DOI: 10.5061/dryad.prr4xgxvd
title: A mathematical model for pancreatic cancer during intraepithelial neoplasia

description: Cancer is the result of complex interactions of intrinsic and extrinsic
 cell processes, which promote sustained proliferation, resistance to
 apoptosis, reprogramming, and reorganization. The evolution of any type of
 cancer emerges from the role of the microenvironmental conditions and the
 impact of some molecular complexes on certain signalling pathways. The
 understanding of the early onset of cancer requires a multiscale analysis
 of the cellular microenvironment. In this paper, we analyse a quantitative
 multiscale model of pancreatic adenocarcinoma by modelling the cellular
 microenvironment through elastic cell interactions and their intercellular
 communication mechanisms, such as growth factors and cytokines. We focus
 on the low-grade dysplasia (PanIN 1) and moderate dysplasia (PanIN 2)
 stages of pancreatic adenocarcinoma. To this end, we propose a gene
 regulatory network associated with the processes of proliferation and
 apoptosis of pancreatic cells and its kinetics in terms of delayed
 differential equations to mimic cell development. Likewise, we couple the
 cell cycle with the spatial distribution of cells and the transport of
 growth factors to show that the adenocarcinoma evolution is triggered by
 inflammatory processes. We show that the oncogene RAS may be an important
 target for developing anti-inflammatory strategies that limit the
 emergence of more aggressive adenocarcinomas.
description: We considered a genetic regulatory network in the development of
 pancreatic cancer and modified it to observe only the cellular phenotypes
 that give rise to proliferation and apoptosis in healthy and cancerous
 cells. We proposed a dynamic model with differential equations with delay
 to show that the accumulation of mutations generates regressions in the
 genetic network of healthy cells causing the transition to cells with
 cancer. The delay in the actions of the Ras gene is considered the main
 trigger of neoplasia and inflammation in tissues. We built a spatial
 model, with polynomial cells, to show the correlation between
 inflammation, the regulatory network and the proliferation and apoptosis
 rates of cells in the tissue.
description: # A mathematical model for pancreatic cancer during intraepithelial
 neoplasia
  [https://zenodo.org/doi/10.5281/zenodo.13787992](https://zenodo.org/doi/10.5281/zenodo.13787992) The data files contain the numerical simulation programs used to model the delay equations of the genetic regulatory network, the interaction of cytokinins in a Lotka-Volterra model, and the evolution of cellular phenotypes in a two-dimensional array of voronoi-type cells. ## Description of the data All programs can run independently using GitHub's open in Colab. They can also be executed using classic Python tools. The programs can run independently using Jupyter Notebooks with classic Python tools. Also they can be executed using our GitHub's repository ([https://github.com/joshbrx/biomath_model.git](https://github.com/joshbrx/biomath_model.git)) and run them in Jupyter Notebooks with Open Colab application. Here, the data scripts contain the evolution of cells in the reduced genetic network. In the script `full_GRN.ipynb` you will find the code to simulate healthy and cancer cells with the reduced genetic network. The script `Vornoi_cell.ipynb` simulates the evolution of acinar cells with Voronoi diagrams. Also, the script is used it to determine the cell prototypes and inflammatory process during early intraepithelial neoplasia.