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Modeling of Pharmacokinetic/Pharmacodynamic (PK/PD) Relationships: Concepts and Perspectives

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Abstract

Pharmacokinetic/pharmacodynamic (PK/PD)-modeling links dose-concentration relationships (PK) and concentration-effect relationships (PD), thereby facilitating the description and prediction of the time course of drug effects resulting from a certain dosing regimen. PK/PD-modeling approaches can basically be distinguished by four major attributes. The first characterizes the link between measured drug concentration and the response system, direct link versus indirect link. The second considers how the response system relates effect site concentration to the observed outcome, direct versus indirect response. The third regards what clinically or experimentally assessed information is used to establish the link between concentration and effect, hard link versus soft link. And the fourth considers the time dependency of pharmacodynamic model parameters, distinguishing between time-variant versus time-invariant. Application of PK/PD-modeling concepts has been identified as potentially beneficial in all phases of preclinical and clinical drug development. Although today predominantly limited to research, broader application of PK/PD-concepts in clinical therapy will provide a more rational basis for patient-specific dosage individualization and may thus guide applied pharmacotherapy to a higher level of performance.

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REFERENCES

  1. G. Levy. Kinetics of drug action: an overview. J. Allergy Clin. Immunol. 78:754–761 (1986).

    Google Scholar 

  2. N. H. G. Holford and L. B. Sheiner. Kinetics of pharmacological response. Pharmacol. Ther. 16:143–166 (1982).

    Google Scholar 

  3. G. Levy, M. Gibaldi, and W. J. Jusko. Multicompartment pharmacokinetic models and pharmacologic effects. J. Pharm. Sci. 58:422–424 (1969).

    Google Scholar 

  4. G. Levy. Kinetics of drug action in man. Acta Pharmacol. Toxicol. Copenh. 29Suppl. 3:203–210 (1971).

    Google Scholar 

  5. M. Gibaldi, G. Levy, and H. Weintraub. Drug distribution and pharmacologic effects. Clin. Pharmacol. Ther. 12:734–742 (1971).

    Google Scholar 

  6. J. G. Wagner. Kinetics of pharmacologic response: I. Proposed relationship between response and drug concentration in the intact animal and man. J. Theor. Biol. 20:173–201 (1968).

    Google Scholar 

  7. 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. 25:358–371 (1979).

    Google Scholar 

  8. N. H. G. Holford and L. B. Sheiner. Pharmacokinetic and pharmacodynamic modeling in vivo. CRC Crit. Rev. Bioeng. 5:273–322 (1981).

    Google Scholar 

  9. B. Oosterhuis and C. J. van Boxtel. Kinetics of drug effects in man. Ther. Drug Monit. 10:121–132 (1988).

    Google Scholar 

  10. J. D. Unadkat, F. Bartha, and L. B. Sheiner. Simultaneous modeling of pharmacokinetics and pharmacodynamics with nonparametric kinetic and dynamic models. Clin. Pharmacol. Ther. 40:86–93 (1986).

    Google Scholar 

  11. E. Fuseau and L. B. Sheiner. Simultaneous modeling of pharmacokinetics and pharmacodynamics with a nonparametric pharmacodynamic model. Clin. Pharmacol. Ther. 35:733–741 (1984).

    Google Scholar 

  12. E. Chan, A. McLachlan, R. O'Reilly, and M. Rowland. Stereochemical aspects of warfarin drug interactions: use of a combined pharmacokinetic-pharmacodynamic model. Clin. Pharmacol. Ther. 56:286–294 (1994).

    Google Scholar 

  13. M. Thibonnier, N. H. G. Holford, R. A. Upton, C. D. Blume, and R. L. Williams. Pharmacokinetic-pharmacodynamic analysis of unbound disopyramide directly measured in serial plasma samples in man. J. Pharmacokinet. Biopharm. 12:559–573 (1984).

    Google Scholar 

  14. S. Rohatagi, U. Tauber, K. Richter, and H. Derendorf. Pharmacokinetic/pharmacodynamic modeling of cortisol suppression after oral administration of fluocortolone. J. Clin. Pharmacol. 36:311–314 (1996).

    Google Scholar 

  15. B. Meibohm and H. Derendorf. Basic concepts of pharmacokinetic/pharmacodynamic (PK/PD) modeling. Int. J. Clin. Pharmacol. Ther. 35:401–413 (1997).

    Google Scholar 

  16. H. Derendorf and G. Hochhaus, Handbook of Pharmacokinetic/Pharmacodynamic Correlation, CRC Press, Boca Raton, 1995.

    Google Scholar 

  17. M. O. Karlsson, V. Molnar, J. Bergh, A. Freijs, and R. Larsson. A general model for time-dissociated pharmacokinetic-pharmacodynamic relationships exemplified by paclitaxel myelosuppression. Clin. Pharmacol. Ther. 63:11–25 (1998).

    Google Scholar 

  18. D. E. Nix, J. H. Wilton, J. Hyatt, J. Thomas, L. C. Strenkoski-Nix, A. Forrest, and J. J. Schentag. Pharmacodynamic modeling of the in vivo interaction between cefotaxime and ofloxacin by using serum ultrafiltrate inhibitory titers. Antimicrob. Agents Chemother. 41:1108–1114 (1997).

    Google Scholar 

  19. J. W. Mandema and D. R. Stanski. Population pharmacodynamic model for ketorolac analgesia. Clin. Pharmacol. Ther. 60:619–635 (1996).

    Google Scholar 

  20. C. A. Shanks, M. J. Avram, T. C. Krejcie, T. K. Henthorn, and W. B. Gentry. A pharmacokinetic-pharmacodynamic model for quantal responses with thiopental. J. Pharmacokinet. Biopharm. 21:309–321 (1993).

    Google Scholar 

  21. J. W. Blue and W. A. Colburn. Efficacy measures: surrogates or clinical outcomes. J. Clin. Pharmacol. 36:767–770 (1996).

    Google Scholar 

  22. J. W. Lee, J. D. Hulse, and W. A. Colburn. Surrogate biochemical markers: precise measurement for strategic drug and biologics development. J. Clin. Pharmacol. 35:464–470 (1995).

    Google Scholar 

  23. B. G. Reigner, P. E. O. Williams, I. H. Patel, J. L. Steimer, C. C. Peck, and P. van Brummelen. An evaluation of the integration of pharmacokinetic and pharmacodynamic principles in clinical drug development. Clin. Pharmacokinet. 33:142–152 (1997).

    Google Scholar 

  24. V. P. Shah, K. K. Midha, S. Dighe, I. J. McGilveray, J. P. Skelly, A. Yacobi, T. Layloff, et al. Analytical method validation: bioavailability, bioequivalence, and pharmacokinetic studies. J. Pharm. Sci. 81:309–312 (1992).

    Google Scholar 

  25. W. A. Colburn. Selecting and validating biologic markers for drug development. J. Clin. Pharmacol. 37:355–362 (1997).

    Google Scholar 

  26. G. Levy. Mechanism-based pharmacodynamic modeling. Clin. Pharmacol. Ther. 56:356–358 (1994).

    Google Scholar 

  27. W. A. Colburn. Pharmacokinetic/pharmacodynamic modeling: what it is! J. Pharmacokinet. Biopharm. 15:545–555 (1987).

    Google Scholar 

  28. A. Racine-Poon, L. Botta, T. W. Chang, F. M. Davis, D. Gygax, R. S. Liou, P. Rohane, et al. Efficacy, pharmacodynamics, and pharmacokinetics of CGP 51901, an anti-immunglobulin E chimeric monoclonal antibody, in patients with seasonal allergic rhinitis. Clin. Pharmacol. Ther. 62:675–690 (1997).

    Google Scholar 

  29. J. O. Auler, E. B. Espada, E. Crivelli, T. B. G. Quintavalle, A. Kurata, N. A. G. Stolf, A. M. Issy, et al. Diclofenac plasma protein binding: PK-PD modeling in cardiac patients submitted to cardiopulmonary bypass. Braz. J. Med. Biol. Res. 30:369–374 (1997).

    Google Scholar 

  30. G. Hochhaus, E. W. Schmidt, K. L. Rominger, and H. Möllmann. Pharmacokinetic/dynamic correlation of pulmonary and cardiac effects of fenoterol in asthmatic patients after different routes of administration. Pharm. Res. 9:291–297 (1992).

    Google Scholar 

  31. W. G. Kramer, A. J. Kolibash, R. P. Lewis, M. S. Bathala, J. A. Visconti, and R. H. Reuning. Pharmacokinetics of digoxin: Relationship between response intensity and predicted compartmental drug levels in man. J. Pharmacokinet. Biopharm. 7:47–61 (1979).

    Google Scholar 

  32. G. Segre. Kinetics of interaction between drugs and biological systems. Farmaco. Sci. 23:907–918 (1968).

    Google Scholar 

  33. W. A. Colburn. Simultaneous pharmacokinetic and pharmacodynamic modeling. J. Pharmacokinet. Biopharm. 9:367–388 (1981).

    Google Scholar 

  34. J. Dingemanse, J. Häussler, W. Hering, H. Ihmsen, S. Albrecht, M. Zell, H. Schwilden, and J. Schüttler. Pharmacokinetic-pharmacodynamic modeling of the EEG effects of RO 48-6791, a new short-acting benzodiazepine, in young and elderly subjects. Br. J. Anaesth. 79:567–574 (1997).

    Google Scholar 

  35. D. E. Salazar, D. R. Much, P. S. Nichola, J. R. Seibold, D. Shindler, and P. H. Slugg. A pharmacokinetic-pharmacodynamic model of d-sotalol Q-Tc prolongation during intravenous administration to healthy subjects. J. Clin. Pharmacol. 37:799–809 (1997).

    Google Scholar 

  36. R. Nagashima, R. A. O'Reilly, and G. Levy. Kinetics of pharmacologic effects in man: the anticoagulant action of warfarin. Clin. Pharmacol. Ther. 10:22–35 (1969).

    Google Scholar 

  37. N. L. Dayneka, V. Garg, and W. J. Jusko. Comparision of four basic models of indirect pharmacodynamic responses. J. Pharmocokinet. Biopharm. 21:457–478 (1993).

    Google Scholar 

  38. A. Sharma and W. J. Jusko. Characteristics of indirect pharmacodynamic models and applications to clinical drug responses. Br. J. Clin. Pharmacol. 45:229–239 (1998).

    Google Scholar 

  39. D. Verotta and L. B. Sheiner. A general conceptual model for non-steady state pharmacokinetic/pharmacodynamic data. J Pharmacokinet. Biopharm. 23:1–4 (1995).

    Google Scholar 

  40. L. B. Sheiner and D. Verotta. Further notes on physiologic indirect response models. Clin. Pharmacol. Ther. 58:238–240 (1995).

    Google Scholar 

  41. M. Wakelkamp, G. Alvan, and G. Paintaud. The time of maximum effect for model selection in pharmacokinetic-pharmacodynamic analysis applied to frusemide. Br. J. Clin. Pharmacol. 45:63–70 (1998).

    Google Scholar 

  42. S. Rohatagi, A. Bye, C. Falcoz, A. E. Mackie, B. Meibohm, H. Möllmann, and H. Derendorf. Dynamic modeling of cortisol reduction after inhaled administration of fluticasone propionate. J. Clin. Pharmacol. 36:938–941 (1996).

    Google Scholar 

  43. W. J. Jusko and H. C. Ko. Physiologic indirect response models characterize diverse types of pharmacodynamic effects. Clin. Pharmacol. Ther. 56:406–419 (1994).

    Google Scholar 

  44. Z. X. Xu, Y. N. Sun, D. C. DuBois, R. R. Almon, and W. J. Jusko. Third-generation model for corticosteroid pharmacodynamics: Roles of glucocorticoid receptor mRNA and tyrosine aminotransferase mRNA in rat liver. J. Pharmacokinet. Biopharm. 23:163–181 (1995).

    Google Scholar 

  45. A. I. Nichols, F. D. Boudinot, and W. J. Jusko. Second generation model for prednisolone pharmacodynamics in the rat. J. Pharmacokinet. Biopharm. 17:209–227 (1989).

    Google Scholar 

  46. H. Derendorf, G. Hochhaus, H. Möllmann, J. Barth, M. Krieg, S. Tunn, and C. Möllmann. Receptor-based pharmacokinetic-pharmacodynamic analysis of corticosteroids. J. Clin. Pharmacol. 33:115–123 (1993).

    Google Scholar 

  47. R. E. Jonkers, M. C. P. Braat, R. P. Koopmans, and C. J. van Boxtel. Pharmacodynamic modeling of the drug-induced down-regulation of a β2-adrenoceptor mediated response and lack of restoration of receptor function after a single high dose of prednisone. Eur. J. Clin. Pharmacol. 49:37–44 (1995).

    Google Scholar 

  48. B. Meibohm, G. Hochhaus, and H. Derendorf. Time dependency of the pharmacologic response to glucocorticoids. Clin. Pharmacol. Ther. 61:155 (1997).

    Google Scholar 

  49. M. J. Chow, J. J. Ambre, T. I. Ruo, A. J. Atkinson, D. J. Bowsher, and M. W. Fischman. Kinetics of cocaine distribution, elimination, and chronotropic effects. Clin. Pharmacol. Ther. 38:318–324 (1985).

    Google Scholar 

  50. J. J. Ambre. Acute tolerance to pressor effects of cocaine in humans. Ther. Drug Monit. 15:537–540 (1993).

    Google Scholar 

  51. H. C. Porchet, N. L. Benowitz, and L. B. Sheiner. Pharmacodynamic model of tolerance: application to nicotine. J. Pharmacol. Exp. Ther. 244:231–236 (1988).

    Google Scholar 

  52. J. A. Bauer and H. L. Fung. Pharmacodynamic models of nitroglycerin-induced hemodynamic tolerance in experimental heart failure. Pharm. Res. 11:816–823 (1994).

    Google Scholar 

  53. M. Wakelkamp, G. Alvan, J. Gabrielsson, and G. Paintaud. Pharmacodynamic modeling of furosemide tolerance after multiple intravenous administration. Clin. Pharmacol. Ther. 60:75–88 (1996).

    Google Scholar 

  54. Y. Hashimoto and L. B. Sheiner. Designs for population pharmacodynamics: Value of pharmacokinetic data and population analysis. J. Pharmacokinet. Biopharm. 19:333–353 (1991).

    Google Scholar 

  55. L. B. Sheiner and T. M. Ludden. Population pharmacokinetics/dynamics. Ann. Rev. Pharmacol. Toxicol. 32:185–209 (1992).

    Google Scholar 

  56. L. Yuh, S. Beal, M. Davidian, F. Harrison, A. Hester, K. Kowalski, E. Vonesh, and R. Wolfinger. Population pharmacokinetic/pharmacodynamic methodology and applications: a bibliography. Biometrics 50:566–575 (1994).

    Google Scholar 

  57. S. Vozeh, J. L. Steimer, M. Rowland, P. Morselli, F. Mentre, L. P. Balant, and L. Aarons. The use of population pharmacokinetis in drug development. Clin. Pharmacokinet. 30:81–93 (1996).

    Google Scholar 

  58. C. C. Peck, W. H. Barr, L. Z. Benet, J. Collins, R. E. Desjardins, D. E. Furst, J. G. Harter, et al. Opportunities for integration of pharmacokinetics, pharmacodynamics, and toxicokinetics in rational drug development. J. Clin. Pharmacol. 34:111–119 (1994).

    Google Scholar 

  59. P. D. Kroboth, V. D. Schmith, and R. B. Smith. Pharmacodynamic modeling: Application to new drug development. Clin. Pharmacokinet. 20:91–98 (1991).

    Google Scholar 

  60. R. Lieberman and J. McMichael. Role of pharmacokinetic-pharmacodynamic principles in rational and cost-effective drug development. Ther. Drug Monit. 18:423–427 (1996).

    Google Scholar 

  61. D. D. Breimer and M. Danhof. Relevance of the application of pharmacokinetic-pharmacodynamic modeling concepts in drug development. Clin. Pharmacokinet. 32:259–267 (1997).

    Google Scholar 

  62. F. Mentre, F. Pousset, E. Comets, B. Plaud, B. Diquet, G. Montalescot, A. Ankri, et al. Population pharmacokinetic-pharmacodynamic analysis of fluindione in patients. Clin. Pharmacol. Ther. 63:64–78 (1998).

    Google Scholar 

  63. M. Hale, W. Gillespie, S. Gupta, B. Tuk, and N. H. G. Holford. Clinical trial simulation: Streamlining your drug development process. Appl. Clin. Trials 5:35–40 (1996).

    Google Scholar 

  64. R. Gieschke, B. G. Reigner, and J. L. Steimer. Exploring clinical study design by computer simulation based on pharmacokinetic/pharmacodynamic modeling. Int. J. Clin. Pharmacol. Ther. 35:469–474 (1997).

    Google Scholar 

  65. N. H. G. Holford. The target concentration approach to clinical drug development. Clin. Pharmacokinet. 29:287–291 (1995).

    Google Scholar 

  66. Z. X. Xu, A. Rakhit, I. H. Patel, and P. van Brummelen. PK/PD modeling approach to support clinical development of a long-acting interferon (RO 25-3036) for the treatment of chronic hepatitis C. Clin. Pharmacol. Ther. 63:162 (1998).

    Google Scholar 

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Derendorf, H., Meibohm, B. Modeling of Pharmacokinetic/Pharmacodynamic (PK/PD) Relationships: Concepts and Perspectives. Pharm Res 16, 176–185 (1999). https://doi.org/10.1023/A:1011907920641

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