The local environment plays an important role in tumor progression. Not only can it hinder tumor development, but it can also promote it, as demonstrated by numerous studies over the past decades [1-3]. Tumor cells can interact with, modify, and utilize their local environment to enhance their ability to grow and invade. Angiogenesis, vasculogenesis, extracellular matrix components, other healthy cells, and even chronic inflammation are all examples of potential resources that tumors can exploit [4,5]. Several cancer therapies now aim to target the tumor's local environment in order to reduce its ability to take advantage of its surrounding [6,7].

The interactions between a tumor and its local environment involve many complex mechanisms, making the resulting dynamics difficult to capture and comprehend. Therefore, mathematical modeling serves as an efficient tool to analyze, identify, and quantify the roles of these mechanisms.

 

It has been recognized that healthy yet senescent cells can play a major role in cancer development [8]. The work of Almeida et al. aims to improve our understanding of the role these cells play in early cancer invasion [9]. They focus on carcinoma, an epithelial tumor. During the invasion process, tumor cells must escape their original compartment to reach the surrounding connective tissue. To do so, they must break through the basement membrane enclosing their compartment by digesting it using enzymatic proteins. These proteins are produced in an inactive form by senescent cells and activated by tumor cells. To analyze this process, the authors employ mathematical and numerical modeling, which allows them to fully control the system's complexity by carefully adjusting modeling hypotheses. This approach enables them to easily explore different invasion scenarios and compare their progression rates.

The authors propose an original model that provides a detailed temporal and spatial description of the biochemical reactions involved in basement membrane digestion. The model accounts for protein reactions and exchanges between the connective tissue and basement membrane. Their approach significantly enhances the accuracy of the biochemical description of basement membrane digestion. Additionally, through dimensionality reduction, they manage to represent the basement membrane as an infinitely thin layer while still maintaining an accurate biochemical and biophysical description of the system.

A clever modeling strategy is then employed. The authors first introduce a comprehensive model, which, due to its complexity, has low tractability. By analyzing the relative influence of various parameters, they derive a reduced model, which they validate using relevant data from the literature—a remarkable achievement in itself. Their results show that the reduced model accurately represents the system’s dynamics while being more manageable. However, the reduced model exhibits greater sensitivity to certain parameters, which the authors carefully analyze to establish safeguards for potential users.

The codes developed by the authors to analyze the models are open-source [10].

 

Almeida et al. explore several biological scenarios, and their results qualitatively align with existing literature. In addition to their impressive, consistent, and tractable modeling framework, Almeida et al.’s work provides a compelling explanation of why and how the presence of senescent cells in the stroma can accelerate basement membrane digestion and, consequently, tumor invasion. Moreover, the authors identify the key parameters—and thus, the essential tumor characteristics—that are central to basement membrane digestion.

This study represents a major step forward in understanding the role of senescent cells in carcinoma invasion and provides a powerful tool with significant potential. More generally, this work demonstrates that mathematical models are highly suited for studying the role of the stroma in cancer progression.

 

 

[1] J. Wu, Sheng ,Su-rui, Liang ,Xin-hua, et Y. and Tang, « The role of tumor microenvironment in collective tumor cell invasion », Future Oncology, vol. 13, no 11, p. 991‑1002, 2017, https://doi.org/10.2217/fon-2016-0501

[2] F. Entschladen, D. Palm, Theodore L. Drell IV, K. Lang, et K. S. Zaenker, « Connecting A Tumor to the Environment », Current Pharmaceutical Design, vol. 13, no 33, p. 3440‑3444, 2007, https://doi.org/10.2174/138161207782360573

[3] H. Li, X. Fan, et J. Houghton, « Tumor microenvironment: The role of the tumor stroma in cancer », Journal of Cellular Biochemistry, vol. 101, no 4, p. 805‑815, 2007, https://doi.org/10.1002/jcb.21159

[4] J. M. Brown, « Vasculogenesis: a crucial player in the resistance of solid tumours to radiotherapy », Br J Radiol, vol. 87, no 1035, p. 20130686, 2014, https://doi.org/10.1259/bjr.20130686

[5] P. Allavena, A. Sica, G. Solinas, C. Porta, et A. Mantovani, « The inflammatory micro-environment in tumor progression: The role of tumor-associated macrophages », Critical Reviews in Oncology/Hematology, vol. 66, no 1, p. 1‑9, 2008, https://doi.org/10.1016/j.critrevonc.2007.07.004

[6] L. Xu et al., « Reshaping the systemic tumor immune environment (STIE) and tumor immune microenvironment (TIME) to enhance immunotherapy efficacy in solid tumors », J Hematol Oncol, vol. 15, no 1, p. 87, 2022, https://doi.org/10.1186/s13045-022-01307-2

[7] N. E. Sounni et A. Noel, « Targeting the Tumor Microenvironment for Cancer Therapy », Clinical Chemistry, vol. 59, no 1, p. 85‑93, 2013, https://doi.org/10.1373/clinchem.2012.185363

[8] D. Hanahan, « Hallmarks of Cancer: New Dimensions », Cancer Discovery, vol. 12, no 1, p. 31‑46, 2022, https://doi.org/10.1158/2159-8290.CD-21-1059

[9] L. Almeida, A. Poulain, A. Pourtier, et C. Villa, « Mathematical modelling of the contribution of senescent fibroblasts to basement membrane digestion during carcinoma invasion », HAL, ver.3 peer-reviewed and recommended by PCI Mathematical and Computational Biology, 2025. https://hal.science/hal-04574340v3

[10] A. Poulain, alexandrepoulain/TumInvasion-BM: BM rupture code, 2024. Zenodo. https://doi.org/10.5281/zenodo.12654067 / https://github.com/alexandrepoulain/TumInvasion-BM