biophBiomedical PhotonicsBiomedical Photonics2413-9432Non-profit partnership for development of domestic photodynamic therapy and photodiagnosis10.24931/2413-9432-2022-11-2-4-11bioph-538Research ArticleОРИГИНАЛЬНЫЕ СТАТЬИORIGINAL ARTICLESМодель выживаемости опухолевых клеток после фотодинамической терапииCancer cell survival model after photodynamic therapyKarami-GadalloL.Karami-GadalloL.

Тегеран

Tehran

PouladianM.PouladianM.

Тегеран

Tehran

Исламский Университет АзадИранIslamic Azad UniversityIslamic Republic of Iran202226072022112411Copyright © Karami-Gadallo L., Pouladian M., 20222022Karami-Gadallo L., Pouladian M.Karami-Gadallo L., Pouladian M.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.pdt-journal.com/jour/article/view/538

При проведении фотодинамической терапии (ФДТ) индекс выживаемости (жизнеспособность) клеток в зависимости от концентрации 1O2 или плотности мощности облучения на графике представляет собой кривую. В этой статье была предложена математическая модель с возможностью построения зеркально-сигмовидной кривой, которая, по мнению авторов, может быть использована для любых экспериментальных данных, касающихся жизнеспособности клеток или вероятности выживания, путем настройки трех параметров. Это было подтверждено демонстрацией совпадения кривой с данными, полученными в эксперименте in vitro для ФДТ с 5-аминолевулиновой кислотой клеток рака легкого.

Была предпринята попытка определить взаимосвязь между параметрами биологической модели и формой участков кривой. При низких дозах наблюдали на кривой участок плато (нечувствительная часть), при средних дозах – участок крутого подъема (высокочувствительная часть) и при высоких дозах – стационарное состояние (низкочувствительная часть). Авторы считают, что предложенная ими модель может быть применена к описанию любых данных, представляющих собой показатель выживаемости клеток, в зависимости от дозы воздействия при любом методе лечения рака (например, при лучевой терапии). Хотя это утверждение оказалось верным для ФДТ, представляется перспективной оценка пригодности предложенной модели для других данных.

Photodynamic therapy (PDT) is known as a routine treatment method in which cell survival index like viability plotted versus 1O2 concentration or light fluence in the form of a curve. In this paper, a mathematical model was proposed with ability of generating a mirrored-sigmoid curve which seems to be fitted to any experimental data relating to cell viability, survival probability or any cellular index representing living conditions through adjusting three parameters. It was validated by showing an excellent curve fitting relatively with data obtained from cancerous lung cells under ALA-PDT process in vitro. 

It was tried to define the relations between model’s parameters and biological/clinical factors with the curve regions of plateau (at low doses; non- sensitive part), steep (high-sensitive part), and steady state (at high doses; low-sensitive part). It seems this model could be excellently fitted to any data presenting the cell-living index versus the killer agent in «any cancer therapy technique (e.g. radiotherapy)». Although this claim showed to be correct for PDT, different relevant data of other researchers should also be used for this model and other usual models too, in order to compare their fitness rates.

кривые выживаемости клетокматематическое моделированиефотодинамическая терапияcell survival curvemathematical modelingphotodynamic therapyReferencesGirotti A. Photodynamic Therapy of Neoplastic Disease // CRC Press; Boca Raton, FL, USA: 1990.Girotti A. Photodynamic Therapy of Neoplastic Disease, CRC Press, Boca Raton, FL, USA: 1990.Filonenko E.V. Clinical implementation and scientific development of photodynamic therapy in Russia in 2010-2020 // Biomedical Photonics. – 2021. – Т. 10, № 4. – С. 4–22. doi: 10.24931/2413-9432- 2021-9-4-4-22Filonenko E.V. Clinical implementation and scientific development of photodynamic therapy in Russia in 2010- 2020, Biomedical Photonics, 2021, vol. 10, no. 4, pp. 4–22. doi: 10.24931/2413–9432–2021–9-4-4-22Sokolov V.V., Filonenko E.V., Telegina L.V., Boulgakova N.N., Smirnov V.V. Combination of fluorescence imaging and local spectrophotometry in fluorescence diagnostics of early cancer of larynx and bronchi // Quantum Electronics. – 2002. – Vol. 32(11). – P. 963–969. doi: 10.1070/QE2002v032n11ABEH002329Sokolov V.V., Filonenko E.V., Telegina L.V. et al. Combination of fluorescence imaging and local spectrophotometry in fluorescence diagnostics of early cancer of larynx and bronchi, Quantum Electronics, 2002, vol. 32, no. 11, рр. 963–969. doi: 10.1070/QE2002v032n11ABEH002329Agostinis P. et al. Photodynamic therapy of cancer: an update // CA Cancer J. Clin. – 2004. Vol. 61 (4) – P. 250–281.Agostinis P. et al. Photodynamic therapy of cancer: an update, CA Cancer J. Clin., 2011, vol. 61 (4), pp. 250–281.Filonenko, E.V., Kaprin, A.D., Raszhivina, A.A., Urlova, A.N., Nechipai, A.M. Fluorescence diagnostics of colon malignant and premalignant lesions using 5-aminolevulinic acid // International Journal of Photoenergy. – 2014. – № 378673 Doi: 10.1155/2014/378673Filonenko E.V., Kaprin A.D., Raszhivina A.A., Urlova A.N., Nechipai A.M. Fluorescence diagnostics of colon malignant and premalignant lesions using 5-aminolevulinic acid, International Journal of Photoenergy, 2014, no. 378673. doi: 10.1155/2014/378673Filonenko E.V., Ivanova-Radkevich V.I. Photodynamic therapy in the treatment of patients with mycosis fungoides // Biomedical Photonics. – 2022. – Т. 11, № 1. – С. 27–36. doi: 10.24931/2413– 9432–2022–11-1-27-36.Filonenko E.V., Ivanova-Radkevich V.I. Photodynamic therapy in the treatment of patients with mycosis fungoides, Biomedical Photonics, 2022, vol. 11, no. 1, pp. 27–36. doi: 10.24931/2413– 9432–2022–11-1-27-36.Henderson B.W., Dougherty T.J. How does photodynamic therapy work? // Photochem. Photobiol. – 1992. – Vol. 55. – P. 145–157.Henderson B.W., Dougherty T.J. How does photodynamic therapy work? Photochem. Photobiol., 1992, vol. 55, pp. 145– 157.Filonenko E.V. The history of development of fluorescence diagnosis and photodynamic therapy and their capabilities in oncology // Russian Journal of General Chemistry. – 2015. – Vol. 85(1). – P. 211–216. doi: 10.1134/S1070363215010399Filonenko E.V. The history of development of fluorescence diagnosis and photodynamic therapy and their capabilities in oncology, Russian Journal of General Chemistry, 2015, vol. 85(1), pp. 211–216. doi: 10.1134/S1070363215010399Helander L., Krokan H.E., Johnsson A., Gederaas O.A., Plaetzer K. Red versus blue light illumination in hexyl 5-aminolevulinate photodynamic therapy: the influence of light color and irradiance on the treatment outcome in vitro // Journal of Biomedical Optics. – 2014. – Vol. 19(8). – P. 088002.Helander L., Krokan H.E., Johnsson A., Gederaas O.A., Plaetzer K. Red versus blue light illumination in hexyl 5-aminolevulinate photodynamic therapy: the influence of light color and irradiance on the treatment outcome in vitro, Journal of Biomedical Optics, 2014, vol. 19(8), pp. 088002.Jerjes W., Upile T., Betz C.S., El Maaytah M., Abbas S., Wright A. et al. The application of photodynamic therapy in the head and neck // Dent Update. 2017. – Vol. 34. – P. 478-486.Jerjes W., Upile T., Betz C.S., El Maaytah M., Abbas S., Wright A. et al. The application of photodynamic therapy in the head and neck, Dent Update, 2017, vol. 34, pp. 478-486.Zheng Huang et al. Photodynamic therapy for treatment of solid tumors – potential and technical challenges // Technol Cancer Res Treat. – 2008. – Vol. 7(4). – P. 309–320.Zheng Huang et al. Photodynamic therapy for treatment of solid tumors – potential and technical challenges, Technol Cancer Res Treat, 2008, vol. 7(4), pp. 309–320.Jarvi M.T., Patterson M.S., Wilson B.C. Insights into Photodynamic Therapy Dosimetry: Simultaneous Singlet Oxygen Luminescence and Photosensitizer Photobleaching Measurements // Biophysical Journal Volume. – 2012. – Vol. 102. – P. 661–671.Jarvi M.T., Patterson M.S., Wilson B.C. Insights into Photodynamic Therapy Dosimetry: Simultaneous Singlet Oxygen Luminescence and Photosensitizer Photobleaching Measurements, Biophysical Journal Volume, 2012, vol. 102, pp. 661–671.Foster, T.H., Murant R.S., Bryant R.G., Knox R.S., Gibson S. L. and Hilf R. Oxygen consumption and diffusion effects in photodynamic therapy // Radiat. Res. – 1991. – Vol. 126. – P. 296–303.Foster, T.H., Murant R.S., Bryant R.G., Knox R.S., Gibson S. L. and Hilf R. Oxygen consumption and diffusion effects in photodynamic therapy, Radiat. Res., 1991, vol. 126, pp. 296–303.Valentine R.M., Ibbotson S.H., Wood K., Brown C.T. Modelling fluorescence in clinical photodynamic therapy // Photochem Photobiol Sci. – 2013. – Vol. 12(1). – P. 203–13 [PubMed: 23128146]Valentine R.M., Ibbotson S.H., Wood K., Brown C.T. Modelling fluorescence in clinical photodynamic therapy, Photochem Photobiol Sci, 2013, vol. 12(1), pp. 203–13 [PubMed: 23128146]Pelicano H., Carney D. and Huang P. ROS stress in cancer cells and therapeutic implications // Drug Resist. Updat. – 2014. – Vol. 7. – P. 97–110.Pelicano H., Carney D. and Huang P. ROS stress in cancer cells and therapeutic implications, Drug Resist. Updat., 2014, vol. 7, pp. 97–110.Belousova I. M., Mironova N.G. and Yur’ev M.S. A mathematical model of the photodynamic fullerene-oxygen action on biological tissues // Opt. Spectrosc. – 2015. –Vol. 98. – P. 349–356.Belousova I. M., Mironova N.G. and Yur’ev M.S. A mathematical model of the photodynamic fullerene-oxygen action on biological tissues, Opt. Spectrosc, 2015, vol. 98, pp. 349–356.Ioannis Gkigkitzis, Yuanming Feng, Chunmei Yang, Jun Q. Lu and Xin-Hua Hu. Modeling of Oxygen Transport and Cell Killing in Type-II Photodynamic Therapy // Photochemistry and Photobiology. – 2012. – Vol. 88. – P. 969–977.Ioannis Gkigkitzis, Yuanming Feng, Chunmei Yang, Jun Q. Lu and Xin-Hua Hu. Modeling of Oxygen Transport and Cell Killing in Type-II Photodynamic Therapy, Photochemistry and Photobiology, 2012, vol. 88, pp. 969–977.Casasa A., Di Venosa G., Hasan T. and Batllea A. Mechanisms of Resistance to Photodynamic Therapy // Curr Med Chem. – 2011. – Vol. 18(16). – P. 2486–2515.Casasa A., Di Venosa G., Hasan T. and Batllea A. Mechanisms of Resistance to Photodynamic Therapy, Curr Med Chem, 2011, vol. 18(16), pp. 2486–2515.Wyld L., Smith O., Lawry J., Reed M.W. and Brown N.J. Cell cycle phase influences tumour cell sensitivity to aminolaevulinic acid- induced photodynamic therapy in vitro // Br J Cancer. 1998. – Vol. 78(1). – P. 50–55.Wyld L., Smith O., Lawry J., Reed M.W. and Brown N.J. Cell cycle phase influences tumour cell sensitivity to aminolaevulinic acid-induced photodynamic therapy in vitro, Br J Cancer, 1998, vol. 78(1), pp. 50–55.Karami Gadallo L., Ghoranneviss M., Ataie-Fashtami L., Pouladian M., Sardari D., Enhancement of Cancerous Cells Treatment by Applying Cold Atmosphere Plasma and Photo Dynamic Therapy Simultaneously // Clinical Plasma Medicine. – 2017. http://dx.doi.org/10.1016/j.cpme.2017.08.002Karami Gadallo L., Ghoranneviss M., Ataie-Fashtami L., Pouladian M., Sardari D., Enhancement of Cancerous Cells Treatment by Applying Cold Atmosphere Plasma and Photo Dynamic Therapy Simultaneously, Clinical Plasma Medicine, 2017 http://dx.doi.org/10.1016/j.cpme.2017.08.002Chen X., Zhao P., Chen F., Li L., and Luo R. Effect and mechanism of 5-aminolevulinic acid-mediated photodynamic therapy in esophageal cancer // Lasers Med Sci. – 2011. –Vol. 26. – P. 69-78.Chen X., Zhao P., Chen F., Li L., and Luo R. Effect and mechanism of 5-aminolevulinic acid-mediated photodynamic therapy in esophageal cancer, Lasers Med Sci, 2011, vol. 26, pp. 69-78.Bodgi L. et al. Mathematical models of radiation action on living cells: From the target theory to the modern approaches. A historical and critical review // Journal of Theoretical Biology. – 2011. – Vol. 394. – P. 93 –101.Bodgi L. et al. Mathematical models of radiation action on living cells: From the target theory to the modern approaches. A historical and critical review, Journal of Theoretical Biology, 2011, vol. 394, pp. 93 –101.Nomiya T. Discussions on target theory: past and present // J Radiat Res. – 2013. – Vol. 54(6). – P. 1161–1163.Nomiya T. Discussions on target theory: past and present, J Radiat Res, 2013, vol. 54(6), pp. 1161–1163.

The authors declare that there are no conflicts of interest present.