Analytical Derivation of Hypothetical Tumor Internal Pressure Using Physically Based Formalism |
| A. Ghanbaria, R. Khordada, M. Ghaderi-Zefreheib
aDepartment of Physics, Yasouj University, Yasouj 75918, Iran bDepartment of Animal Genetics, Yasouj University, Yasouj 75918, Iran |
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| Addressing the open, complex, dynamic and adaptive nature of cancer biology, mathematical formalism that works well at a tumor level is required. Our main goal in this study is to propose such simple mathematical formalism. We try to simplify the model as much as possible, however to such extent as not to leave out the crucial features of the molecular biology or cell physiology. Depending on the variation of the analyzed real data, the tumor physically based formalism allows for insights at the molecular level and for making robust reliable predictions about how a tumor responds to a variety of natural situations and interventions. In this study, by adopting a hypothetical cylindrical tumor shape surrounded in a hypothetical cylindrical-like peripheral tissue, a set of physically based ordinary differential equations (ODEs) was developed to assess the internal pressure of the tumor in the course of a two-dimensional external pressure. The calculation was analytically performed and applied on real data. It turned out that under constant external pressure exerted on a tumor wall, the internal fluid tumor pressure decreased over time. This study, although purely mathematical and abstract in nature, may help further studies on environmental pressures which aim at either deterring or alleviating tumor growth. Researchers should intensify efforts aimed at finding a tissue-specific physically based mathematical model to discover the underlying processes governing cancer formation and development. |
DOI:10.12693/APhysPolA.138.863 topics: tumor, hypothetical, internal pressure, ODEs |