Model composition for biological mathematical systems

Mathematical models are frequently used to model biological process, such as cardiac electrophysiological systems. In order to separate the models from the implementations, and to facilitate curation, domain specific languages (DSLs) have become a popular and effective means of specifying models (Lloyd et al., 2004; Hucka et al., 2004). In previous papers (Gill et al., 2012a; Gill et al., 2012b; McKeever et al., 2013) we have argued for including parameterised modules as part of such DSLs. We presented our prototype Ode language and showed how models could be created in a generic fashion. In this paper we extend our work with concrete examples and simulation results. We show how complex heart models can be constructed by aggregation, encapsulation and subtyping. Our use-case retraces the steps taken by (Niederer et al., 2009), which investigated the common history between cardiac models, and shows how they can be cast in our language to be reused and extended. Our DSL enables ‘physiological model engineering’ through the development of generic modules exploiting high cohesion and low coupling.