A Fractional-order Tumor Growth Inhibition Model in PKPD
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Manycompartmentmodelsassumeakineticallyhomogeneous amount of materials that have well-stirred compartments. However, based on observations from such processes, they have been heuristically fitted by exponential or gamma distributions even though biological media are inho- mogeneous in real environments. Fractional differential equations using a specific kernel in Pharmacokinetic/Pharmacodynamic (PKPD) model are recently introduced to account for abnormal drug disposition. We discuss a tumor growth inhibition (TGI) model using fractional-order derivative from it. This represents a tumor growth delay by cytotoxic agents and additionally show variations in the equilibrium points by the change of fractional order. The result indicates that the equilibrium depends on the tumor size as well as a change of the fractional order. We find that the smaller the fractional order, the smaller the equilibrium value. However, a difference of them is the number of concavities and this indicates that TGI over time profile for fitting or prediction should be determined properly ei- ther fractional order or tumor sizes according to the number of concavities shown in experimental data.
Abstract
Manycompartmentmodelsassumeakineticallyhomogeneous amount of materials that have well-stirred compartments. However, based on observations from such processes, they have been heuristically fitted by exponential or gamma distributions even though biological media are inho- mogeneous in real environments. Fractional differential equations using a specific kernel in Pharmacokinetic/Pharmacodynamic (PKPD) model are recently introduced to account for abnormal drug disposition. We discuss a tumor growth inhibition (TGI) model using fractional-order derivative from it. This represents a tumor growth delay by cytotoxic agents and additionally show variations in the equilibrium points by the change of fractional order. The result indicates that the equilibrium depends on the tumor size as well as a change of the fractional order. We find that the smaller the fractional order, the smaller the equilibrium value. However, a difference of them is the number of concavities and this indicates that TGI over time profile for fitting or prediction should be determined properly ei- ther fractional order or tumor sizes according to the number of concavities shown in experimental data.
참고문헌 (23)
- P. Macheras, "Mod-eling in Biopharmaceutics, Phar-macokinetics and Pharmacody-namics: Homogeneous and Het-erogeneous Approaches. Inter-disciplinary Applied Mathemat-ics" (2016), Springer International Pub-lishing
- Bruce J. West, "Fractal physiology for physi-cists: Lvy statistics", Physics Re-ports, 246(1), pp.1~100 (1994)
- Christopher N Angstmann, "Fractional order compartment models", SIAM Journal on Applied Mathematics, 77(2), pp.430~446 (2017)
- John E. Mittler, "In uence of delayed vi-ral production on viral dynamics in HIV-1 infected patients", Math-ematical Biosciences, 152(2), pp.143~163 (1998)
- Davide Verotta, "Fractional dynamics pharmacokinetics-pharmacodynamic models", Journal of Pharmacokinetics and Pharmacodynamics, 37(3), pp.257~276 (2010)
- Aristides Dokoumetzidis, "A commentary on fractional-ization of multi-compartmental models", Journal of Pharma-cokinetics and Pharmacodynam-ics, 37(2), pp.203~207 (2010)
- Rasiel Toledo-Hernandez, "A fractional calcu-lus approach to the dynamic optimization of biological reac-tive systems. Part I: Fractional models for biological reactions", Chemical Engineering Science, 117, pp.217~228 (2014)
- Dana Copot, "A two-compartment fractional derivative model for propofol diffusion in anesthesia", Control Applications (CCA), 2013 IEEE International Confer-ence on, pp.264~269 (2013), IEEE
- Jovan K. Popovi, "A new approach to the compart-mental analysis in pharmacoki-netics : fractional time evolution of diclofenac", Journal of Pharma-cokinetics and Pharmacodynam-ics, 37(2), pp.119~134 (2010)
- Aristides Dokoumetzidis, "Fractional kinetics in multi-compartmental systems", Journal of Pharmacokinetics and Phar-macodynamics, 37(5), pp.507~524 (2010)
- Jovan K. Popovi, "Two compartmental fractional deriva-tive model with fractional deriva-tives of different order", Com-munications in Nonlinear Sci-ence and Numerical Simulation, 18(9), pp.2507~2514 (2013)
- Aristides Dokoumetzidis, "Fractional kinetics in drug absorption and disposition processes", Journal of Pharmacokinetics and Phar-macodynamics, 36(2), pp.165~178 (2009)
- Prasith Baccam, "Kinetics of in uenza A virus infection in humans", Jour-nal of Virology, 80(15), pp.7590~7599 (2006)
- Yusuke Kakizoe, "A method to determine the duration of the eclipse phase for in vitro infec-tion with a highly pathogenic SHIV strain", Scientific Reports, 5, pp.10371~ (2015)
- Stefan G Samko, "Frac-tional integrals and derivatives", Theory and Applications, 44, pp.1993~ (1993), Gordon and Breach
- B Meibohm, "Ba-sic concepts of pharmacokinetic pharmacodynamic(PK", PD)modelling, 1997, pp.35(10), 401~413
- Kenneth A. Johnson, "The Original Michaelis Constant: Translation of the 1913 MichaelisMenten Paper", Biochemistry, 50(39), pp.8264~8269 (1913)
- Meindert Danhof, "Mechanism-based pharmacokinetic-pharmacodynamic (PK-PD) modeling in translational drug research", Trends in Pharmaco-logical Sciences, 29(4), pp.186~191 (2008)
- Donald E Mager, "Diver-sity of mechanism-based pharma-codynamic models", Drug Metab-olism and Disposition, 31(5), pp.510~518 (2003)
- Shinji Yamazaki, "Pharmacokinetic-Pharmacodynamic Modeling of Biomarker Response and Tumor Growth Inhibition to an Orally Available cMet Kinase Inhibitor in Human Tumor Xenograft Mouse Models", Drug Metabolism and Disposition, 36(7), pp.1267~1274 (2008)
- Vinay G. Vaidya, "Evaluation of some mathematical models for tumor growth", International Jour-nal of Bio-Medical Computing, 13(1), pp.19~35 (1982)
- Malgorzata Turalska, "A search for a spec-tral technique to solve nonlin-ear fractional differential equa-tions", Chaos, Solitons & Fractals, 102, pp.387~395 (2017)
- Pantelis Sopasakis, "Frac-tional calculus in pharmacoki-netics", Journal of Pharma-cokinetics and Pharmacodynam-ics, 45(1), pp.107~125 (2018)