A Hybrid Model for Cellular Dynamics in Colorectal Crypts

Ítalo José Lima de Sousa; Giuseppe Romanazzi

doi:10.5433/1679-0375.2025.v46.53590

A Hybrid Model for Cellular Dynamics in Colorectal Crypts

Authors

Ítalo José Lima de Sousa Universidade Estadual do Maranhão https://orcid.org/0009-0007-9147-7742
Giuseppe Romanazzi Universidade Estadual de Campinas https://orcid.org/0000-0002-4486-7840

DOI:

https://doi.org/10.5433/1679-0375.2025.v46.53590

Keywords:

colon crypt, partial differential equations, tessellation, cell proliferation and differentiation, finite element method

Abstract

Colorectal cancer is believed to originate from abnormal cell proliferation in small cavities of its epithelium called crypts. We present a hybrid framework that couples a Voronoi tessellation-based cell model with a continuous differential model to describe cellular dynamics, proliferation, and differentiation in a colorectal crypt. The framework is implemented numerically using finite difference and finite element methods.
This~allows us to simulate how cells move, proliferate, and differentiate in normal and abnormal scenarios.
We consider in particular the normal homeostatic case for validating the framework, and simulate two abnormal scenarios where perturbations in cell distribution or proliferation are imposed. The benefit of such a hybrid model is that we can freely impose perturbations and show results for cellular dynamics, proliferation, and differentiation at two different scales: a macro continuous scale and a micro cell scale. This framework provides insights into how cell behavior changes under abnormal conditions and how crypt lesions and adenomas may originate from cellular dynamics perturbations.

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Author Biographies

Ítalo José Lima de Sousa, Universidade Estadual do Maranhão

Prof. Me., Department of Mathematics, UEMA, São Luís, MA, Brazil.
Substitute Professor of the Department of Mathematics and Informatics at the State University of Maranhão (UEMA), Brazil. Prof. at SEMED School, São Luís, MA, Brazil.

Giuseppe Romanazzi, Universidade Estadual de Campinas

Professor of the Department of Applied Mathematics of Universidade Estadual de Campinas UNICAMP

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