Investigating Stochastic Differential Equations Modelling for Levodopa Infusion in Patients with Parkinson's Disease

BACKGROUND AND OBJECTIVES: Levodopa concentration in patients with Parkinson's disease is frequently modelled with ordinary differential equations (ODEs). Here, we investigate a pharmacokinetic model of plasma levodopa concentration in patients with Parkinson's disease by introducing stochasticity to separate the intra-individual variability into measurement and system noise, and to account for auto-correlated errors. We also investigate whether the induced stochasticity provides a better fit than the ODE approach. METHODS: In this study, a system noise variable is added to the pharmacokinetic model for duodenal levodopa/carbidopa gel (LCIG) infusion described by three ODEs through a standard Wiener process, leading to a stochastic differential equations (SDE) model. The R package population stochastic modelling (PSM) was used for model fitting with data from previous studies for modelling plasma levodopa concentration and parameter estimation. First, the diffusion scale parameter (σw), measurement noise variance, and bioavailability are estimated with the SDE model. Second, σw is fixed to certain values from 0 to 1 and bioavailability is estimated. Cross-validation was performed to compare the average root mean square errors (RMSE) of predicted plasma levodopa concentration. RESULTS: Both the ODE and the SDE models estimated bioavailability to be approximately 75%. The SDE model converged at different values of σw that were significantly different from zero. The average RMSE for the ODE model was 0.313, and the lowest average RMSE for the SDE model was 0.297 when σw was fixed to 0.9, and these two values are significantly different. CONCLUSIONS: The SDE model provided a better fit for LCIG plasma levodopa concentration by approximately 5.5% in terms of mean percentage change of RMSE

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

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