计算模型中心脏空间异质性的高效表示方法
Efficient Representations of Cardiac Spatial Heterogeneity in Computational Models
AI总结：
针对心脏组织电特性空间异质性的高效建模问题，本研究基于Fenton-Karma模型，通过分段常数/线性函数拟合粗网格参数，发现1.0-1.6cm网格间距即可在复杂动力学状态下实现与真实结果的良好吻合，提升建模效率。
摘要：
通常认为，心脏组织电行为模型中的所有细胞都具有相同的特性。然而，心肌细胞之间存在的差异虽未得到充分表征，却会导致组织电特性的空间异质性。光学标测技术可用于以高空间分辨率获取心脏表面的实验数据。与逐像素考虑参数变化相比，模型参数的变异可以在更粗的网格上定义，从而能够更高效地获得异质组织的表示形式。本文研究了在空间不一致交替（spatially discordant alternans）的复杂动力学状态下，仍能获得准确结果的参数化网格的最粗粒度。我们采用Fenton-Karma模型，将异质性以空间上平滑的非线性梯度形式引入更多模型参数中。为获得更高效的表示，我们假设粗网格点处的精确参数值已知（这些参数值可通过实验数据获取），并以此为基础设定空间各处的参数值。我们通过对空间粗粒度的已知数据拟合分段常数函数或分段线性函数，来分配空间中的参数值。我们旨在确定这类网格点的最大间距，以使复杂状态下动作电位时程的空间分布与真实分布良好吻合。研究发现，对于一系列不同的模型参数以及这些参数在空间上的不同分布函数，约1.0-1.6 cm的粗网格间距通常能得到与真实分布高度一致的空间分布。此外，分段常数函数和分段线性函数的表现相近。我们目前的结果表明，即使在复杂动力学状态下，将心脏组织模型的输出与异质实验数据进行匹配也可以高效完成。
英文摘要：
It is generally assumed that all cells in models of the electrical behavior of cardiac tissue have the same properties. However, there are differences in cardiac cells that are not well characterized but cause spatial heterogeneity of the electrical properties in tissue. Optical mapping can be used to obtain experimental data from cardiac surfaces at high spatial resolution. Variations in model parameters can be defined on a coarser grid than considering each single pixel, which would allow a representation of heterogeneous tissue to be obtained more efficiently. Here, we address how coarse the parameterization grid can be while still obtaining accurate results for complicated dynamical states of spatially discordant alternans. We use the Fenton-Karma model with heterogeneity included as a smooth nonlinear gradient over space for more model parameters. To obtain the more efficient representations, we set parameter values everywhere in space based on the assumption that the exact parameter values are known at the points of the coarser grid; we assume the parameter values could be obtained from experimental data. We assign parameter values in space by fitting either a piecewise-constant or piecewise-linear function to the spatially coarse known data. We wish to identify the maximal grid spacing of such points to obtain good agreement with spatial profiles of action potential duration during complex states. We find that coarse grid spacing of about 1.0-1.6 cm generally results in spatial profiles that agree well with the true profiles for a range of different model parameters and different functions of those parameters over space. In addition, the piecewise-constant and piecewise-linear functions perform similarly. Our results to date suggest that matching the output of models of cardiac tissue to heterogeneous experimental data can be done efficiently, even during complex dynamical states.
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