The morphological instability of solid tumor cells in a nutrient-deficient environment

Chien-Han Yen¹, Yi-Chieh Lai^1*, Kuo-An Wu¹

¹Physics, National Tsing Hua University, Hsinchu, Taiwan

* Presenter:Yi-Chieh Lai, email:sim070500@gmail.com

A phenomenological reaction-diffusion model, that includes a nutrient-regulated growth rate of
tumor cells, is proposed to investigate the morphological instability of solid tumor cells during the
avascular growth. We find that the surface instability could be induced more easily when tumor
cells are placed in a harsher nutrient-deficient environment, while the instability is suppressed
for tumor cells in a nutrient rich environment due to the nutrient-regulated proliferation. In
addition, the surface instability is shown to be influenced by the growth moving speed of tumor
rims. Our analysis reveals that a larger growth movement of the tumor front results in a closer
proximity of tumor cells to a nutrient-rich region, which tends to inhibit the surface instability.
A nourished length that represents the proximity is defined to illustrate its close relation to the
surface instability.

Keywords: Patterns in complex systems, Developmental pattern formation, Tumors