Математические основания метода изобол

Математические основания метода изобол

Панов В. Г.
Сибирский журнал индустриальной математики, 27, 4(100), 84-98 (2024)
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УДК 51-76:514.124:573.2:615.015.2 
DOI: 10.33048/SIBJIM.2024.27.406

Аннотация:

Предлагаются более точные определения понятий и конструкций, используемых в медикобиологических науках для анализа совместного действия факторов с помощью изоболограмм. Приведены формальные определения понятий нулевого взаимодействия, масштабно эквивалентных дозо-ответных функций, многообразия нулевого взаимодействия. Предложена общая конструкция, формализующая условия применимости и основные методы анализа комбинированного действия с помощью изобол. Получены уравнения многообразий нулевого взаимодействия как в случае масштабно эквивалентных, так и для произвольных функций отклика. Приведены примеры.

Литература:
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  13. Myers R. H., Montgomery D. C., Anderson-Cook C. M. Response surface methodology: process and product optimization using designed experiments. New Jersey: Hoboken, 2016.
     
  14. Nazni P., Gracia J. Application of Response Surface Methodology in the Development of Barnyard Millet Bran Incorporated Bread // Int. J. Innov. Res. Sci. Eng. Technol. 2014. V. 3, N 9. Article 16041; DOI: 10.15680/IJIRSET.2014.0309038 

Исследование выполнено за счет субсидий Минобрнауки РФ на выполнение научной темы FUMN-2024-0002. Других источников финансирования проведения или руководства данным конкретным исследованием не было.

В. Г. Панов
  1. Институт промышленной экологии УрО РАН, 
    ул. С. Ковалевской, 20, г. Екатеринбург 620137, Россия

E-mail: vpanov@ecko.uran.ru

Статья поступила 08.11.2022 г.
После доработки — 03.09.2024 г.
Принята к публикации 29.10.2024 г.

Abstract:

More precise definitions of concepts and constructs used in biomedical sciences are proposed to analyze the joint action of factors using isobolograms. Formal definitions of concepts of zero interaction, scale-equivalent dose—response functions, and zero-interaction manifold are given. A general construction is proposed that formalizes the conditions of applicability and the basic methods for analyzing the combined action using isoboles. Equations of zero interaction manifolds are derived both in the case of scale-equivalent and arbitrary dose—response functions.

References:
  1. W. R. Greco, G. Bravo, and J. C. Parsons, “The search for synergy: A critical review from a response surface perspective,” Pharmacol. Rev. 47 (2), 331–385 (1995).
     
  2. J. Tang, K. Wennerberg, and T. Aittokallio, “What is synergy? The Saariselkä agreement revisited,” Front. Pharmacol. 6 (1), 181 (2015). https://doi.org/10.3389/fphar.2015.00181
     
  3. R.-Y. Huang, L. Pei, Q. Liu, S. Chen, H. Dou, G. Shu, Z.-X. Yuan, J. Lin, G. Peng, W. Zhang, and H. Fu, “Isobologram analysis: A comprehensive review of methodology and current research,” Front. Pharmacol. 10 (29), 1222 (2019). https://doi.org/10.3389/fphar.2019.01222
     
  4. J. P. van den Berg, H. E. M. Vereecke, J. H. Proost, D. J. Eleveld, J. K. G.Wietasch, A. R. Absalom, and M. M. R. F. Struys, “Pharmacokinetic and pharmacodynamic interactions in anaesthesia. A review of current knowledge and how it can be used to optimize anaesthetic drug administration,” Br. J. Anaesth. 118 (1), 44–57 (2017). https://doi.org/10.1093/bja/aew312
     
  5. T. G. Short and J. A. Hannam, Pharmacology and Physiology for Anesthesia (Elsevier, Philadelphia, 2019).
     
  6. R. T. Basting, H. M. Spindola, I. M. de Oliveira Sousa, N. C. A. Queiroz, J. R. Trigo, J. J. E. de Carvalho, and M. A. Foglio, “Pterodon pubescens and Cordia verbenacea association promotes a synergistic response in antinociceptive model and improves the anti-inflammatory results in animal models,” Biomed. Pharmacother. 112, 108693 (2019). https://doi.org/10.1016/j.biopha.2019.108693
     
  7. N. Atwal, S. L. Casey, V. A. Mitchell, and C. W. Vaughan, “THC and gabapentin interactions in a mouse neuropathic pain model,” Neuropharmacology 144, 115–121 (2019). https://doi.org/10.1016/j.neuropharm.2018.10.006
     
  8. J. J. Luszczki and A. Wlaz, “Isobolographic analysis of interactions — a pre-clinical perspective,” J. PreClin. Clin. Res. 17 (4), 238–241 (2023). https://doi.org/10.26444/jpccr/177246
     
  9. J. Foucquier and M. Guedj, “Analysis of drug combinations: Current methodological landscape,” Pharmacol. Res. Perspect. 3 (3), e00149 (2015). https://doi.org/10.1002/prp2.149
     
  10. M. A. M. Garcia and M. A. P. Lage, “Dose—response analysis in the joint action of two effectors: A new approach to simulation and identification and modelling of some basic interactions,” PLoS One 8 (4), e61391 (2013). https://doi.org/10.1371/journal.pone.0061391
     
  11. I. Rodea-Palomares, M. González-Pleiter, K. Martin-Betancor, R. Rosal, and F. Fernández-Pĩnas, “Additivity and interactions in ecotoxicity of pollutant mixtures: Some patterns, conclusions, and open questions,” Toxics 3 (4), 342–369 (2015). https://doi.org/10.3390/toxics3040342
     
  12. M. C. Berenbaum, “The expected effect of a combination of agents: The general solution,” J. Theor. Biol. 114 (3), 413–431 (1985). https://doi.org/10.1016/s0022-5193(85)80176-4
     
  13. R. H. Myers, D. C. Montgomery, and C. M. Anderson-Cook, Response Surface Methodology: Process and Product Optimization Using Designed Experiments (Wiley, Hoboken, NJ, 2016).
     
  14. P. Nazni and J. Gracia, “Application of response surface methodology in the development of Barnyard Millet Bran incorporated bread,” Int. J. Innov. Res. Sci. Eng. Technol. 3 (9), 16041 (2014). https://doi.org/10.15680/IJIRSET.2014.0309038