English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we propose a tumor growth model to incorporate and investigatethe spatial effects of autophagy. The cells are classified into two phases:normal cells and autophagic cells, whose dynamics are also coupled with thenutrients. First, we construct a reaction-(cross-)diffusion system describingthe evolution of cell densities, where the drift is determined by the negativegradient of the joint pressure, and the reaction terms manifest the uniquemechanism of autophagy. Next, in the incompressible limit, such a cell densitymodel naturally connects to a free boundary system, describing the geometricmotion of the tumor region. Analyzing the free boundary model in a specialcase, we show that the ratio of the two phases of cells exponentially convergesto a ``well-mixed" limit. Within this ``well-mixed" limit, we obtain ananalytical solution of the free boundary system which indicates the exponentialgrowth of the tumor size in the presence of autophagy in contrast to the lineargrowth without it. Numerical simulations are also provided to illustrate theanalytical properties and to explore more scenarios.

A tumor growth model with autophagy: the reaction-(cross-)diffusion system and its free boundary limit