Modeling of heat and mass transfer processes for the gap-lyophilization system using the mannitol-trehalose-NaCl formulation.

Gap freezing (GF) is a new concept that was developed to reduce the primary drying time using an alternative freezing process. The purpose of this investigation was to determine the gap-tray heat transfer coefficient, Kgtr , and to investigate the effect of gap lyophilization on cycle reduction of a mannitol-trehalose-NaCl (MTN) formulation. The values of Kgtr were measured using the product temperature profiles in three different configurations: (1) shelf freezing followed by shelf drying (denoted as SF-SD), (2) GF followed by SD (denoted as GF-SD), and (3) GF followed by gap drying (denoted as GF-GD). For the lyophilization cycle using shelf drying (SF-SD), 80% of the heat transferred during primary drying was from the bottom shelf to the vial, versus 20% via radiation from the top shelf. For the lyophilization cycle using gap drying (GF-GD), only 37% of the heat transferred during primary drying was from the bottom shelf to the vial versus 63% via radiation from the top shelf. Furthermore, GF in conjunction with annealing significantly reduces the dry layer resistance of the MTN formulation, which is the opposite of what was observed with a conventional freezing cycle.

Gap-freezing approach for shortening the lyophilization cycle time of pharmaceutical formulations-demonstration of the concept.

During gap freezing, vials are placed on a metal tray, which is separated from the shelf surface with a small air gap that eliminates significant conductive heat transfer from the shelf to the bottom of the vial. The purpose of this freezing approach is to reduce the lyophilization cycle time of various amorphous formulations by nearly isothermal freezing. Such isothermal freezing promotes the formation of large ice crystals, and thus large pores throughout the cake, which subsequently accelerates the primary drying rate. The nucleation temperature using gap freezing, for the experimental conditions tested, was in the range of -1°C to -6°C, much higher than the range of -10°C to -14°C found using conventional shelf freezing. Isothermal freezing becomes effective when the gap is greater than 3 mm. The pore sizes and cake resistance during primary drying for various formulations were determined using the pore diffusion model developed by Kuu et al. (Pharm Dev Technol, 2011, 16(4): 343-357). Reductions in primary drying time were 42% (for 10% sucrose), 45% (for 10% trehalose), and 33% (for 5% sucrose).

Quality by design in formulation and process development for a freeze-dried, small molecule parenteral product: a case study.

A case study has been developed to illustrate one way of incorporating a Quality by Design approach into formulation and process development for a small molecule, freeze-dried parenteral product. Sodium ethacrynate was chosen as the model compound. Principal degradation products of sodium ethacrynate result from hydrolysis of the unsaturated ketone in aqueous solution, and dimer formation from a Diels-Alder condensation in the freeze-dried solid state. When the drug crystallizes in a frozen solution, the eutectic melting temperature is above -5°C. Crystallization in the frozen system is affected by pH in the range of pH 6-8 and buffer concentration in the range of 5-50 mM, where higher pH and lower buffer concentration favor crystallization. Physical state of the drug is critical to solid state stability, given the relative instability of amorphous drug. Stability was shown to vary considerably over the ranges of pH and buffer concentration examined, and vial-to-vial variability in degree of crystallinity is a potential concern. The formulation design space was constructed in terms of pH and drug concentration, and assuming a constant 5 mM concentration of buffer. The process design space is constructed to take into account limitations on the process imposed by the product and by equipment capability.

Product mass transfer resistance directly determined during freeze-drying cycle runs using tunable diode laser absorption spectroscopy (TDLAS) and pore diffusion model.

The pore diffusion model is used to express the dry layer mass transfer resistance, [Formula: see text], as a function of the ratio r(e)/?, where r(e) is the effective pore radius and ? is the tortuosity factor of the dry layer. Using this model, the effective pore radius of the dry layer can be estimated from the sublimation rate and product temperature profiles measured during primary drying. Freeze-drying cycle runs were performed using the LyoStar II dryer (FTS Systems), with real-time sublimation rate profiles during freeze drying continuously measured by tunable diode laser absorption spectroscopy (TDLAS). The formulations chosen for demonstration of the proposed approach include 5% mannitol, 5% sucrose, 5% lactose, 3% mannitol plus 2% sucrose, and a parenteral nutrition formulation denoted VitaM12. The three different methods used for determination of the product resistance are: (1) Using both the sublimation rate and product temperature profiles, (2) using the sublimation rate profile alone, and (3) using the product temperate profile alone. Unlike the second and third methods, the computation procedure of first method does not need solution of the complex heat and mass transfer equations.

Rapid freeze-drying cycle optimization using computer programs developed based on heat and mass transfer models and facilitated by tunable diode laser absorption spectroscopy (TDLAS).

Computer programs in FORTRAN were developed to rapidly determine the optimal shelf temperature, T(f), and chamber pressure, P(c), to achieve the shortest primary drying time. The constraint for the optimization is to ensure that the product temperature profile, T(b), is below the target temperature, T(target). Five percent mannitol was chosen as the model formulation. After obtaining the optimal sets of T(f) and P(c), each cycle was assigned with a cycle rank number in terms of the length of drying time. Further optimization was achieved by dividing the drying time into a series of ramping steps for T(f), in a cascading manner (termed the cascading T(f) cycle), to further shorten the cycle time. For the purpose of demonstrating the validity of the optimized T(f) and P(c), four cycles with different predicted lengths of drying time, along with the cascading T(f) cycle, were chosen for experimental cycle runs. Tunable diode laser absorption spectroscopy (TDLAS) was used to continuously measure the sublimation rate. As predicted, maximum product temperatures were controlled slightly below the target temperature of -25 degrees C, and the cascading T(f)-ramping cycle is the most efficient cycle design. In addition, the experimental cycle rank order closely matches with that determined by modeling.

Rapid determination of vial heat transfer parameters using tunable diode laser absorption spectroscopy (TDLAS) in response to step-changes in pressure set-point during freeze-drying.

The purpose of this study was to perform a rapid determination of vial heat transfer parameters, that is, the contact parameter K(cs) and the separation distance l(v), using the sublimation rate profiles measured by tunable diode laser absorption spectroscopy (TDLAS). In this study, each size of vial was filled with pure water followed by a freeze-drying cycle using a LyoStar II dryer (FTS Systems) with step-changes of the chamber pressure set-point at to 25, 50, 100, 200, 300, and 400 mTorr. K(cs) was independently determined by nonlinear parameter estimation using the sublimation rates measured at the pressure set-point of 25 mTorr. After obtaining K(cs), the l(v) value for each vial size was determined by nonlinear parameter estimation using the pooled sublimation rate profiles obtained at 25 to 400 mTorr. The vial heat transfer coefficient K(v), as a function of the chamber pressure, was readily calculated, using the obtained K(cs) and l(v) values. It is interesting to note the significant difference in K(v) of two similar types of 10 mL Schott tubing vials, primary due to the geometry of the vial-bottom, as demonstrated by the images of the contact areas of the vial-bottom.

Determination of shelf heat transfer coefficients along the shelf flow path of a freeze dryer using the shelf fluid temperature perturbation approach.

The spatial distribution of local shelf heat transfer coefficients, Ks, was determined by mapping the transient temperature response of the shelf surface along the serpentine internal channels of the shelf while the temperature of the heat transfer fluid was ramped from -40 degrees to 40 degrees C. The solution of a first-order non-steady-state differential equation resulted in a predicted shelf surface temperature as a function of the shelf fluid temperature at any point along the flow path. During the study, the shelf surfaces were maintained under a thermally insulated condition so that the heat transfers by gas conduction and radiation were negligible. To minimize heat conduction by gas, the chamber was evacuated to a low pressure, such as 100 mTorr. To minimize heat transfers between shelves, shelves were moved close together, with a gap of approximately 3 mm between any two shelves, because the shelf surface temperatures at corresponding vertical locations of two shelves are virtually equal. In addition, this also provides a shielding from radiation heat transfer from shelf to walls. Local heat transfer coefficients at the probed locations h(x) ( approximately Ks) were calculated by fitting the experimental shelf temperature response to the theoretical value. While the resulting values of K(s) are in general agreement with previously reported values, the values of Ks close to the inlet are significantly higher than those of other locations of the shelf channel. This observation is most likely attributed to the variation of the flow pattern of heat transfer fluid within the channels.

Rapid determination of dry layer mass transfer resistance for various pharmaceutical formulations during primary drying using product temperature profiles.

Mass transfer resistance of the dry layer during the primary drying phase of a lyophilizaton cycle is probably the most important factor affecting maximum product temperature and drying time. Product resistance parameters should be determined for each formulation because of their dependence of formulation composition and concentration. The purpose of this study was to determine the dry layer mass transfer resistance, using a simple and rapid method, for various pharmaceutical formulations during primary drying in a laboratory dryer, using monitored product temperature profiles. The mathematical tools used for the determination were a primary drying simulation program in conjunction with Powell's optimization algorithm. For each formulation studied, primary drying was performed using a shelf temperature of -15 or -20 degrees C and the chamber pressure controlled at 100 mTorr (0.1 Torr). The product temperature profiles (T(b)) during primary drying were recorded and became the input data for the parameter estimation. The normalized product resistance, R(pN), as a function of the dry layer thickness, l, can be described by: R(pN) = R(0) + A(1)l/(1 + A(2)l), where the constants R(0), A(1) and A(2) are product resistance parameters of water vapor through the dry layer. Even when the parameter A(1) was negative, indicating that product temperature atypically decreased over time, the dry layer product resistance parameters of the various pharmaceutical formulations could be rapidly and successfully determined using the proposed approach. The product resistance equation obtained in this work for 5% marmitol, expressed as R(pN) = 0.0002025 + 20.23l, is similar to that obtained by Pikal [Pikal, M.J., 1985. Use of laboratory data in freeze drying process design: heat and product resistance parameters and the compute simulation of freeze drying. J. Parent. Sci. Technol. 39, 115-138.] using the microbalance method, expressed as R(pN) = 1.40 + 16.0l. The product resistance values obtained for the 3% lactose-LDH formulation are also very close to those obtained by (Milton, N., Pikal, M.J., Roy, M.L., Nail, S.L., 1997. Evaluation of manometric temperature measurement as a method of monitoring product temperature during lyophilization. PDA J. Pharm. Sci. Technol. 51, 7-16.) for 5% lactose using the MTM (manometric temperature measurement) method. With the obtained values of the parameters R(0), A(1), and A(2), simulations can be performed to determine the maximum product temperature and the drying time during primary drying. As such, optimum cycle parameters can be determined to avoid collapse of the product. The proposed approach requires only accurately measured product temperature profiles, easily obtained in a laboratory dryer.

Correlation of laboratory and production freeze drying cycles.

The purpose of this study was to develop the correlation of cycle parameters between a laboratory and a production freeze-dryer. With the established correlation, key cycle parameters obtained using a laboratory dryer may be converted to those for a production dryer with minimal experimental efforts. In order to develop the correlation, it was important to consider the contributions from the following freeze-drying components: (1) the dryer, (2) the vial, and (3) the formulation. The critical parameters for the dryer are the shelf heat transfer coefficient and shelf surface radiation emissivity. The critical parameters for the vial are the vial bottom heat transfer coefficients (the contact parameter Kcs and separation distance lv), and vial top heat transfer coefficient. The critical parameter of the formulation is the dry layer mass transfer coefficient. The above heat and mass transfer coefficients were determined by freeze-drying experiments in conjunction with mathematical modeling. With the obtained heat and mass transfer coefficients, the maximum product temperature, Tbmax, during primary drying was simulated using a primary drying subroutine as a function of the shelf temperature and chamber pressure. The required shelf temperature and chamber pressure, in order to perform a successful cycle run without product collapse, were then simulated based on the resulting values of Tbmax. The established correlation approach was demonstrated by the primary drying of the model formulation 5% mannitol solution. The cycle runs were performed using a LyoStar dryer as the laboratory dryer and a BOC Edwards dryer as the production dryer. The determined normalized dried layer mass transfer resistance for 5% mannitol is expressed as RpN=0.7313+17.19l, where l is the receding dry layer thickness. After demonstrating the correlation approach using the model formulation 5% mannitol, a practical comparison study was performed for the actual product, the lactate dehydrogenase (LDH) formulation. The determined normalized dried layer mass transfer resistance for the LDH formulation is expressed as RpN=4.344+10.85l. The operational templates Tbmax and primary drying time were also generated by simulation. The cycle run for the LDH formulation using the Edwards production dryer verified that the cycle developed in a laboratory freeze-dryer was transferable at the production scale.

Determination of in-process limits during parenteral solution manufacturing using Monte Carlo Simulation.

The purpose of this study is to utilize Monte Carlo Simulation methodology to determine the in-process limits for the parenteral solution manufacturing process. The Monte Carlo Simulation predicts the distribution of a dependable variable (such as drug concentration) in a naturally occurring process through random value generation considering the variability associated with the depended variable. The propagation of variation in drug concentration from batch to batch is cascading in nature during the following four formulation steps: 1) determination of drug raw material potency (or purity), 2) weighing of drug raw material, 3) measurement of batch volume, and 4) determination of drug concentration in the mix tank. The coefficients of variation for these four steps are denoted as CV1, CV2, CV3, and CV4, respectively. The Monte Carlo Simulation was performed for each of the above four cascading steps. The results of the simulation demonstrate that the in-process limits of the drug can be successfully determined using the Monte Carlo Simulation. Once the specification limits are determined, the Monte Carlo Simulation can be used to study the effect of each variability on the percent out of specification limits (OOL) for the in-process testing. Demonstrations were performed using the acceptance criterion of less than 5% of OOL batches, and the typical values of CV2 and CV3 being equal to 0.03% and 0.5%, respectively. The results show that for the in-process limits of +/- 1%, the values of CV1 and CV4 should not be greater than 0.1%. These assay requirements appear to be difficult to achieve for a given chemical analytical method. By comparison, for the In-process limits of +/- 4%, the requirements are much easier to achieve. The values of CV1 and CV4 should not be greater than 1.38%. In addition, the relationship between the percent OOL versus CV1 or CV4 is nonlinear per se. The number of OOL batches increases rapidly with increasing variability of CV1 or CV4.