A stochastic differential equation model for drug dissolution and its parameters

Area of Science:

• Pharmacokinetics and Pharmaceutical Sciences
• Mathematical Modeling
• Stochastic Processes

Background:

• Classical deterministic models for drug dissolution often assume constant rates, which may not reflect real-world variability.
• Stochastic processes offer a more realistic framework for modeling dynamic biological and chemical phenomena, including drug dissolution.

Purpose of the Study:

• To present a generalized stochastic differential equation model for drug dissolution.
• To investigate the half-dissolution time within the stochastic framework.
• To develop and apply parameter estimation methods (Maximum Likelihood and Bayes) for the stochastic model.

Main Methods:

• Formulation of a stochastic differential equation (SDE) to describe drug dissolution, incorporating white noise.
• Analysis of the half-dissolution time based on the proposed SDE.
• Development of Maximum Likelihood and Bayes estimation techniques for model parameters.
• Validation of the model and estimation methods using experimental drug dissolution data.

Main Results:

• The stochastic model generalizes the deterministic first-order dissolution model by introducing randomness.
• Parameter estimation methods (Maximum Likelihood and Bayes) were successfully developed and applied.
• Estimates for the fractional dissolution rate from the stochastic model were systematically lower than those from the deterministic model, attributed to nonlinear relationships.

Conclusions:

• The stochastic differential equation model provides a more nuanced understanding of drug dissolution compared to deterministic models.
• The developed estimation methods are effective for characterizing drug dissolution under variability.
• The findings highlight the importance of considering stochasticity in dissolution modeling for accurate pharmacokinetic predictions.