(432d) 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

Rajniak, P., Merck & Co., Inc.
Mifkovich, C., Merck & Co., Inc.
Farber, L., Merck & Co., Inc.

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 Rskin = 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 Rskin = 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.