Development of Fractional Mathematical Model Analysis for the Effects of Medicine Supplies to a solid Tumor Cells Density According to Recovery of Three Organs

Mohammed Abdulhameed, M. S. Adamu, Salisu Lukunti, Abdulsalam Yau Gital

Abstract


This study presents a generalized mathematical model to simulate the dynamic supply of medicine to a solid tumor based on the density of tumor cells and the recovery trajectories of three critical organs: the kidney, liver, and heart. The aim is to optimize drug dosage schedules that will balance tumor reduction with minimizing toxicity to healthy tissue. The generalized model that integrates pharmacokinetics and pharmacodynamics with tumor growth and organ recovery functions was solved analytically using the integral transformation method. By simulating varying levels of drug delivery and tracking the response of each organ, this solution allows for predicting optimal dosing regimens that can achieve effective tumor control without compromising organ function. The validation is carried out with a classical computational model, providing a basis for potential application in personalized cancer treatment strategies. The results show that the distribution of controlled medicine can significantly impact both tumor reduction and organ recovery. This model has a highly significant impact on clinical decision-making processes.


Full Text:

PDF

References


Dewhirst, M. W., & Secomb, T. W. (2017). Transport of drugs from blood vessels to tumour tissue. Nature Reviews Cancer, 17(12), 738-750.

Mattheolabakis, G., & Mikelis, C. M. (2019). Nanoparticle delivery and tumor vascular normalization: the chicken or the egg?. Frontiers in oncology, 9, 1227.

Teleanu, R. I., Chircov, C., Grumezescu, A. M., & Teleanu, D. M. (2019). Tumor angiogenesis and anti-angiogenic strategies for cancer treatment. Journal of clinical medicine, 9(1), 84.

Jain, R. K., & Baxter, L. T. (1988). Mechanisms of heterogeneous distribution of monoclonal antibodies and other macromolecules in tumors: significance of elevated interstitial pressure. Cancer research, 48(24_Part_1), 7022-7032.

Baxter, L. T., & Jain, R. K. (1989). Transport of fluid and macromolecules in tumors. I. Role of interstitial pressure and convection. Microvascular research, 37(1), 77-104.

Baxter, L. T., & Jain, R. K. (1990). Transport of fluid and macromolecules in tumors. II. Role of heterogeneous perfusion and lymphatics. Microvascular research, 40(2), 246-263.

Baxter, L. T., & Jain, R. K. (1991). Transport of fluid and macromolecules in tumors: III. Role of binding and metabolism. Microvascular research, 41(1), 5-23.

Soltani, M., & Chen, P. (2012). Effect of tumor shape and size on drug delivery to solid tumors. Journal of biological engineering, 6, 1-15.

Soltani, M., & Chen, P. (2013). Numerical modeling of interstitial fluid flow coupled with blood flow through a remodeled solid tumor microvascular network. PloS one, 8(6), e67025.

Vazifehshenas, F. H., & Bahadori, F. (2019). Investigation of Soret effect on drug delivery in a tumor without necrotic core. Journal of the Taiwan Institute of Chemical Engineers, 102, 17-24.

Hadjicharalambous, M., Wijeratne, P. A., & Vavourakis, V. (2021). From tumour perfusion to drug delivery and clinical translation of in silico cancer models. Methods, 185, 82-93.

Sedaghatkish, A., Rezaeian, M., Heydari, H., Ranjbar, A. M., & Soltani, M. (2020). Acoustic streaming and thermosensitive liposomes for drug delivery into hepatocellular carcinoma tumor adjacent to major hepatic veins; an acoustics–thermal–fluid-mass transport coupling model. International Journal of Thermal Sciences, 158, 106540.

Kashkooli, F. M., Rezaeian, M., & Soltani, M. (2022). Drug delivery through nanoparticles in solid tumors: A mechanistic understanding. Nanomedicine, 17(10), 695-716.

Rezaeian, M., Soltani, M., Naseri Karimvand, A., & Raahemifar, K. (2022). Mathematical modeling of targeted drug delivery using magnetic nanoparticles during intraperitoneal chemotherapy. Pharmaceutics, 14(2), 324.

Go, J. (2021). Mathematical analysis for the effects of medicine supplies to a solid Tumor. Symmetry, 13(11), 1988. [Ionescu, C. M., & Ghita, M. (2022). Model-Based Regional Control with Anomalous Diffusion of Multi-Drug Combined Cancer Therapy for Volume Predictions. Symmetry, 15(1), 51]

Omame, A., & Zaman, F. D. (2023). Analytic solution of a fractional order mathematical model for tumour with polyclonality and cell mutation. Partial Differential Equations in Applied Mathematics, 8, 100545.

Baleanu, D., Jajarmi, A., Mohammadi, H., & Rezapour, S. (2020). A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative. Chaos, Solitons & Fractals, 134, 109705.

Sweilam, N. H., Al-Mekhlafi, S. M., Assiri, T., & Atangana, A. (2020). Optimal control for cancer treatment mathematical model using Atangana–Baleanu–Caputo fractional derivative. Advances in Difference Equations, 2020(1), 1-21.

Mishra, M. N., & Aljohani, A. F. (2022). Mathematical modelling of growth of tumour cells with chemotherapeutic cells by using Yang–Abdel–Cattani fractional derivative operator. Journal of Taibah University for Science, 16(1), 1133-1141.

Valko, P., Abate, J. (2004) Comparison of sequence accelerators for the Gaver method of numerical Laplace transform inversion. Computers & Mathematics with Applications, 48(34), 629-636.

Vieru, D., Fetecau, C., Ahmed, N., Shah, N. A., (2021). A generalized kinetic model of the advection-dispersion process in a sorbing medium, Math. Model. Nat. Phenom., 16, Article 39, 1-28.

Tarasov, V. E. (2013). Review of some promising fractional physical models. Int. J. of Modern Phys. B, 27 (9) 1330005, 1-32.

Hristov, J. (2023). Non-local kinetics: Revisiting and updates emphasizing fractional calculus applications. Symmetry, 15, 632, 1-46.

Kuznetsov, A. (2013). On the convergence of the Gaver-Stehfest algorithm. SIAM J. Numer. Anal. 51 (6), 2984-2998.


Refbacks

  • There are currently no refbacks.