Journal of Pharmacokinetics and Pharmacodynamics

, Volume 46, Issue 1, pp 89–101 | Cite as

Indirect pharmacodynamic models for responses with circadian removal

  • Vivaswath S. Ayyar
  • Wojciech Krzyzanski
  • William J. JuskoEmail author
Original Paper


Rhythmicity in baseline responses over a 24-h period for an indirect pharmacological effect R(t) can arise from either a periodic time-dependent input rate \( k_{in} \left( t \right) \) or a periodic time-dependent loss constant \( k_{out} \left( t \right) \). If either \( k_{in} \left( t \right) \) or \( k_{out} \left( t \right) \) follows some nonstationary biological rhythm (e.g., circadian), then the response R(t) also displays a periodic behavior. Indirect response models assuming time-dependent input rates \( \left[ {k_{in} \left( t \right)} \right] \) have been utilized to capture drug effects on various physiological responses such as hormone suppression, immune cell trafficking, and gene expression in tissues. This paradigm was extended to consider responses with circadian-controlled loss \( \left[ {k_{out} \left( t \right)} \right] \) mechanisms. Theoretical equations describing this model are presented and simulations were performed to examine expected response behaviors. The model was able to capture the chronobiology and pharmacodynamics of applicable drug responses, including the uricosuric effects of lesinurad in humans, suppression of the beta amyloid (Aβ) peptide by a gamma-secretase inhibitor in mouse brain, and the modulation of extracellular dopamine by a dopamine transporter inhibitor in rat brain. This type of model has a mechanistic basis and shows utility for capturing drug responses displaying nonstationary baselines controlled by removal mechanism(s).


Circadian rhythm Nonstationary baseline Pharmacodynamics Indirect response model Periodic removal Mathematical modeling 



This work was supported by the National Institutes of Health - National Institute of General Medical Sciences [Grant GM24211].

Supplementary material

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Supplementary material 1 (XLSX 702 kb)
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Supplementary material 2 (DOCX 829 kb)
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Supplementary material 3 (DOCX 32 kb)


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Pharmaceutical Sciences, School of Pharmacy and Pharmaceutical SciencesState University of New York at BuffaloBuffaloUSA

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