Development of a new conductance catheter system taking account of heterogeneous current distribution

1.使用心室和胸腔的简化形状模型，我们数值分析了电流如何响应于来自导管末端的电刺激而在心室腔、心肌和周围组织上不均匀地分布。1）数值分析和非线性分析的开发：在第一年，我们将问题描述为偏导数方程的解，Vxx+Vyy+Vzz=0，边界条件Vn=0，在内皮细胞处，V=+/-V0，在两个刺激电极处。由于其轴对称性质，我们使用柱坐标系表示该方程，并代入t=log（r），得到exp（-2t）Vtt+Vzz=0。这些考虑使我们想到了一种方法来有效地离散r，使其对数等间距。2）任意旋转形状下的数值分析：我们开发了一个软件来分析任意旋转形状下的电流分布和非线性。3）体外非线性检测：我们检测了电极宽度为1 mm、电极间距为1 mm的导管的非线性。我们证实，90%的电流被限制在距离导管3.3mm的范围内。2.我们研制了一个电导容积系统，它用计算机数字化地产生交流电流和测定有效值。这使得能够小型化和省电，从而能够在有意识的小动物（例如大鼠）中通过植入装置进行连续体积测定。与所产生的AC同步的数据采样使得在两个频率下的RMS计算仅通过加法和减法成为可能。

1.Using a simplified shape model of ventricle and thorax, we analyzed numerically how currents distribute heterogeneously over ventricular cavity, myocardium, and surrounding tissue in response to electrical stimulation from catheter ends.1)Development of numerical analysis and analysis of nonlinearity : In the first year, we characterized the problem as a solution of a partial derivative equation, Vxx+Vyy+Vzz=0 with boundary conditions Vn=0 at endocardium and V=+/-V0 at both stimulating electrodes. We expressed the equation using cylindrical coordinate system, due to its axisymmetrical nature, and substituted t=log(r), resulting in exp(-2t)Vtt+Vzz=0. These considerations led us to a method to efficiently discretize r with its logarithm equi-spaced. With this numerical analysis we identified the nonlinear relation between ventricular volume and its conductance.2)Numerical analysis in arbitray rotational shapes : We have developed a software to analyze current distribution and nonlinearity in arbitrary rotational shapes.3)Examination of nonlinearity in vitro : We examined the nonlinearity with a catheter of electrode width of 1mm and interelectrode distance of 1mm. We confirmed that 90% of currents were confined within 3.3mm from the catheter. Compared to the preveious reports, the range was wider ; however was similar to our numerical; analysis2.We developed a conductance volumetric system, in which generation of AC currents as well as determination of RMS values is performed digitally with a computer. This enables miniaturization and power-saving, and thereby continuous volumetry by an implanted device in a conscious small animals such as in rats. Data sampling synchronous to generated AC made RMS calculation at two frequencies possible with only addition and subtraction.