Stochastic differential equations modelling of levodopa concentration in patients with Parkinson's disease

• The purpose of this study is to investigate a pharmacokinetic model of levodopa concentration in patients with Parkinson's disease by introducing stochasticity so that inter-individual variability may be separated into measurement and system noise. It also aims to investigate whether the stochastic differential equations (SDE) model provide better fits than its ordinary differential equations (ODE) counterpart, by using a real data set. Westin et al. developed a pharmacokinetic-pharmacodynamic model for duodenal levodopa infusion described by four ODEs, the first three of which define the pharmacokinetic model. In this study, system noise variables are added to the aforementioned first three equations through a standard Wiener process, also known as Brownian motion. The R package PSM for mixed-effects models is used on data from previous studies for modelling levodopa concentration and parameter estimation. First, the diffusion scale parameter, σ, and bioavailability are estimated with the SDE model. Second, σ is fixed to integer values between 1 and 5, and bioavailability is estimated. Cross-validation is performed to determine whether the SDE based model explains the observed data better or not by comparingthe average root mean squared errors (RMSE) of predicted levodopa concentration. Both ODE and SDE models estimated bioavailability to be about 88%. The SDE model converged at different values of σ that were signicantly different from zero while estimating bioavailability to be about 88%. The average RMSE for the ODE model wasfound to be 0.2980, and the lowest average RMSE for the SDE model was 0.2748 when σ was xed to 4. Both models estimated similar values for bioavailability, and the non-zero σ estimate implies that the inter-individual variability may be separated. However, the improvement in the predictive performance of the SDE model turned out to be rather small, compared to the ODE model.

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Nyckelord

levodopa

parkinson's disease

pharmacokinetic model

stochastic modelling

PSM.

Allmänt Mikrodataaanalys - metod

General Microdata Analysis - methods

Publikations- och innehållstyp

vet (ämneskategori)

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