Application of Stochastic Differential Equations to Disease Progression in a Neuropathic Pain Model in Rats
V.L. Di Iorio(1), M. Danhof(1), O. E. Della Pasqua(1,2)
(1) Division of Pharmacology, Leiden/Amsterdam Center for Drug Research, Leiden, the Netherlands; (2) GlaxoSmithKline, Clinical Pharmacology Modelling and Simulation, Stockley Park, UK
Background: In nonlinear mixed-effects modelling the variability may be decomposed into an inter-individual, an inter-occasion and a residual component. Stochastic Differential Equations (SDE) can be used instead of Ordinary Differential Equations (ODE) to further decompose the residual variability into system and measurement noise. The former may reflect true physiological fluctuations in the biological system, whilst the latter encompasses measurement errors and other unexplained sources of variability.
Objectives: The aim of this work was to evaluate the feasibility of using SDEs in a model of Neuropathic Pain in rats, as compared to the use of Ordinary Differential Equation.
Methods: Neuropathic Pain was induced in rats by Chronic Constrictive Injury (CCI), i.e. applying loose ligatures around the sciatic nerve. Pawn Withdrawal Threshold (PWT), measured in grams, was used as a measure of response. For the current analysis only placebo data were available. PKPD models were built with both SDE and ODE. Subsequently, the models derived were used to perform simulation in order to compare performances of ODE and SDE. Several scenarios were also used to determine the impact of different sampling schedules on the predictive value of the models. Data analysis was performed in NONMEM v7. R was used for data manipulation, statistical and graphical summaries.
Results: Despite the increased complexity, the use of SDEs does not seem to capture time dependent changes in CCI-induced allodynia. The results of the simulations suggest that limitations in the sampling scheme may contribute to the limited performance of SDEs.
Conclusions: Our findings demonstrate that SDEs are a valuable tool in modelling of disease progression. However, their usefulness in capturing time-dependent oscillations in system-specific parameters is very sensitive to sampling frequency.
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