Skip to main content

Advertisement

SpringerLink
Log in

Lifespan based indirect response models

  • Published:
Journal of Pharmacokinetics and Pharmacodynamics Aims and scope Submit manuscript

Abstract

In the field of hematology, several mechanism-based pharmacokinetic-pharmacodynamic models have been developed to understand the dynamics of several blood cell populations under different clinical conditions while accounting for the essential underlying principles of pharmacology, physiology and pathology. In general, a population of blood cells is basically controlled by two processes: the cell production and cell loss. The assumption that each cell exits the population when its lifespan expires implies that the cell loss rate is equal to the cell production rate delayed by the lifespan and justifies the use of delayed differential equations for compartmental modeling. This review is focused on lifespan models based on delayed differential equations and presents the structure and properties of the basic lifespan indirect response (LIDR) models for drugs affecting cell production or cell lifespan distribution. The LIDR models for drugs affecting the precursor cell production or decreasing the precursor cell population are also presented and their properties are discussed. The interpretation of transit compartment models as LIDR models is reviewed as the basis for introducing a new LIDR for drugs affecting the cell lifespan distribution. Finally, the applications and limitations of the LIDR models are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Perez-Ruixo JJ, de Ridder F, Kimko H, Samtani M, Cox E, Mohanty S, Vermeulen A (2008) Simulation in clinical drug development. In: Bertau M, Mosekilde E, Westerhoff HV (eds) Biosimulation in drug development. Wiley-VCH Verlag GmbH & Co KGaA, Weinheim, pp 3–24

    Google Scholar 

  2. Mager DE, Wyska E, Jusko WJ (2003) Diversity of mechanism-based pharmacodynamic models. Drug Metab Dispos 31:510–519

    Article  PubMed  CAS  Google Scholar 

  3. Mackey MC (1996) Mathematical models of hematopoietic cell replication and control. In: Othamer HG (ed) The art of mathematical modeling: case ctudies in ecology, physiology and biofluids. Prentice Hall, New York

    Google Scholar 

  4. Krzyzanski W, Ramakrishnan R, Jusko WJ (1999) Basic pharmacodynamic models for agents that alter production of natural cells. J Pharmacokinet Biopharm 27:467–489

    PubMed  CAS  Google Scholar 

  5. Krzyzanski W, Perez-Ruixo JJ, Vermeulen A (2008) Basic pharmacodynamic models for agents that alter the lifespan distribution of natural cells. J Pharmacokin Pharmacodyn 35:349–377

    Article  CAS  Google Scholar 

  6. Krzyzanski W, Jusko WJ (2002) Multiple-pool cell lifespan model of hematologic effects of anticancer agents. J Pharmacokin Pharmacodyn 29:311–337

    Article  CAS  Google Scholar 

  7. Harker LA, Roskos LK, Marzec UM, Carter RA, Cherry JK, Sundell B, Cheung EL, Terry D, Sheridan W (2000) Effects of megakaryocyte growth and development factor on platelet production, platelet life span, and platelet function in healthy human volunteers. Blood 95:2514–2522

    PubMed  CAS  Google Scholar 

  8. Roskos LK, Lum Lockbaum P, Schwab G, Yang B-B (2006) Pharmacokinetic/pharmacodynamic modeling of pegfilgrastim in healthy subjects. J Clin Pharmacol 46:747–757

    Article  PubMed  CAS  Google Scholar 

  9. Wang YM, Krzyzanski W, Doshi S, Xiao JJ, Pérez-Ruixo JJ AT, Chow AT (2010) Pharmacodynamics-mediated drug disposition (PDMDD) and precursor pool lifespan model for single dose of romiplostim in healthy subjects. AAPS J 12:729–740

    Article  PubMed  CAS  Google Scholar 

  10. Pérez-Ruixo JJ, Krzyzanski W, Bouman-Thio E, Miller B, Jang H, Bai SA, Zhou H, Yohrling J, Cohen A, Burggraaf J, Franson K, Davis HM (2009) Pharmacokinetics and pharmacodynamics of the erythropoietin Mimetibody construct CNTO 528 in healthy subjects. Clin Pharmacokinet 48:601–613

    Article  PubMed  Google Scholar 

  11. Foley C, Mackey MC (2009) Mathematical model for G-CSF administration after chemotherapy. J Theor Biol 257:27–44

    Article  PubMed  CAS  Google Scholar 

  12. Friberg LE, Karlsson MO (2003) Mechanistic models for myelosuppression. Invest New Drugs 21:183–194

    Article  PubMed  CAS  Google Scholar 

  13. Doshi S, Chow A, Pérez Ruixo JJ (2010) Exposure-response modeling of darbepoetin alfa in anemic patients with chronic kidney disease not receiving dialysis. J Clin Pharmacol 50(9 Suppl):75S–90S

    Article  PubMed  CAS  Google Scholar 

  14. Sun YN, DuBois DC, Almon RR, Jusko WJ (1998) Fourth-generation model for corticosteroid pharmacodynamics: a model for methylprednisolone effects on receptor/gene mediated glucocorticoid receptor down-regulation and tyrosine aminotransferase induction in rat liver. J Pharmacokinet Biopharm 26:289–317

    Article  PubMed  CAS  Google Scholar 

  15. Perlstein I, Stepansky D, Krzyzanski W, Hofman A (2002) A signal transduction pharmacodynamic model of the kinetics of parasympathomimetic activity of low-dose scopolamine and atropine in rats. J Pharm Sci 91:2500–2510

    Article  PubMed  CAS  Google Scholar 

  16. Mager DE, Jusko WJ (2001) Pharmacodynamic modeling of time-dependent transduction systems. Clin Pharmacol Ther 70:210–216

    Article  PubMed  CAS  Google Scholar 

  17. Loeffler M, Wichmann HE (1985) Structure of the model. In: Wichmann HE, Loeffler (eds) Mathematical modeling of cell proliferation: stem cell regulation in hemopoiesis, vol 1. CRC Press, Boca Raton

    Google Scholar 

  18. Loeffler M, Pantel K, Wulff H, Wichmann HE (1989) A mathematical model of erythropoiesis in mice and rats, Part 1: Structure of the model. Cell Tissue Kinet 22:13–30

    PubMed  CAS  Google Scholar 

  19. Schmitz S, Franke H, Brusis J, Wichmann HE (1993) Quantification of the cell kinetic effects of G-CSF using a model of human granulopoiesis. Exp Hematol 21:755–760

    PubMed  CAS  Google Scholar 

  20. Wichmann HE, Gerhardts MD, Spechtmeyer H, Gross R (1979) Mathematical model of thrombopoiesis in rats. Cell Tissue Kinet 12:551–567

    PubMed  CAS  Google Scholar 

  21. Freise KJ, Widness JA, Schmidt RL, Veng-Pedersen P (2007) Pharmacodynamic analysis of time-variant cellular disposition: reticulocyte disposition changes in phlebotomized sheep. J Pharmacokinet Pharmacodyn 34:519–547

    Article  PubMed  CAS  Google Scholar 

  22. Freise FJ, Widness JA, Schmidt RL, Veng-Pedersen P (2008) Modeling time variant distributions of cellular lifespans: increase in circulating reticulocyte lifespans following double phlebotomies in sheep. J Pharmacokinet Pharmacodyn 35:285–324

    Article  PubMed  Google Scholar 

  23. Freise FJ, Schmidt RL, Widness JA, Veng-Pedersen P (2008) Pharmacodynamic modeling of the effect of changes in the environment on cellular lifespan and cellular response. J Pharmacokinet Pharmacodyn 35:527–552

    Article  PubMed  Google Scholar 

  24. Krzyzanski W, Woo S, Jusko WJ (2006) Pharmacodynamic models for agents that alter production of natural. J Pharmacokinet Pharmacodyn 33:125–165

    Article  PubMed  CAS  Google Scholar 

  25. Dayneka NL, Garg W, Jusko WJ (1993) Comparison of four basic models of indirect pharmacodynamic responses. J Pharmacokinet Biopharm 21:457–478

    Article  PubMed  CAS  Google Scholar 

  26. Krzyzanski W, Jusko WJ (1997) Mathematical formalism for the properties of four basic models of indirect pharmacodynamic responses. J Pharmacokinet Biopharm 25:107–123

    Article  PubMed  CAS  Google Scholar 

  27. Krzyzanski W, Jusko WJ (1998) Integrated functions of four basic models of indirect pharmacodynamic response. J Pharm Sci 87:67–72

    Article  PubMed  CAS  Google Scholar 

  28. Friberg LE, Henningsson A, Maas H, Nguyen L, Karlsson MO (2002) Model of chemotherapy-induced myelosuppression with parameter consistency across drugs. J Clin Oncol 20:4713–4721

    Article  PubMed  Google Scholar 

  29. Krzyzanski W, Wiczling P, Lowe P, Pigeolet E, Fink M, Berghout A, Balser S (2010) Population modeling of filgrastim PK-PD in healthy adults following intravenous and subcutaneous administrations. J Clin Pharmacol 50(9 Suppl):101S–112S

    Article  PubMed  CAS  Google Scholar 

  30. Perez-Ruixo JJ, Krzyzanski W, Hing J (2008) Pharmacodynamic analysis of recombinant human erythropoietin effect on reticulocyte production rate and age distribution in healthy subjects. Clin Pharmacokinet 47:399–415

    Article  PubMed  CAS  Google Scholar 

  31. Hamrén B, Björk E, Sunzel M, Karlsson M (2008) Models for plasma glucose, HbA1c, and hemoglobin interrelationships in patients with type 2 diabetes following tesaglitazar treatment. Clin Pharmacol Ther 84:228–235

    Article  PubMed  Google Scholar 

  32. Agoram B, Heatherington AC, Gastonguay MR (2006) Development and evaluation of a population pharmacokinetic-pharmacodynamic model of darbepoetin alfa in patients with nonmyeloid malignancies undergoing multicycle chemotherapy. AAPS J 8:E552–E563

    Article  PubMed  CAS  Google Scholar 

  33. Krzyzanski W (2011) Interpretation of transit compartments pharmacodynamic models as lifespan based indirect response models. J Pharmacokinet Pharmacodyn 38:179–204

    Article  PubMed  Google Scholar 

  34. Holford N (2005) Pharmacokinetic/pharmacodynamic models for red cell responses to hematopoietic stimulation with and without chemotherapy. American Society of Clinical Pharmacology and Therapeutics Annual Meeting, Orlando, FL, March 2–5

  35. Budha NR, Kovar A, Meibohm B (2011) Comparative performance of cell lifespan and cell transit models for describing erythropoietic drug effects. AAPS J 13:650–661

    Article  PubMed  CAS  Google Scholar 

  36. Soto E, Staab A, Doege C, Freiwald M, Munzert G, Trocóniz IF (2011) Comparison of different semi-mechanistic models for chemotherapy-related neutropenia: application to BI 2536 a Plk-1 inhibitor. Cancer Chemother Pharmacol 68:1517–1527

    Article  PubMed  CAS  Google Scholar 

  37. Woo S, Krzyzanski W, Jusko WJ (2006) Pharmacokinetic and pharmacodynamic modeling of recombinant human erythropoietin after intravenous and subcutaneous administration in rats. J Pharmacol Exp Ther 319:1297-06

    Article  Google Scholar 

  38. Ramakrishnan R, Cheung WK, Farrell F, Joffee L, Jusko WJ (2003) Pharmacokinetic and pharmacodynamic modeling of recombinant human erythropoietin after intravenous and subcutaneous dose administration in cynomolgus monkeys. J Pharmacol Exp Ther 306:324–331

    Article  PubMed  CAS  Google Scholar 

  39. Ramakrishnan R, Cheung WK, Wacholtz MC, Minton N, Jusko WJ (2004) Pharmacokinetic and pharmacodynamic modeling of recombinant human erythropoietin after single and multiple doses in healthy volunteers. J Clin Pharmacol 44:991–1002

    Article  PubMed  CAS  Google Scholar 

  40. Krzyzanski W, Jusko WJ, Wacholtz MC, Minton N, Cheung WK (2005) Pharmacokinetic and pharmacodynamic modeling of recombinant human erythropoietin after multiple subcutaneous doses in healthy subjects. Eur J Pharm Sci 26:295–306

    Article  PubMed  CAS  Google Scholar 

  41. Woo S, Krzyzanski W, Duliege AM, Stead RB, Jusko WJ (2008) Population pharmacokinetics and pharmacodynamics of peptidic erythropoiesis receptor agonist (ERA) in healthy volunteers. J Clin Pharmacol 48:43–52

    Article  PubMed  CAS  Google Scholar 

  42. Uehlinger DE, Gotch FA, Sheiner LB (1992) A pharmacodynamic model of erythropoietin therapy for uremic anemia. Clin Pharmacol Ther 51:76–89

    Article  PubMed  CAS  Google Scholar 

  43. Freise KJ, Widness JA, Veng-Pedersen P (2010) Erythropoietic response to endogenous erythropoietin in premature very low birth weight infants. J Pharmacol Exp Ther 332:229–237

    Article  PubMed  CAS  Google Scholar 

  44. Samtani MN, Perez-Ruixo JJ, Brown K, Cerneus D, Molloy C (2009) Pharmacokinetic and pharmacodynamic modeling of pegylated thrombopoietin mimetic peptide (PEG-TPOm) after single intravenous dose in healthy subjects. J Clin Pharmacol 49:336–350

    Article  PubMed  CAS  Google Scholar 

  45. Mager DE, Woo S, Jusko WJ (2009) Scaling pharmacodynamics from in vitro and preclinical animal studies to humans. Drug Metab Pharmacokinet 24:16–24

    Article  PubMed  CAS  Google Scholar 

  46. Krzyzanski W, Perez-Ruixo JJ (2007) An assessment of recombinant human erythropoietin effect on reticulocyte production rate and lifespan distribution in healthy subjects. Pharm Res 24:758–771

    Article  PubMed  CAS  Google Scholar 

  47. Woo S, Krzyzanski W, Jusko WJ (2008) Pharmacodynamic model for chemotherapy induced anemia in rats. Cancer Chemother Pharmacol 62:123–133

    Article  PubMed  CAS  Google Scholar 

  48. Fetterly GJ, Tamburlin JM, Straubinger RM (2001) Paclitaxel pharmacodynamics: application of a mechanism-based neutropenia model. Biopharm Drug Dispos 22:251–261

    Article  PubMed  CAS  Google Scholar 

  49. Bulitta JB, Zhao P, Arnold RD, Kessler DR, Daifuku R, Pratt J, Luciano G, Hanauske A-R, Gelderblom H, Awada A, Jusko WJ (2009) Multiple-pool cell lifespan models for neutropenia to assess the population pharmacodynamics of unbound paclitaxel from two formulations in cancer patients. Cancer Chemother Pharmacol 63:1035–1048

    Article  PubMed  CAS  Google Scholar 

  50. Hairer E, Norsett SP, Wanner G (1993) Solving ordinary differential equations I: nonstiff problems. Springer, Berlin

    Google Scholar 

  51. Krzyzanski W, Bauer RJ (2011) Solving delay differential equations in S-ADAPT by methods of steps. p. 20 Abstr 2144 [www.page-meeting.org/?abstract=2144]

  52. Perez-Ruixo JJ, Kimko HC, Chow AT, Piotrovsky V, Krzyzanski W, Jusko WJ (2005) Population cell life span models for effects of drugs following indirect mechanisms of action. J Pharmacokinet Pharmacodyn 32:767–793

    Article  PubMed  Google Scholar 

  53. McKenzie SB (1996) Textbook of hematology. Williams & Wilkins, Baltimore

    Google Scholar 

  54. Miyasata M, Tanaka T (2010) Lymphocyte trafficking across high endothelial venules: Dogmas and enigmas. Nat Rev Immunol 4:360–370

    Article  Google Scholar 

  55. Krzyzanski W, Dmochowski J, Matsushima N, Jusko WJ (2006) Assessment of dosing impact on intra-individual variability in estimation of parameters for basic indirect response models. J Pharmacokinet Pharmacodyn 33:635–655

    Article  PubMed  Google Scholar 

  56. Khinkis LA, Krzyzanski W, Jusko WJ, Greco WR (2009) D-optimal designs for parameter estimation for indirect pharmacodynamics response models. J Pharmacokinet Pharmacodyn 36:523–539

    Article  PubMed  Google Scholar 

Download references

Acknowledgment

This work was supported in part by NIH grant GM57980.

Author information

Authors and Affiliations

  1. Department of Pharmaceutical Sciences, University at Buffalo, Buffalo, NY, USA

    Wojciech Krzyzanski

  2. Amgen Inc., Pharmacokinetics and Drug Metabolism, Thousand Oaks, CA, USA

    Juan Jose Perez Ruixo

Authors
  1. Wojciech Krzyzanski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juan Jose Perez Ruixo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wojciech Krzyzanski.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krzyzanski, W., Perez Ruixo, J.J. Lifespan based indirect response models. J Pharmacokinet Pharmacodyn 39, 109–123 (2012). https://doi.org/10.1007/s10928-011-9236-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10928-011-9236-y

Keywords

Search

Navigation