Experimental and Theoretical Study of Lyophilization From a Packing of Vials: Using of Tunable Diode Laser Absorption Spectroscopy (TDLAS) for Process Monitoring and Model Calibration

Objectives: 1/experimentally evaluate water sublimation and lyophilization of a pharmaceutical formulation from a packing of vials at different conditions; 2/monitor total sublimation and desorption rate using a tunable diode laser absorption spectroscopy (TDLAS) sensor; 3/evaluate distribution of heat transfer coefficients from gravimetric water sublimation studies; 4/develop mathematical models for water sublimation and primary drying from a packing of vials; 5/evaluate cake resistance parameters from the primary drying sublimation rates monitored by the TDLAS; 6/perform a qualitative comparison between the SEM images of cakes manufactured at different freezing conditions and cake properties evaluated by the model.

Methods: A simple gravimetric method was used to evaluate the mass of water sublimed at different locations within a laboratory scale (FTS-Lyostar II) lyophilizer. Unidirectional mathematical model for ice sublimation from a single vial was used for evaluation of heat transfer coefficients between the shelf and bottom of vials at different locations. Different cumulative distribution functions were tested for calculation of distribution of evaluated heat transfer coefficients. A mathematical model combining the distribution of heat transfer coefficients with the unidirectional model of primary drying in a vial was developed and employed for calculation of sublimation rates from a packing of vials. A simple optimization procedure was developed for evaluation of the cake resistance parameters (pore size and skin resistance) by fitting the model predictions to the TDLAS mass flux data. SEM imaging was used for visualization of the cake morphology.

Results: Weibull cumulative distribution function accurately describes the distribution of heat transfer coefficients of an inhomogeneous shelf.  Mathematical models for both, the pure ice sublimation and sublimation of water from a pharmaceutical (sucrose-based) formulation satisfactorily simulate the sublimation rates measured experimentally. A model assuming  a homogeneous porous cake was unable to describe experimental observation of a lyophilization cycle without annealing. On the other hand, a model assuming the presence of a skin (skin resistance R_skin = 0.7) at the cake surface followed by a porous structure with pore radii 70 microns  very well describes experimental observations. A faster sublimation was measured using the TDLAS for a cycle with annealing. The experimental mass flux can be satisfactorily predicted using a cake model with a thinner skin at the surface (skin resistance R_skin = 0.1) followed by a porous structure with pore radii 90 microns. SEM imaging nicely supports results of theoretical evaluation showing a thicker skin followed by smaller pores for cakes from the cycle without annealing. 

Conclusions: A multi-dimensional mathematical model of lyophilization from packing of vials in combination with the TDLAS probe is a useful tool for better understanding and faster development and scale-up of lyophilization processes.