Modeling, Stability and Numerical Simulation of Doxorubicin Transport and Uptake in Tumors.
DOI:
https://doi.org/10.5540/03.2023.010.01.0072Keywords:
Difusion-Convection, Interstitium, StabilityAbstract
This work analyzes the transport and effect of the chemotherapy drug doxorubicin in tumors. Specifically, we model the diffusion-convection process of doxorubicin delivered by bolus injection across the tumor and interstitium by a system of partial differential equations. We present a stability analysis of the system solution and implement a finite difference method to approximate it.
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References
L. T. Baxter and R. K. Jain. “Transport of fluid and macromolecules in tumors. I. Role of interstitial pressure and convection”. In: Microvascular Research 1 (1989), pp. 77–104. doi: 10.1016/0026-2862(89)90074-5.
J. S. Borges et al. “Drug release from viscoelastic polymeric matrices-a stable and supraconvergent FDM”. In: Computers & Mathematics with Applications (2021), pp. 257–269. doi: 10.1016/j.camwa.2021.08.007.
G. C. M Campos, J.A. Ferreira, and G. Romanazzi. “Density-pressure IBVP: Numerical analysis, simulation and cell dynamics in a colonic crypt”. In: Applied Mathematics and Computation 424.127037 (2022).
S. Eikenberry. “A tumor cord model for doxorubicin delivery and dose optimization in solid tumors”. In: Theoretical Biology and Medical Modelling 1 (2009), pp. 1–20. doi: 10.1186/1742-4682-6-16.
The MathWorks Inc. MATLAB version: 9.13.0 (R2022b). Natick, Massachusetts, United States, 2022. url: https://www.mathworks.com.
A. W. El-Kareh and T. W. Secomb. “A mathematical model for comparison of bolus injection, continuous infusion, and liposomal delivery of doxorubicin to tumor cells”. In: Neoplasia 4 (2000), pp. 325–338. doi: 10.1038/sj.neo.7900096.
W. Zhan, W. Gedroyc, and X. Yun Xu. “Mathematical modelling of drug transport and uptake in a realistic model of solid tumour”. In: Protein and Peptide Letters 11 (2014), pp. 1146–1156. doi: 10.2174/0929866521666140807115629.