### Cell growth on a sphere cell

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Hi,

are there parameters which influence the shape of a single cell in a 3D lattice beside the target volume/surface and the lambda multiplier?

Since the real volume of a sphere is almost identical with the surface out of voxels and the surface of the voxel sphere is by a factor 1.5 larger than the realistic surface, it is possible to calculate the realistic volume and surface and multiply this surface by 1.5 for the growth of a cell. With the algorithm to draw the cell it is possible to read out the volume and surface values out of CC3D. Then the factor between the real sphere surface and the voxel sphere surface can be calculated.

The algorithm to draw the cell consider the corner length of a voxel as steplength. With this approach it is checked if the center of the voxel is inside the sphere or not.

The following cell is drawn with an radius of 10 voxel

The cell after 500 MCS

are there parameters which influence the shape of a single cell in a 3D lattice beside the target volume/surface and the lambda multiplier?

Since the real volume of a sphere is almost identical with the surface out of voxels and the surface of the voxel sphere is by a factor 1.5 larger than the realistic surface, it is possible to calculate the realistic volume and surface and multiply this surface by 1.5 for the growth of a cell. With the algorithm to draw the cell it is possible to read out the volume and surface values out of CC3D. Then the factor between the real sphere surface and the voxel sphere surface can be calculated.

The algorithm to draw the cell consider the corner length of a voxel as steplength. With this approach it is checked if the center of the voxel is inside the sphere or not.

```
for xr in xrange(xStart, xEnd):
for yr in xrange(yStart, yEnd):
for zr in xrange(zStart, zEnd):
rd = sqrt(
((xr+(((xr+stepLength) - xr)/2.)) - x0) ** 2 +
((yr+(((yr+stepLength) - yr)/2.)) - y0) ** 2 +
((zr+(((zr+stepLength) - zr)/2.)) - z0) ** 2)
if (rd <= radiusPx):
steppable.cellField[xr, yr, zr] = cell
```

The following cell is drawn with an radius of 10 voxel

During the simulation the cell looses the desired structure and become a cube again. Even the volume and surface values as well as the target volume and target surface values match the values of the drawn voxel spheres

The cell after 500 MCS

Since this is not a perfect smooth cube and in other simulations there were more edges and peaks, I can imagine that this cell meets also the volume and surface values.

Are there any techniques to keep the shape of the sphere during the simulation?

Is it maybe not possible because for a given volume and surface there are infinite possible 3D objects?

Thank you,

Thorsten

Community: CompuCell3D

### 1 Answer

0

In addition to the volume and surface constraints the adhesion energies will also affect the sphericity of a cell. Is the system trying to not only maintain the cell's target volume and surface but also trying to avoid adhesion energy penalties? In general all of these will affect the sphericity of a cell;

This would be an interesting question to explore with a parameter scan.

Usually though, cells aren't spherical anyway since they are in contact with each other and those contacts are generally flat faces.

- target and lambda volume
- target and lambda surface
- adhesion energies (e.g., cell to medium)
- neighbor order in pixel copy
- neighbor order in adhesion
- square vs. hexagonal lattice
- Potts temperature (which controls how quickly the surface fluctuates)

This would be an interesting question to explore with a parameter scan.

Usually though, cells aren't spherical anyway since they are in contact with each other and those contacts are generally flat faces.

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