Mathematical analysis of nonlinear combination drug delivery

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Abstract

This study examined a single-compartment pharmacokinetic model with intravenous and oral administration. It investigated the trends in steady-state drug exposure and average steady-state plasma drug concentration under multiple dosing regimens. First, the combined drug administration model was a non-autonomous system, and we approximated the solution of the model by estimating the exact upper and lower bounds in conjunction with the comparison theorem for differential equations. We also demonstrated the existence, uniqueness, and stability of the solution. Second, we derived the steady-state drug exposure and compared it with the solution of the intravenous drug delivery model alone. The results indicate that the combined drug delivery scheme offers superior performance. Finally, we theoretically proved the change rule of average steady-state blood drug concentration under different dosing regimens, and verified its feasibility and rationality by combining the numerical simulation results of Phenytoin sodium.

Keywords

pharmacokinetic model / combined drug administration / steady-state drug exposure / average steady-state concentration

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References

[1] R. Panchagnula, N. S. Thomas, Biopharmaceutics and pharmacokinetics in drug research, Int. J. Pharm., 201 (2000), 131-150. https://doi.org/10.1016/s0378-5173(00)00344-6

[2] M. A. Hedaya, Basic Pharmacokinetics , Routledge, 2023. https://doi.org/10.1016/b978-0-12-815499-1.00050-8

[3] X. H. Huang, Q. S. Zheng, Pharmacokinetic and pharmacodynamic data analysis: concepts and applications, Am. J. Pharm. Educ., 74 (2010). https://doi.org/10.5688/aj740353b

[4] C. Csajka, D. Verotta, Pharmacokinetic-pharmacodynamic modelling: history and perspectives, J. Pharmacokinet. Pharmacodyn., 33 (2006), 227-279. https://doi.org/10.1007/s10928-005-9002-0

[5] W. Wang, E. Q. Wang, J. P. Balthasar, Monoclonal antibody pharmacokinetics and pharmacodynamics, Clin. Pharmacol. Ther., 84 (2008), 548-558. https://doi.org/10.1038/clpt.2008.170

[6] Y. M. C. Wang, B. Sloey, T. Wong, P. Khandelwal, R. Melara, Y. N. Sun, Investigation of the pharmacokinetics of romiplostim in rodents with a focus on the clearance mechanism, Pharm. Res., 28 (2011), 1931-1938. https://doi.org/10.1007/s11095-011-0420-y

[7] S. Kozawa, N. Yukawa, J. Liu, A. Shimamoto, E. Kakizaki, T. Fujimiya, Effect of chronic ethanol administration on disposition of ethanol and its metabolites in rat, Alcohol, 41 (2007), 87-93. https://doi.org/10.1016/j.alcohol.2007.03.002

[8] P. H. van der Graaf, N. Benson, L. A. Peletier, Topics in mathematical pharmacology, J. Dyn. Differ. Equations, 28 (2016), 1337-1356. https://doi.org/10.1007/s10884-015-9468-4

[9] H. Moore, R. Allen, What can mathematics do for drug development?, Bull. Math. Biol., 81 (2019), 3421-3424. https://doi.org/10.1007/s11538-019-00632-x

[10] S. Tang, Y. Xiao, One-compartment model with Michaelis-Menten elimination kinetics and therapeutic window: an analytical approach, J. Pharmacokinet. Pharmacodyn., 34 (2007), 807-827. https://doi.org/10.1007/s10928-007-9070-4

[11] A. Dokoumetzidis, R. Magin, P. Macheras, Fractional kinetics in multi-compartmental systems, J. Pharmacokinet. Pharmacodyn., 37, (2010), 507-524. https://doi.org/10.1007/s10928-010-9170-4

[12] X. Wu, J. Li, F. Nekka, Closed form solutions and dominant elimination pathways of simultaneous first-order and Michaelis-Menten kinetics, J. Pharmacokinet. Pharmacodyn., 42 (2015), 151-161. https://doi.org/10.1007/s10928-015-9407-3

[13] X. Wu, F. Nekka, J. Li, Analytical solution and exposure analysis of a pharmacokinetic model with simultaneous elimination pathways and endogenous production: The case of multiple dosing administration, Bull. Math. Biol., 81 (2019), 3436-3459. https://doi.org/10.1007/s11538-019-00651-8

[14] N. A. Daryakenari, M. De Florio, K. Shukla, G. E. Karniadakis, Al-Aristotle: A physics-informed framework for systems biologygray-box identification, PLoS Comput. Biol., 20 (2024), e1011916. https://doi.org/10.1371/journal.pcbi.1011916

[15] N. A. Daryakenari, S. Wang, G. Karniadakis, CMINNs: Compartment model informed neural networks-Unlocking drug dynamics, Comput. Biol. Med., 184, (2025), 109392. https://doi.org/10.1016/j.compbiomed.2024.109392

[16] R. Panaccione, S. Ghosh, S. Middleton, J. R. Marquez, B. B. Scott, L. Flint, et al., Combination therapy with infliximab and azathioprine is superior to monotherapy with either agent in ulcerative colitis, Gastroenterology, 146 (2014), 392-400. https://doi.org/10.1053/j.gastro.2013.10.052

[17] N. M. Maruthur, E. Tseng, S. Hutfless, L. M. Wilson, C. Suarez-Cuervo, Z. Berger, et al., Diabetes medications as monotherapy or metformin-based combination therapy for type 2 diabetes: a systematic review and meta-analysis, Ann. Intern. Med., 164 (2016), 740-751. https://doi.org/10.7326/M15-2650

[18] Y. Ma, Q. Chen, Y. Zhang, J. Xue, Q. Liu, Y. Zhao, et al., Pharmacokinetics, safety, tolerability, and feasibility of apatinib in combination with gefitinib in stage IIIB-IV EGFR-mutated non-squamous NSCLC: a drug-drug interaction study, Cancer Chemother. Pharmacol., 92 (2023), 411-418. https://doi.org/10.1007/s00280-023-04563-2

[19] L. Hanum, Q. Ertiningsih, N. Susyanto, Sensitivity analysis unveils the interplay of drug-sensitive and drug-resistant Glioma cells: Implications of chemotherapy and anti-angiogenic therapy, Electron. Res. Arch., 32 (2024), 72-89. https://doi.org/10.3934/era.2024004

[20] X. Tan, S. Fan, K. Duan, M. Xu, J. Zhang, P. Sun, et al., A novel drug-drug interactions prediction method based on a graph attention network, Electron. Res. Arch., 31 (2023), 5632-5648. https://doi.org/10.3934/era.2023286

[21] N. Erawaty, N. Aris, A mathematical study of effects of delays arising from the interaction of anti-drug antibody and therapeutic protein in the immune response system, AIMS Math., 5 (2020), 7176-7199. https://doi.org/10.3934/math.2020460

[22] T. Gould, R. J. Roberts, Therapeutic problems arising from the use of the intravenous route for drug administration, J. Pediatr., 95 (1979), 465-471. https://doi.org/10.1016/s0022-3476(79)80538-7

[23] P. Fasinu, V. Pillay, V. M. K. Ndesendo, L. C. du Toit, Y. E. Choonara, Diverse approaches for the enhancement of oral drug bioavailability, Biopharm. Drug Dispos., 32 (2011), 185-209. https://doi.org/10.1002/bdd.750

[24] R. Selimov, E. Goncharova, P. Koriakovtsev, D. Gabidullina, J. Karsakova, S. Kozlov, et al., Comparative pharmacokinetics of florfenicol in heifers after intramuscular and subcutaneous administration, J. Vet. Pharmacol. Ther., 46 (2023), 177-184. https://doi.org/10.1111/jvp.13110

[25] N. Z. Kerin, R. D. Blevins, H. Frumin, K. Faitel, M. Rubenfire, Intravenous and oral loading versus oral loading alone with amiodarone for chronic refractory ventricular arrhythmias, Am. J. Cardiol., 55 (1985), 89-91. https://doi.org/10.1016/0002-9149(85)90305-4

[26] H. U. Xiao-hu, T. San-yi, Approximate Solutions to the Nonlinear Compartmental Model for Extravascular Administration, Appl. Math. Mech., 35 (2014), 1033-1045. https://doi.org/10.3879/j.issn.1000-0887.2014.09.009

[27] S. H. Jang, P. M. Colangelo, J. V. S. Gobburu, Exposure-response of posaconazole used for prophylaxis against invasive fungal infections: evaluating the need to adjust doses based on drug concentrations in plasma, Clin. Pharmacol. Ther., 88 (2010), 115-119. https://doi.org/10.1038/clpt.2010.64

[28] M. Prasad, P. R. Krishnan, R. Sequeira, Khaldoon. Al-Roomi, Anticonvulsant therapy for status epilepticus, Cochrane Database Syst. Rev., 2014. https://doi.org/10.1002/14651858.CD003723.pub3

[29] E. H. Reynolds, D. Chadwick, A. W. Galbraith, One drug(phenytoin) in the treatment of epilepsy, The lancet, 307 (1976), 923-926. https://doi.org/10.1016/s0140-6736(76)92881-6

[30] J. Patocka, Q. Wu, E. Nepovimova, K. Kuca, Phenytoin-An anti-seizure drug: Overview of its chemistry, pharmacology and toxicology, Food Chem. Toxicol., 142 (2020), 111393. https://doi.org/10.1016/j.fct.2020.111393

[31] W. J. Jusko, J. R. Koup, G. Alvan, Nonlinear assessment of phenytoin bioavailability, J. Pharmacokinet. Biopharm., 4 (1976), 327-336. https://doi.org/10.1007/bf01063122

[32] R. Gugler, C. V. Manion, D. L. Azarnoff, Phenytoin: pharmacokinetics and bioavailability, Clin. Pharmacol. Ther., 19 (1976), 135-142. https://doi.org/10.1002/cpt1976192135

[33] L. Osterberg, T. Blaschke, Adherence to medication, N. Engl. J. Med., 353 (2005), 487-497. https://doi.org/10.7748/ns.25.2.59.s53

[34] B. Vrijens, S. De Geest, D. A. Hughes, K. Przemyslaw, J. Demonceau, T. Ruppar, et al., A new taxonomy for describing and defining adherence to medications, Br. J. Clin. Pharmacol., 73 (2012), 691-705. https://doi.org/10.1111/j.1365-2125.2012.04167.x

[35] M. E. Csete, J. C. Doyle, Reverse engineering of biological complexity, Science, 295 (2002), 1664-1669. https://doi.org/10.1126/science.1069981

[36] B. Munos, Lessons from 60 years of pharmaceutical innovation, Nat. Rev. Drug Discov., 8 (2009), 959-968. https://doi.org/10.1038/nrd2961