Distributed Parameter Biological Function Model Simulation with User-Provided PDE Numerical Solution Scheme

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  • 形式的に記述されたPDE解法スキームに基づく分布定数系生体機能モデルシミュレーションコード生成システム
  • ケイシキテキ ニ キジュツ サレタ PDEカイホウ スキーム ニ モトズク ブンプ テイスウケイ セイタイ キノウ モデルシミュレーションコード セイセイ システム

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The coupling of cellular processes at the tissue and organ level usually involves the handling of partial differential equations (PDEs). Since physiological computational models using PDEs have varied greatly in terms of complexity, most solutions are tailored for specific problems. Space-time discretization schemes like FTCS (Forward-Time Centered-Space), BTCS (Backward-Time Centered-Space), Dufort-Frankel, Crank-Nicolson and Lax-Friedrichs exist. We propose a general approach for handling PDEs in computational models using a replacement scheme for discretization. The replacement scheme involves substituting all the partial differential terms with the numerical solution equations. During the replacement algorithm, the time and spatial indices are also appended to the model variables. This method allows for handling of different forms of equation. Once the derivatives are replaced with the discretized terms, the resulting equations are then written in a recurrence relation form. Finally, the equations for solving the unknown variables are generated. The solution to the linear system of equations uses iterative methods like Gauss-Jacobi and Gauss-Seidel algorithm. If the system is explicit, corresponding loop structure is generated as program code to solve the system. We could successfully generate an excitation propagation simulation program for FTCS scheme with a complex cell model.

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