A CellML simulation compiler and code generator using ODE solving schemes

Models written in description languages such as CellML are becoming a popular solution to the handling of complex cellular physiological models in biological function simulations. However, in order to fully simulate a model, boundary conditions and ordinary differential equation (ODE) solving schemes have to be combined with it. Though boundary conditions can be described in CellML, it is difficult to explicitly specify ODE solving schemes using existing tools. In this study, we define an ODE solving scheme description language-based on XML and propose a code generation system for biological function simulations. In the proposed system, biological simulation programs using various ODE solving schemes can be easily generated. We designed a two-stage approach where the system generates the equation set associating the physiological model variable values at a certain time t with values at t + Δt in the first stage. The second stage generates the simulation code for the model. This approach enables the flexible construction of code generation modules that can support complex sets of formulas. We evaluate the relationship between models and their calculation accuracies by simulating complex biological models using various ODE solving schemes. Using the FHN model simulation, results showed good qualitative and quantitative correspondence with the theoretical predictions. Results for the Luo-Rudy 1991 model showed that only first order precision was achieved. In addition, running the generated code in parallel on a GPU made it possible to speed up the calculation time by a factor of 50. The CellML Compiler source code is available for download at http://sourceforge.net/projects/cellmlcompiler.