Modular mathematical modelling of biological systems

Mathematical models are frequently used to model biological systems, particularly within the field of cardiac electrophysiology. Such systems are typically modelled in a continuous fashion using ordinary differential equations (ODEs) and simulated using custom computer programs created in general purpose languages. Several domain specific languages (DSLs) have been created to ease the difficulty in programming biological models, including CellML. However models in such DSLs are monolithic, interdependent systems, hindering possibilities for reuse and specialisation. In this paper we introduce the Ode language; a typed DSL for describing ODE-based biological models in a structured manner. The type system is used to validate models and includes automated checking and conversion of units of measure. We introduce a module system influenced by parameterised modules from OCaml that allows specialised instantiation at compile-time. Module parameterisation provides great flexibility, enabling the creation of reusable, abstracted model components. These components may be composed and specialised to create larger models. The type system is used to generate module interfaces that guide successful module composition. Parameterised modules may be used, for instance, to abstract a models stimulus protocol or modify its parameters. Several examples are given and the implementation details are discussed.