A Graphical Approach for Hybrid Simulation of 3D Diffusion Bio-Models via Coloured Hybrid Petri Nets

Three-dimensional modelling of biological systems is imperative to study the behaviour of dynamic systems that require the analysis of how their components interact in space. However, there are only a few formal tools that offer a convenient modelling of such systems. The traditional approach to construct and simulate 3D models is to build a system of partial differential equations (PDEs). Although this approach may be computationally efficient and has been employed by many researchers over the years, it is not always intuitive since it does not provide a visual depiction of the modelled systems. Indeed, a visual modelling can help to conceive a mental image which eventually contributes to the understanding of the problem under study. Coloured Hybrid Petri Nets (HPNC) are a high-level representation of classical Petri nets that offer hybrid as well as spatial modelling of biological systems. In addition to their graphical representations, HPNC models are also scalable. This paper shows how HPNC can be used to construct and simulate systems that require three-dimensional as well as hybrid (stochastic/continuous) modelling. We use calcium diffusion in three dimensions to illustrate our main ideas. More specifically, we show that creating 3D models using HPNC can yield more flexible models as the structure can be easily scaled up and down by just modifying a few parameters. This advantage of convenient model configuration facilitates the design of different experiments without the need to alter the model structure.