The AAPS Journal

, Volume 17, Issue 2, pp 447–456 | Cite as

Stochastic Process Pharmacodynamics: Dose Timing in Neonatal Gentamicin Therapy as an Example

  • Tomas Radivoyevitch
  • Nopphon Siranart
  • Lynn Hlatky
  • Rainer SachsEmail author
Research Article


We consider dosing regimens designed to cure patients by eradicating colony forming units (CFU) such as bacteria. In the field of “population” pharmaco-kinetics/dynamics (PK/PD), inter-individual variability (IIV) of patients is estimated using model parameter statistical distributions. We consider a more probabilistic approach to IIV called stochastic process theory, motivated by the fact that tumor treatment planning uses both approaches. Stochastic process PD can supply additional insights and suggest different dosing regimens due to its emphasis on the probability of complete CFU eradication and its predictions on “pure chance” fluctuations of CFU number per patient when treatment has reduced this integer to less than ~100. To exemplify the contrast between stochastic process PD models and standard deterministic PD models, which track only average CFU number, we analyze, neglecting immune responses, neonatal intravenous gentamicin dosing regimens directed against Escherichia coli. Our stochastic calculations predict that the first dose is crucial for CFU eradication. For example, a single 6 mg/kg dose is predicted to have a higher eradication probability than four daily 4 mg/kg doses. We conclude: (1) neonatal gentamicin dosing regimens with larger first doses but smaller total doses deserve investigation; (2) in general, if standard PK/PD models predict average CFU number drops substantially below 100, the models should be modified to incorporate stochastic effects more accurately, and will then usually make more favorable, or less unfavorable, predictions for front boosting (“hit hard early”). Various caveats against over-interpreting the calculations are given.


anti-bacterial dosing regimens front boosting PK/PD eradication probability small-number stochastic fluctuations stochastic birth-death cell population dynamics 



Support from NIH NCI ICBP U54CA149233 (LH and RKS), from the University of California Undergraduate Research Program (NS), and from the Cleveland Clinic Foundation (TR) is gratefully acknowledged. We thank Prof. L. Hanin for useful criticisms.

Conflict of interest

There are no conflicts of interest related to the work in the manuscript.


Use of the information in this manuscript for commercial, noncommercial, research, or purposes other than peer review not permitted prior to publication without the expressed written permission from the author.

Supplementary material

12248_2014_9715_MOESM1_ESM.docx (242 kb)
ESM 1 (DOCX 241 kb)


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Copyright information

© American Association of Pharmaceutical Scientists 2015

Authors and Affiliations

  • Tomas Radivoyevitch
    • 1
  • Nopphon Siranart
    • 2
  • Lynn Hlatky
    • 3
  • Rainer Sachs
    • 2
    Email author
  1. 1.Department of Quantitative Health SciencesCleveland ClinicClevelandUSA
  2. 2.Department MathematicsUniversity of CaliforniaBerkeleyUSA
  3. 3.Center of Cancer Systems Biology, GRITufts University School of MedicineBostonUSA

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