Mathematical modeling of spherical shell-type pattern of tumor invasion
Date
2023
Authors
Amereh, Meitham
Struchtrup, Henning
Nadler, Ben
Journal Title
Journal ISSN
Volume Title
Publisher
Symmetry
Abstract
Cancer cell migration, as the principal element of tumor invasion, involves different cellular
mechanisms. Various modes of cell migration including single and collective motions contribute
to the invasion patterns. The competition between adhesive cell–cell and cell–matrix forces is a key
factor that determines such patterns. In this paper, we study a distinct shell-type mode of tumor
invasion observed in brain and breast tumors. In this mode, cells at the outer layer of the tumor
collectively move away from the core and form a shell-type shape. Both the core and the shell sustain
a sharp interface between cells and the surrounding matrix. To model the preserved interface, we
adopted a Cahn–Hilliard-type free energy relation with the contribution of the interfacial stress.
This nonconvex form of free energy allows for cells to remain together and preserve the tumor
core via adhesive cell–cell forces while separating the core from the surrounding matrix across
a continuous sharp interface. In addition, the motion of the shell was modeled using the chemotactic
migration of cells in response to the gradient of nutrients. The associated fluxes of cells were
implemented in a general form of balance law. A non-Michaelis–Menten kinetics model was adopted
for the proliferation rate of cells. The flux of nutrients was also modeled using a simple diffusion
equation. The comparison between the model predictions and experimental observations indicates
the ability of the model to manifest the salient features of the invasion pattern.
Description
Keywords
tumor modeling, shell-type invasion, chemotaxis
Citation
Amereh, M., Struchtrup, H., & Nadler, B. (2023). “Mathematical modeling of spherical shell-type pattern of tumor invasion.” Symmetry, 15(2), 283. https://doi.org/10.3390/sym15020283