Advertisement

Feedback control indirect response models

  • Yaping Zhang
  • David Z. D’ArgenioEmail author
Original Paper

Abstract

A general framework is introduced for modeling pharmacodynamic processes that are subject to autoregulation, which combines the indirect response (IDR) model approach with methods from classical feedback control of engineered systems. The canonical IDR models are modified to incorporate linear combinations of feedback control terms related to the time course of the difference (the error signal) between the pharmacodynamic response and its basal value. Following the well-established approach of traditional engineering control theory, the proposed feedback control indirect response models incorporate terms proportional to the error signal itself, the integral of the error signal, the derivative of the error signal or combinations thereof. Simulations are presented to illustrate the types of responses produced by the proposed feedback control indirect response model framework, and to illustrate comparisons with other PK/PD modeling approaches incorporating feedback. In addition, four examples from literature are used to illustrate the implementation and applicability of the proposed feedback control framework. The examples reflect each of the four mechanisms of drug action as modeled by each of the four canonical IDR models and include: selective serotonin reuptake inhibitors and extracellular serotonin; histamine H2-receptor antagonists and gastric acid; growth hormone secretagogues and circulating growth hormone; β2-selective adrenergic agonists and potassium. The proposed feedback control indirect response approach may serve as an exploratory modeling tool and may provide a bridge for development of more mechanistic systems pharmacology models.

Keywords

Autoregulation Feedback control Biological control theory Indirect response models Integral feedback 

Notes

Acknowledgments

The authors gratefully acknowledge Professor Donald E. Mager for his many insightful suggestions. This work was supported by Grant NIH/NIBIB P41-EB001978 (DZD).

Compliance with ethical standards

Conflict of interest

Y. Zhang and D.Z. D’Argenio declare no conflict of interests. Y. Zhang is currently employed at Genentech.

References

  1. 1.
    Grodins FS, Gray JS, Schroeder KR, Norins AL, Jones RW (1954) Respiratory responses to CO2 inhalation; a theoretical study of a nonlinear biological regulator. J Appl Physiol 7(3):283–308PubMedGoogle Scholar
  2. 2.
    Arthur CG, Carl EJ, Thomas GC (1973) Circulatory physiology: cardiac output and its regulation. W.B. Saunders Company, PhiladelphiaGoogle Scholar
  3. 3.
    Sherman PM, Stark L (1957) A servoanalytic study of consensual pupil reflex to light. J Neurophysiol 20(1):17–26PubMedGoogle Scholar
  4. 4.
    Bolie VW (1961) Coefficients of normal blood glucose regulation. J Appl Physiol 16:783–788PubMedGoogle Scholar
  5. 5.
    Yates FE, Urquhart J (1962) Control of plasma concentrations of adrenocortical hormones. Physiol Rev 42:359–433PubMedGoogle Scholar
  6. 6.
    Euler CV (1964) The gain of the hypothalamic temperature regulating mechanisms. Prog Brain Res 5:127–131CrossRefGoogle Scholar
  7. 7.
    Milhorn HT (1966) Application of control theory to physiological Systems. W. B. Saunders Company, PhiladelphiaGoogle Scholar
  8. 8.
    Yi TM, Huang Y, Simon MI, Doyle J (2000) Robust perfect adaptation in bacterial chemotaxis through integral feedback control. Proc Natl Acad Sci USA 97(9):4649–4653CrossRefPubMedPubMedCentralGoogle Scholar
  9. 9.
    Koulnis M, Liu Y, Hallstrom K, Socolovsky M (2011) Negative autoregulation by Fas stabilizes adult erythropoiesis and accelerates its stress response. PLoS One 6(7):e21192. doi: 10.1371/journal.pone.0021192 CrossRefPubMedPubMedCentralGoogle Scholar
  10. 10.
    Sturm OE, Orton R, Grindlay J, Birtwistle M, Vyshemirsky V, Gilbert D, Calder M, Pitt A, Kholodenko B, Kolch W (2010) The mammalian MAPK/ERK pathway exhibits properties of a negative feedback amplifier. Sci Signal 3(153):ra90. doi: 10.1126/scisignal.2001212 CrossRefPubMedGoogle Scholar
  11. 11.
    Gabrielsson J, Peletier LA (2008) A flexible nonlinear feedback system that captures diverse patterns of adaptation and rebound. AAPS J 10(1):70–83. doi: 10.1208/s12248-008-9007-x CrossRefPubMedPubMedCentralGoogle Scholar
  12. 12.
    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(24):4713–4721CrossRefPubMedGoogle Scholar
  13. 13.
    Woo S, Krzyzanski W, Jusko WJ (2008) Pharmacodynamic model for chemotherapy-induced anemia in rats. Cancer Chemother Pharmacol 62(1):123–133. doi: 10.1007/s00280-007-0582-9 CrossRefPubMedGoogle Scholar
  14. 14.
    Bundgaard C, Larsen F, Jorgensen M, Gabrielsson J (2006) Mechanistic model of acute autoinhibitory feedback action after administration of SSRIs in rats: application to escitalopram-induced effects on brain serotonin levels. Eur J Pharm Sci 29(5):394–404. doi: 10.1016/j.ejps.2006.08.004 CrossRefPubMedGoogle Scholar
  15. 15.
    Dayneka NL, Garg V, Jusko WJ (1993) Comparison of four basic models of indirect pharmacodynamic responses. J Pharmacokinet Biopharm 21(4):457–478CrossRefPubMedPubMedCentralGoogle Scholar
  16. 16.
    Astrom KJ, Murray RM (2010) Feedback systems. Princeton University Press, PrincetonGoogle Scholar
  17. 17.
    Ahlstrom C, Kroon T, Peletier LA, Gabrielsson J (2013) Feedback modeling of non-esterified fatty acids in obese Zucker rats after nicotinic acid infusions. J Pharmacokinet Pharmacodyn 40(6):623–638. doi: 10.1007/s10928-013-9335-z CrossRefPubMedGoogle Scholar
  18. 18.
    Wakelkamp M, Alvan G, Gabrielsson J, Paintaud G (1996) Pharmacodynamic modeling of furosemide tolerance after multiple intravenous administration. Clin Pharmacol Ther 60(1):75–88. doi: 10.1016/S0009-9236(96)90170-8 CrossRefPubMedGoogle Scholar
  19. 19.
    D’Argenio DZ, Schumtizky A, Wang X (2009) ADAPT 5 user’s guide: pharmacokinetic/pharmacodynamic systems analysis software. Biomedical Simulations Resource, Los AngelesGoogle Scholar
  20. 20.
    Harrold JM, Straubinger RM, Mager DE (2012) Combinatorial chemotherapeutic efficacy in non-Hodgkin lymphoma can be predicted by a signaling model of CD20 pharmacodynamics. Cancer Res 72(7):1632–1641. doi: 10.1158/0008-5472.CAN-11-2432 CrossRefPubMedPubMedCentralGoogle Scholar
  21. 21.
    Sharma A, Ebling WF, Jusko WJ (1998) Precursor-dependent indirect pharmacodynamic response model for tolerance and rebound phenomena. J Pharm Sci 87(12):1577–1584CrossRefPubMedGoogle Scholar
  22. 22.
    Pineyro G, Blier P (1999) Autoregulation of serotonin neurons: role in antidepressant drug action. Pharmacol Rev 51(3):533–591PubMedGoogle Scholar
  23. 23.
    Mathot RA, Geus WP (1999) Pharmacodynamic modeling of the acid inhibitory effect of ranitidine in patients in an intensive care unit during prolonged dosing: characterization of tolerance. Clin Pharmacol Ther 66(2):140–151. doi: 10.1053/cp.1999.v66.99988 CrossRefPubMedGoogle Scholar
  24. 24.
    Shulkes A, Read M (1991) Regulation of somatostatin secretion by gastrin- and acid-dependent mechanisms. Endocrinology 129(5):2329–2334. doi: 10.1210/endo-129-5-2329 CrossRefPubMedGoogle Scholar
  25. 25.
    Nwokolo CU, Smith JT, Sawyerr AM, Pounder RE (1991) Rebound intragastric hyperacidity after abrupt withdrawal of histamine H2 receptor blockade. Gut 32(12):1455–1460CrossRefPubMedPubMedCentralGoogle Scholar
  26. 26.
    Muller EE, Locatelli V, Cocchi D (1999) Neuroendocrine control of growth hormone secretion. Physiol Rev 79(2):511–607PubMedGoogle Scholar
  27. 27.
    Agerso H, Ynddal L, Sogaard B, Zdravkovic M (2001) Pharmacokinetic and pharmacodynamic modeling of NN703, a growth hormone secretagogue, after a single po dose to human volunteers. J Clin Pharmacol 41(2):163–169CrossRefPubMedGoogle Scholar
  28. 28.
    Greenlee M, Wingo CS, McDonough AA, Youn JH, Kone BC (2009) Narrative review: evolving concepts in potassium homeostasis and hypokalemia. Ann Intern Med 150(9):619–625CrossRefPubMedPubMedCentralGoogle Scholar
  29. 29.
    Jonkers R, Van Boxtel CJ, Oosterhuis B (1987) Beta-2-adrenoceptor-mediated hypokalemia and its abolishment by oxprenolol. Clin Pharmacol Ther 42(6):627–633CrossRefPubMedGoogle Scholar
  30. 30.
    Adolph EF (1961) Early concepts of physiological regulations. Physiol Rev 41:737–770PubMedGoogle Scholar
  31. 31.
    Cannon WB (1929) Organization for physiological homeostasis. Physiol Rev 9(3):399–431Google Scholar
  32. 32.
    Yamashiro SM, Grodins FS (1971) Optimal regulation of respiratory airflow. J Appl Physiol 30(5):597–602PubMedGoogle Scholar
  33. 33.
    D’Argenio DZ, Yamashiro SM, Grodins FS (1979) Minimum energy expenditure as a basis for myocardial regulation. Fed Proceedings 38:890Google Scholar
  34. 34.
    Isaacs FJ, Hasty J, Cantor CR, Collins JJ (2003) Prediction and measurement of an autoregulatory genetic module. Proc Natl Acad Sci USA 100(13):7714–7719. doi: 10.1073/pnas.1332628100 CrossRefPubMedPubMedCentralGoogle Scholar
  35. 35.
    Urquhart J (2003) History-informed perspectives on the modeling and simulation of therapeutic drug actions. In: Kimko HC, Duffull SB (eds) Simulation for designing clinical trials. Marcel Dekker, New York, pp 245–269Google Scholar
  36. 36.
    Cole KS (1949) Dynamic electrical characteristics of the squid axon membrane. Annu Rev Physiol 3:253–258Google Scholar
  37. 37.
    Donald DE, Milburn SE, Shepherd JT (1964) Effect of cardiac denervation on the maximal capacity for exercise in the racing greyhound. J Appl Physiol 19:849–852PubMedGoogle Scholar
  38. 38.
    Khoo MCK (2000) Physiological control systems. Wiley-IEEE Press, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Biomedical EngineeringUniversity of Southern CaliforniaLos AngelesUSA

Personalised recommendations