Table 1.

Existing model assumptions.

Model type	Assumptions/comments
Exponential growth	- Cell number increases proportionally to the number of cells present
	- Only output is cell number; does not have spatial information
Reaction diffusion (RD)	- Tumor growth is affected by 3 parameters: proliferation rate, diffusion coefficient, and carrying capacity
	- Only average cell behaviors are considered
	- Cannot resolve individual cell trajectories or cell-cell interactions
Reaction diffusion convection (RDC)	- Directed, non-random movement (e.g. chemotaxis) is also considered
	- Cannot resolve individual cell trajectories or interactions
Agent based (AB)/individual-cell based lattice	- For computational efficiency, cell movements and/or division events are confined to a lattice of specified size
	- Interactions below the spatial scale of the lattice cannot be modeled
	- Migration is often modeled as cells ‘jumping’ from one lattice location to the next, or otherwise cell movement only occurs after a proliferation event when the new cell occupies a free lattice location
Agent based (AB)/individual-cell based	- Individual cells (‘agents’) and their interactions are modeled
	- Computationally very expensive
Hybrid AB and RD	- Combines the computational speed of RD with the stochasticity of AB models to show relevant activity at the cell and tissue levels