Modelling problem

[TobiasDuswald]

Experiment

Running the experiment with only 1 initial agent results in the following simulation output, from which I conclude that there must be another reason why we see the straight lines in the full simulation. Furthermore, we can conclude that the splitting is actually random and there's no problem with the random generator.

[TobiasDuswald]

Adding an exponential decay sounds feasible to reduce the "reach" of the nutrients. To numerically test this hypothesis, we simulate the following equations on a 2D disk with radius 2.8:

We use MFEM, a NURBS mesh, second order elements, and a forward euler for time integration. We simulate with dt=0.0001 and for a total T=1. The results are the following:

Left aplpha = 4 , right alpha = 0. We see that the values towards the outside get lowerd by a factor of 10 while the center values get lowerd by a factor two and a bit. Thus, the exponential decay is a good approach to supply nutrients more locally.

[TobiasDuswald]

Publication for TumorCell sizes:

Hao, S.-J., Wan, Y., Xia, Y.-Q., Zou, X., & Zheng, S.-Y. (2018). Size-based separation methods of circulating tumor cells. Advanced Drug Delivery Reviews, 125, 3–20. https://doi.org/10.1016/j.addr.2018.01.002

Google search for blood

It ranges from a diameter of about 25 millimeters for the aorta to only 8 micrometers in the capillaries. This comes out to about a 3000-fold range. Wikipedia

Conclusion

The blood vessel size can be in the order of the tumor cells, but can also get significantly smaller (half the size).