# CPM

## 1D PDE Barkley Model

Derived from the seminal Hodgkin-Huxley and FitzHugh-Nagumo models, the Barkley model is probably the simplest continuous model for excitable media. It replaces the cubic term in the FitzHugh-Nagumo model with a piece-wise linear term as a simplification that enables fast simulation.

## Try the Examples

Examples Menu To explore the potential and modeling features, it is the best to learn by example. Morpheus comes with a range of fully functional example models showcasing a number of model formalism and modeling features.

## Step-by-Step Example

To show SBML support in Morpheus as of version 2.1 in practice, we give a step-by-step example of how to download, import and extend an SBML model. 1. Get an SBML Model from BioModels First, we browse the BioModels model repository and select a model.

## Convert to 2D

Converting the model from the previous chapter into a 2D model is trivial in Morpheus. In the Space section, you only need to change the Size of the Lattice to e.

## Convert to 3D

Now we finally arrive at the 3D model. As an example, we further develop the coupled PDE and CPM model with mechanical interaction. Similar to the 1D to 2D case, it is straighforward to extend the dimensionality to 3D.

## Conclusion

In this course, we have shown how to convert a 1D PDE model into a 3D multiscale tissue model in Morpheus using 3 steps: Convert a PDE model into a cell-discrete diffusion model, add motility and cell mechanics using cellular Potts sampling, couple intracellular dynamics and tissue mechanics.

## A Multiscale Mini Model

A Word on the Word ‘Multiscale’ First, let’s clarify what we mean by the somewhat hyped term ‘multiscale’. Generally, the term refers to mathematical and computational models that simultaneously describe processes at multiple time and spatial scales.

## Example

Let’s go through an example. We’ll construct a model in which an intracellular cell cycle network (ODE) regulates the division of motile cells which (CPM) release a diffusive cytokine (PDE) which, in turn, controls the cell cycle (ODE).

## Relative Time Scales

At this point, you may be asking yourself: ‘All nice and well, but how can I control the relative time scales between the various models?’ And I’d respond:

## Conclusion

In this course, we have constructed a small multiscale model in which an ODE model, a CPM model and a PDE model are mutually coupled to each other. The main aim was to show how one can couple such models with relative ease in Morpheus and how you can control such couplings.