，该过程去除了这种细节水平，将其并入一些组织参数中。以这种方式，可以包括例如心肌缺血对小的微域上的细胞外空间的变化的影响，然后计算所需的bidomain参数以预测整个心脏对缺血的响应。 在过去的一年中，我们已经扩大了微域模型的范围，132个细胞，这是现在足够大，以代表激活的蔓延和测量传导速度都沿着和跨纤维方向。 这个新模型是一篇已提交的期刊文章的基础，第二篇已接近完成最终评审。 特别是第二篇文章的新颖之处在于，它描述了在具有相同物理尺寸和特性的微域和双域模型中激发的传播的比较。 我们能够证明，在合理的条件范围内，即，改变参数，例如细胞外空间和间隙连接传导率，以代表正常和缺血心肌，两种模型产生相同的结果。 然而，这是唯一正确的，如果bidomain的体电导率参数来自微区模拟。 因此，我们已经开发出一种方法，明确的微观几何形状或电导率的变化与相关的bidomain参数的变化，以前只可能通过非常粗略的近似链接。 这两篇文章，沿着之前的两篇描述微域的被动特性的期刊出版物，应该形成一个坚实的工作主体，沿着我们继续展示这些结果的会议，将建立这种方法。 进行模拟所需的软件代表了SCIRun和由杜克计算电生理小组开发的Cardiowave软件的合并，可通过CIBC网站获得。

This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. MATHEMATICAL MODELING AND SIMULATION Subproject Description As a Center, we have established expertise in the area of simulation in bioelectric fields, have built on that expertise in the current funding period, and propose to continue to make this form of simulation a centerpiece of our future research activities. At the start of the Center, our focus was on passive electrical characteristics of the torso and head and their response to endogenous bioelectric sources (the heart and brain); we solved both forward problems based on known sources as well as inverse problems, in which we sought to identify and localize bioelectric sources from measurements on (or outside) the body surface. In recent years, we have also begun to simulate the bioelectric activity itself and thus to study the nature of bioelectric sources; these sources are highly dynamic and increased knowledge of their behavior will help improve our ability to predict the consequences of their function and disfunction in disease. We propose to continue this research, with emphasis on simulating the effects of myocardial ischemia and defibrillation on the heart and epilepsy and deep brain stimulation in the brain. In order to translate the discoveries and computational developments within the Center to the broader biomedical user community, we will continue to develop, publish, release, and support software that will incorporate models of dynamic bioelectric sources as well as the tools with which to create efficient solutions to the associated forward and inverse problems. One application of the simulation of bioelectric activity has been in the computation of the spread of excitation in microscopic models of myocardial tissue. The goal of this research was to address a long standing gap in the multiscale modeling of cardiac electrophysiology between the very evolved and well characterized behavior of cardiac cell membranes and the simulation of electrical activity in the whole heart. Simulation of the heart has advance mainly because there exist models at each of the meaningful scales, from stochastic models of ion channels to whole heart and torso. However, there is a need for simplification at each transition of scale and hence a requirement that results at one scale find an associated expression at the next. For example, a model of tissue must be able to incorporate the effects of changes in the behavior of the cell in order to mimic or predict pathophysiology of the mechanisms of pharmaceutics. It is also essential, and until recently a significant omission, in this translation across scales that changes in microscopic structure find expression in tissue level models. We have addressed this omission. The approach we have developed, which we have named "microdomain" modeling, is meant to incorporate structural information at the microscopic scale and then general parameters that feed into the tissue level simulation framework known as the "bidomain" approach. Each microdomain model we have created contains a modest number (30--150) of cardiac myocytes surrounded by a discrete extracellular space, which is also an explicit part of the model. The information for these models comes from microscopy and histology together with basic conductivities of electrolytes and the gap junctions that link myocytes. By tessellating the microdomain into millions of finite elements, it is possible to compute bulk values for both intracellular and extracellular, anisotropic conductivities, which are the equivalent parameters in the bidomain. The bidomain is the product of a homogenization process that removes this level of detail, incorporating it in a few tissue parameters. In this way, it is possible to include the effects of, for example, myocardial ischemia on changes in extracellular space on a small, microdomain and then compute the required bidomain parameters to predict the response of the whole heart to ischemia. In the past year, we have expanded the scope of the microdomain models to 132 cells, which is now large enough to represent the spread of activation and measure conduction velocities both along and across he fiber direction. This new model is the basis for one journal article submitted and a second nearing completion of final review. The novel aspect of especially the second article is that it describes a comparison of the spread of excitation in a microdomain and in a bidomain model with the same physical size and characteristics. We were able to show that under a reasonable range of conditions, i.e., varying parameters such as extracellular space and gap junction conductivities to represent both normal and ischemic myocardium, both models generate the same results. However, this is only true if the bulk conductivity parameters of the bidomain are derived from the microdomain simulations. Thus, we have developed a means of linking explicitly variations in microscopic geometry or electrical conductivity with the resulting variations in associated bidomain parameters, a link that was previously only possible through very coarse approximation. These two articles, along with two previous journal publications describing the passive characteristics of the microdomain, should form a solid body of work that, along with the conferences at which we continue to present these results, will establish this approach. The software required to carry out the simulations represents a merging of SCIRun and the Cardiowave software developed by the Duke Computational Electrophysiology group and is available through the CIBC website.