Geodesic
Numerical modeling of space-time distribution of a drug agent in biological tissue
Matematičeskoe modelirovanie, Tome 33 (2021) no. 11, pp. 3-17

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A mathematical model of the pharmacokinetics of anticancer drugs is presented. The model uses the biological tissue as a randomly inhomogeneous medium. Model is based on reaction-diffusion equation system, coefficients of which are random functions of space and time. The coefficients of the model are calculated based on the probability of processes occurring in living tissue. Proposed approach is applied for two drugs: for “Cisplatin”, which is used in cancer chemotherapy, and “Boron-phenylalanine”, which was proposed as an agent, increasing the dose during irradiation. The model demonstrates a good agreement with experimental results. The described method of modeling of pharmacokinetics of drugs can serve as universal approach for study of the space-time distributions for many drugs, including those using nanoparticles. The simulation results allow to propose optimization of the existing protocols for chemotherapeutic and radiological treatment.
Keywords: model, kinetics, therapy, oncology, drug, cells. 
@article{MM_2021_33_11_a0,
     author = {A. F. Ginevsky and D. A. Ginevsky and P. V. Izhevsky},
     title = {Numerical modeling of space-time distribution of a drug agent in biological tissue},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--17},
     publisher = {mathdoc},
     volume = {33},
     number = {11},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2021_33_11_a0/}
}
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A. F. Ginevsky; D. A. Ginevsky; P. V. Izhevsky. Numerical modeling of space-time distribution of a drug agent in biological tissue. Matematičeskoe modelirovanie, Tome 33 (2021) no. 11, pp. 3-17. http://geodesic.mathdoc.fr/item/MM_2021_33_11_a0/