A population growth model of dissolution

Area of Science:

• Pharmaceutical Sciences
• Physical Chemistry
• Pharmacokinetics

Background:

• Traditional drug dissolution models often rely on Fick's law of diffusion and assume time continuity.
• These assumptions limit applicability to homogeneous systems and may not accurately reflect complex biological environments.
• A need exists for a more versatile dissolution model applicable to both homogeneous and heterogeneous media.

Purpose of the Study:

• To develop a novel drug dissolution model independent of time continuity and Fick's law.
• To create a model applicable to both homogeneous and heterogeneous dissolution media.
• To facilitate the correlation of in vitro dissolution data with in vivo observations.

Main Methods:

• A discrete time model was developed, considering mass dissolved as a function of discrete time generations (n).
• A recurrence equation was derived: phi n+1 = phi n + r(1 - phi n)(1 - phi n X0/theta).
• The model incorporates dimensionless parameters r (proportionality constant) and theta/X0 (related to drug solubility and dose).

Main Results:

• The model exhibits two steady-state solutions based on the ratio of drug dose (X0) to solubility (theta).
• It accurately describes dissolution profiles, showing monotonic exponential increases to a steady state.
• The model successfully fitted danazol dissolution data after time scale transformation and predicted fraction of dose absorbed for highly permeable drugs.

Conclusions:

• The developed model offers a new approach to drug dissolution, free from diffusion principles.
• Its applicability to both homogeneous and heterogeneous media enhances its utility for in vitro-in vivo correlations.
• This model can bridge the gap between laboratory dissolution studies and the complex biological environment of the gastrointestinal tract.