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Combining Mechanisms of Growth Arrest in Solid Tumours: A Mathematical Investigation
- Source :
- Bulletin of mathematical biology. 84(8)
- Publication Year :
- 2022
-
Abstract
- The processes underpinning solid tumour growth involve the interactions between various healthy and tumour tissue components and the vasculature, and can be affected in different ways by cancer treatment. In particular, the growth-limiting mechanisms at play may influence tumour responses to treatment. In this paper, we propose a simple ordinary differential equation model of solid tumour growth to investigate how tumour-specific mechanisms of growth arrest may affect tumour response to different combination cancer therapies. We consider the interactions of tumour cells with the physical space in which they proliferate and a nutrient supplied by the tumour vasculature, with the aim of representing two distinct growth arrest mechanisms. More specifically, we wish to consider growth arrest due to (1) nutrient deficiency, which corresponds to balancing cell proliferation and death rates, and (2) competition for space, which corresponds to cessation of proliferation without cell death. We perform numerical simulations of the model and a steady-state analysis to determine the possible tumour growth scenarios described by the model. We find that there are three distinct growth regimes: the nutrient- and spatially limited regimes and a bi-stable regime, in which both growth arrest mechanisms are simultaneously active. Thus, the proposed model has the features required to investigate and distinguish tumour responses to different cancer treatments.
- Subjects :
- Pharmacology
General Mathematics
General Neuroscience
Immunology
Mathematical Concepts
Models, Biological
General Biochemistry, Genetics and Molecular Biology
Computational Theory and Mathematics
Neoplasms
Humans
Computer Simulation
General Agricultural and Biological Sciences
Mathematics
General Environmental Science
Subjects
Details
- ISSN :
- 15229602
- Volume :
- 84
- Issue :
- 8
- Database :
- OpenAIRE
- Journal :
- Bulletin of mathematical biology
- Accession number :
- edsair.doi.dedup.....47d63d732b933ef7f417bfda450036bc