Mathematical modelling of the impact of chemotherapy on the state of a cancerous tumor based on fractional calculus
| dc.citation.epage | 182 | |
| dc.citation.issue | 2 | |
| dc.citation.journalTitle | Комп’ютерні системи проектування. Теорія і практика | |
| dc.citation.spage | 172 | |
| dc.citation.volume | 6 | |
| dc.contributor.affiliation | Національний університет “Львівська політехніка” | |
| dc.contributor.affiliation | Національний університет “Львівська політехніка” | |
| dc.contributor.affiliation | Національний лісотехнічний університет України | |
| dc.contributor.affiliation | Lviv Polytechnic National University | |
| dc.contributor.affiliation | Lviv Polytechnic National University | |
| dc.contributor.affiliation | Ukrainian National Forestry University | |
| dc.contributor.author | Вільчинська, Олеся-Оксана | |
| dc.contributor.author | Соколовський, Ярослав | |
| dc.contributor.author | Мокрицький, Андрій | |
| dc.contributor.author | Vilchynska, Olesia-Oksana | |
| dc.contributor.author | Sokolovskyi, Yaroslav | |
| dc.contributor.author | Mokrytskyi, Andrii | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-12-15T08:11:12Z | |
| dc.date.created | 2024-08-10 | |
| dc.date.issued | 2024-08-10 | |
| dc.description.abstract | У статті побудовано різницеві апроксимації фрактальних операторів математичної моделі впливу хіміотерапії на стан ракової пухлини на підставі апарату дробового диференціювання з використанням похідної Капуто. Подано математичну модель стовбурових клітин і хіміотерапії. Побудовано числові алгоритми для реалізації математичних моделей дробового порядку з викорис- танням методу Атангана – Туфіка. Описано UML-діаграму програмного застосунку та наведено його розроблення. Проаналізовано вплив фрактальних характеристик (довготривалої пам’яті) хіміотерапії на стан ракової пухлини. Наявність дробового порядку похідної за часом як параметра розв’язків дає важливу інформацію про прогнозування впливу хіміотерапії на стан ракової пухлини. | |
| dc.description.abstract | The article is dedicated to constructing difference approximations of fractal operators in a mathematical model of the impact of chemotherapy on the state of a cancerous tumor, based on fractional calculus using the Caputo derivative. A mathematical model of stem cells and chemotherapy is presented. Numerical algorithms for implementing fractional-order mathematical models have been developed using the Atangana-Toufik method. The UML diagram of the software application and its development process are described. The impact of fractal characteristics (longterm memory) of chemotherapy on the state of a cancerous tumor is analysed. The presence of a fractional-order time derivative as a parameter of the solutions provides important information for predicting the effects of chemotherapy on the tumor’s state | |
| dc.format.extent | 172-182 | |
| dc.format.pages | 11 | |
| dc.identifier.citation | Vilchynska O. Mathematical modelling of the impact of chemotherapy on the state of a cancerous tumor based on fractional calculus / Olesia-Oksana Vilchynska, Yaroslav Sokolovskyi, Andrii Mokrytskyi // Computer Systems of Design. Theory and Practice. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 6. — No 2. — P. 172–182. | |
| dc.identifier.citation2015 | Vilchynska O., Mokrytskyi A. Mathematical modelling of the impact of chemotherapy on the state of a cancerous tumor based on fractional calculus // Computer Systems of Design. Theory and Practice, Lviv. 2024. Vol 6. No 2. P. 172–182. | |
| dc.identifier.citationenAPA | Vilchynska, O., Sokolovskyi, Y., & Mokrytskyi, A. (2024). Mathematical modelling of the impact of chemotherapy on the state of a cancerous tumor based on fractional calculus. Computer Systems of Design. Theory and Practice, 6(2), 172-182. Lviv Politechnic Publishing House.. | |
| dc.identifier.citationenCHICAGO | Vilchynska O., Sokolovskyi Y., Mokrytskyi A. (2024) Mathematical modelling of the impact of chemotherapy on the state of a cancerous tumor based on fractional calculus. Computer Systems of Design. Theory and Practice (Lviv), vol. 6, no 2, pp. 172-182. | |
| dc.identifier.doi | https://doi.org/10.23939/cds2024.02.172 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/124051 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Комп’ютерні системи проектування. Теорія і практика, 2 (6), 2024 | |
| dc.relation.ispartof | Computer Systems of Design. Theory and Practice, 2 (6), 2024 | |
| dc.relation.references | [1] Medina, M. A. Mathematical modeling of cancer metabolism. Crit. Rev. Oncol./Hematol. 2018, 124, 37–40. https://doi.org/10.1016/j.critrevonc.2018.02.004 | |
| dc.relation.references | [2] Bellomo, N.; Bellouquid, A.; Delitala, M. Mathematical topics on the modeling of multicellular systems in competition between tumor and immune cells. Math. Models Methods Appl. Sci., 2004, 14, 1683–1733.https://doi.org/10.1142/S0218202504003799 | |
| dc.relation.references | [3] Sierociuk, Dominik, et al. “Modelling heat transfer in heterogeneous media using fractional calculus”. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371.1990(2013): 20120146. https://doi.org/10.1098/rsta.2012.0146 | |
| dc.relation.references | [4] Iomin, Alexander. “Superdiffusion of cancer on a comb structure”. Journal of Physics: conference series. Vol. 7. No. 1. IOP Publishing, 2005. https://doi.org/10.1088/1742-6596/7/1/005 | |
| dc.relation.references | [5] Alinei-Poiana, T., Dulf, Eh. and Кovacs L. Дробове числення в математичній онкології. Sci. Rep., 13,10083 (2023). https://doi.org/10.1038/s41598-023-37196-9 | |
| dc.relation.references | [6] Erturk, V. S.; Zaman, G.; Momani, S. A numeric analytic method for approximating a giving up smoking model containing fractional derivatives. Comput.Math. Appl. 2012, 64, 3068–3074. https://doi.org/10.1016/j.camwa.2012.02.002 | |
| dc.relation.references | [7] Manar A. Alqudah Cancer treatment by stem cells and chemotherapy as a mathematical model with numerical simulations. Alexandria Engineering Journal, Vol. 59, Issue 4, August 2020, 1953–1957.https://doi.org/10.1016/j.aej.2019.12.025 | |
| dc.relation.references | [8] Sweilam, N. H., Al-Mekhlafi, S. M., Assiri, T. et al. Optimal control for cancer treatment mathematical model using Atangana – Baleanu – Caputo fractional derivative. Adv. Differ. Equ., 2020, 334 (2020).https://doi.org/10.1186/s13662-020-02793-9 | |
| dc.relation.references | [9] Abdon Atangana and Dumitru Baleanu. “New fractional derivatives with non-local and non-singular kernel. Theory and Application to Heat Transfer Model”. Year 2016, Vol. 20, No. 2, 763–769.https://doi.org/10.2298/TSCI160111018A | |
| dc.relation.references | [10]G .F. Webb, A nonlinear cell population model of periodic chemotherapy treatment. Vol. I of Recent Trends in Ordinary Differential Equations. Series in Applicable Analysis. World Scientic (1992) 569–583.https://doi.org/10.2298/TSCI160111018A | |
| dc.relation.references | [11] J. C. Panetta and J. Adam, A mathematical model of cycle-specic chemotherapy. Math. Comput. Model,22 (1995), 67–82. https://doi.org/10.1016/0895-7177(95)00112-F | |
| dc.relation.references | [12]Z. Liu and C. Yang, A mathematical model of cancer treatment by radiotherapy. Comput. Math. Methods Med., 2014 (2014), 172–192. https://doi.org/10.1155/2014/172923 | |
| dc.relation.references | [13] J. C. Panetta, A mathematical model of breast and ovarian cancer treated with Paclitaxel. Math. Biosci., 146 (1997), 89–113. https://doi.org/10.1016/S0025-5564(97)00077-1 | |
| dc.relation.references | [14]P. Unni and P. Seshaiyer, Mathematical modeling, analysis, and simulation of tumor dynamics with drug interventions. Comput. Math. Methods Med., 2019 (2019), 407–429. https://doi.org/10.1155/2019/4079298 | |
| dc.relation.references | [15]H. N. Weerasinghe, P. M. Burrage, K. Burrage and D. V. Nicolau Jr., Mathematical models of cancer cell plasticity. J. Oncol., 2019 (2019), 240–253. https://doi.org/10.1155/2019/2403483 | |
| dc.relation.references | [16]E. Ucar, N.Ozdemir and E. Altun, Fractional order model of immune cells inuenced by cancer cells. MMNP, 14 (2019), 308–321. https://doi.org/10.1051/mmnp/2019002 | |
| dc.relation.references | [17]D. Dingli, M. D. Cascino, K. Josic, S. J. Russell and Z. Bajzer, Mathematical modeling of cancer radiovirotherapy. Math Biosci., 199 (2006), 55–78. https://doi.org/10.1016/j.mbs.2005.11.001 | |
| dc.relation.references | [18]A. Yin, D. J. A. R. Moes, J. G. C. van Hasselt, J. J. Swen and H. J. Guchelaar, A review of mathematical models for tumor dynamics and treatment resistance evolution of solid tumors. CPT Pharmacometrics Syst. Pharmacol., 8 (2019), 720–737. https://doi.org/10.1002/psp4.12450 | |
| dc.relation.references | [19]S. Wang and H. Schattler, Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Math. BioSciences, 13 (2016), 1223–1240. https://doi.org/10.3934/mbe.2016040 | |
| dc.relation.references | [20]O. G. Isaeva and V. A. Osipov, Different strategies for cancer treatment: mathematical modeling. Comput. Math. Methods Med., 10 (2009), 453–472. https://doi.org/10.1080/17486700802536054 | |
| dc.relation.referencesen | [1] Medina, M. A. Mathematical modeling of cancer metabolism. Crit. Rev. Oncol./Hematol. 2018, 124, 37–40. https://doi.org/10.1016/j.critrevonc.2018.02.004 | |
| dc.relation.referencesen | [2] Bellomo, N.; Bellouquid, A.; Delitala, M. Mathematical topics on the modeling of multicellular systems in competition between tumor and immune cells. Math. Models Methods Appl. Sci., 2004, 14, 1683–1733.https://doi.org/10.1142/S0218202504003799 | |
| dc.relation.referencesen | [3] Sierociuk, Dominik, et al. "Modelling heat transfer in heterogeneous media using fractional calculus". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371.1990(2013): 20120146. https://doi.org/10.1098/rsta.2012.0146 | |
| dc.relation.referencesen | [4] Iomin, Alexander. "Superdiffusion of cancer on a comb structure". Journal of Physics: conference series. Vol. 7. No. 1. IOP Publishing, 2005. https://doi.org/10.1088/1742-6596/7/1/005 | |
| dc.relation.referencesen | [5] Alinei-Poiana, T., Dulf, Eh. and Kovacs L. Drobove chyslennia v matematychnii onkolohii. Sci. Rep., 13,10083 (2023). https://doi.org/10.1038/s41598-023-37196-9 | |
| dc.relation.referencesen | [6] Erturk, V. S.; Zaman, G.; Momani, S. A numeric analytic method for approximating a giving up smoking model containing fractional derivatives. Comput.Math. Appl. 2012, 64, 3068–3074. https://doi.org/10.1016/j.camwa.2012.02.002 | |
| dc.relation.referencesen | [7] Manar A. Alqudah Cancer treatment by stem cells and chemotherapy as a mathematical model with numerical simulations. Alexandria Engineering Journal, Vol. 59, Issue 4, August 2020, 1953–1957.https://doi.org/10.1016/j.aej.2019.12.025 | |
| dc.relation.referencesen | [8] Sweilam, N. H., Al-Mekhlafi, S. M., Assiri, T. et al. Optimal control for cancer treatment mathematical model using Atangana – Baleanu – Caputo fractional derivative. Adv. Differ. Equ., 2020, 334 (2020).https://doi.org/10.1186/s13662-020-02793-9 | |
| dc.relation.referencesen | [9] Abdon Atangana and Dumitru Baleanu. "New fractional derivatives with non-local and non-singular kernel. Theory and Application to Heat Transfer Model". Year 2016, Vol. 20, No. 2, 763–769.https://doi.org/10.2298/TSCI160111018A | |
| dc.relation.referencesen | [10]G .F. Webb, A nonlinear cell population model of periodic chemotherapy treatment. Vol. I of Recent Trends in Ordinary Differential Equations. Series in Applicable Analysis. World Scientic (1992) 569–583.https://doi.org/10.2298/TSCI160111018A | |
| dc.relation.referencesen | [11] J. C. Panetta and J. Adam, A mathematical model of cycle-specic chemotherapy. Math. Comput. Model,22 (1995), 67–82. https://doi.org/10.1016/0895-7177(95)00112-F | |
| dc.relation.referencesen | [12]Z. Liu and C. Yang, A mathematical model of cancer treatment by radiotherapy. Comput. Math. Methods Med., 2014 (2014), 172–192. https://doi.org/10.1155/2014/172923 | |
| dc.relation.referencesen | [13] J. C. Panetta, A mathematical model of breast and ovarian cancer treated with Paclitaxel. Math. Biosci., 146 (1997), 89–113. https://doi.org/10.1016/S0025-5564(97)00077-1 | |
| dc.relation.referencesen | [14]P. Unni and P. Seshaiyer, Mathematical modeling, analysis, and simulation of tumor dynamics with drug interventions. Comput. Math. Methods Med., 2019 (2019), 407–429. https://doi.org/10.1155/2019/4079298 | |
| dc.relation.referencesen | [15]H. N. Weerasinghe, P. M. Burrage, K. Burrage and D. V. Nicolau Jr., Mathematical models of cancer cell plasticity. J. Oncol., 2019 (2019), 240–253. https://doi.org/10.1155/2019/2403483 | |
| dc.relation.referencesen | [16]E. Ucar, N.Ozdemir and E. Altun, Fractional order model of immune cells inuenced by cancer cells. MMNP, 14 (2019), 308–321. https://doi.org/10.1051/mmnp/2019002 | |
| dc.relation.referencesen | [17]D. Dingli, M. D. Cascino, K. Josic, S. J. Russell and Z. Bajzer, Mathematical modeling of cancer radiovirotherapy. Math Biosci., 199 (2006), 55–78. https://doi.org/10.1016/j.mbs.2005.11.001 | |
| dc.relation.referencesen | [18]A. Yin, D. J. A. R. Moes, J. G. C. van Hasselt, J. J. Swen and H. J. Guchelaar, A review of mathematical models for tumor dynamics and treatment resistance evolution of solid tumors. CPT Pharmacometrics Syst. Pharmacol., 8 (2019), 720–737. https://doi.org/10.1002/psp4.12450 | |
| dc.relation.referencesen | [19]S. Wang and H. Schattler, Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Math. BioSciences, 13 (2016), 1223–1240. https://doi.org/10.3934/mbe.2016040 | |
| dc.relation.referencesen | [20]O. G. Isaeva and V. A. Osipov, Different strategies for cancer treatment: mathematical modeling. Comput. Math. Methods Med., 10 (2009), 453–472. https://doi.org/10.1080/17486700802536054 | |
| dc.relation.uri | https://doi.org/10.1016/j.critrevonc.2018.02.004 | |
| dc.relation.uri | https://doi.org/10.1142/S0218202504003799 | |
| dc.relation.uri | https://doi.org/10.1098/rsta.2012.0146 | |
| dc.relation.uri | https://doi.org/10.1088/1742-6596/7/1/005 | |
| dc.relation.uri | https://doi.org/10.1038/s41598-023-37196-9 | |
| dc.relation.uri | https://doi.org/10.1016/j.camwa.2012.02.002 | |
| dc.relation.uri | https://doi.org/10.1016/j.aej.2019.12.025 | |
| dc.relation.uri | https://doi.org/10.1186/s13662-020-02793-9 | |
| dc.relation.uri | https://doi.org/10.2298/TSCI160111018A | |
| dc.relation.uri | https://doi.org/10.1016/0895-7177(95)00112-F | |
| dc.relation.uri | https://doi.org/10.1155/2014/172923 | |
| dc.relation.uri | https://doi.org/10.1016/S0025-5564(97)00077-1 | |
| dc.relation.uri | https://doi.org/10.1155/2019/4079298 | |
| dc.relation.uri | https://doi.org/10.1155/2019/2403483 | |
| dc.relation.uri | https://doi.org/10.1051/mmnp/2019002 | |
| dc.relation.uri | https://doi.org/10.1016/j.mbs.2005.11.001 | |
| dc.relation.uri | https://doi.org/10.1002/psp4.12450 | |
| dc.relation.uri | https://doi.org/10.3934/mbe.2016040 | |
| dc.relation.uri | https://doi.org/10.1080/17486700802536054 | |
| dc.rights.holder | © Національний університет „Львівська політехніка“, 2024 | |
| dc.rights.holder | © Vilchynska O.-O., Sokolovskyi Ya., Mokrytskyi A., 2024 | |
| dc.subject | модель дробового порядку | |
| dc.subject | дробові оператори | |
| dc.subject | метод Атангана – Туфіка | |
| dc.subject | ракова пухлина | |
| dc.subject | Python | |
| dc.subject | мова R | |
| dc.subject | fractional order model | |
| dc.subject | fractional operators | |
| dc.subject | atangana–toufik method | |
| dc.subject | cancer tumor python | |
| dc.subject | R language | |
| dc.title | Mathematical modelling of the impact of chemotherapy on the state of a cancerous tumor based on fractional calculus | |
| dc.title.alternative | Математичне моделювання впливу хіміотерапії на стан ракової пухлини на підставі апарату дробового диференціювання | |
| dc.type | Article |