Add subcellular element model

[MILeach]

Subcellular Element Model

Aim

This pull request will add subcellular element functionality to chaste and close #110

Features

• Generation of cells with or without boundaries
• Ability to model complex cell shapes

New Code

• SemElement
• SemMesh
• SemMeshReader
• SemMeshWriter
• SemBasedCellPopulation
• SemCellsGenerator
• SemInterCellularForce
• SemIntraCellularForce

To Do

• Get existing code building
• Implement CPU version of SEM in Chaste
  • Clarify algorithm
  • Map to chaste, i.e. nodes, elements etc.
  • Implement basic algorithm
  • Add supporting features, e.g. mesh writers, readers
• Add tests
• Tutorial
• Documentation
• Integrate FLAME GPU with the chaste build process
• FLAME GPU implementation of SEM
• Plan for remaining work
• Update github issue / pull request

Subcellular Element Method Overview

The Subcellular Element Method (SEM) is a lagrangian (i.e. particle based rather than grid based) method for simulating cells & cell shapes. An individual cell is modelled as a collection of particles which interact with each other via two potential fields, one modelling inter-cellular forces, and the other modelling intra-cellular forces.

Each particle has an associated interaction radius and different functions/coefficients can be used to modify the properties of the cells. To support interaction between cells, each particle has an identifier stating which cell it is a part of.

Interaction forces are summed over each other particle within the interaction range. Particles with the same cell id use the intra-ceullular force model, and particles with differing cell ids use the inter-cellular force model.

Mapping SEM to chaste

Components

• Each SEM particle will correspond to a chaste node (derived from node)
• Each cell will correspond to a chaste SemElement (derived from element)
  • Has a unique cell id
  • Maintains a set of ‘layers’ of particles. Used to determine force interactions
• A collection of cells will correspond to a chaste SemBasedCellPopulation (derived from off lattice cell population)
• SemCellsGenerator - generates cells
• SemMesh - keeps track of elements
• SemInterCellularForce
  • By default produces interactions between all particles of differing cell-id
  • Mode to specify interaction between specific cell-ids and/or particular ‘layers’
  • Multiple forces can be enabled at once
• SemIntraCellularForce
  • By default used for all intra-cellular interactions
  • Possible to specify that the force is to be used for specific layers
  • Multiple forces can be enabled at once
• Relevant implementations within:
  • Cell writers
  • Population writers
  • Serialisation
  • MeshWriter
  • MeshReader
• Cell Division
• Cell Death

Notes

Implementation uses the concept of 'interaction layers'. Forces can be specified to act between specific layers.

• Paper

Update 23/02/2024

• Basic core functionality implemented, i.e:
  • Sem cell population can be created
  • Intra-cellular forces work for a simple force model. This should be improved
  • Inter-cellular forces can be added but do not currently generate forces.
  • Some writers work, others need implementation details adding
  • Results visually verified
  • There are various print statements for development/debugging currently committed in this branch

Next Steps

• Implement inter-cellular force model
• Create tests for each class
• Go back over classes - some methods have been commented out or need functionality adding
• Add mesh readers/writers & serialization
• Check functionality for cell division / cell death is working
• Identify how to sensibly test a representative simulation