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Transforming parts of a differential equations system to difference equations as a method for run-time savings in NONMEM
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
2010 (English)In: Journal of Pharmacokinetics and Pharmacodynamics, ISSN 1567-567X, E-ISSN 1573-8744, Vol. 37, no 5, 493-506 p.Article in journal (Refereed) Published
Abstract [en]

Computer models of biological systems grow more complex as computing power increase. Often these models are defined as differential equations and no analytical solutions exist. Numerical integration is used to approximate the solution; this can be computationally intensive, time consuming and be a large proportion of the total computer runtime. The performance of different integration methods depend on the mathematical properties of the differential equations system at hand. In this paper we investigate the possibility of runtime gains by calculating parts of or the whole differential equations system at given time intervals, outside of the differential equations solver. This approach was tested on nine models defined as differential equations with the goal to reduce runtime while maintaining model fit, based on the objective function value. The software used was NONMEM. In four models the computational runtime was successfully reduced (by 59-96%). The differences in parameter estimates, compared to using only the differential equations solver were less than 12% for all fixed effects parameters. For the variance parameters, estimates were within 10% for the majority of the parameters. Population and individual predictions were similar and the differences in OFV were between 1 and -14 units. When computational runtime seriously affects the usefulness of a model we suggest evaluating this approach for repetitive elements of model building and evaluation such as covariate inclusions or bootstraps.

Place, publisher, year, edition, pages
2010. Vol. 37, no 5, 493-506 p.
Keyword [en]
Population modeling, NONMEM, Differential equations solver, Run times
National Category
Medical and Health Sciences
URN: urn:nbn:se:uu:diva-134141DOI: 10.1007/s10928-010-9169-xISI: 000282873500003OAI: oai:DiVA.org:uu-134141DiVA: diva2:372154
Available from: 2010-11-24 Created: 2010-11-22 Last updated: 2012-08-01Bibliographically approved
In thesis
1. Population Pharmacodynamic Modeling and Methods for D2-receptor Antagonists
Open this publication in new window or tab >>Population Pharmacodynamic Modeling and Methods for D2-receptor Antagonists
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Early predictions of a potential drug candidate’s time-course of effect and side-effects, based on models describing drug concentrations, drug effects and disease progression, would be valuable to make drug development more efficient. Pharmacodynamic modeling can incorporate and propagate prior knowledge and be used for simulations of different scenarios.

In this thesis three population pharmacodynamic models were developed to describe the antipsychotic effects and the side-effects prolactin elevation and Extra Pyramidal Symptoms (EPS) following administration of D2-receptor antagonists, commonly used in the treatment of schizophrenia.

Model parameter estimates of prolactin elevating potencies of six compounds correlated with in vitro values of receptor affinities, and parameters related to diurnal prolactin variation and tolerance were similar for the different compounds. The developed prolactin model can thereby be used to predict the time-course of prolactin elevation in patients for a drug candidate using information on in vitro affinity to the D2-receptor. Furthermore, the clinical antipsychotic effect and the prolactin elevation was found to correlate on the individual level for the three antipsychotic compounds investigated and a quantitative relation between D2-receptor occupancy in the brain and prolactin elevation was established. These results support the use of prolactin concentrations as a biomarker in drug development or for individual dose adjustments in clinical care.

The developed model for spontaneously reported EPS adverse events, following treatment with one of five antipsychotics drugs, characterized both the duration and severity of EPS. The model successfully described both the proportions and number of transitions between severity grades and was shown to adequately simulate longitudinal categorical EPS data.

Complex pharmacodynamic models are often associated with long estimation times and non-normal distributions of individual parameters. A method for shortening computation times by substituting differential equations for difference equations was evaluated and shown to be valuable for some models. In addition, transformation of distributions allowed for non-normal distributions of between-subject variability to be better characterized and thereby simulation properties were improved.

In conclusion, population pharmacodynamic models for a range of D2-receptor antagonists were developed and together with the investigated methods the models can facilitate prediction of effects and side-effects in drug development.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2012. 69 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy, ISSN 1651-6192 ; 161
population modeling, schizophrenia, D2-antagonists, pharmacodynamics, drug development
National Category
Pharmaceutical Sciences
urn:nbn:se:uu:diva-172540 (URN)978-91-554-8346-3 (ISBN)
Public defence
2012-05-25, B41, Biomedicinskt Centrum, Husargatan 3, Uppsala, 13:15 (English)
Available from: 2012-05-03 Created: 2012-04-11 Last updated: 2012-08-01Bibliographically approved

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Friberg, Lena E.Karlsson, Mats O.
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