Scale-Up Procedure for Primary Drying Process in Lyophilizer by Using the Vial Heat Transfer and the Drying Resistance

Abstract

The objective of this study is to design primary drying conditions in a production lyophilizer based on a pilot lyophilizer. Although the shelf temperature and the chamber pressure need to be designed to maintain the sublimation interface temperature of the formulation below the collapse temperature, it is difficult to utilize a production lyophilizer to optimize cycle parameters for manufacturing. In this report, we assumed that the water vapor transfer resistance (R_p) in the pilot lyophilizer can be used in the commercial lyophilizer without any correction, under the condition where both lyophilizers were operated in the high efficiency particulate air (HEPA)-filtrated airflow condition. The shelf temperature and the drying time for the commercial manufacturing were designed based on the maximum R_p value calculated from the pilot lyophilizer (1008 vials) under HEPA-filtrated airflow condition and from the vial heat transfer coefficient of the production lyophilizer (6000 vials). And, the cycle parameters were verified using the production lyophilizer of 60000 vials. It was therefore concluded that the operation of lab- or pilot-scale lyophilizer under HEPA-filtrated airflow condition was one of important factors for the scale-up.

In order to store drug products for an extended-period of time and to maintain their storage characteristics, an appropriate drying method should be applied to remove water from the drug products because it deteriorates the product quality. Various drying technologies have been developed, including the lyophilization,¹⁾ spray drying,^2,3) and reduced-pressure drying.⁴⁾ In the manufacturing of pharmaceutical drug products such as unstable chemicals and sterile products, the lyophilization has been widely used as an effective means.^1,5) For the commercial manufacturing, a scale-up of lyophilization at lab-scale has been carried out. Some researchers have proposed two main approaches including the robust design space⁶⁾ and the trial-and-error method.^7,8) Specifically, the design of operating conditions tends to rely on trial-and-error experiments, which often causes variations in product quality and increases manufacturing costs. Thus, it is well-known that the existing scale-up theory is far from being sufficient. Then, the control method for the lyophilization process at a commercial scale needs to be improved.

The establishment of scale-up theory requires the deeper understanding on the principle of lyophilization. The lyophilization process that is commonly used consists of three stages: (1) freezing stage, (2) primary drying stage, and (3) secondary drying stage.

• – The freezing stage has been well understood in terms of physicochemical and engineering aspects. If water is used as a solvent, water turns into ice during the freezing stage to separate from other solute components. The freezing is usually completed within a few hours.^9,10)
• – The primary drying stage is also called as a sublimation drying stage. In this stage, the chamber pressure is reduced below the equilibrium vapor pressure of ice, and the heat will be transferred from the shelf surface to the product. This prevents the decrease in the product temperature due to sublimation and promotes sublimation. The sublimated vapor is transferred to the condenser and then turns into ice again. The heat removed from the product as a latent heat of sublimation will be supplied again from the shelf.¹¹⁾ Generally, the primary drying stage lasts the longest among three stages in the lyophilization process. Optimizing and shortening this procedure can reduce the cost significantly.
• – The secondary drying stage is the diffusion and desorption drying stage. It is a procedure to remove the water that did not turn into ice during the freezing phase and was captured inside the solute components as nonfreezing water. The objective of secondary drying is to reduce the final residual water content to acceptable level for stability assurance. This stage requires a higher temperature setting than the primary drying stage, but the drying is usually completed within a few hours.

In order to avoid the trial-and-error approach, the control of three stages mentioned above has been studied. Of three stages, the primary drying stage takes longest time. Therefore, the shortening of primary drying stage is always an issue in terms of economical cost at a commercial scale.

As the understanding on the lyophilization process has progressed, the mathematical models based on parameters that dominate the lyophilization process have been developed.^7,8,12–14) In recent years, the higher temperature of products and reduction of resistance of the frost layer to vapor flow results in the improvement of the primary drying efficiency.^12–14)

If the product temperature rises too much during the drying stage, a collapse (improper freeze drying) of the product occurs.¹⁵⁾ When a bulk solution is continuously cooled down under the atmospheric pressure, the solution maintains a super-cooled state even below the freezing temperature. And the temperature increases up to around the equilibrium freezing point due to the heat of crystallization caused by the ice nucleation. When the heat is removed continuously by cooling it down, the ice crystal will grow. Moreover, water is captured in solute components, excluding the non-freezing water, will be transferred to the ice.¹⁶⁾ When the cryopreservation proceeds, solute components are concentrated. Once the temperature reaches the eutectic temperature (T_e), water and solute components will become independent from each other, forming the eutectic mixture through the crystallization. Mannitol, glycine, sodium chloride, and phosphate buffer are known to crystallize during the freezing process at a certain concentration.¹⁷⁾ Generally, drugs or excipients that are developed to use as injection products have high affinity with water, and they rarely form eutectic crystals during the freezing process. When solute components are concentrated, below the glass-transition temperature (T_g′), they turn into amorphous solids that have a low molecular mobility. This phenomenon is called glass transition. The T_g′ value can be determined by the low-temperature differential scanning calorimetry (DSC). The collapse temperature (T_c) that can be determined by the freeze drying microscopy is also the important index of the lyophilization process. Cake collapse temperature is the temperature above which the lyophilized product loses its macroscopic structure and cake collapses during the primary drying process. Generally, it is known that T_c is approximately 2°C higher than T_g′.¹⁸⁾ In order to produce an acceptable lyophilized product, it is always required to perform the primary drying at the temperature lower than T_c.

Another factor for the improved efficiency of the drying is the transfer resistance of dried layer to water vapor flow. The primary drying stage is controlled by the heat transfer and the mass transfer, as illustrated schematically in Fig. 1. The heat which was transferred from the heat medium to the shelf is transferred to the shelf surface. Then, the heat is transferred to the bottom of the vial via the gas (mainly vapor) that is present between the shelf surface that comes into contact with the bottom of the vial and the bottom surface of the vial that comes into contact with the shelf. During this heat transfer, the radiation heat from the walls of the lyophilizer is also transferred to the vial.¹⁹⁾ The heat transferred to the bottom of the vial is transferred to the sublimation interface via the frost layer, and consumed as the latent heat of sublimation. Accordingly, these heat transfers induce the conversion from ice to vapor. The progression of ice sublimation forms the dried layer to play a role for the resistor against the sublimation, suppressing the sublimation rate. If this drying resistance (R_p: water vapor transfer resistance of the dried layer) is well controlled, the heat input to the product would be able to be controlled, and the optimal primary drying temperature will be secured.

Fig. 1. Schematic Illustration of Heat Transfer and Mass Transfer of Vial Near the Wall

In the practical equipment, the excess heat input troubles the lyophilization process. The radiation from the shelf and from chamber walls affects the heat transfer to the product.²⁰⁾ It is the vials at the edge position that are influenced by the radiation. The production lyophilization at large scale possesses the high portion of vials at the edge position to ones at the central position than the lab-scale lyophilization. Pisano et al. proposed to place the empty vial at the edge of the shelf.¹³⁾ This recipe burden the practitioner. Generally, the preservation of the dynamics in the lyophilization between lab- and production-scale is needed for the successful scale-up, i.e., the R_p values at lab- and production-scale are equivalent.¹²⁾ Meanwhile, the operating condition where the R_p values at lab- and production scale are equivalent has been still unclear. The commercial lyophilizers are strictly operated under the dust-free condition. Then, the operation of lab- and pilot-scale lyophilizer under the dust-free condition, as well as the commercial level, might meet the requirement of the equivalent dynamics.

The major objective in this research is to establish the practical scale-up procedure for primary drying process. We assumed that the R_p obtained using pilot lyophilizer under high efficiency particulate air (HEPA)-filtrated airflow condition can reflect R_p to be obtained using production under Class 100 environment condition. Firstly, the T_g′ and T_c values for the target formulation were evaluated. Secondly, the vial heat transfer coefficient (K_v) for the pilot and the production lyophilizers were evaluated by using 1008 and 6000 vials, respectively. Thirdly, the lyophilization cycle for the formulation was performed in the pilot lyophilizer under HEPA-filtrated airflow condition in order to protect airborne ice-nucleating particles and R_p for the formulation was calculated using the K_v value of the pilot lyophilizer. At last, the lyophilization cycle for the commercial manufacturing was designed based on the maximum value of R_p calculated from manufacture with the pilot lyophilizer and from the vial heat transfer coefficient of the production lyophilizer, and then the cycle parameters were verified using the production lyophilizer of 60000 vials under Class 100 production environment.

Experimental

Materials

Flomoxef sodium solution for injection (molecular weight: 518.45, CAS No. 92823-03-5) was used for the investigation. The formulation included sodium chloride as stabilizing agent. The total solid content of the solution was 31% (w/w, liquid density: 1.156 g/mL), with all solid material dissolved in water for injection. The 14 mL vials manufactured from clear, colorless, round borosilicate glass tubing that meet United States Pharmacopeia (USP) criteria for Type I glass and the stoppers suitable for lyophilization manufactured from chlorinated butyl elastomer were used for the investigation.

Physical Property Evaluation of Flomoxef Sodium Bulk Solution

The T_g′ of samples can be estimated by DSC. Thirty one percent Flomoxef sodium bulk solution was loaded into the measurement cell of the DSC (TA Instruments, Q2000). The sample was then equilibrated at −80°C to freeze the liquid and held isothermally for 30 min. Afterwards, the temperature elevated by a rate of 2°C/min up to 20°C.

The T_c value was determined according to the lyophylization microscopy technique by using the lyophilization microscope (Linkam Scientific Instruments, Linksys 32). The bulk solution was poured into the observation cell and equilibrated at −40°C to be frozen. This sample was kept isothermal at −40°C for 5 min. Furthermore, the atmosphere within a measurement cell approached vacuum by decreasing the pressure. After the pressure was stabilized, the temperature was elevated at a rate of 1°C/min to 0°C.

Estimate of Vial Heat Transfer Coefficient

The schematic illustration with respect to the primary drying of vial in dry chamber is shown in Fig. 1. Lyophilizer RL-402BS (total shelf area of 1.8 m²) manufactured by Kyowa Vacuum Enginerering Co., Ltd. (KYOWAC, Japan) was utilized for the pilot scale experiments. Lyophilizer RL-4536BS (total shelf area of 36.1 m²) manufactured by KYOWAC was utilized for the production scale experiments. 3024 vials and 60000 vials of 14 mL vial can be placed in the pilot lyophilizer RL-402BS and the production lyophilizer RL-4536BS, respectively. Five milliliters of water for injection was filled in the number of vials to be placed fully on at least one shelf in the lyophilizer for this evaluation (pilot lyophilizer: at least 1008 vials, production lyophilizer: at least 6000 vials), and the mass before lyophilization was measured. The vials were packed tightly on the shelf (hexagonal arrangement). The freezing procedure was performed at −40°C for 4h, and the primary drying in the pilot machine was performed at 4, 10, and 20 Pa with a shelf temperature of −10°C for 7 h, and the primary drying in the production machine was performed at 2, 10, and 20 Pa with a shelf temperature of −5°C for 7 h, respectively.

In order to monitor the product temperature during the lyophilization, the thermocouples were installed in the vials and placed in the center as well as the edge of the shelf. In addition, in order to monitor the temperature of the shelf surface, the thermocouples were taped on the shelf surfaces that are located at the inlet as well as the outlet of the heat medium.

The mass loss over time (dm/dt) after the lyophilization was measured to determine the amount of water used for sublimation. At last, the K_v values were calculated from the shelf surface temperature (T_s), product temperature (T_b), latent heat of ice (ΔH_s), cross sectional area of vial calculated from its outer diameter (A_v), and dm/dt, according to the following Eq. 1. See Appendix A for the details.

  

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Evaluation of the Water Vapor Transfer Resistance of the Dried Layer

Pilot lyophilizer RL-402BS (total shelf area of 1.8 m²) manufactured by KYOWAC was utilized for the pilot scale experiments. Prior to lyophilization, Flomoxef sodium bulk solution was filtered through a 0.2 µm filter. 3.15 mL of filtered Flomoxef sodium bulk solution was filled in 1008 vials to be placed fully on one shelf in the lyophilizer under HEPA-filtrated airflow condition. After filling, the vials were semi-stoppered and loaded into the lyophilizer, and lyophilized. The freezing procedure was performed at −41.5°C for 2h, and the primary drying was performed at −10°C under 6.7 Pa pressure for 24 h, and the secondary drying was performed at 50°C under 2 Pa pressure for 4 h. Thermocouples were installed in the vials filled with the Flomoxef sodium solution in such a manner that the end part of the thermocouple comes in the center of the bottom of the vials. If the sensor touches the inside wall of the vial, the vial temperature will be measured, instead of the product temperature. The thermocouples were taped on the shelf surfaces that are located at the inlet as well as the outlet of the heat medium. While lyophilization was performed, the shelf temperature, the product temperature, and pressure were monitored. The point at which T_b increases sharply toward the established shelf temperature was determined as the drying endpoint for analysis. From T_s, T_b, and pressure profile of the equilibrium vapor pressure of ice (P_ice) on the sublimation interface and the vacuum pressure (P_c) in the lyophilizer, the R_p value of dried layer with a cross-sectional area (A_p) was calculated according to Eq. 2. The drying time was also calculated from this equation. The procedures for the analysis are shown below.

  

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Verification Study in the Production Lyophilizer

Lyophilizer RL-4536BS (total shelf area of 36.1 m²) manufactured by KYOWAC was utilized for the production scale experiments. Prior to lyophilization, Flomoxef sodium bulk solution was filtered through a 0.2 µm filter. 3.15 mL of filtered Flomoxef sodium bulk solution was filled in 60000 vials to be placed fully on ten shelves in the lyophilizer under Class 100 production environment. After filling, the vials were semi-stoppered and loaded into the lyophilizer, and lyophilized. The freezing procedure was performed at −41.5°C, and the primary drying was performed at −10°C under 6.7 Pa pressure, and the secondary drying was performed at 50°C under 2 Pa pressure. Since the product temperature during the primary drying should be preferably 2 to 5°C lower than the collapse temperature,²¹⁾ the target product temperature was controlled to be −33 to −30°C considering the collapse temperature of the Flomoxef sodium bulk solution. In order to maintain the sublimation interface temperature at −30°C or less and to prevent the cake collapse during the primary drying stage, the shelf temperature was expected to be designed at −11°C or less. In this verification study, the shelf temperature was designed at −10°C (predicted product temperature: −29°C) as a boundary condition in order to assure the suitability of the design for the shelf temperature of −11°C or less during primary drying stage.

Results and Discussion

Physical Property Evaluation of Flomoxef Sodium Bulk Solution

Collapse should be avoided over the primary drying. Both the T_g′ and T_c values are therefore the critical physical parameter of the primary drying. The T_g′ value of target solution, Flomoxef sodium solution was estimated from the DSC measurement. Figure 2(a) depicts the DSC curve for the target. A slightly decrease in heat flow observed at around −31°C was corresponding with the glass-transition. For a solute system which does not crystallize but remains amorphous, this maximum temperature is generally equivalent to the T_c value.¹⁵⁾ The T_c value was measured by the freeze drying microscope technique. Accordingly, a process of primary drying of Flomoxef sodium bulk solution was observed microscopically, as shown in Fig. 2(b). At −30°C, the sublimation interface between the frozen layer and dried one was definitely observed as shown in Fig. 2(b1). At −28°C, a partial cake collapse was observed as demonstrated in the arrow in Fig. 2(b2). Furthermore, this partial collapse was, at −26°C, spread along the sublimation interface (Fig. 2(b3)). Thereby, the T_c value was determined to be −28°C. The above results was in agreement with the finding¹⁸⁾ that T_c is higher than T_g′ by approximately 2°C.

Fig. 2. (a) DSC Thermograms of Flomoxef Sodium Bulk Solution and (b) Freeze Dry Microscopy Photographs of Flomoxef Sodium Bulk Solution

(1) Cake collapse was not observed in the sublimation interface at −30°C. (2) Onset of partial cake collapse was observed at −28°C. (3) Full cake collapse was observed at −26°C. (Color figure can be accessed in the online version.)

Comparison of Sublimation Behavior in Both Machines

The sublimation behavior in both pilot lyophilizer (RL-402BS) and the production lyophilizer (RL-4536BS) was investigated in the primary drying process. The sublimation behavior is subjective to the radiation from chamber walls, in particular of production lyophlilizer.¹⁹⁾ To evaluate the influence the edge and center positions of lyophilizer on the heat transfer, the sublimation behavior was investigated at only one shelf. That is to say, the sublimation amount of 1008 of whole 3024 vials for RL-402BS, and 6000 of whole 60000 vials for RL-4536BS were monitored.

Figure 3 shows the distribution of sublimation amount (m) in the both machines at the certain time under 10 Pa. The m value was 2.0–3.0 g at the edge position of pilot machine whereas 1.5–2.0 g in the center position (Fig. 3(a)). In contrast, the m value was 2.0–3.5 g at the edge position of the production machine although the 1.5–2.5 g at the center position. It was obvious, in both the machines, that more amount of ice was sublimated at the edge position as compared with the center position. This result implied that the vial heat transfer at the edge position of the machine was strongly affected by the radiation heat input,^12,19,20) accelerating the sublimation rate. It was considered that such a distribution of sublimation resulted from the position-dependency of heat transfer characteristics.

Fig. 3. 3D-Distribution of the Mass of Ice Sublimed in a (a) Pilot and (b) Production Lyophilizer

(a) 1008 vials filled with WFI were used for the sublimation test. Shelf temperature, chamber pressure and primary drying time were −10°C, 10 Pa, and 7h, respectively. (b) 6000 vials filled with WFI were used for the sublimation test. Shelf temperaute, chamber pressure and primary drying time were −5°C, 10 Pa, and 7h, respetively. (Color figure can be accessed in the online version.)

Accordingly, the K_v value was estimated from Eq. 1. For this, the slope of dm/dt was coarsely estimated from Fig. 3: i.e., dm/dt=m(t)−m(0)/t. The K_v value was then estimated by using ΔH_s=669 cal/g, A_v=4.71 cm², the T_s and T_b values during the primary drying, and the dm/dt value. The result of K_v values are shown in Table 1. At P_c=4 Pa, the 10⁴ K_v values at the edge and center positions were 3.40±0.37 and 2.38±0.18 cal/(s·cm²·°C), respectively. The K_v value at the edge was higher than that at the center position. This is attributed to the radiation heat transfer from the wall of machine as shown in Fig. 1. In addition, the increase in chamber pressure up to 20 Pa elevated the K_v value. This attributes to the increased amount of gas (vapor) that is present in the gap between the shelf surface and the bottom of the vial. In contrast, the decrease in chamber pressure during the primary drying stage enlarged the difference (Edge/Center) in the K_v value between the edge and center positions (from 1.27 at 20 Pa to 1.48 at 4 Pa). This occurs because the vapor amount in the chamber decreases under a highly vacuumed chamber pressure condition, which will diminish the effects of the gas heat transfer and will relatively increase the effects of radiation heat transfer. The same was true for the production machine (right column in Table 1). Furthermore, the K_v values between both machines were compared. At 10 Pa, the pilot machine indicated the K_v value is higher than the production machine, at both edge and center. The same was true for the comparison at 20 Pa. Meanwhile, the difference in Edge/Center of production machine (=1.27) surpassed that of pilot machine (=1.33) at 20 Pa. Thus, the scale up of lyophilizer appeared to reduce the heat transfer property of vials.

Table 1. Analysis of Vial Heat Transfer Coefficient with Pilot and Production Lyophilizer

Chamber pressure (Pa)	Pilot machine 104 Kv (cal/s·cm2·°C)			Production machine 104 Kv (cal/s·cm2·°C)
	Center	Edge	Edge/Center	Center	Edge	Edge/Center
2	—	—	—	1.46±0.04	2.64±0.09	1.81
4	2.38±0.18	3.40±0.37	1.48	—	—	—
10	3.78±0.26	5.17±0.55	1.37	3.54±0.08	4.61±0.11	1.30
20	5.07±0.35	6.46±0.52	1.27	4.57±0.10	6.10±0.11	1.33

All the experiments were performed at least three times.

Contribution of Elemental Process of Heat Transfer to Vial Heat Transfer

The vial heat transfer process consists of the contact heat transfer, gas heat transfer, and radiation heat transfer. Their heat transfer coefficients were defined as K_c, K_g, and K_r, respectively (see Appendix B). According to the previous reports,^15,23) K_c and K_r do not depend on P_c and K_g depends on P_c. K_g was described as a function of P_c as follows.

  

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where

  

Λ₀ represents the free molecular heat conductivity of water vapor at 0°C, and λ₀ is the thermal heat conductivity of water vapor at ambient pressure, α is a function of the energy accommodation coefficient, α_c is the parameter, and T is the absolute temperature of the water vapor.

The K_v value obtained in the last section was plotted against the corresponding P_c value. The dependency of K_v on chamber pressure is theoretically written by Eq. 4 (see Appendix B).

  

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Nonlinear regression analysis of Eq. 4 was performed by using Λ₀=6.34×10⁻³ cal/(s·cm²·°C), λ₀=4.29×10⁻⁵ cal/(s·cm·°C). Also, α_c=0.67 was used.¹⁵⁾ The results of analysis are shown in Fig. 4. Overall, the experimental data were well fitted with the theoretical curves. Approaching P_c to 0 Pa, the contribution of gas heat transfer diminished. In other words, the intercept of K_v in Fig. 4 meant the contribution of K_c and K_r. Both pilot and production machines indicated the higher intercept of K_v values at the edge position than those at the center position. This resulted from the radiation from the wall.²²⁾ According to the study by Fissore and Barresi,¹²⁾ the vials paced in the central part of the shelf are not affected by the radiation from chamber walls. The contribution of K_g was elevated by more than 3 times as compared with other two factors.

Fig. 4. Dependency of Vial Heat Transfer Coefficients on Chamber Pressure with Pilot and Production Lyophilizer

Solid curves: center position; dotted curves: edge position. Experimental data: K_v values for the center position for the pilot (closed circle) and prudction (closed triangel); K_v values for the edge position for the pilot (open circle) and prudction (open triangel). The pilot lyophilizer (RL-402BS) and Lyophilizer RL-4536BS as production machine were used to estimate K_v value at −10 and −5°C, respectively. Those curves were best fit with experimental data summarized in Table 1. The details for calculation using Eq. 4 are described in Appendix B.

Monitoring of Temperature Profile for Design of Operation Conditions

Another important parameter to predict the primary drying process is the water vapor transfer resistance of the dried layer R_p. The amount of airborne particles may have impact on ice-nucleation temperature and cause larger variability in R_p, and hence the manufacture in pilot lyophilizer was implemented under HEPA-filtrated airflow condition in order to assume R_p to be obtained in production lyophilizer under Class 100 production environment. The dried layer generally grows dependent of the T_b value. Figure 5(a) shows the T_b-profile of the vial placed at the center position in the pilot lyophilizer during the primary and secondary drying stage, monitored by thermocouples. At T_s=−10°C, the T_b value gradually increased to approached the constant T_b at around −30°C and represented the steady state ice sublimation, followed by a sharp increase step to the shelf temperature after 18.5 h and essentially equilibrated to the shelf temperature after 24 h. After the completion of primary drying stage, the T_b value indicated the stepwise increase accompanied with the shift of T_s up to 50°C during secondary drying stage. Based on the T_b-profile obtained during the primary drying in the pilot lyophilizer, the R_p value was then calculated using Eq. 2. The values of parameters for calculations are as follows: the filling volume W_fill=3.64 g, the ice density ρ_ice=0.918 g/mL, the liquid density ρ=1.16 g/mL, the solute concentration C=0.31 g/g, A_p=3.84 cm², A_v=4.71 cm², the thickness of the maximum frozen layer L_max=0.73 cm, the moisture content in 1 vial Δm_H2O=2.51 g/vial, ΔH_s=669 cal/g, 10⁴ K_v (at 6.7 Pa)=3.02 cal/(s·cm²·°C). The variation of R_p as a function of dried layer thickness defined as (L_max−L_ice) is shown in Fig. 5(b). Completing the sublimation of ice, the dried layer thickness approached to 0.73 cm (equivalent to L_max), at which the R_p value indicated the maximum value being 7.9 Torr·cm²·h/g at 6.7 Pa.

Fig. 5. (a) Temperature Profile for Vial and (b) Resistance of Dried Product Layer as a Function of Time during Primary Drying

The pilot lyophilizer (RL-402BS; 1008 vials) was used to estimate R_p value. The values of parameters are as follows: W_fill=3.64 g, ρ_ice=0.918 g/mL, ρ=1.16 g/mL, C=0.31 g/g, A_p=3.84 cm², A_v=4.71 cm², L_max=0.73 cm, Δm_H2O=2.51 g/vial, ΔH_s=669 cal/g, 10⁴ K_v=3.02 cal/(s·cm²·°C) at P_c=6.7 Pa. The details for calculation are described in Appendix C.

Scale-Up of Pilot to Production Lyophilizer

In order to produce an acceptable lyophilized product, it is always required to perform primary drying at the temperature lower than T_c. Then, the T_s in the production lyophilizer need to be designed at −5°C or less because of −28°C of the cake collapse temperature for Flomoxef sodium drug product. For this, both the sublimation interface temperature (T_ice) during the primary drying step and the drying time, at the production scale, can be established based on the maximum R_p value calculated from manufacture with the pilot lyophilizer (RL-402BS) and from the K_v value of the production lyophilizer (RL-4536BS). Specifically, when the R_p value is known, the design of operational variables T_s and P_c can give the T_ice and T_b values according to the following Eq. 5, followed by prediction of the drying time according to Eq. 2. This detailed treatment is described in Appendix C.

  

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From the last section, R_p,max=7.9 Torr·cm²·h/g at P_c=6.7 Pa was obtained. Thereby, the Eq. 5 gave the T_b and T_ice under the designed T_s. The predicted values were summarized in Table 2. Varying T_s from −15 to −5°C, the T_b and T_ice values similarly altered from −31 to −28°C. The corresponding time for drying operation was calculated to be ranged from 25 to 17 h. The primary drying stage requires the occurrence of the product cake collapse. Therefore, we selected T_s=−11 ca. 10°C and the needed time for primary drying stage was around 21 ca. 20 h as the optimal condition. In this verification study, the shelf temperature was designed at −10°C (predicted product temperature: −29°C) as a boundary condition.

Table 2. Predicted Sublimation Interface Temperature and Drying Time for the Production Lyophilizer at R_p=7.9 in the Pilot Lyophilizer

Set value		Predicted value
Shelf temperature Ts (°C)	Chamber pressure Pc (Pa)	Product temperature Tb (°C)	Sublimation interface temperature Tice (°C)	Drying time (h)
−15	6.7	−31	−31	25
−14	6.7	−30	−31	24
−13	6.7	−30	−30	23
−12	6.7	−30	−30	22
−11	6.7	−29	−30	21
−10	6.7	−29	−29	20
−5	6.7	−28	−28	17

The values of parameters are same as ones in Fig. 5(b) except 10⁴ K_v (6.7 Pa)=2.54 cal/(s·cm²·°C) and R_p=7.9 Torr·cm²·h/g.

In order to establish scientific evidence that a lyophilization process is capable of consistently delivering quality product, consecutive three batches of Flomoxef sodium drug product were then manufactured in 60000 vials scale which is the commercial scale. Lyophilizer RL-4536BS was utilized for the production scale-verification study. Visual inspection was carried out for 60000 lyophilized vials and the yield of the three batches was 99% or more (99.6, 99.7, 99.3%, respectively). Acceptable lyophilized products were observed with preventing the occurrence of product cake collapses. It was considered that the obtained yield was sufficient for routine production.

Thus, the scale-up theory using combination of the vial heat transfer of lyophilizers with the resistance of dried product layer obtained under HEPA-filtrated airflow condition could bridge the gap between the pilot scale (3024 vials) and the production scale (60000 vials) to the extent where the product was sufficiently acceptable.

Conclusion

The position of vials on the shelf gives the position-dependency of K_v value, which possibly becomes the obstacle to establish the scale-up theory for the production lyophilizer. It was first revealed that the K_v value estimated from the sublimated amount of ice at the position in the shelfs (1008 and 6000 vials) was influenced by the radiation heat transfer from the wall of machine. We separately treated the K_v values at the edge and center positions in the shelf, which were dependent on the P_c. The R_p value was also determined by using the pilot lyophilizer (1008 vials) under HEPA-filtrated airflow condition. From these investigations, we established the scale-up theory for the lyophilization of 60000-vial scale.

It is noted that the dynamics of lyophization in pilot lyophilizer was assumed to be same as that in production-scale lyophilizer, i.e., the R_p value at each scale were equivalent. The determination of K_v and R_p values could then predict the target parameters T_b, T_ice, and the drying time during the primary drying stage. The verification study based on our predictions demonstrated that the lyophilization of 60000 vials succeeded in the yield of 99% or more, thus indicating a robust operation with satisfactory. Thus, the operation of pilot lyophilizer under HEPA-filtrated airflow condition was considered to be one of possible conditions that give the same dynamics of primary drying in the pilot- and production lyophilizer.

This scale-up theory, which bridges the gap between the laboratory scale and the production scale, would enable us to perform an efficient and robust process design. A lyophilizer has a desired operational condition where chamber pressure cannot be controlled (i.e., choked flow limit) in a highly vacuumed condition or at an accelerated sublimation rate. By taking these factors into consideration, the desired operational condition where the product quality is not damaged, and at the same time, where stable manufacturing can be performed is expected to be established (i.e., design space).²⁴⁾ Our scale-up theory would give a certain impact on the determination of design space.

Appendix A Elucidation of K_v Based on the Heat/Mass Transfer

The heat transfer to the product during the primary drying consists of three types of heat transfer.⁹⁾ The first one is the contact heat transfer (Q_c) from the surface that directly comes into contact with the shelf as well as the bottom of the vial. The second one is the gas heat transfer (Q_g) via the gas (mainly vapor) that is present in the gap between the shelf surface and the bottom of the vial. The third one is the radiation heat transfer (Q_r). When a vial is used as a container, the gas heat transfer is estimated as the main heat transfer.²⁵⁾ However, compared to the vial that is placed in the center of the lyophilizer, the vial placed at the edge of the lyophilizer has a faster sublimation rate. This indicates that the effects of the radiation heat transfer cannot be ignored.²⁰⁾ In addition, the gas heat transfer depends on the chamber pressure. When the chamber pressure decreases, the gas heat transfer increases. When the chamber pressure is over 13.3 Pa, the gas heat transfer becomes the most dominant of the 3 types of heat transfer: a contact heat transfer coefficient, gas heat transfer coefficient, and radiation heat transfer coefficient.²⁶⁾ Accordingly, we estimated the gas heat transfer by using the K_v value as follows.

The heat transfer caused by the difference between the shelf surface temperature and the product temperature is shown in Eq. A1. The conversion from the heat transfer to the material transfer by sublimation is shown in Eq. A).

  

(A1)

  

(A2)

Both Eqs. A1 and A2 yielded the Eq. 1 to determine the K_v value.

  

(1)

By using Eq. 1, the K_v value can be estimated based on the heat/mass transfer.

Appendix B Decomposition of K_v into Elemental Factors

The vial heat transfer process consists of the contact heat transfer, gas heat transfer, and radiation heat transfer. Their heat transfer coefficients are defined as K_c, K_g, and K_r, respectively. The relationship among them were then given as K_v=K_c+K_g+K_r, according to the previous report.⁵⁾ In details, as shown in Fig. 1, the heat flow into a vial from the outside corresponds three heat flows: (i) the contact heat transfer (Q_c) from the surface that directly comes into contact with the shelf as well as the bottom of the vial; (ii) the gas heat transfer (Q_g) via the gas (mainly vapor) that is present in the gap between the shelf surface and the bottom of the vial; (iii) the radiation heat transfer from the shelf and wall (Q_r). That is to say,

  

(B1)

Three different heat flows may be considered to be driven by the same temperature difference (T_s−T_b), assuming the vial far from the wall; i.e., the contribution of radiation heat transfer from the wall being negligible. Therefore, each heat balance equation can be described as follows.

  

(B2)

  

(B3)

  

(B4)

Eqs. A1 and B2 to B4 are substituted into (B1) yields the following equation.

  

(B5)

Then,

  

(B6)

Thus, K_v can be decomposed into three elemental factors. Defining as a=K_c+K_r, b=αΛ₀, and c=l_v (αΛ₀/λ₀), the combination of Eqs. B6 and 3 yielded Eq. 4.

  

(4)

Appendix C Prediction of T_b and T_ice for Verification Test

The mass transfer is generated from the difference between the P_ice and P_c in the lyophilizer, and R_p determines the sublimation rate.¹¹⁾ In acutual, there is a resistance of the rubber stopper. Since this resistance is, however, extremely small compared to the drying resistance, it can be ignored. The relational expression is shown using Eq. C1.

  

(C1)

When Eq. B1 is converted, the R_p value is shown using Eq. 2. The required drying time can be calculated from the integration of Eq. 2.

  

(2)

The conversion factor between the heat flow (dQ/dt) and the mass of substance (m) can be expressed using Eq. C2. The conversion factor used herein is to be 0.1833 as previously reported.¹⁵⁾ The term dm/dt is the sublimation rate in g/h, and the coefficient 0.1833 is the factor to convert the sublimation rate of pure water from g/h to cal/s.

  

(C2)

The thickness of the maximum frozen layer is defined as L_max. Thereby, the thickness of the frost layer (L_ice) can be shown using Eq. C3.

  

(C3)

Assuming the percentage of the ice deposit in solutes as ε, L_max can be defined as follows.

  

(C4)

Since the heat quantity (dQ/dt) that was supplied from the shelf surface to the product is transferred to the sublimation interface via the frozen layer. The T_ice value can be expressed in Eq. C5.

  

(C5)

Furthermore, from Eq. A1 and Eq. C5, T_ice can be expressed in Eq. C6.

  

(C6)

On the other hand, if the difference between the T_b and T_ice values is expressed in Eq. C7,^27–29) T_ice can also be calculated using Eq. C8.

  

(C7)

  

(C8)

The P_ice value is expressed in Eq. C9, by substituting this formula into Eq. 2, the R_p value at a specific time can be calculated.

  

(C9)

In addition, from Eq. C1 and Eq. C2, Eq. C10 can be elucidated.

  

(C10)

Furthermore, a substitution of Eqs. C8 and C9 into Eq. C10 give Eq. 5.

  

(5)

When the R_p value is known, the design of T_s and P_c can give the T_ice and T_b values.

Conflict of Interest

The authors declare no conflict of interest.

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