### Would SteadyStateDiffusionSolver2D be appropriate to be used with Chemotaxis

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I have my model based on the paper "Emergent Stratification in Solid Tumors Selects for Reduced Cohesion of Tumor Cells: A Multi-Cell, Virtual-Tissue Model of Tumor Evolution Using CompuCell3D" for tumor growth. However, I would like to have my cells to move towards higher glucose and additionally oxygen. Both these nutrients would have high diffusion constants. Using "DiffusionSolverFE" is making my simulations very slow as has been mentioned in the tutorials. Hence, I was wondering if I use SteadyStateDiffusionSolver as has been used in the above paper, would chemotaxis be appropriate?

Community: CompuCell3D

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You should be able to use any module for solving your field and use that for chemotaxis. When you change the diffusion solver, also update the ChemicalField Source under the Chemotaxis plugin.

written
6 months ago by
priyomadhyapok

### 1 Answer

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Any solver can be used with chemotaxis but for large diffusion constants we typically use SteadyState solver that essentially solves Helmholtz equation in Cartesian coordinates

(d/dx)(du/dx) + (d/dy)(du/dy) + lambda*u = f(x,y).

As you can see there is no dependence on time here and this is the limiting case for the diffusion equation when d/dt term is zero because the field stopped evolving (i.e. at large t.) Clearly this is an approximation so you have to be aware of it and double check if this approximation is appropriate for your problem. However using the field from SteadyState solvers in Chemotaxis plugin is fine

(d/dx)(du/dx) + (d/dy)(du/dy) + lambda*u = f(x,y).

As you can see there is no dependence on time here and this is the limiting case for the diffusion equation when d/dt term is zero because the field stopped evolving (i.e. at large t.) Clearly this is an approximation so you have to be aware of it and double check if this approximation is appropriate for your problem. However using the field from SteadyState solvers in Chemotaxis plugin is fine

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