Explicit reformulations of the Lambert W-omega function for calculations of the solutions to one-compartment pharmacokinetic models with Michaelis-Menten elimination kinetics

European Journal of Drug Metabolism and Pharmacokinetics

Volumn 36, Issue 3, 2011, Pages 121-127

  Goličnik, Marko ^a  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

Author keywords

Kinetic parameter analysis; Lambert W omega function; Michaelis menten elimination kinetics; Nonlinear pharmacokinetics

Indexed keywords

ACCURACY; ANALYTIC METHOD; ARTICLE; CALCULATION; COMPARTMENT MODEL; COMPUTER PROGRAM; CONCENTRATION (PARAMETERS); CONTROLLED STUDY; DRUG MONITORING; INTERMETHOD COMPARISON; LAMBERT W OMEGA FUNCTION; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MICHAELIS MENTEN KINETICS; NONLINEAR REGRESSION ANALYSIS; SIMULATION; STATISTICAL CONCEPTS; STATISTICAL MODEL; BIOLOGICAL MODEL; HUMAN; MATHEMATICS; PHARMACOKINETICS;

HUMANS; MATHEMATICS; MODELS, BIOLOGICAL; PHARMACOKINETICS; SOFTWARE;

EID: 84856375867     PISSN: 03787966     EISSN: 21070180     Source Type: Journal    
DOI: 10.1007/s13318-011-0040-2     Document Type: Article

References (17)

1. Barry DA, Barry SJ, Culligen-Hensley PJ (1995) Algorithm 743: a Fortran routine for calculating real values of the W function. ACM Trans Math Softw 21:172-181
2. Barry DA, Parlange JY, Li L, Prommer H, Cunningham CJ, Stagnitti F (2000) Analytical approximations for real values of the Lambert W-function. Math Comp Simul 53:95-103
3. Bonate P (2006) Pharmacokinetic-pharmacodynamic modeling and simulation. Springer, New York
4. Burgess DS, Frei CR, Lewis JS, Fiebelkorn KR, Jorgensen JH (2007) The contribution of pharmacokinetic-pharmacodynamic modeling with Monte Carlo simulation to the development of susceptibility breakpoints for Neisseria meningitides. Clin Microbiol Infect 13:33-39 (Pubitemid 44869205)
5. Chan PLS, Jacqmin P, Lavielle M, McFadyen L, Weatherley B (2011) The use of the SAEM algorithm in MONOLIX software for estimation of population pharmacokinetic-pharmacodynamic-viral dynamics parameters of maraviroc in asymptomatic HIV subjects. J Pharmacokin Pharmacodyn 38:41-61
6. Corless RM, Gonnet GH, Hare DEG, Jeffrey DJ, Knuth DE (1996) On the Lambert W function. Adv Comput Math 5:329-359 (Pubitemid 126729167)
7. Goličnik M (2010) Explicit reformulations of time-dependent solution for a Michaelis-Menten enzyme reaction model. Anal Biochem 406:94-96
8. Goličnik M (2011) Evaluation of enzyme kinetic parameters using explicit analytic approximations to the solution of the Michaelis-Menten equation. Biochem Eng J 53:234-238
9. Goudar CT, Harris SK, McInerney MJ, Suflita JM (2004) Progress curve analysis for enzyme and microbial kinetic reactions using explicit solutions based on the Lambert W function. J Microbiol Methods 59:317-326 (Pubitemid 39370794)
10. Huisinga W, Telgman R, Wulkow M (2006) The virtual laboratory approach to pharmacokinetics: design principles and concepts. Drug Discov Today 11:800-805 (Pubitemid 44280017)
11. Keller F, Hartman B, Czock D (2009) Explicit solution of the integrated 1-exp equation for predicting accumulation and decline of concentrations for drugs obeying nonlinear saturation kinetics. Ther Drug Monit 31:783-785
12. Lave T, Parrott N, Grimm HP, Fleury A, Reddy M (2007) Challenges and opportunities with modeling and simulation in drug discovery and drug development. Xenobiotica 37:1295-1310 (Pubitemid 350035528)
13. Pillia G, Mentre F, Steimer JL (2005) Non-linear mixed effects modeling-from methodology and software development to driving implementation in drug science. J Pharmacokin Pharmacodyn 32:161-183 (Pubitemid 41712738)
14. Schnell S, Mendoza C (1997) Closed form solution for timedependent enzyme kinetics. J Theor Biol 187:207-212 (Pubitemid 27359368)
15. Tang S, Xiao Y (2007) One-compartment model with Michaelis-Menten elimination kinetics and therapeutic window: an analytical approach. J Pharmacokin Pharmacodyn 34:807-827 (Pubitemid 350165275)
16. von Kleist M, Huisinga W (2007) Physiologically based pharmacokinetic modeling: a sub-compartmentalized model of tissue distribution. J Pharmacokinet Pharmacodyn 34:789-806 (Pubitemid 350165276)
17. Zavrel M, Kochanowski K, Spiess AC (2010) Comparison of different approaches and computer programs of progress curve analysis of enzyme kinetics. Eng Life Sci 10:191-200