Determination for dry layer resistance of sucrose under various primary drying conditions using a novel simulation program for designing pharmaceutical lyophilization cycle

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ARTICLE IN PRESS International Journal of Pharmaceutics xxx (2013) xxx–xxx

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Determination for dry layer resistance of sucrose under various primary drying conditions using a novel simulation program for designing pharmaceutical lyophilization cycle Tatsuhiro Kodama a,∗ , Hiroyuki Sawada b , Hiroshi Hosomi b , Masahito Takeuchi a , Naoki Wakiyama a , Etsuo Yonemochi c , Katsuhide Terada c a

Formulation Technology Research Laboratories, Daiichi Sankyo Co., Ltd., 1-12-1 Shinomiya, Hiratsuka, Kanagawa 254-0014, Japan Technical Department, Kyowa Vacuum Engineering, Co., Ltd., 5-60 Menumahigashi, Kumagaya, Saitama 360-0202, Japan c Faculty of Pharmaceutical Sciences, Toho University, 2-2-1 Miyama, Funabashi, Chiba 274-8510, Japan b

a r t i c l e

i n f o

Article history: Received 19 January 2013 Received in revised form 12 April 2013 Accepted 30 April 2013 Available online xxx Keywords: Dry layer mass transfer resistance Simulation Predictive model Heat and mass transfer model

a b s t r a c t Dry layer resistance, which is the resistance of dried cake against water vapor flow generated from sublimation, is one of the important parameters to predict maximum product temperature and drying time during primary drying in lyophilization. The purpose of this study was to develop the predictive model of dry layer resistance under various primary drying conditions using the dry layer resistance obtained from a preliminary lyophilization run. When the maximum dry layer resistance was modified under the assumption that the chamber pressure is zero, the modified dry layer resistance, which is defined as specific dry layer resistance, correlated well with the sublimation rate. From this correlation, the novel predictive model including the empirical formula of sublimation rate and specific dry layer resistance is proposed. In this model, the dry layer resistance under various conditions of shelf temperature and chamber pressure was successfully predicted based on the relationship of the sublimation rate and specific dry layer resistance of the edge and center vials obtained from the product temperature in one preliminary cycle run. It is expected that this predictive model could be a practical and useful tool to predict product temperature during primary drying. © 2013 Elsevier B.V. All rights reserved.

1. Introduction In the pharmaceutical industry, lyophilization is commonly used in the development of parenteral injection to stabilize the drug product. The lyophilization cycle mainly consists of freezing, primary drying, and secondary drying. In particular, the primary drying, where ice is removed by sublimation under vacuum, requires a long time and consumes a large amount of energy. Thereby, primary drying at a higher heat transfer rate is of great importance to minimize the process time, resulting in a higher product temperature. On the other hand, collapse of the lyophilized product, which is generated at the product temperature over the collapse temperature, should be avoided (Bellows and King, 1972; Pikal and Shah, 1990). This is because collapse of the lyophilized cake potentially affects the stability of lyophilized product. Hence, enormous efforts have been spent to minimize the primary drying time without collapse of the lyophilized cake by adjusting the shelf temperature and chamber pressure, considering a point of

∗ Corresponding author. Tel.: +81 463 31 6325; fax: +81 463 31 6478. E-mail address: [email protected] (T. Kodama).

compromise between manufacturing efficiency and product quality in the pharmaceutical development. In order to resolve these problems, the mathematical model for the prediction of the optimized product temperature is thought to be useful. The mathematical model expressed by heat and mass transfer has been utilized to understand the sublimation phenomenon by many researchers (Ho and Roseman, 1979; Jennings, 1988; Kuu et al., 2006; Nail, 1980; Pikal et al., 1984). In the heat and mass transfer model, two parameters of heat transfer coefficient and dry layer resistance are most important. The heat transfer coefficient for estimation of the heat transfer rate depends on the lyophilizer and the container of glass vial and stopper, and is experimentally determined by a water sublimation test (Pikal, 1985; Rambhatla et al., 2006; Schneid et al., 2009). On the other hand, dry layer resistance means the resistance of the dried cake against the water vapor flow generated from the interface of sublimation of the frozen layer. In order to determine dry layer resistance, a preliminary lyophilization run using drug solution is essential for individual formulation, because dry layer resistance is dependent on the component and the concentration in the formulation, as some authors have reported (Overcashier De Fau-Patapoff et al., 1999; Pikal et al., 1983).

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Please cite this article in press as: Kodama, T., et al., Determination for dry layer resistance of sucrose under various primary drying conditions using a novel simulation program for designing pharmaceutical lyophilization cycle. Int J Pharmaceut (2013), http://dx.doi.org/10.1016/j.ijpharm.2013.04.081

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2

The heat transfer coefficient and dry layer resistance experimentally obtained by two preliminary lyophilization experiments using pure water and drug solution allows us to estimate the product temperature during primary drying at a given shelf temperature and chamber pressure. Recently, the simulation program for the prediction of the product temperature, which is based on the heat and mass transfer model, has been practically evaluated (Koganti et al., 2011; Kuu and Nail, 2009). These programs are thought to be useful tools for searching the optimized shelf temperature and chamber pressure. On the other hand, it is known that dry layer resistance is not a constant curve and is affected by the shelf temperature and chamber pressure. Pikal et al. reported that low dry layer resistance was observed at a high shelf temperature and chamber pressure (Pikal et al., 1983). The variations of dry layer resistance were explained by the pore size of lyophilized cake and the molecular collision between the water vapor and gas, when the shelf temperature and chamber pressure were changed. Moreover, Milton et al. and Overcasher et al. indicated that the mechanism for the variation of dry layer resistance was explained by the micro scale hole of the lyophilized cake, which was called “micro-collapse” (Milton et al., 1997; Overcashier De Fau-Patapoff et al., 1999). This variety of dry layer resistance above probably causes the obstacle to accurately simulate the product temperature at various shelf temperature and chamber pressure during primary drying. However, little attention has been paid to the predictive model of variable dry layer resistance under different primary drying conditions from the dry layer resistance in the preliminary run. Therefore, the aim of study is to develop the novel predictive model for dry layer resistance focusing on the change of shelf temperature and chamber pressure in the primary drying process. 2. Materials and methods 2.1. Mathematical model of primary drying Dry layer resistance can be mathematically calculated, as follows. The overall heat transfer rate around the glass vial comprises of three kinds of heat transfer rates, which are (1) the shelf heat transfer rate from the shelf to the bottom of the glass vial, Qsh, (2) the conductive heat transfer rate from the tray flame to the side of the glass vial, Qt, and (3) the radiative heat transfer rate from the chamber wall to the top and side of the glass vial, Qr. Qsh is mathematically expressed by Eq. (1). Qsh = Kc · Ae · (Tsh − Tb)

g lv + (Lp/Pc)

(2)

(3)

Where At is the side area of the glass vial, Tt is the temperature of the tray flame. The tray heat transfer coefficient, Kt, is expressed as the function of the chamber pressure, Pc in Eq. (4). Kt =

g lt + (Lp/Pc)

1

·  · Ar · (Tw4 − Tb4 )

(5)

Where 1 is the radiation factor related to the emissivity of thermal radiation for the chamber wall and glass vial,  is the Stefan Boltzmann constant, Ar is the top and side area of the glass vial, Tw is the wall temperature in lyophilizer. From three kinds of heat transfer rates, the sublimation rate, dm/dt, can be calculated as a pseudo steady state that the overall heat quantity is spent for latent heat of sublimation (Pikal et al., 2005). Qsh + Qt + Qr dm = dt Hs

(6)

Where Hs is the latent heat of sublimation. In Eq. (6), Qt is used for estimation of the heat transfer rate of the “edge vial”, which is placed on the peripheral position on the shelf, and has a direct contact with the tray flame. In the case of the “center vial” placed on the center position of shelves, the heat transfer rate for the center vial was calculated by the sum of Qsh and Qr. The temperature at the interface of sublimation, Ti, can be converted from the experimentally measured product temperature during primary drying by Eq. (7). Ti =

Tb − (Qsh + Qt + Qr) · S K1 · Av

(7)

Where S is the dry layer thickness, Av is the area of sublimation per vial (calculated based on the inside diameter). K1 , is the thermal conductivity of the frozen layer. Here, the thermal conductivity of ice was tentatively used for K1 . Then, the pressure at the interface of sublimation, Pi, is calculated with Ti in Eq. (8). Pi = e6144.96/Ti+28.911

(8)

Finally, the dry layer resistance, Rp, can be calculated with dm/dt and Pi which are determined from Eqs. (6) and (8), respectively. Rp =

Pi − Pc dm/dt

(9)

2.2. Water sublimation test for shelf heat transfer coefficient

Where g is the free molecular thermal conductivity of the gas, lv is the mean separation distance between the shelf and the bottom of the glass vial, Lp is a constant value related to the molecular mean free path. Qt is also explained by the following equation. Qt = Kt · At · (Tt − Tb)

Qr =

(1)

Where Ae is the cross sectional area of glass vial (calculated based on the outside diameter), Tsh is the shelf temperature during primary drying, Tb is the product temperature at the bottom center of the glass vial, and the shelf heat transfer coefficient, Kc, is expressed as the function of the chamber pressure, Pc in Eq. (2). Kc =

Where g is the free molecular thermal conductivity of the gas, lt is the mean separation distance between the tray flame and glass vial. In this paper, the fixed value (5 × 10−4 m) was tentatively used. Lp is a constant value related to the molecular mean free path. Qr is determined by Eq. (5).

(4)

The shelf heat transfer coefficient, Kc, can be determined by a water sublimation test (Pikal, 1985; Rambhatla et al., 2006; Schneid et al., 2009). This test was performed using a laboratory scale lyophilizer (DFM-09A-S, ULVAC, Inc., in Japan, shelf area: 0.3 m2 ). Five mL of pure water was filled into each 20 mL vial (Transparent Type 1 glass vial, Japan Glass Industry Co., Ltd, outside diameter: 30 mm, inside diameter: 27 mm), and the filled vials were partially stoppered with rubber stoppers (Two leg 20 mm gray butyl rubber stoppers, Daikyo Seiko, Ltd). The partially stoppered vials were loaded onto a shelf of the lyophilizer (320 vials per shelf). In this process, the weight of some vials were weighed in advance and loaded at the peripheral and center positions on the shelf. The setting parameters used in this study for freezing, annealing, and primary drying process were as follows: (1) cooling from 5 ◦ C to −45 ◦ C (0.28 ◦ C/min), (2) holding at −45 ◦ C for 2 h, (3) heating from −45 ◦ C to −10 ◦ C (0.58 ◦ C/min), (4) holding at −10 ◦ C for 2 h, (5) cooling from −10 ◦ C to −45 ◦ C (0.58 ◦ C/min), (6) holding at −45 ◦ C for 2 h, (7) turning on the vacuum and waiting until the chamber pressure has reached less than 13.3 Pa, (8) heating from −45 ◦ C to −20 ◦ C (0.42 ◦ C/min), and (9) holding the shelf temperature at −20 ◦ C and the chamber pressure at 10 Pa. During lyophilization,

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the shelf temperature, chamber pressure, and product temperature at the bottom center of the vial, were continuously recorded by thermocouples and a capacitance manometer (MKS, Baratron). After the total elapsed time was finished, the chamber pressure in the lyophilizer was returned to atmospheric pressure, and the vials were stoppered immediately. After the selected vials in the peripheral and center space on the shelf were unloaded, the amount of water was determined by the gravimetrical method. Subsequently, the total sublimated amount of water, Mtmeas. , was determined from the weight loss of these vials. The calculated total sublimated amount of water, Mtcal. , was obtained from the sum of the calculated sublimation rate, dm/dt, at each interval time, t, in Eq. (10). The sublimation rate should be calculated from the model expressed by Eqs. (1)–(6).



Mtcal. =

dm

dtt

Mtcal. = Mtmeas.

Rp (kPam2s/kg)

300

The mean separation distance between the shelf and the glass vial, lv, in Eq. (2) was adjusted so that that the calculated value of the total sublimated amount, Mtcal. , was in agreement with the measured value, Mtmeas. The shelf heat transfer coefficient, Kc, in Eq. (1) was continuously calculated as well. 2.3. Measurement of dry layer resistance of 10 w/v% sucrose The dry layer resistance of the aqueous solution containing 10 w/v% sucrose (purchased from Merck) was determined by one lyophilization experiment as a preliminary run. The procedure to measure the dry layer resistance is described below. Five mL of 10 w/v% sucrose was filled into each 20 mL vial, and 320 vials were positioned on a shelf in a laboratory scale lyophilizer. Then, some thermocouples were placed at the bottom center of some vials on the peripheral and center space on a shelf. After lyophilization was completed under the same conditions as that employed in the water sublimation test, the product temperature of the edge and center vials were recorded during primary drying. Based on the product temperature of the edge and center vials, each dry layer resistance was calculated as mentioned in the section “Mathematical model of primary drying”. The software “Kyowa FD program”, which was provided by Kyowa Vacuum Engineering Co., Ltd in Japan, was applied to calculate the dry layer resistance. In order to collect a series of data of the dry layer resistance, lyophilization experiments were repeated under various primary drying conditions. In this study, five different lyophilization programs were undertaken by changing the shelf temperature (−20 ◦ C to 0 ◦ C) and chamber pressure (5–15 Pa). Each dry layer resistance of the edge and center vials were calculated by Kyowa FD program, based on the product temperature recorded during primary drying. 2.4. Prediction of maximum product temperature and primary drying time of 10 w/v% sucrose The lyophilization experiments were carried out under the same condition as that in Section 2.3 except for primary drying. The primary drying conditions were set at −20 ◦ C of the constant shelf temperature and at 5 Pa or 10 Pa of the chamber pressure. From the product temperature recorded during primary drying, the measured maximum product temperature of the edge vial and the measured primary drying time at the center vial were obtained. The product temperature profiles at −20 ◦ C of the constant shelf temperature and 5 Pa or 10 Pa of chamber pressure were predicted, and the predicted maximum product temperature of the edge vial and the predicted primary drying time of the center vial were determined by the Kyowa FD program mentioned above. The basic

200

100

0 0

1

2

3

4

5

6

Dry layer thickness (mm)

(10) (11)

3

Fig. 1. Dry layer resistance profiles of 10 w/v% sucrose in the edge vial (open circles) and the center vial (close circles). The profiles were converted from the product temperature profiles recorded during primary drying (shelf temperature; −20 ◦ C, chamber pressure; 10 Pa).

procedure programmed in the software is as follows. The sublimation rate was estimated from the mathematical model in Eqs. (1–7), and the dry layer resistance was measured at −20 ◦ C of shelf temperature and 10 Pa of chamber pressure (Section 2.3). The pressure at the interface of sublimation was calculated in Eq. (9) by the sublimation rate, dry layer resistance, and chamber pressure. Then, the temperature at the interface of sublimation was determined from the pressure at the interface of sublimation in Eq. (8). Finally, the product temperature was calculated from Eq. (12) as described below. Tb =

Ti + (Qsh + Qt + Qr) · S K1 · Av

(12)

3. Results and discussion 3.1. Determination of parameters related to primary drying The shelf heat transfer coefficient is one of the most important parameters to estimate the heat transfer rate from the shelf to the bottom of the vial. The dry layer resistance is of great importance to affect the product temperature as well in the heat and mass transfer model. First, in order to obtain the shelf heat transfer coefficient between the shelf and the glass vial, the water sublimation test was carried out under the following conditions, at −20 ◦ C of shelf temperature and 10 Pa of chamber pressure. According to Eqs. (1)–(7), (9), and (10), the amount of sublimated water in the sublimation test was used for calculation. As a result, the mean separation distance and the shelf heat transfer coefficient were calculated to be 5.9 × 10−3 m and 10.3 kcal/hrm2 ◦ C, respectively. When the chamber pressure is changed, the shelf heat transfer coefficient was recalculated according to Eqs. (1) and (2) in this report. Second, the dry layer resistance of 10 w/v% sucrose was calculated for each edge and center vial based on the product temperature which was obtained in a preliminary run of lyophilization (Fig. 1). The shelf temperature and chamber pressure conditions in the primary drying process were at −20 ◦ C and 10 Pa, respectively. The dry layer resistance of each edge and center vial was different, and the characteristics of the dry layer resistance profile are shown below. In the case of the edge vial, the maximum dry layer resistance was observed in the early period of profile. On the other hand, the maximum dry layer resistance was observed in the later period of the profile of the center vial.

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In order to optimize the lyophilization program, it is significant to monitor the product temperature of each edge and center vial located on the peripheral and center positions on the shelves. Edge vials show the higher sublimation rate due to additional heat transfer from the chamber wall or tray flame (Rambhatla and Pikal, 2003). The higher heat transfer causes the higher product temperature, which is closer to the collapse temperature. On the other hand, the sublimation rate of the center vial is inversely the slowest among all vials due to the smallest radiation heat transfer from the chamber wall. The endpoint of primary drying is often estimated from the product temperature of the center vial. For this reason, the product temperature of each edge and center vial was predicted. The prediction was made for the product temperature of each edge and center vial during primary drying at 5 and 10 Pa at −20 ◦ C, utilizing the shelf heat transfer coefficient measured by the water sublimation test mentioned above and the dry layer resistance measured by a preliminary run. Then, the maximum product temperature of the edge vial and the primary drying time of the center vial were predicted under each primary drying condition. Two experiments were also conducted under these same conditions, and the maximum product temperature and drying time were experimentally determined. As summarized in Table 1, the predicted primary drying time was comparable with the measured time under both conditions. Overcashier et al. observed a similar phenomenon that the sublimation rate was less affected by the variation of dry layer resistance (Overcashier De Fau-Patapoff et al., 1999). This suggested that the primary drying time can be roughly predicted, even if the fixed profile of dry layer resistance is used for the simulation program. On the other hand, the maximum product temperature predicted at −20 ◦ C and 10 Pa, which was the same condition employed in a preliminary run for the measurement of dry layer resistance, was almost the same as the measured value. There was 2.7 ◦ C difference, however, in maximum product temperature between the predicted and measured values at the primary drying of −20 ◦ C and 5 Pa, where the primary drying condition is different from that used for a preliminary run of lyophilization. The temperature difference was not thought to be negligible even considering the possible error of the thermocouple. In our present program, the heat transfer coefficient is corrected according to Eqs. (1) and (2) with the chamber pressure. On the other hand, a fixed profile of dry layer resistance obtained from a preliminary run is used, even if any chamber pressure is set. Therefore, it was suggested that the predictive model for dry layer resistance was required for accurate prediction of product temperature, when the dry layer resistance that was determined from a different primary drying condition was applied. To support this hypothesis, the contribution of shelf temperature and chamber pressure on the dry layer resistance was evaluated. 3.3. Effects of shelf temperature and chamber pressure on the dry layer resistance Though the prediction of the product temperature during primary drying was challenged using the shelf heat transfer coefficient and the dry layer resistance obtained from a preliminary run, the prediction for maximum product temperature was unsuccessful due to different dry layer resistance. In order to investigate the cause of the deviation of prediction, it was evaluated whether dry layer resistance changes or not depending upon conditions of shelf temperature and chamber pressure. The data of product temperature of each edge and center vial during primary drying was collected with five different programs in terms of shelf temperature

(A) 300

Rp (kPam2s/kg)

3.2. Prediction of maximum product temperature and primary drying time

200

100

0 0

1

2

3

4

5

6

5

6

Dry layer thickness (mm)

(B) 300

Rp (kPam2s/kg)

4

200

100

0 0

1

2

3

4

Dry layer thickness (mm) Fig. 2. Effects of chamber pressure on the dry layer resistance profiles of 10 w/v% sucrose in the edge vial (A) and the center vial (B). The setting parameters of shelf temperature and chamber pressure during primary drying were 5 Pa (open circles), 10 Pa (open triangles), and 15 Pa (open diamonds) at a constant shelf temperature (−20 ◦ C).

and chamber pressure. In these programs, the shelf temperature and chamber pressure were set at a range of −20 ◦ C to 0 ◦ C and 5–15 Pa, respectively. The dry layer resistance of each edge and center vial was calculated from individual product temperature experimentally obtained above. Fig. 2A and B shows the relationship between the dry layer thickness of edge and center vials and dry layer resistance at 5, 10, and 15 Pa of chamber pressure at constant shelf temperature of −20 ◦ C. Each dry layer resistance profile is depicted as a curve and was dependent on dry layer thickness. Such profiles have often been observed in the formulation containing sucrose (Johnson et al., 2010; Overcashier De Fau-Patapoff et al., 1999). It is apparent from the graphs that the lower chamber pressure resulted in higher maximum dry layer resistance. The maximum dry layer resistance measured at 5 Pa was approximately two-fold higher than those measured at 10 Pa. This phenomenon was commonly observed regardless of the position of vials. This result indicates that the low heat transfer rate to the glass vial, derived from the decrease of chamber pressure, raises maximum dry layer resistance. Similarly, the effects of shelf temperature on dry layer resistance were investigated at constant chamber pressure of 5 Pa. In Fig. 3A and B, dry layer resistance of each edge and center vial was plotted as a function of the dry layer thickness at different shelf temperature between −20 ◦ C and 0 ◦ C. As a result, when the lower shelf temperature was set, higher dry layer resistance was observed. It is clear that an increase in heat transfer rate due to higher shelf temperature ascribes lower dry resistance. These results are

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Table 1 The results of prediction of maximum product temperature and the primary drying time. The measured dry layer resistance profile at −20 ◦ C of shelf temperature and 10 Pa of chamber pressure was used for the prediction. Shelf temperature (◦ C)

Chamber pressure (Pa)

−20 −20

Maximum product temperature of edge vial

Primary drying time of center vial

Predicted

Predicted

Measured

38 h 30 h

38 h 30 h

◦

supported by a previous report, where say the dry layer resistance varies depending upon the shelf temperature and chamber pressure (Pikal et al., 1983). As shown in Figs. 2 and 3, the maximum dry layer resistance of the edge vial was lower than that of the center vial. As previously mentioned, the edge vial is exposed to radiative heating from the chamber wall and to conductive heating from the tray flame. The higher heat transfer rate probably allows the edge vial to raise the product temperature (and the temperature at the interface of sublimation), and to form a dry layer of rough porous structure due to the micro-collapse, resulting in lower resistance against water vapor flow. Consequently, these results indicated that dry layer resistance varied depending upon the extent of the heat transfer rate to the glass vial. As explained in Section 3.2, our results indicated that the maximum product temperature was not accurately predicted at different primary drying conditions where dry layer resistance was measured. This suggested that the temperature variation between prediction and measurement was caused by inputting the mistaken dry layer resistance to the simulation program. Therefore, it was thought that the predictive model of dry layer resistance

Rp (kPam2s/kg)

300

(A)

200

100

0 1

2

3

4

5

6

Dry layer thickness (mm) 300

(B)

200

−34.1 C −33.3 ◦ C

needs to be developed, and is a useful tool to predict the product temperature during primary drying. In the following sections, various correlations for development of the predictive model were attempted. 3.4. Predictive model of dry layer resistance The way of predicting dry layer resistance under different conditions of shelf temperature and chamber pressure from the measured dry layer resistance at a preliminary run was investigated. When the operating parameters of shelf temperature and chamber pressure change, the heat transfer rate and sublimation rate change (see Eqs. (1)–(6)). Thereby, in order to evaluate the two parameters of shelf temperature and chamber pressure, these parameters were converted to the sublimation rate to investigate the relationship with dry layer resistance. On the other hand, maximum dry layer resistance is the most important factor affecting the maximum product temperature during primary drying, which is available as an index of collapse of the lyophilized product. Accordingly, an attempt was made to develop a predictive model for dry layer resistance under various primary drying conditions by evaluating the relationship between the sublimation rate and maximum dry layer resistance. As shown in Fig. 4A, the maximum dry layer resistance of the edge and center vials was plotted as the function of the sublimation rate which was obtained from the five different lyophilization programs at a range of −20 ◦ C to 0 ◦ C and 5–15 Pa. As a result, apparent correlation was not observed between these parameters (R2 = 0.46). As mentioned in “Mathematical model of primary drying”, dry layer resistance is expressed as a function for the differential pressure between the pressure at the interface of the sublimation and the chamber pressure in Eq. (9). Thus, dry layer resistance against water vapor flow is determined by not only the structure of dried cake but also the chamber pressure. When the dry layer resistance is modified under the assumption that the chamber pressure is considered to be zero, the modified dry layer resistance can be defined as the parameter depending on the dried cake structure alone. Thus, Eq. (9) was converted to Eq. (13) to exclude the effects of the chamber pressure. Rp =

Rp (kPam2s/kg)

◦

−36.8 C −33.4 ◦ C

5 10

0

Measured

Pi − Pc dm/dt

Rps = limPc→0 Rp = limPc→0 100

0 0

1

2

3

4

5

6

Dry layer thickness (mm) Fig. 3. Effects of shelf temperature on the dry layer resistance profiles of 10 w/v% sucrose in the edge vial (A) and the center vial (B). The setting parameters of shelf temperature during primary drying were −20 ◦ C (open circles), −10 ◦ C (close triangles), and 0 ◦ C (close diamonds) at a constant chamber pressure (5 Pa).

Pi − Pc Pi = dm/dt dm/dt

(13)

The dry layer resistance obtained here was named “Specific dry layer resistance (Rps)”. If the maximum of specific dry layer resistance, Rps-max, is successfully predicted, the maximum dry layer resistance is also predicted from Eqs. (9) and (13). The maximum of specific dry layer resistance, Rps-max, was plotted as functions of the sublimation rate in Fig. 4B. It was found that the correlation coefficient between the maximum of specific dry layer resistance and sublimation rate was remarkably improved to 0.93. Furthermore, higher correlation coefficient (0.96) was obtained between Ln(Rps-max) and Ln(dm/dt), when the maximum of specific dry layer resistance and sublimation rate were expressed as a

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Then Eqs. (16) and (17) can be expressed using the measured and predicted values of Pi and dm/dt.

300

Rp-max (kPam2s/kg)

(A)

Pimeas. = eb + 200

Pipre. = eb + 100

0 0.1

0.2

0.3

(16)

dm

(17)

1+a dtpre.

Where Pimeas. and dm/dtmeas. are the measured values of the pressure at the interface of sublimation and the sublimation rate. Pipre. and dm/dtpre. are the predicted pressure at the interface of sublimation and the predicted sublimation rate. Then, the novel empirical formula was derived from the combination of Eqs. (16) and (17).

y = -1630x + 273 R² = 0.46 0.0

dm 1+a dtmeas.

0.4



dm/dt (g/hr/vial)

Pipre. = Pimeas. +

300

dm/dtpre. dm/dtmeas.

1+a

Rps-max (kPam2s/kg)

(B)

Rpspre. =

Rppre. =

(19)

0.0

0.1

0.2

0.3

0.4

dm/dt (g/hr/vial)

(C)

5.0

4.5 y = -0.79 x + 3.7 R² = 0.96 4.0 -2.0

-1.5

-1.0

Ln (dm/dt) Fig. 4. Correlation between maximum dry layer resistance (or maximum specific dry layer resistance) and sublimation rate of the edge vial (open circles) and the center vial (close circles). The relationship between X-axis and Y-axis in these graphs are below; (A) sublimation rate, dm/dt, and maximum dry layer resistance, Rp-max, (B) sublimation rate, dm/dt, and maximum of specific dry layer resistance, Rps-max, and (C) logarithm of sublimation rate, Ln(dm/dt), and logarithm of maximum of specific dry layer resistance, Ln(Rps-max).

logarithm in Fig. 4C. The empirical formula in Eq. (14) was derived from such high correlation. Ln(Rps − max) = a × Ln

 dm  dt

+b

(14)

Where “a” and “b” are the slope and the intercept, respectively. Eqs. (13) and (14) can be expressed as the equation of the pressure at the interface of sublimation in Eq. (15). dm dt 1+a

(20)

3.5. Predictive procedure for dry layer resistance

5.5

-2.5

1+a Pimeas. − Pc + dm/dtpre. /dm/dtmeas. dm/dtpre.

In these formulas of Eqs. (15)–(20), when the dry layer resistance showed the maximum value, the corresponding values of Pi, Rps, and dm/dt is used. The newly introduced predictive formula (Eq. (20)) was applied to “the mathematical model of primary drying”, and then the novel predictive model of dry layer resistance was proposed.

100

0

Ln (Rps-max)

1+a

200

y = -3730 x + 618 R² = 0.93

Pi = eb +

Pimeas. + (dm/dtpre. /dm/dtmeas. ) dm/dtpre.

(18)

(15)

In order to predict the dry layer resistance, Eq. (20) needs to be resolved. The measured values of the pressure at the interface of sublimation, Pimeas. , and the measured sublimation rate, dm/dtmeas. , can be determined from the maximum product temperature in a preliminary run. Besides, the predicted sublimation rate, dm/dtpre. , at various conditions of shelf temperature and chamber pressure can be obtained by estimation of the heat transfer rate to the vial in Eqs. (1)–(6). Then, at least two sets of measured maximum of specific dry layer resistance and the sublimation rate are necessary to determine “slope a” in Eq. (14). As already mentioned, the heat transfer rates between the edge and center vials are different because the edge vial is positioned closer to the chamber wall and the tray flame than the center vial, and is exposed more to the radiative heating from the chamber wall and to the conductive heating from the tray flame. Similarly, the specific dry layer resistance and the sublimation rate are also different between the edge and center vials for the difference of heat transfer to glass vial. Thus, these two sets of measured parameters, the maximum of specific dry layer resistance and the sublimation rate, are available from the product temperature of each edge and center vial in a preliminary run. In this report, two sets of maximum of specific dry layer resistance and the sublimation rate of the edge and center vials were calculated from the maximum product temperature of each edge and center vial obtained from a preliminary run, where the primary drying was conducted at −20 ◦ C of shelf temperature and 10 Pa of chamber pressure. From the calculation, the “slope a” was determined to be −0.85 by the linear regression, and this value was comparable with −0.79 (=slope a) in Fig. 4. Utilizing the obtained value of −0.85 (=slope a), the maximum dry layer resistance at different primary drying conditions was predicted by resolving Eq. (20) with “Mathematical model of primary drying”. The predicted dry layer resistance profile was obtained by multiplying the measured dry layer resistance profile obtained from a preliminary run

Please cite this article in press as: Kodama, T., et al., Determination for dry layer resistance of sucrose under various primary drying conditions using a novel simulation program for designing pharmaceutical lyophilization cycle. Int J Pharmaceut (2013), http://dx.doi.org/10.1016/j.ijpharm.2013.04.081

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Table 2 Comparison of the predicted and measured maximum dry layer resistance at various parameters of shelf temperature and chamber pressure. Shelf temperature (◦ C)

Chamber pressure (Pa)

−20 −20 −20 −10 0

5 10 15 5 5

Maximum dry layer resistance of edge vial (kPa m2 s/kg)

Maximum dry layer resistance of center vial (kPa m2 s/kg)

Predicted

Measured

Predicted

Measured

213 124 77 158 125

207 122 86 150 121

265 144 85 191 148

251 145 103 194 149

by the ratio of maximum dry layer resistance between the predicted and measured values. As an example, Fig. 5 shows the predicted and measured dry layer resistance for 10 w/v% sucrose of the edge vial under the primary drying condition of −20 ◦ C and 5 Pa. The measured dry layer resistance at −20 ◦ C and 10 Pa in a preliminary run are shown as a reference profile. The predicted dry layer resistance profile at −20 ◦ C and 5 Pa was calculated from the measured dry layer resistance profile at −20 ◦ C and 10 Pa. Then, the predicted dry layer resistance profile of sucrose was almost identical to the measured dry layer resistance profile. Consequently, it was demonstrated that the dry layer resistance could be easily predicted by the product temperature of each edge and center vial measured from one preliminary lyophilization run. 3.6. Experimental verification for prediction of maximum dry layer resistance under various primary drying conditions Utilizing the dry layer resistance measured at −20 ◦ C of shelf temperature and 10 Pa of chamber pressure in a preliminary run, the maximum dry layer resistance of each edge and center vial under various primary drying conditions at a range of −20 ◦ C to 0 ◦ C and 5 Pa to 15 Pa was predicted. These predicted values of maximum dry layer resistance were compared with the measured values obtained from the lyophilization cycles conducted under individual primary drying conditions. As can be seen from Table 2, these predicted values of maximum dry layer resistance were highly consistent with the measured values for both edge and center vials, demonstrating that the simulation model would be applicable to the prediction of dry layer resistance under various primary drying conditions where the shelf temperature and chamber pressure are different from those of a preliminary run.

Rp (kPam2s/kg)

300

200

100

0 0

1

2 3 4 Dry layer thickness (mm)

5

6

Fig. 5. Predicted and measured dry layer resistance profiles of 10 w/v% sucrose. Open and close circles are the predicted and measured dry layer resistance profiles of edge vial at −20 ◦ C of shelf temperature and 5 Pa of chamber pressure. Open triangles are the measured dry layer resistance profiles of the edge vial at −20 ◦ C of shelf temperature and 10 Pa of chamber pressure in a preliminary run.

4. Conclusion In order to predict the dry layer resistance under various shelf temperature and chamber pressure, the novel predictive model of dry layer resistance was developed. The predictive model is derived from the empirical formula consisting of the sublimation rate and the specific dry layer resistance, which is defined as the dry layer resistance under assumption that the chamber pressure is considered to be zero. In the lyophilization experiments, it was demonstrated that this model could successfully predict the dry layer resistance under various shelf temperature and chamber pressure based on relationship of the sublimation rate and specific dry layer resistance obtained from the product temperature of the edge and center vials in one preliminary run. Therefore, it is expected that the predictive model of dry layer resistance is applied to accurately predict the product temperature. References Bellows, R.J., King, C.J., 1972. Freeze-drying of aqueous solutions: maximum allowable operating temperature. Cryobiology 9, 559–561. Ho, N.F., Roseman, T.J., 1979. Lyophilization of pharmaceutical injections: theoretical physical model. J. Pharm. Sci. 68, 1170–1174. Jennings, T.A., 1988. Discussion of primary drying during lyophilization. J. Parenter. Sci. Technol. 42, 118–121. Johnson, R.E., Oldroyd, M.E., Ahmed, S.S., Gieseler, H., Lewis, L.M., 2010. Use of manometric temperature measurements (MTM) to characterize the freeze-drying behavior of amorphous protein formulations. J. Pharm. Sci. 99, 2863–2873. Koganti, V.R., Shalaev, E.Y., Berry, M.R., Osterberg, T., Youssef, M., Hiebert, D.N., Kanka, F.A., Nolan, M., Barrett, R., Scalzo, G., Fitzpatrick, G., Fitzgibbon, N., Luthra, S., Zhang, L., 2011. Investigation of design space for freeze-drying: use of modeling for primary drying segment of a freeze-drying cycle. AAPS PharmSciTech 12, 854–861. Kuu, W.Y., Hardwick, L.M., Akers, M.J., 2006. Rapid determination of dry layer mass transfer resistance for various pharmaceutical formulations during primary drying using product temperature profiles. Int. J. Pharm. 313, 99–113. Kuu, W.Y., Nail, S.L., 2009. 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). J. Pharm. Sci. 98, 3469–3482. 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. Pharmaceut. Sci. Technol. 51, 7–16. Nail, S.L., 1980. The effect of chamber pressure on heat transfer in the freeze drying of parenteral solutions. J. Parenter. Drug Assoc. 34, 358–368. Overcashier De Fau-Patapoff, T.W., Patapoff Tw Fau-Hsu, C.C., Hsu, C.C., 1999. Lyophilization of protein formulations in vials: investigation of the relationship between resistance to vapor flow during primary drying and small-scale product collapse. J. Pharm. Sci. 88. Pikal, M.J., 1985. Use of laboratory data in freeze drying process design: heat and mass transfer coefficients and the computer simulation of freeze drying. J. Parenter. Sci. Technol. 39, 115–139. Pikal, M.J., Cardon, S., Bhugra, C., Jameel, F., Rambhatla, S., Mascarenhas, W.J., Akay, H.U., 2005. The nonsteady state modeling of freeze drying: in-process product temperature and moisture content mapping and pharmaceutical product quality applications. Pharmaceut. Dev. Technol. 10, 17–32. Pikal, M.J., Roy, M.L., Shah, S., 1984. Mass and heat transfer in vial freeze-drying of pharmaceuticals: role of the vial. J. Pharm. Sci. 73, 1224–1237. Pikal, M.J., Shah, S., 1990. The collapse temperature in freeze drying: dependence on measurement methodology and rate of water removal from the glassy phase. Int. J. Pharm. 62, 165–186. Pikal, M.J., Shah, S., Senior, D., Lang, J.E., 1983. Physical chemistry of freeze-drying: measurement of sublimation rates for frozen aqueous solutions by a microbalance technique. J. Pharm. Sci. 72, 635–650.

Please cite this article in press as: Kodama, T., et al., Determination for dry layer resistance of sucrose under various primary drying conditions using a novel simulation program for designing pharmaceutical lyophilization cycle. Int J Pharmaceut (2013), http://dx.doi.org/10.1016/j.ijpharm.2013.04.081

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dryer differences via operational qualification tests. AAPS PharmSciTech 7, E39. Schneid, S.C., Gieseler, H., Kessler, W.J., Pikal, M.J., 2009. Non-invasive product temperature determination during primary drying using tunable diode laser absorption spectroscopy. J. Pharm. Sci. 98, 3406–3418.

Please cite this article in press as: Kodama, T., et al., Determination for dry layer resistance of sucrose under various primary drying conditions using a novel simulation program for designing pharmaceutical lyophilization cycle. Int J Pharmaceut (2013), http://dx.doi.org/10.1016/j.ijpharm.2013.04.081