New developments in using stochastic recipe for multi-compartment model: Inter-compartment traveling route, residence time, and exponential convolution expansion

Mathematical Biosciences and Engineering

Volumn 6, Issue 3, 2009, Pages 663-682

  Zhao, Liang ^a,b  

^a OHIO STATE UNIVERSITY   (United States)

^b 1 Medimmune Way ^*  (United States)

Author keywords

Convolution; Laplace transform; Markovian; Pharmacokinetics and pharmacodynamics; Residence time

Indexed keywords

DRUG;

ARTICLE; BIOLOGICAL MODEL; COMPARATIVE STUDY; HUMAN; METABOLIC CLEARANCE RATE; METABOLISM; PHARMACOKINETICS; PROBABILITY; STATISTICAL MODEL;

HUMANS; MARKOV CHAINS; METABOLIC CLEARANCE RATE; MODELS, BIOLOGICAL; MODELS, STATISTICAL; PHARMACEUTICAL PREPARATIONS; PHARMACOKINETICS;

EID: 70349650812     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2009.6.663     Document Type: Article

References (22)

1. B. D. Beck, R. L. Mattuck, T. S. Bowers, J. T. Cohen and E. O'Flaherty, The development of a stochastic physiologically-based pharmacokinetic model for lead, Sci. Total Environ., 274 (2001), 15-19.
2. L. Z. Benet and J. S. Turi, Use of general partial fraction theorem for obtaining inverse laplace transforms in pharmacokinetic analysis, J. Pharm. Sci., 60 (1971), 1593-1594.
3. H. Cheng and W. R. Gillespie, Volumes of distribution and mean residence time of drugs with linear tissue distribution and binding and nonlinear protein binding, J. Pharmacokinet. Biopharm., 24 (1996), 389-402.
4. N. L. Dayneka, V. Garg and W. J. Jusko, Comparison of four basic models of indirect pharmacodynamic responses, J. Pharmacokinet. Biopharm., 21 (1993), 457-478.
5. W. R. Gillespie and P. Veng-Pedersen, The determination of mean residence time using statistical moments: it is correct, J. Pharmacokinet. Biopharm., 13 (1985), 549-554.
6. S. H. Jang, M. G. Wientjes and J. L. Au, Determinants of paclitaxel uptake, accumulation and retention in solid tumors, Invest. New Drugs, 19 (2001), 113-123.
7. N. R. Kristensen, H. Madsen and S. H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn., 32 (2005), 109-141.
8. W. Krzyzanski and W. J. Jusko, Mathematical formalism for the properties of four basic models of indirect pharmacodynamic responses, J. Pharmacokinet. Biopharm., 25 (1997), 107-123.
9. P. Lansky, A stochastic model for circulatory transport in pharmacokinetics, Math. Biosci., 132 (1996), 141-167.
10. J. H. Matis, T. R. Kiffe, T. I. Matis and D. E. Stevenson, Nonlinear stochastic modeling of aphid population growth, Math. Biosci., 198 (2005), 148-168.
11. J. H. Matis and T. E. Wehrly, Generalized stochastic compartmental models with erlang transit times, J. Pharmacokinet. Biopharm., 18 (1990), 589-607.
12. J. H. Matis and T. E. Wehrly, A general approach to non-markovian compartmental models, J. Pharmacokinet. Biopharm., 26 (1998), 437-456.
13. J. H. Matis, T. E. Wehrly and C. M. Metzler, On some stochastic formulations and related statistical moments of pharmacokinetic models, J. Pharmacokinet. Biopharm., 11 (1983), 77-92.
14. T. Moriwaki, H. Yasui and A. Yamamoto, A recirculatory model with enterohepatic circulation by measuring portal and systemic blood concentration difference, J. Pharmacokinet. Biopharm., 30 (2003), 119-144.
15. T. Moriwaki, H. Yasui and A. Yamamoto, Pharmacokinetic analysis of ramatroban using a recirculatory model with enterohepatic circulation by measuring portal and systemic blood concentration difference in sprague-dawley and eisai hyperbilirubinemia rats, Pharm. Res., 21 (2004), 1055-1064.
16. E. Nakashima and L. Z. Benet, An integrated approach to pharmacokinetic analysis for linear mammillary systems in which input and exit may occur in/from any compartment, J. Pharmacokinet. Biopharm., 17 (1989), 673-686.
17. L. B. Sheiner, D. R. Stanski, S. Vozeh, R. D. Miller and J. Ham, Simultaneous modeling of pharmacokinetics and pharmacodynamics: Application to d-tubocurarine, Clin. Pharmacol. Ther., 25 (1979), 358-371.
18. C. E. Smith, P. Lansky and T. H. Lung, Cycle-time and residence-time density approximations in a stochastic model for circulatory transport, Bull. Math. Biol., 59 (1997), 1-22.
19. P. Veng-Pedersen, Stochastic interpretation of linear pharmacokinetics: A linear system analysis approach, J. Pharm. Sci., 80 (1991), 621-631.
20. P. Veng-Pedersen and W. R. Gillespie, The mean residence time of drugs in the systemic circulation, J. Pharm. Sci., 74 (1985), 791-792.
21. J. Yu and T. E. Wehrly, An approach to the residence time distribution for stochastic multicompartment models, Math. Biosci., 19X (2004), 185-205.
22. J. H. Zheng, C. T. Chen, J. L. Au and M. G. Wientjes, Time- and concentration-dependent penetration of doxorubicin in prostate tumors, AAPS Pharm Sci., 3 (2001), E15.