Lyophilization of pharmaceutical injections: theoretical physical model

A physical model for the lyophilization kinetics of parenteral formulations is presented. Mathematical relationships are derived, which involve the simultaneous change in the receding boundary of the ice-vapor interface with time as well as water vapor diffusion across the dry porous matrix and boundary layer. Heat from an external heat source is transferred across the frozen solution to the receding ice surface. The model predicts that the water lost and the receding boundary distance are linearly related to the square root of time when lyophilization is matrix controlled. The mathematical descriptions are predictive of the physicochemical and transport events and can lead to the design of quantitative experiments to relate theory to formulation design.