Analytical Solution of Solid Cancer Growth model with Angiogenesis using Differential Transform Method

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K. D. Patel , H. S. Patel, D. C. Joshi

Abstract

The mathematical model to describe the solid cancer growth dynamics producing angiogenesis in the absence of cancer controlling mechanism is analysed. Differential Transform Method is applied for analytical solution of the model. The influence of initial conditions supplied to the system and the interacting parameters involved, on dynamical trajectories of tumour growth is observed graphically. At the same time, our results are also compared with Numerical simulation to prove the efficacy of the proposed approach. Result obtained by differential transform method (DTM) shows good agreement with Numerical result.

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References

Chaplain, M. A. J. (2000). Mathematical Modelling of Angiogenesis. Journal of Neuro-Oncology, 50, 37–51.

Chaplain, M. A. J., McDougall, S. R., & Anderson, A. R. A. (2006). Mathematical modeling of tumor-induced angiogenesis. Annual Review of Biomedical Engineering, 8, 233–257.

Hassan, I. H. A.-H. (2008). Application to differential transformation method for solving systems of differential equations. Applied Mathematical Modelling, 32(12), 2552–2559.

Hogea, C. S., Murray, B. T., & Sethian, J. A. (2006). Simulating complex tumor dynamics from avascular to vascular growth using a general level-set method. Journal of Mathematical Biology, 53(1), 86–134.

Patel, Y. F. (2017). Application of differential transform method to compartment modelling. SVNIT Surat, Gujarat, INDIA.

SP, G., Ananthaswamy, V., & Rajendran, L. (2014). Mathematical modeling and analysis of solid cancer growth with angiogenesis. Canadian Open Mathematical Modeling and Applied Computing Journal, 1(1), 1–19.

Yang, H. M. (2012). Mathematical modeling of solid cancer growth with angiogenesis. Theoretical Biology & Medical Modelling, 9(2), 1–39.

Zhou, J. K. (1986). Differential transformation and its applications for electrical circuits.