Feedback control indirect response models

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


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.


Autoregulation Feedback control Biological control theory Indirect response models Integral feedback 



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.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

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

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