An equivalent cardiac source for the anisotropic muscle based on the bidomain theory and its application to the inverse problem in electrocardiology

基于双胞体模型，我们开发了一种等效的各向异性心肌电源，并讨论了在心脏表面重建（宏观）跨膜电位的方法。首先，我们用积分方程的形式给出了有界非均匀体积导体的胞外电势。通过了解肌纤维的几何特性和心肌的各向异性电导率，可以从心脏的跨膜电位分布计算出场电位。其次，我们讨论了利用上述方程从体表图估计（原位）跨膜电位的方法。据预测，如果细胞内与细胞外电导率在所有方向上的比率相等，则由于心肌组织各向异性引起的体积积分消失，因此只能使用心脏表面跨膜电位的表面积分来确定场电位。因此，在这种情况下，心脏表面的原位跨膜电位分布可以从体表测量的电位图中唯一地计算出来。我们正在开发一种从体表图计算原位跨膜电位的程序。由于原位跨膜电位与心肌细胞的电活动直接相关，因此有望成为诊断梗死面积和梗死面积最有效的方法。

We developed an equivalent electric source for anisotropic cardiac muscle based on the bidomain (bisyncytia) model and then discussed a method of reconstructing (macroscopic) transmembrane potentials over the heart surface.First, we gave the extracelluar potential in a bounded inhomogeneous volume conductor in the form of an integral equation. It is possible to calculate the field potential from the transmembrane potential distribution in the heart, with a knowledge of geometrical property of muscle fibers as well as anisotropic conductivity of the heart muscle. Second, we discussed the method of estimating the (in situ) transmembrane potentials from the body surface map using the above equation. It is predicted that, if ratios of intracellular to extracellular conductivity along all directions are equal, the field potentials can be determined only using surface integral of the transmembrane potentials over the heart surface since the volume integral arising from the tissue anisotropy of cardiac muscle vanishes. Therefore, in that case, the in situ transmembrane potential distribution on the heart surface can be calculated uniquely from potential maps measured on the body surface.We are developing a procedure of calculating the in situ transmembrane potentials from the body surface maps. It is expected that the in situ transmembrane potentials will be most effective in diagnosing of infarcted area and size since it is directly related to electric activity of heart muscle cells.