Applications of the Tunable Diode Laser Absorption Spectroscopy: In-Process Estimation of Primary Drying Heterogeneity and Product Temperature During Lyophilization

Journal of Pharmaceutical Sciences xxx (2018) 1-15

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Research Article

Applications of the Tunable Diode Laser Absorption Spectroscopy: In-Process Estimation of Primary Drying Heterogeneity and Product Temperature During Lyophilization Puneet Sharma 1, *, William J. Kessler 2, Robin Bogner 1, Meena Thakur 1, Michael J. Pikal 1, y 1 2

Department of Pharmaceutical Sciences, School of Pharmacy, University of Connecticut, Storrs, Connecticut 06269 Physical Sciences, Inc., Andover, Massachusetts 01810

a r t i c l e i n f o

a b s t r a c t

Article history: Received 16 March 2018 Revised 8 July 2018 Accepted 17 July 2018

The aim of this research was to evaluate the impact of variability in ice sublimation rate (dm/dt) measurement and vial heat transfer coefficient (Kv) on product temperature prediction during the primary drying phase of lyophilization. The mathematical model used for primary drying uses dm/dt and Kv as inputs to predict product temperature. A second-generation tunable diode laser absorption spectroscopy (TDLAS)ebased sensor was used to measure dm/dt. In addition, a new approach to calculate drying heterogeneity in a batch during primary drying is described. The TDLAS dm/dt measurements were found to be within 5%-10% of gravimetric measurement for laboratory- and pilot-scale lyophilizers. Intersupplier variability in Kv was high for the same “type” of vials, which can lead to erroneous product temperature prediction if “one value” of vial heat transfer coefficient is used for “all vial types” from different suppliers. Studies conducted in both a laboratory- and a pilot-scale lyophilizer showed TDLAS product temperature to be within ±1 C of average thermocouple temperature during primary drying. Using TDLAS data and calculations to estimate drying heterogeneity (number of vials undergoing primary drying), good agreement was obtained between theoretical and experimental results, demonstrating usefulness of the new approach. © 2018 Published by Elsevier Inc. on behalf of the American Pharmacists Association.

Keywords: freeze drying/lyophilization process analytical technology (PAT) mathematical model simulation

Introduction Primary drying is the longest phase in the lyophilization process during which sublimation of ice takes place under vacuum and low temperature conditions. The temperature of the product during primary drying is controlled by adjusting the shelf temperature and chamber pressure. An increase in product temperature above a critical temperature can adversely affect product quality, perhaps causing loss of cake structure (collapse), so product temperature estimation during primary drying is critical. The traditional

Current address for Sharma: Genentech, South San Francisco, California. Current address for Thakur: Amgen, Cambridge, Massachusetts. Note: The research data used in preparation of the article is available upon request to the corresponding author. This article contains supplementary material available from the authors by request or via the Internet at https://doi.org/10.1016/j.xphs.2018.07.031. * Correspondence to: Puneet Sharma (Telephone: þ1 650 467 6064). E-mail address: [email protected] (P. Sharma). y In Loving Memory of Professor Michael J. Pikal.

approach for product temperature measurement on a commercialscale dryer is to use thermocouples, which has some major limitations. First, placing/positioning the thermocouple sensor into aseptically filled vials during commercial manufacturing may compromise the sterility of the batch. Therefore, it is preferred to use thermocouples only during scale up/technical transfer studies when having a sterile product is not always a requirement. Second, it is now well known that the product temperature measurement using thermocouples is only directly relevant to the vials that contain thermocouples and is not representative of the entire batch. Presence of a temperature sensor in the vial also alters the temperature history by changing the ice nucleation temperature.1 Finally, using thermocouples in dryers equipped with automated loading-unloading system is challenging. Thermocouples are either not used or they are only placed in the vials in the first few rows of the shelf near the door of the dryer. Wireless temperature sensors are available for product temperature measurement; however, limitations similar to use of thermocouples still exist in terms of data being applicable only to the vials having wireless sensors. This problem with the temperature sensor impacting the ice nucleation

https://doi.org/10.1016/j.xphs.2018.07.031 0022-3549/© 2018 Published by Elsevier Inc. on behalf of the American Pharmacists Association.

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temperature can be solved by using controlled ice nucleation, which, however, is currently not commonly used in manufacturing. Annealing approach can be used to normalize for ice nucleation differences due to the use of temperature sensors. However, depending on the formulation composition and fill volume, considerable efforts may be required to develop an optimized annealing process that does not adversely impact product quality and increases the overall cycle time. Knowledge of reliable in-process product temperature can be extremely valuable in selecting “optimum” lyophilization process parameters (shelf temperature, pressure, and time) for manufacturing-scale lyophilization cycles. Lyophilization cycles on manufacturing scale are conducted using process parameters that keep the product temperature below the critical product temperature in an effort to minimize cycle time. In the absence of in-process product temperature data, lyophilization cycles are designed conservatively such that the product temperature remains far below the critical product temperature, and the primary drying hold time is much longer than necessary. At the other extreme, the process can be inadvertently designed to be aggressive such that the product temperature is close to critical product temperature and risks product loss due to very minor process variations, even calibration errors. A process analytical technology compatible with the aseptic environment of a manufacturing-scale lyophilizer that provides information on “batch average” product temperature and temperature of slow drying vials is highly desirable. Such a technology is beneficial for the pharmaceutical industry in situations where lyophilized products are scaled up or transferred between dryers of different mechanical designs/layout or if the process is briefly out of control. For example, if there is loss of pressure control, data from a process analytical technology tool can support investigations verifying the impact of process excursion on product temperature and possible impact on product quality attributes. Schneid et al. have shown the applicability of using a tunable diode laser absorption spectroscopy (TDLAS) sensor to estimate batch average product temperature (Tb) at the bottom center of the vial using a steady-state heat and mass transfer model2 using Equation 1:

Tb ¼ Ts 

! DHs $dm dt ; Av $Kv $N

(1)

where dm/dt is amass flow rate (g/s) measured using TDLAS, DHs is the heat of sublimation of ice (cal/g), Av is the outer cross sectional area of the vial (cm2), and Kv is the average vial heat transfer coefficient (cal s1 cm2 K1); Ts is the shelf surface temperature ( C), N is the number of vials in the batch undergoing primary drying, and Tb is the product temperature at the bottom center of the vial ( C). The TDLAS sensor is installed in the duct connecting the lyophilizer chamber and condenser. The sensor measures water vapor concentration and water vapor flow velocity across the duct enabling the calculation of the batch average water vapor mass flow rate, dm/dt. The “uncertainty” of Tb measurement using Equation 1 depends on the combined “uncertainty” of the input parameters. Of all the parameters on the right side of the equation, inaccurate values of Kv are most problematic. Kv data are obtained using “unique procedures,” and therefore, if these “procedures” are not performed carefully, Kv errors can lead to errors in Tb measurement. The Kv in Equation 1 refers to the average Kv for all vials in the batch, including vials on the edge of the vial array as well as interior or center vials. Edge vials have a higher heat transfer coefficient than that same vial in the center of the vial array, and this difference, denoted the “edge vial effect,” may be estimated from heat transfer theory.3 Even for a given position in the vial array, variability in Kv values is introduced by the lack of perfect control of the

vial bottom contour during vial manufacturing. In addition, the impact of dryer design on the fraction of edge and center vials as well as on the magnitude of the edge vial effect needs to be taken into account when using an average Kv value obtained on a laboratory-scale dryer for Tb estimation on a production-scale dryer.3 The average laboratory Kv value needs to be adjusted to correspond with the average Kv that vials will have in a manufacturing operation. Recent studies suggest this adjustment can be made with acceptable accuracy.3 The measurement accuracy and sensitivity of dm/dt by the TDLAS sensor are dependent on the velocity and water concentration measurements. In the study of Schneid et al.,2 a first-generation TDLAS sensor using laser propagation in one line of sight at 45 across the lyophilizer duct was used to monitor dm/dt. This study evaluated a second-generation TDLAS sensor that was developed to improve the accuracy and sensitivity of velocity measurement. Since some improvements have been made in the sensor to improve the mass flow rate measurement, the “proof of concept” established in the study of Schneid et al. for use of the TDLAS sensor in product temperature measurement needs to be updated or “reverified,” and error estimates made of the temperature measurement, including the impact of likely inter-batch variation in Kv. The focus of the studies described in this article was to evaluate the accuracy of the real-time estimation of Tb using the improved TDLAS-based water vapor mass flow rate measurement and more accurate Kv values. The studies described here present the following aspects: (1) Impact of variability in average Kv values characteristic of different batches of vials produced by different vial manufacturers on Tb estimation. (2) Accuracy and sensitivity in dm/dt measurement obtained using a second-generation TDLAS sensor in laboratory- and pilot-scale lyophilizers. (3) Comparison of Tb values obtained using thermocouples and Equation 1 (where dm/dt values obtained from the TDLAS sensor are used) for runs performed in laboratory- and pilotscale lyophilizers. (4) A TDLAS-based procedure to estimate drying heterogeneity in a batch of vials; accuracy of the procedure and use of the procedure to estimate drying heterogeneity when using controlled ice nucleation.

Materials Bovine serum albumin (BSA), sodium chloride, and sucrose were purchased from Sigma-Aldrich (St Louis, MO). Tubing vials of 20 cc were purchased from West Pharmaceuticals Company (Lionville, PA) and Cole-Parmer Instrument Company (Vernon Hills, IL). Experiments were also performed using 20-cc tubing vials obtained from Nipro Glass Americas (NGA, Formerly Amcor, Millville, NJ). Two-leg 20-mm gray butyl stoppers were used (Fisher Scientific, Waltham, MA). Thirty-gauge T-type copper constantan thermocouples were purchased from Omega Engineering (Stamford, CT) to measure Tb. Thirty-gauge T-type copper constantan surface adhesive thermocouples (Omega Engineering, Stamford, CT) were used to measure shelf surface temperature. Methods Lyophilization Experiments were performed using laboratory- (LyoStar II; SP Industries) and pilot-scale (IMA Life North America Inc.)

P. Sharma et al. / Journal of Pharmaceutical Sciences xxx (2018) 1-15 Table 1 Selected Specifications of the Laboratory- (LyoStar II) and Pilot-Scale Lyophilizers and TDLAS Sensor Assembly

Chamber volume (L) Duct diameter (cm) Duct area (cm2) Total shelf surface area (m2) Path length (cm) Measurement angle

LyoStar II

Pilot-Scale Dryer

107.5 9.72 74.36 0.46 13.15 45.0 and 135.0

950.3 33.70 892.00 2.25 50.10 47.4 and 132.6

lyophilizers with approximately 0.45 m2 and 2 m2 shelf surface areas, respectively. The basic differences between the 2 lyophilizers are listed in Table 1. Vial Heat Transfer Coefficient (Kv) Kv is defined as the area normalized ratio of heat flow rate (dQ/ dt) to the temperature difference between the shelf surface and bottom of the product.4

Kv ¼

dQ =dt Av $ðTs  Tb Þ

(2)

The heat transfer coefficient (Kv) can be divided into 3 component mechanisms4; (1) radiation heat transfer (Kr) to the bottom, top, and sides of the vial, (2) heat transfer due to gas conduction (Kg) in the space between the vial bottom and shelf surface, and (3) heat transfer due to direct conduction (Kc) between the contact points at the vial bottom and shelf surface. Although Kc and Kr are independent of chamber pressure, Kg can be written as a function of pressure as follows4:

Kg ¼

a$L0 $P   ; 1 þ lv a$Ll00 P

(3)

where L0 is the free molecular flow heat conductivity of the gas at 0 C, l0 is the heat conductivity of the gas at ambient pressure, P is the gas pressure, lv is the constant “effective” distance characterizing the gap between the shelf and the vial bottom, and a is a term related to the energy accommodation coefficient (ac) and the square root of the absolute temperature, T. Batch average Kv as a function of pressure (P) can be represented as follows5:

Kv ¼ KC þ

KP$P ; 1 þ KD$P

(4)

where KC is the sum of contact parameters, Kc and the radiative term Kr, KP is the product of a and L0 , and KD is the combination of terms, lv  (a  L0 /l0). For all the vials, KP is 0.00332.4 The regression fit of Kv and P (Torr) yields KC and KD. Once KD is determined, lv can be calculated using literature values of a, L0 , and l0.5 The tubing vial manufacturing process generates vials with variability in the contour of the vial bottom. Variability in the degree of physical contact between vial bottom and shelf translates into differences in the parameters Kc and lv (gap between shelf and vial bottom). Variation in the term “lv” can lead to differences in the heat transfer through Kg, and variation in contact impacts the pressure-independent term in Kv. Such differences may mean significant differences in Kv for vials from different suppliers and may, in principle, also lead to differences in batch average Kv for different batches from the same supplier. Therefore, it is critical to have a good estimate of the interbatch differences in the Kv of vials from

3

the same supplier. The impact of uncertainty in Kv estimation on the uncertainty in product temperature estimation can be represented as follows:

dTb ¼

ðTS  Tb Þ  dKv ; Kv

(5)

where the symbol d represents uncertainty in the respective parameters (see Appendix I for derivation). Determination of 20-cc vial (20 mm neck diameter) Kv values was performed using deionized water sublimation tests at 10 C shelf temperature and 65, 100, and 150 mT chamber pressures. The Kv was determined gravimetrically using procedures similar to those described in the literature.4 The individual vials were weighed before and after a steady-state sublimation period of 6 h to determine vial-specific sublimation rate (mi). During the sublimation tests, 10 mL of water was filled into 160 vials that covered 1 full shelf of the LyoStar II lyophilizer. Each of the 20-mm stoppers used for this study was fully inserted into the vials, and a small precision bore stainless steel tube (length ¼ 1.497 cm, internal diameter 0.217 cm) was inserted. This tube eliminates variability introduced in mass transfer due to variation in stopper placement and ensures constant mass transfer resistance across the stopper in all vials,4 meaning all variation in sublimation rate is due to variation in heat transfer. Of the 160 vials used for the sublimation test, 110 vials were at the “center” position and 50 vials were at the “edge” position. Vials were treated as “center” vials when they were surrounded by other vials in a hexagonal close pack configuration; otherwise they were treated as “edge” vials. Tb was measured in 5 vials placed at center and edge locations in the array using 30-gauge thermocouples. Ts was measured using 2 surface adhesive thermocouples placed close to the shelf heat transfer fluid inlet and outlet ports on each shelf. An aluminum foil cover was attached to the inside of the front door of the lyophilizers to partially shield the vials from the “extra” radiation effects of the acrylic door, relative to a production dryer that typically has a polished stainless steel door. After loading the vials, the shelf temperature was lowered to 40 C to freeze the water. Following freezing and chamber evacuation, the shelf temperature was raised at approximately 2 C per min to 10 C. Once the Tb was close to 10 C, the sublimation test was initiated at the chosen chamber pressure, and the Tb quickly dropped to approximately 35 C. This procedure for Kv estimation ensures that heat flow from shelf to the product is near “steady state” in the study. After 6 h of sublimation, the chamber pressure was released to atmospheric pressure and the shelf temperature was raised to thaw the ice. The time for the sublimation studies was selected such that total weight loss was between 5% and 20% at selected sublimation conditions to avoid excessive sublimation of ice that might compromise contact between the ice and the vial bottom. The average vial heat transfer coefficient for vials containing 1 thermocouples, KTC cm2 K1) is calculated using4 v,i , (cal s

K TC v;i

¼

E D 0:1833$ m_ TC i Av $ðTS  Tb Þ

;

(6)

_ TC where m i is the mean sublimation rate of the thermocouple vials, and Av is the outer cross sectional area of the vials (cm2). The numerical factor 0.1833 arises from unit conversion and introducing the heat of sublimation of ice (660 cal/g). The value of the average temperature difference, (Ts  Tb), is obtained by integration over the 6-h run. From KTC v,i , the vial heat transfer coefficient of each vial Kv,i is calculated as follows4:

4

P. Sharma et al. / Journal of Pharmaceutical Sciences xxx (2018) 1-15

" Kv;i ¼

K TC v;i $

1þ

# ! E  D m_ i TC 4  1 $ 1:2 þ 0:04$10 $ K v;i ; m_ TC i

(7)

_ i is the vial-specific sublimation rate that is determined where m gravimetrically as described previously. For details regarding the derivation of Equation 3, refer the study by Pikal et al.4 The term in square brackets allows calculation of the individual vial Kv,i from the average of the thermocouple KTC v,i and the ratio of the sublima_ i and the average sublimation rate tion rate of the vial of interest m 4 _ TC of the thermocouple vials, m i . The average Kv for the batch is then determined from the average of all Kv,i for center vials and edge vials. Equation 7 is necessary because the average of the KTC v,i is not necessarily the same as the average for the batch as a whole, and no temperature measurements are available for the vials not containing thermocouples. The variability between batch average Kv values of the different batches and different manufacturers of vials was assessed. Assessment was also performed for differences in the Kv values of center and edge vials of different batches.

Laboratory- and Pilot-Scale Testing of the Second-Generation TDLAS Sensor The LyoFlux 200 (TDLAS system; Physical Sciences Inc., Andover, MA) was installed on the FTS LyoStar II laboratory-scale lyophilizer and a pilot-scale lyophilizer at IMA Life North America Inc. The TDLAS sensor was installed in the duct connecting the chamber and condenser. The details of the TDLAS technology have been previously described.6 Briefly, the TDLAS sensor optically measures (1) N, water vapor concentration or number density, and (2) v, gas flow velocity. From these values, the instantaneous mass flow rate (dm/dt) is calculated using the following relation: dm/dt ¼ N v A, where A is the cross-sectional area of the duct. Sensor operation and reporting of the average dm/dt values was provided by the LyoFlux 200 software (Physical Sciences Inc., Andover, MA). At the beginning of each experiment, before raising the freeze dryer shelf temperature to initiate sublimation, a sensor zero velocity offset (ZVO) determination was performed. The ZVO determination was performed with product in the chamber at a low temperature (e.g., 40 C) and at the target sublimation pressure (e.g., 100 mT). The isolation valve between the dryer chamber and condenser was closed to provide a zero net flow velocity condition. Three 1-min measurements were made to determine the velocity with the valve closed. The averaged measured velocity in the absence of flow (typically <±0.5 m/s) was then subtracted from each subsequent measurement to account for electronic offsets, optical noise, etc. We note that typical velocities vary between ~20 and 150 m/s during primary drying and 2 and 20 m/s during secondary drying. The offset corrected velocities were used in combination with the water concentration measurements to calculate the batch average water vapor mass flow rates. The first-generation TDLAS sensor2,5 utilized a single, 45 angle line-of-sight optical absorption measurement across the freeze dryer duct. A second measurement across a sealed, low-pressure (~500 mT neat water vapor) glass cell was simultaneously made to enable the measurement of the gas flow velocity. The secondgeneration TDLAS sensor used during these experiments used 2 line-of-sight measurements (45 and 135 with respect to the gas flow axis) across the freeze dryer duct. This new configuration resulted in twice the velocity measurement sensitivity (due to each absorption feature shifting in opposite directions) and eliminated potential measurement errors associated with pressure-induced shifts in the wavelength or frequency position of the absorption feature (compared to the reference absorption cell). These errors originate from referencing the absorption lineshape measurement

in the freeze dryer duct (typically at ~100 mT) to the absorption lineshape measurement in the sealed cell maintained at ~500 mT of neat water vapor. The 2 line-of-sight measurement configuration enabled determination of the velocity-induced frequency shift using 2 measurements within the duct at the same pressure and gas constituency conditions, greatly simplifying the analysis algorithm and eliminating potential measurement errors. Following installation of the sensor, a series of ice slab sublimation tests were conducted to assess the dm/dt measurement accuracy of the LyoFlux 200 software. Ice slab tests were periodically performed throughout the study each time a hardware or software change was made to the system to verify the dm/dt measurement accuracy. Ice slab sublimation tests were performed to enable a direct comparison of the measurement of total water removed using both the LyoFlux 200 monitor and gravimetric measurements. The weight of total water removed during the sublimation experiment was considered the “gold standard” for accuracy determination. There is no direct comparison for the 2 independent measurements (water vapor concentration and gas flow velocity) made by the sensor, but only for the integrated mass flow rate determination. Ice slabs were formed on the shelves of the lyophilizer by lining the “bottom-less trays” (i.e., the metal bands used with bottom-less trays) with thin black plastic (3 mil). The plastic-lined trays were filled with known weights of liquid water. To begin sublimation study, the shelf temperature was reduced to 40 C to form the ice slabs. After ice slab formation (>1 h), the pressure within the lyophilizer chamber was reduced to the desired set point (typically between 65 mT and 500 mT). After pressure stabilization, the isolation valve between the dryer chamber and condenser was closed to enable determination of the sensor ZVO. The lyophilizer isolation valve was opened after ZVO estimation, and the chamber pressure was restabilized to the desired set point. Sensor data collection was initiated, and the shelf temperature was increased to the desired set point. Ice slab sublimation was typically conducted under near steady-state conditions (constant shelf temperature and pressure set point) to remove 50% of the water added to the dryer shelves to avoid excessive loss of thermal contact between the ice and the pan plastic bottom. Once the desired sublimation time was reached, LyoFlux 200 data collection was stopped, the chamber was vented to atmospheric pressure, and the remaining ice was melted by raising the dryer shelf temperature. The remaining water was removed and weighed to determine the total amount of water removed during the sublimation experiment. The LyoFlux 200 mass flow rate determinations were integrated as a function of time to calculate the amount of water removed. Integration was performed from the time the ZVO measurement was complete (isolation valve is opened and pressure restabilized to set point) to the time sublimation test was complete. The calculated amount of water removed was compared to the gravimetric measurements. Note that the water removed before the time the pressure was restabilized (after ZVO determination) was not included in the calculation of total water removed. Before pressure restabilization (after ZVO determination) and during the evacuation and initial pressure stabilization phase, ice crystals from the top layer of the ice slab, empty shelves (not loaded with ice slabs), and silicone oil hoses undergoes sublimation. It is expected that at low temperature and short duration of this “initial” sublimation phase, only negligible amount of water will be removed and hence is insignificant for the purposes of the study. Nevertheless, if needed, water removed during the initial sublimation phase could be estimated if the ZVO was performed at a slightly higher pressure (~150 mT) before the typical onset of sublimation with the ice slab held at 40 C.

0.0 0.8 0.6 0.77 0.0 0.4 0.3 0.38

0.7 1.2

0.0 0.2 0.1 0.14

0.3 0.6 0.1 0.2

3.0 3.7 4.6

0.0 0.1 0.1

0.1 0.25 4.5 5.8

3.0 (0.2) 3.8 (0.2) 4.6 (0.3)

Run 1

4.5 (0.3) 5.7 (0.4) 4.5 (0.2) 5.7 (0.3)

0.4 0.1 3.6 3.5 (0.2) 3.5 (0.2) 3.6 (0.1)

Run 2 Run 1 K

Run 2

cm

4.6 (0.3) 5.9 (0.4)

Low Sublimation Rate (Ts  Tb ¼ 5 C)

3.0 (0.2) 3.7 (0.2) 4.5 (0.3) Average

65 100 150

4.6 (0.2) 6.0 (0.4) 100 150

Run 1

3.6 (0.2)

Run 1

10 cal s mT

65

s Tb ( C) s Kv Mean Kv Batch 1 and 2 Mean Kv Batch 2

1 2 1 4

Mean Kv Batch 1

Uncertainty in Tb is shown as a function of sublimation rate. s represents uncertainty. Values in parenthesis are sample standard deviation in Kv of 110 center vials.

Table 2 presents the uncertainty in Tb as a function of uncertainty in Kv introduced due to the use of different batches of 20-cc

NGA Av ¼ 7.21 cm2

Impact of Variability in Kv Values in Different Batches of Vials Produced by Different Vial Manufacturers on Tb Estimation

West Pharmaceuticals Company Av ¼ 6.93 cm2

Results and Discussion

Pressure

Test Setup for the Pilot-Scale Lyophilizer Two runs were conducted on the pilot-scale lyophilizer both using 20-cc tubing vials. One lyophilization run was conducted with 2% (w/w) BSA and 5% (w/w) sucrose as formulation, and second lyophilization run with 5% (w/w) BSA with 2% (w/w) sucrose formulation. Fill volumes of the formulations and lyophilization cycle conditions were similar to the laboratory-scale lyophilization runs described previously. Three shelf loads of 1620 vials were used for each run. On each shelf, 4 stainless steel bottomless tray bands (length  width  height ¼ 44.5 cm  29 cm  2.5 cm) each containing 135 vials were placed such that 2 bands were in the front and 2 were in the rear of each shelf. Six thermocouples were used for each run; 3 in the edge vials (1 on each shelfdleft, right, and front) and 3 in the center vials (one of each shelf). Before the freeze-drying experiments, the readouts of all product thermocouples were tested to read 0.0 C when the thermocouples were immersed in an ice slush. The vial configuration on each shelf was such that there were 30 edge vials on the sides touching the bands, 30 edge vials on the sides not touching the bands, and 36 vials in the front and back touching the bands. The distinction between vials touching the band and not touching the band is described here to be able to calculate the edge vial effect (DKEv) using the methodology described by Pikal et al.3

Table 2 Predicted Uncertainty in Tb (Product Temperature at the Bottom of Vial) as a Function of Difference in Mean Kv From Different Batches of Vials

Test Setup for the Laboratory-Scale Lyophilizer For the laboratory-scale lyophilizer, 1 shelf load of 160 (50 vials on the edge and 110 in the center) vials was used. Thermocouple placement was as follows: In the laboratory-scale dryer, 8 thermocouples were used for each run; 4 in the vials placed on edges (front, rear, and side rows) and 4 in the center vials. Before the freeze-drying experiments, the readouts of all product thermocouples were tested to read 0.0 C when the thermocouples were immersed in an ice slush. A sharp drop in Pirani baseline pressure during primary drying was used to determine the end point of primary drying for nearly all vials in the dryer.

Moderate Sublimation Rate (Ts  Tb ¼ 15 C)

Tb was predicted via TDLAS using Equation 1 and measured by thermocouples (Copper Constantan thermocouples; Omega Engineering, Inc., CT) for 2 model products on the laboratory- and pilotscale lyophilizers. In all the studies, thermocouples were carefully positioned touching the bottom center of the vials. The shelf surface temperature (Ts) was measured as described previously. BSA was used as a model protein, with 2% (w/w) BSA and 5% (w/w) sucrose in 1 formulation, and 5% (w/w) BSA with 2% (w/w) sucrose in another formulation. The experiments were performed using 20-cc tubing vials. The fill volume was 5 mL per vial. During drying, the shelf temperature was periodically adjusted to maintain Tb near the target product temperature, which was 32 C for 2% BSA/5% sucrose and 30 C for 5% BSA/2.5% sucrose formulations. Note that the target product temperature was for the sublimation interface instead of Tb. For the studies described in this article, the temperature difference between bottom and sublimation interface was calculated to be <0.5 C. The cycles with protein formulations were conducted at 65 mT chamber pressure. The shelf temperatures for the 2 formulations were between 21 C and 26 C.

0.1

High Sublimation Rate (Ts  Tb ¼ 30 C)

Product Temperature Measurement

5

0.8

P. Sharma et al. / Journal of Pharmaceutical Sciences xxx (2018) 1-15

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P. Sharma et al. / Journal of Pharmaceutical Sciences xxx (2018) 1-15

Table 3 Results for Ice Slab Sublimation Tests Performed on a FTS LyoStar II Freeze Dryer Sublimation Conditions (Pressure/Shelf Temperature)

Loading/No. of Trays

Error (%)

Ratio TDLAS/Gravimetric

Number Density (mol/cc)

Velocity (m/s)

dm/dt (g/s)

100 mT/20 C 100 mT/10 C 200 mT/35 C 200 mT/15 C 65 mT/25 C 200 mT/15 C

3 3 1 3 3 3

3.7 4.9 1.7 7.2 3.7 7.2

1.04 1.05 1.02 1.07 1.04 1.07

2.80Eþ15 2.59Eþ15 5.27Eþ15 5.91Eþ15 1.58Eþ15 5.75Eþ15

76.4 117.6 1.8 102.4 104.2 107.5

0.0037 0.0053 0.0002 0.0110 0.0028 0.0114

vials obtained from a given supplier, for each of 2 suppliers, West Pharmaceuticals Company and NGA. Only center vials have been used for uncertainty estimation because the intrabatch variation is smaller for center vials. For each batch of vials from West Pharmaceuticals Company, 2 sublimation tests were performed to calculate systematic variability in the Kv estimation protocol. Only one sublimation test was performed for each batch of vials from NGA. Kv evaluations were performed at 3 representative pressures. Interpolated Kv values reported for West Pharmaceuticals Company vials at 65, 100, and 150 mT were obtained using KC and KD values, which were in turn estimated using a nonlinear fit (Eq. 6) of Kv values obtained at 51, 92, and 144 mTorr pressures. For NGA vials, Kv values were directly obtained at 65, 100, and 150 mT pressure. The temperature difference between shelf surface and product has been used to represent typical values for low, moderate, and high sublimation rate. At low sublimation rate, a 5%-7% uncertainty in Kv values relates to 0.2 C-0.3 C uncertainty in the product temperature, whereas at high sublimation rates, the uncertainty in product temperature is on the order of 1 C. It should be noted that during the course of a lyophilization run where a constant shelf temperature is used during primary drying, the average sublimation rate of a batch decreases over time. Therefore, the uncertainty in product temperature is larger in initial hours of the steady-state regime of primary drying but smaller during the most critical part for product quality late in primary drying where the product temperature at the sublimation interface is normally at maximum (and the error in the TDLAS based temperature determination is lower). Both West Pharmaceuticals Company and NGA vials show a 5%-6% variability (% relative standard deviation) in the Kv values in each sublimation test, which shows that there is reasonably good repeatability in the vial bottom contour for each manufacturer. At the same chamber pressure, the absolute difference in mean Kv between West Pharmaceuticals Company and NGA vials is on the order of 15%-30%, which can lead to more than 2 C difference in predicted Tb at moderate and high sublimation rates. Therefore, for the most accurate Tb estimation using Equation 1, Kv values used should be for the same vial type as used for Kv estimation. Using “one value” of vial heat transfer coefficient for “all vial types” from different suppliers can lead to erroneous Tb prediction. LyoStar II Lyophilizer Sublimation Tests (Laboratory Scale) Ice slab tests were performed at a number of different shelf temperatures and chamber pressures. These parameters affect both

the temperature of the ice slab and the sublimation rate. Experiments were performed over a range of conditions to determine if there are systematic errors associated with the TDLAS sensor and operating parameters. The results of 1 set of sublimation tests on the LyoStar II lyophilizer are shown in Table 3. The results show measurement errors in integrated water mass removed ranging from þ1% to þ7%. There appears to be no correlation of measurement error with pressure, shelf temperature, or gas flow velocity. This is consistent (data not shown) with prior observations during tests with a single line-of-sight instrument. The TDLAS error is biased to overpredicting the total amount of water removed. Of course, there is some error associated with the gravimetric procedure, but this error should normally be less than several percent, so it is likely some of the differences between gravimetric and TDLAS reside in the TDLAS measurement. The TDLAS sensor used the same calibration factor, the laser wavelength (or frequency) increment per data point, as it tunes across the water absorption feature. It is possible that this factor was too high. It is also possible that the electronic gain in signal amplifier circuits was higher than expected. This factor would only affect the water concentration measurements, not the velocity measurement. Pilot-Scale Lyophilizer Sublimation Tests Initially, 4 sublimation tests were performed using a LyoFlux 200 (2 line of sight) instrument on the pilot-scale lyophilizer. The results (Table 4) reveal significant errors between TDLAS and gravimetric mass flow rates. Two sources of error were identified upon investigation. The first was related to an amplifier gain value used to process the voltage data and its conversion to water number density, [H2O] (molecules cm3), or water concentration. The value based upon the circuit components suggested a gain of 2.00. Subsequent experiments revealed that this value was 2.22. This error resulted in an 11% overprediction of water concentration and thus mass flow rate and was easily corrected using the experimental value of the gain, 2.22, instead of the nominal value of 2.00. The other error, which is velocity dependent, is related to the configuration of the lyophilizer. The pilot-scale dryer is equipped with a clean-in-place/sterilization-in-place system that includes stainless steel piping and spray balls, which distribute hot water and steam within the dryer. One of the pipes and spray balls was located at the entrance to the optical spool causing a disturbance in the gas flow within the spool. Figure 1 shows a 3-dimensional mechanical drawing of the IMA Life pilot-scale dryer. Figure 2

Table 4 Results for Initial Ice Slab Sublimation Tests Performed on a Pilot-Scale Freeze Dryer Sublimation Conditions (Pressure/Shelf Temperature)

Loading/No. of Trays

Error (%)

Ratio TDLAS/Gravimetric

Number Density (mol/cc)

Velocity (m/s)

dm/dt (g/s)

65 mT/10 C 65 mT/30 C 65 mT/25 C 100 mT/30 C

4 4 4 4

14.7 11.3 10.2 9.5

1.15 1.11 1.02 1.09

2.50Eþ15 2.49Eþ15 2.52Eþ15 3.81Eþ15

54.5 21.7 32.6 14.4

0.287 0.109 0.169 0.110

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average flow velocity of 17.4 m/s, showed an under prediction error of ~12%. This is unexpected, as flow perturbations due to the cleanin-place/sterilization-in-place piping at low velocities were predicted to return to the expected flow regime before the optical detection region within the spool. This apparent anomaly could also be due to errors in gravimetric measurement of amount of ice sublimed. Limited program resources and access to the pilot-scale dryer at IMA did not enable repetition of this sublimation test to check repeatability. The results of the other 4 sublimation tests clearly demonstrate improved sensor measurement performance needed for application of the sensor for determining product temperature and product resistance to drying.

Figure 1. Three-dimensional assembly drawing of the IMA Edwards pilot-scale dryer showing the freeze dryer chamber (and 4 shelves), the spool connecting the chamber to the condenser (including the optical access ports), and the freeze dryer condenser.

shows the dryer and a gas velocity prediction from a computational fluid dynamic (CFD) model of the sublimation test run under conditions of 65 mT chamber pressure and 10 C shelf temperature. The average TDLAS-predicted velocity under these conditions is ~57 m/s. The CFD results clearly indicate the development of a perturbation in the gas flow downstream of the spray ball, extending into the optical measurement zone indicated by the 2 vertical lines in the spool. Note that the error for this sublimation experiment is 14.7%, of which ~11% was due to the amplifier error and 3.7% would then be attributed to the flow perturbation (as the data analysis algorithm assumes axi-symmetric flow). Figure 3 shows CFD velocity map profile slices at the optical transmitter and receiver locations within the spool. The velocity map at the upstream optical port clearly shows a “donut” pattern, which was washed out by the time the gas reaches the downstream optical port. Figure 4 shows the predicted velocity profiles for the 65 mT, 30 C shelf temperature sublimation test. The TDLASpredicted velocity was 21.7 m/s. The velocity profiles do not predict a donut pattern for this test. This was consistent with the lower total water removed measurement error (~10%) attributable only to the amplifier error and not to the flow perturbation error. Five additional sublimation tests were performed using the pilot-scale lyophilizer and the LyoFlux 200 mass flow meter. The meter data analysis software was modified to include the velocity-dependent scaling factor shown in Figure 5. The results of the corrected sublimation tests are shown in Table 5. Applying the sensor gain correction and the velocity-dependent scaling factor resulted in 4 out of 5 sublimation test results demonstrating a sensor measurement accuracy within the ±5% goal. One of the tests, with an

Comparison of Tb Values Obtained Using Thermocouples and Equation 1 for Runs Performed in Laboratory- and Pilot-Scale Lyophilizers Tb Measurement in the Laboratory-Scale Lyophilizer Figure 6 shows the lyophilization cycle primary drying data for the 5% BSA/2.5% sucrose formulation using the laboratory-scale dryer, and Figure 7 shows the corresponding data obtained from the TDLAS sensor. The Ts during the run was at ~ 20 C. Using the Pirani gauge, MKS gauge (Capacitance Manometer) difference as the indicator, the end point of primary drying was estimated at about 37 h. The target product temperature for this formulation was 30 C. While in primary drying, the edge vial Tb and particularly the center vial Tb values were in excellent agreement among the vials measured (difference between all edge vials Tb < 1.5 C and for center vials less than 1 C). The Tb for one of the edge vials increased sharply from the steady-state value at 22 h, with the average time for this event for the 4 edge vials containing thermocouples being 25 h. The time point marking the beginning of the sharp rise in Tb was considered the end of primary drying for that particular vial. The thermocouples in the center vials did not begin to show this sharp rise until 32 h, with an average time of 35 h. Thus, there is a difference of 10 h between the average primary drying time for edge vials and center vials. Note that the primary drying time for the last center vial containing a thermocouple was 40 h. The difference in the average thermocouple temperature between edge and center vials was ~1 C with the edge vials drying at higher temperature, as expected. The maximum temperature difference between an edge and a center vial was ~3 C. The water vapor concentration in the chamber during primary drying was approximately constant (1.86  1015 molecules/cm3) throughout the primary drying phase, as expected (Fig. 7). This profile of water vapor concentration was qualitatively similar to the Pirani profile in Figure 6. At the beginning of primary drying, the

Figure 2. CFD model results of the predicted gas flow velocity within the pilot-scale lyophilizer spool for the 65 mT pressure, 10 C shelf temperature sublimation test. The condenser is on the left, and the drying chamber is on the right. The bar code to the right identifies by color the flow velocity.

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P. Sharma et al. / Journal of Pharmaceutical Sciences xxx (2018) 1-15

Figure 3. CFD model results showing the velocity profiles at the TDLAS sensor upstream and downstream window ports for the 65 mT pressure, 10 C shelf temperature sublimation test. The drying chamber is on the right.

velocity of water vapor from the chamber to condenser was ~28 m/ s. During primary drying, there was a drop in the velocity of water vapor to 20 m/s at 20 h before dropping again toward the end of primary drying. Because the sublimation rate was a function of velocity and the concentration of water vapor was nearly constant, the temporal profile of sublimation rate follows the same trend as that of velocity. The first drop in the velocity in the first few hours of

primary drying was a result of increased dry layer resistance in the product to the flow of water vapor, the slope of which becomes less steep by 20 h. The second drop in the velocity at 20 h occurred largely because of heterogeneity in the drying rate of vials in the batch; that is, some vials had finished primary drying. Using the sublimation rate from TDLAS in Equation 1, batch average Tb was estimated. The TDLAS Tb profile was compared with

Figure 4. CFD model results showing the velocity profiles at the TDLAS sensor upstream and downstream window ports for the 65 mT pressure, 30 C shelf temperature sublimation test. The drying chamber is on the right.

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Figure 5. Calculated velocity scaling factor as a function of gas flow velocity used to mitigate the effects of clean-in-place/sterilization-in-place piping created noneaxi-symmetric gas flow within the pilot-scale dryer spool.

the average thermocouple Tb profile (Fig. 8). The average thermocouple Tb used for comparison is number-weighted average values calculated by accounting for the total number of edge and center vials in a batch. The difference between the thermocouples and TDLAS Tb is within ±1 C throughout most of the primary drying stage. Note that based on expected uncertainty in both Kv and TDLAS sublimation rate, an uncertainty of about 1 C is expected for the TDLAS Tb (Appendix A). A similar agreement (±1 C) between product thermocouples and TDLAS Tb was observed for 2% BSA/5% sucrose (Fig. 9). For 5% BSA/2.5% sucrose formulation, a comparison between TDLAS Tb calculated using Kv for edge vials (3.8  104 cal s1 cm2 K1) and average of thermocouple data of 4 edge vials shows agreement within 1 C, whereas a comparison between TDLAS Tb calculated using Kv for center vials (2.9  104 cal s1 cm2 K1) and average of thermocouple data of 4 center vials shows agreement within 2 C. Note that during the initial stage of primary drying while the shelf temperature was raised to the set point, the assumption of pseudo steady state between heat and mass transfer is not valid, so temperature comparisons between thermocouple and TDLAS during this time are not necessarily meaningful; however, as shown in Figure 9, a small change in shelf temperature produces a change in the TDLAS Tb in response to this change that is in good agreement with thermocouple Tb. The TDLAS temperature data were calculated using the average Kv value for the 20-cc vials, which was weighted for the number and the heat transfer coefficient of edge and center vials. As the edge vials dry, the calculation of number-weighted average temperature values are not strictly valid because the calculation assumes that all vials are in primary drying. However, agreement between TDLAS product temperature and average thermocouple

temperature remains relatively good, largely, because as some vials dry early, dm/dt decreases correspondingly, thereby increasing the calculated value of Tb (Eq. 1). Product Temperature Measurement in the Pilot-Scale Lyophilizer To use the TDLAS-based technique to estimate Tb during commercial-scale lyophilization using Equation 1, 2 parameters are needed: (a) batch average Kv and (b) the mass flow measurement, dm/dt, from the TDLAS unit. For vials of identical dimensions, the value of batch average Kv on a pilot- or commercial-scale lyophilizer is different from a laboratory lyophilizer. For accurate estimation of Tb, this difference in Kv needs to be considered or corrected for during scale up and transfer of lyophilization cycles between lyophilizers. These differences arise from differences in the contribution of radiation heat transfer caused by emissivity and/or wall/door surface temperature differences between dryers and different percentages of “edge vials.” In general, the percentage of “edge vials” (i.e., the vials at edge of the vial array on the dryer shelf) decreases in going from laboratory- to pilot- or manufacturing-scale dryers and increases when considering processes where less than 100% of “full load” is used. The scale-up adjustment that needs to be made for contribution of radiation is different for center and edge vials. For center vials, the emissivity of the shelf upon which the vials are placed is replaced by the emissivity of the shelf of the commercial-scale lyophilizer. This is represented by Equation 8.

  K Cv ðdryer AÞ  K cv ðdryer BÞz 104 $Av $ eA  eB ;

(8)

where eA and eB are the emissivities of the shelf in dryers A and B, respectively. In this present study, emissivity differences between

Table 5 Results for Ice Slab Sublimation Tests Performed on a Pilot-Scale Freeze Dryer as Corrected for Known Systematic Errors. (See Text) Sublimation Conditions (Pressure/Shelf Temperature) 65 65 65 65

mT/30 C mT/25 C mT/10 C mT/0 C

Loading/No. of Trays

Error (%)

Ratio TDLAS/Gravimetric

Average Velocity Correction Factor (mol/cc)

Velocity (m/s)

dm/dt (g/s)

4 4 4 4

2.8 0.2 2.2 4.9

1.03 1.00 1.02 1.05

0.969 0.963 0.950 0.949

29.9 37.4 63.5 84.8

0.139 0.179 0.316 0.415

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P. Sharma et al. / Journal of Pharmaceutical Sciences xxx (2018) 1-15

Figure 6. Primary drying temporal profile of temperature and pressure for 5% BSA/2.5% sucrose lyophilization run on the laboratory-scale lyophilizer. Chamber pressure set point: 65 mT. Number-weighted average vial heat transfer coefficient, Kv: 3.1  104 cal s1 cm2 K1. CM, capacitance manometer; TC, thermocouple.

the laboratory- and pilot-scale lyophilizers were considered negligible and heat transfer coefficient of center vials for the laboratory-scale lyophilizer was used for scale-up calculations. For edge vials, the scale-up calculations are described by Pikal et al.3 Difference in the average Kv for edge vials between 2 dryers depends on emissivity of the dryer wall, shelf surface, wall temperature, and view factors for edge vials and wall, as well as the use of bands around the vial array. To calculate the DKEv , the side wall temperature, back wall temperature, door temperature, band-to-wall view factor, and vial-to-wall view factor (sides) were used directly from the study by Pikal et al3 for a pilot-scale lyophilizer, band temperature was calculated using the procedure described in the study by Pikal et al.3 Shelf spacing was 10 cm, and band circumference on each shelf was 294 cm. Using a center vial heat transfer coefficient

from the laboratory-scale lyophilizer (2.9  104 cal s1 cm2 K1) and edge vial heat transfer coefficient using the methodology described by Pikal et al. (5.2  104 cal s1 cm2 K1), the number-weighted average heat transfer coefficient value for the vials used for the pilot-scale lyophilization run for 2% (w/w) BSA and 5% (w/w) sucrose formulation was calculated as 3.3  104 cal s1 cm2 K1. For comparison, the number-weighted average heat transfer coefficient value for the vials used for the laboratory-scale lyophilization run for 2% (w/w) BSA and 5% (w/ w) sucrose formulation was also calculated as 3.3  104 cal s1 cm2 K1. For the vials used for 5% (w/w) BSA and 2% (w/w) sucrose formulation, the number-weighted average heat transfer coefficient values for laboratory- and pilot-scale lyophilizers were 3.1  104 cal s1 cm2 K1 and 3.4  104 cal s1 cm2 K1, respectively.

Figure 7. Primary drying TDLAS temporal profile for 5% BSA/2.5% sucrose lyophilization run on the laboratory dryer.

P. Sharma et al. / Journal of Pharmaceutical Sciences xxx (2018) 1-15

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Figure 8. Primary drying temporal profile of temperature and pressure for 5% BSA/2.5% sucrose lyophilization run. Chamber pressure set point: 65 mT. Number-weighted average vial heat transfer coefficient, Kv: 3.1  104 cal s1 cm2 K1.

Figure 10 shows temporal profile of the difference in the weighted average thermocouple temperature and TDLAS temperature in a pilot-scale lyophilizer during primary drying for 2% BSA/5% sucrose and 5% BSA/2.5% sucrose. Similar to the laboratory results, the agreement between thermocouple temperature data and TDLAS temperature data remains good even after primary drying of the average vial was complete. As demonstrated in Figure 10 for both the formulations, the TDLAS-predicted temperature was within ±1 C of the average thermocouple temperature during entire primary drying step for all vials containing thermocouples.

TDLAS Procedure to Estimate Drying Heterogeneity in a Batch of Vials: Fraction of Vials in Primary Drying Versus Time Here, we describe the use of TDLAS data to evaluate the fraction of vials undergoing primary drying. The methodology described here is useful in providing an estimate of drying homogeneity during primary drying. The Tb obtained using Equation 1 is a batch average temperature for all vials in primary drying. That is, it is assumed that “N” remains constant throughout the process. However, there is heterogeneity in the drying of vials during primary drying and not all vials finish primary drying at the same time. The

Figure 9. Primary drying temporal profile of temperature for 2% BSA/5% sucrose lyophilization run in the laboratory-scale lyophilizer. Chamber pressure set point: 65 mT. Numberweighted average vial heat transfer coefficient, Kv: 3.3  104 cal s1 cm2 K1.

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P. Sharma et al. / Journal of Pharmaceutical Sciences xxx (2018) 1-15

mðtÞ Lice ¼ Lice ð0Þ  Lice ð0Þ$ ; mð0Þ

(12)

where Lice (0) is the thickness of frozen layer at time 0 (cm), m(0) is the initial mass of water (g) per vial, and m(t) is the cumulative mass of ice sublimed at time t (g) that is calculated by integrating the TDLAS dm/dt. L is the thickness of the dry layer (cm) and may be calculated as a function of time (t) as L ¼ Lice (0)  Lice. Resistance Rps as a function of dry layer thickness L can be represented as5

Rps ¼ R0 þ

Figure 10. Difference in product temperature between the weighted average thermocouples and TDLAS temperature in a pilot-scale freeze dryer during primary drying for 2% BSA/5% sucrose and 5% BSA/2.5% sucrose, respectively. Due to an unexpected error in the data acquisition system, thermocouple temperature data were lost for initial 9 h for the 2% BSA/5% sucrose run. The duration selected to estimate the temperature difference excludes initial nonesteady-state temperature (~5 h). In addition, the difference was only calculated for vials undergoing primary drying and discontinued past the point primary drying completed in the first vial as indicated by thermocouple data.

vials with higher Kv and lower degree of supercooling during freezing (large ice crystals) approach the end of primary drying faster relative to the vials with lower Kv and higher degree of supercooling (small ice crystals). To evaluate drying heterogeneity during primary drying, a novel approach was developed. This approach requires estimation of the “resistance to mass transfer of water vapor” (Rps) during primary drying, which can be calculated using TDLAS-based dm/dt coupled with a steady-state heat and mass transfer model. Assuming steady-state sublimation process, the mass transfer of water vapor through the dried product layer can be represented by Equation 9:

P  Pc ; Rps ¼ Ap $ ice dm=dt

(9)

where Rps (cm2.Torr.h.g1) is the combined resistance of the product and stopper (stopper contribution normally negligible), Ap is the internal cross-sectional area of the vial (cm2), Pice is the vapor pressure of ice (Torr) at the sublimation interface, Pc is the chamber pressure (Torr), and dm/dt is the sublimation rate per vial (g/h/vial). Pice can be expressed as5

Pice ¼ 2:69$1013 $e6144:96=Tice ;

(10)

where Tice is the temperature of the ice at the sublimation interface (K), which can be expressed as5

 Tice ¼ Tb 

dQ dt

 $Lice

Av $k

Tb is the temperature at the bottom center of the vial (K), dQ/dt is the heat transfer rate, which is calculated using the relation dQ/ dt ¼ DH  dm/dt (cal/s), Lice is the thickness of the frozen layer (cm), Av is the outer cross-sectional area of the vial (cm2), and k is the thermal conductivity of ice (cal h1 cm1 K1). Here, dm/dt is obtained from TDLAS. Lice may be calculated as a function of time (t) using

(13)

The parameters R0, A, and B are constants and can be evaluated from a fit of Equation 12 to data using regression analysis. Once a significant number of vials have finished primary drying, the TDLAS product temperature becomes higher than the temperature of those product vials still undergoing sublimation and the calculated resistance becomes too unrealistically high. We emphasize that the dm/dt in Equation 9 is evaluated from the total sublimation rate by TDLAS and the total number of vials in the dryer, not just the number still in primary drying. L and time (t) are monotonically related (though not proportionally), and therefore, Equation 13 can also be represented as

  Rps or Rps=cor ¼ R0 þ

A0 $t ; 1 þ B0 $t

(14)

where A’ and B’ in Equation 14 are not necessarily the same as A and B in Equation 13. Note that both Equations 13 and 14 are empirical equations but fit well to the data. As mentioned previously, Equation 14 can be used to describe the relationship between Rps and time (t) until the fast running (edge) vials start to dry. Assuming the edge and center vials are drying homogenously within each class, Equation 14 can be extrapolated to the end of primary drying to obtain the values of Rps for homogenous drying, denoted Rps/cor, as shown in Figure 11. From Figure 11, one can observe that Pice can also be represented (empirically) using an expression similar to Equation 14 over the time when essentially all vials are in primary drying.

  Pice or Pice=cor ¼ P0 þ

A} $t 1 þ B} $t

(15)

The parameters P0, A”, and B” are constants, different from those in Equations 13 and 14, and can be calculated using regression analysis. Here, P0 represents the vapor pressure of ice at the beginning of primary drying. Assuming homogenous drying within each class (edge and center), treatment similar to Rps is performed to obtain a corrected value of the vapor pressure of ice at the sublimation interface, Pice/cor. Using Rps/cor and Pice/cor, Ncor, the number of vials actually in primary drying as a function of time, can be represented by modifying Equation 9 as

Ncor ¼ (11)

A$L 1 þ B$L

R $dm  ps=cor dt  ; Ap $ Pice=cor  Pc

(16)

where Rps/cor and Pice/cor are the corrected values of dry layer resistance and vapor pressure over ice, dm/dt is the mass flow rate of water vapor as obtained using TDLAS, Ap is the internal horizontal cross-sectional area of the vial, and Pc is the chamber pressure. This procedure assumes that the vapor pressure of the ice (P0) and the dry layer resistance (Rps) at times when some vials are finished with primary drying can be extrapolated from such data

P. Sharma et al. / Journal of Pharmaceutical Sciences xxx (2018) 1-15

13

Figure 11. Extrapolation of dry layer resistance and vapor pressure of ice past the time when essentially all vials are in primary drying. Temporal profile of apparent dry layer resistance (Rps) calculated using Equation 8 and apparent vapor pressure over ice (Pice) calculated using Equation 9 are shown in the figure. “Corrected” dry layer resistance assuming homogenous drying (Rps/cor) calculated using Equation 13 and “corrected” vapor pressure over ice assuming homogenous drying (Pice/cor) calculated using Equation 14 are shown as smooth lines for a 5% (w/v) NaCl/0.2% (w/v) sucrose formulation. Using Rps/cor and Pice/cor, Ncor, the number of vials actually undergoing primary drying as a function of time can be calculated using Equation 15 (Fig. 12).

obtained when all vials in the dryer are known to be in primary drying. The accuracy of Equation 16 was evaluated from lyophilization experiments performed using 5% (w/v) NaCl with 0.2% (w/v) sucrose as a binder at 3 mL fill volume in 20-cc vials. This “formulation” was used to facilitate detection of incomplete drying of all vials in a batch because eutectic melt of NaCl can be visually detected for quick evaluation of each vial. The aim of these experiments was to predict the number of vials in primary drying using Equation 15 and through physical observation of eutectic melt of

those vials for which primary drying was incomplete. The freeze drying cycle was abruptly stopped before all vials finished primary drying. One shelf load of 160 vials was used for these studies. Two lyophilization experiments were performed: run A at 20 C shelf temperature and 60 mT chamber pressure and run B at 17.5 C shelf temperature and 60 mT chamber pressure. After stoppering and unloading, the vials were maintained at room temperature for ~60 min to allow any ice to melt and then visually observed. Three types of vials were observed: collapsed, semidried, and dried product. The vials containing ice resulted in massive collapse of the

Figure 12. Comparison of theoretical and experimental results for the change in fraction of vials in primary drying with time near the end of primary drying in all vials. Theoretical results were calculated using Equation 15. Run A used 20 C shelf temperature and 60 mT chamber pressure and run B used 17.5 C shelf temperature and 60 mT chamber pressure during primary drying. Good agreement was obtained between theoretical and experimental results, which indicates acceptable accuracy of Equation 15 for estimation of drying heterogeneity.

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P. Sharma et al. / Journal of Pharmaceutical Sciences xxx (2018) 1-15

Figure 13. Comparison of temporal trends of fraction of vials in primary drying and water concentration in drying chamber for lyophilization runs conducted with controlled and uncontrolled nucleation during freezing. Note the shorter times for a decrease in response for both fraction of vials in primary drying and water concentration in the chamber for the controlled nucleation process, indicating faster primary drying. Note also the steeper slope for the decrease of fraction vials in primary drying for the controlled ice nucleation example, indicating more homogeneous primary drying in the batch.

product, and visual presence of water was detected. Vials containing high residual moisture content also collapsed (severe shrinkage of the solid mass), but because water was not detected, these were considered semidried and were considered as finished with primary drying. This procedure was used to estimate the number of vials in a batch that had not completed primary drying. Using Equation 16, Ncor was determined as a function of time. Figure 12 shows the experimental and theoretical or “calculated” results. Good agreement was obtained, which indicates acceptable accuracy of Equation 16 for estimation of drying heterogeneity. Using the corrected value of number of vials in primary drying, Ncor, the temperature of the vials remaining in primary drying even after most are finished can be calculated from

Tb=cor ¼ Ts 

DHs $dm dt Av $Kv $Ncor

!

lyophilization runs conducted by both controlled and uncontrolled ice nucleation. Ice nucleation was conducted at 5 C using a customized “ice fog technique” as described by Rambhatla et al.8 The rest of the experimental setup and drying conditions were similar to that of 5% BSA/2.5% sucrose formulation as described in the previous section. When ice nucleation was used, both fraction of vials in primary drying and water concentration show faster primary drying, and the steeper slope of the fraction of vials in primary drying versus time indicates more homogeneity. Of course, due to variations in heat transfer, there is still significant heterogeneity in primary drying even with little to no contribution from variation in ice structure. Conclusions

(17)

This equation gives a result equivalent to an extrapolation of temperature for “lagging vials” from a base established when all vials were in primary drying. Figure 12 also shows the water vapor concentration temporal profile for runs A and B. As expected (Eq. 1), a decrease in water concentration is not observed until most of the vials are finished with primary drying. When the water concentration begins to decline, more than 50% of the vials in run A and more than 80% of the vials in run B completed sublimation. It is notable that in run B, ice in ~20% of the vials was sufficient to maintain the chamber composition at essentially 100% water vapor. The use of controlled ice nucleation during freezing has been known to increase drying homogeneity in a batch of vials by reducing intervial ice nucleation differences.7 In other words, controlled ice nucleation allows relatively homogenous dry layer resistance in a batch of vials, and when a relatively high ice nucleation temperature is used, lower product resistance and faster drying. Equation 16 can be used to quantitatively demonstrate the impact of controlled ice nucleation on drying heterogeneity. Figure 13 shows the temporal trend of fraction of vials in primary drying and water concentration in the drying chamber for

TDLAS product temperature measurement can be accomplished with sufficient accuracy on both laboratory- and pilot-scale lyophilizers. Accuracy is dependent on both KV and mass flow rate measurement accuracy. Given the excellent reproducibility in Kv demonstrated by vial manufacturers, interbatch variations in Kv appear to contribute less than 1 C in product temperature error. Of course, this conclusion may not extend to all manufacturers. However, differences in batch average Kv for the same type of vial from different manufacturers are much larger, and one cannot assume equivalence in Kv for purposes of TDLAS product temperature measurement. Throughout the study, TDLAS-predicted temperature was within 1 C of the thermocouple temperature for the laboratory- and about 2 C for the pilot-scale lyophilizer. Measurement of drying heterogeneity using the new methodology allows heterogeneity in primary drying behavior to be documented in quantitative fashion. Acknowledgments Authors would like to thank Frank DeMarco, Tim Zwack, and Len Amico from IMA Life North America Inc. for their support during

P. Sharma et al. / Journal of Pharmaceutical Sciences xxx (2018) 1-15

the execution of this study and access to the pilot-scale lyophilizer. Authors would also like to thank Nipro Glass Americas for supplying vials for this study. This work was supported by the National Institutes of Health National Cancer Institute (NIH/NCI) under contract HHSN261200900023C.

References 1. Roy ML, Pikal MJ. Process control in freeze drying: determination of the end point of sublimation drying by an electronic moisture sensor. J Parenter Sci Technol. 1989;43(2):60-66. 2. Schneid SC, Gieseler H, Kessler WJ, Pikal MJ. Non-invasive product temperature determination during primary drying using tunable diode laser absorption spectroscopy. J Pharm Sci. 2009;98(9):3406-3418.

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3. Pikal MJ, Bogner R, Mudhivarthi V, Sharma P, Sane P. Freeze-drying process development and scale-up: scale-up of edge vial versus center vial heat transfer coefficients. J Pharm Sci. 2016;105(11):3333-3343. 4. Pikal MJ, Roy ML, Shah S. Mass and heat transfer in vial freezedrying of pharmaceuticals: role of the vial. J Pharm Sci. 1984;73(9): 1224-1237. 5. Pikal MJ. 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. 1985;39(3):115-139. 6. Gieseler H, Kessler WJ, Finson M, et al. Evaluation of tunable diode laser absorption spectroscopy for in-process water vapor mass flux measurements during freeze drying. J Pharm Sci. 2007;96(7):1776-1793. 7. Searles JA, Carpenter JF, Randolph TW. The ice nucleation temperature determines the primary drying rate of lyophilization for samples frozen on a temperature-controlled shelf. J Pharm Sci. 2001;90(7):860-871. 8. Rambhatla S, Ramot R, Bhugra C, Pikal MJ. Heat and mass transfer scale-up issues during freeze drying: II. Control and characterization of the degree of supercooling. AAPS PharmSciTech. 2004;5(4):54-62.