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Sensitivity Study to Assess the Robustness of Primary Drying Process in Pharmaceutical Lyophilization
Journal Pre-proof Sensitivity Study to Assess the Robustness of Primary Drying Process in Pharmaceutical Lyophilization Nirajan Adhikari, Tong Zhu, Feroz Jameel, Ted Tharp, Sherwin Shang, Alina Alexeenko PII:
S0022-3549(19)30647-1
DOI:
https://doi.org/10.1016/j.xphs.2019.10.012
Reference:
XPHS 1738
To appear in:
Journal of Pharmaceutical Sciences
Received Date: 12 June 2019 Revised Date:
16 September 2019
Accepted Date: 4 October 2019
Please cite this article as: Adhikari N, Zhu T, Jameel F, Tharp T, Shang S, Alexeenko A, Sensitivity Study to Assess the Robustness of Primary Drying Process in Pharmaceutical Lyophilization, Journal of Pharmaceutical Sciences (2019), doi: https://doi.org/10.1016/j.xphs.2019.10.012. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Inc. on behalf of the American Pharmacists Association.
Sensitivity Study to Assess the Robustness of Primary Drying Process in Pharmaceutical Lyophilization 1
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Nirajan Adhikari , Tong Zhu , Feroz Jameel , Ted Tharp , Sherwin Shang , Alina Alexeenko
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Affiliations: 1
School of Aeronautics and Astronautics, Purdue University, West Lafayette, Indiana, United
States 2
Drug Product Development, AbbVie Inc., North Chicago, Illinois, United States
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Science and Technology, AbbVie Inc., North Chicago, Illinois, United States
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Corresponding Author
Corresponding Author: Alina Alexeenko, PhD School of Aeronautics and Astronautics, Purdue University Address: 701 W. Stadium Ave, West Lafayette, IN 47907 OFFICE: 765-496-1864 EMAIL: [email protected]
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Abstract The objective of this work is to apply a sensitivity study to assess the robustness of the primary drying step of pharmaceutical lyophilization with respect to deviations in process parameters. The sensitivity study can provide valuable information regarding the effect of process input parameters on the product quality that can aid in designing robust lyophilization processes. In this study, the output response is related to its inputs using Smolyak sparse grid generalized Polynomial Chaos method and the sensitivity was calculated using Elementary Effects method. Sensitivity of chamber pressure and shelf temperature on product temperature of two sucrose-based and one mannitol-based formulation was studied and the results were analyzed in terms of risk of adverse effects due to process deviations on the product quality. The study revealed that the sensitivity varies among formulations and preliminary information regarding the possible impact of process deviations can be obtained from the process cycle diagram. The product temperature showed greater sensitivity towards the change in the shelf temperature than the chamber pressure for the greater part of the primary drying stage. An aggressive process deviation scenario at the late stage of primary drying was also studied for different formulations and the results were consistent with the sensitivity study.
Keywords: Lyophilization, Freeze-drying, Mechanistic modeling, Processing, Mathematical model(s), Quality by design (QBD), Uncertainty Quantification (UQ), Sensitivity, Process deviation, Excursion study, Product robustness
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Introduction
Sensitivity study is a powerful statistical technique that quantifies the level of uncertainty in a mathematical model of a physical process. The study can assist in identifying a set of key factors among many variables and parameters involved in a model that can ultimately provide valuable insight to a realistic process prone to uncertainty in its input process parameters. In a lyophilization process, deviation of process parameters during primary drying can significantly compromise the quality of the end product. Most common deviations in the process parameters during a primary drying process arise from deviations in chamber pressure and shelf temperature from a set point often referred to as pressure and temperature excursions respectively. The quality of a freeze dried product is compromised when the product temperature at any point reaches above the critical temperature limit (Tcri) which is often determined using freeze drying microscopy and/or differential scanning calorimetry. Various studies in the literature [1-5] have examined the impact of elevated process temperature on the product quality. Study in [1] has shown partial collapse of the dried product even when the temperature of the product exceeded 0
the collapse temperature only by 1 C. Some of the studies have also revealed the long-term effects associated with the product stability after storage when the product temperature during the primary drying process reached above the critical temperature limit [2]. In another study in [3] with controlled pressure deviations in both experimental and theoretical models, it was revealed that the primary drying time can change by a significant amount in the presence of such deviations despite the product temperature being under the safety limit. The study also suggests extension of the design space beyond the one usually obtained through limited amount of experiments using a mechanistic process modeling. The use of such mechanistic process modeling helps to extend the experiment conditions and maximize the productivity while maintaining an acceptable product quality. The uncertainty due to the variability of chamber pressure and shelf temperature also adds up to the uncertainties of other important parameters like the heat transfer coefficient (Kv) and product resistance (Rp). Kv and Rp are direct or indirect functions of chamber pressure and shelf temperature. Kv and Rp are usually calculated as a batch average and can vary based on locations of the vials on a shelf. The study in [6] includes investigation of Kv variability in the vials inside a lyophilizer based on their positions. The variability of Kv and Rp alone can have adverse impact on the product quality. Furthermore, with added
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uncertainty due to process deviations, the impact on product quality can become even more significant. However, the study presented in this paper only includes uncertainty in process parameters that can occur in the event of pressure and temperature excursions. On a manufacturing scale, pressure and temperature excursions can compromise the quality of an entire batch of manufactured product which can add up to a significant amount of cost. Such excursions can occur randomly at any instant of a primary drying process which makes it difficult to predict the impact of excursions on the product quality. Keeping this idea in mind, the objective of this research was to aid the designing of a robust lyophilization process using sensitivity study that will provide a better understanding of the impacts of random occurrences of process deviations on the quality of a product. Presence of process deviations can have different impact on the primary drying process like elevated product temperature, lyophilizer equipment limit, extension/shortening of primary drying time, etc. Since the product temperature directly relates to the quality of the product, it has been identified as the most important parameter of interest. This study only assesses the impact of process deviation in terms of product temperature and other possible impact parameters are beyond the scope of this study. Three different formulation recipes- two sucrose-based and one pure mannitol-based- were considered in this study. The sensitivity of the product temperature (Tpr) to the chamber pressure (Pch) and the shelf temperature (Tsh) were quantified throughout the primary drying process that is mathematically modeled using quasi-steady state heat and mass transfer in vials [7], commonly referred as LyoCalc. The sensitivity study was performed using an open-source PRISM Uncertainty Quantification (PUQ) tool developed at Purdue University [8]. The organization of the remainder of the paper is as follows. First, the non-intrusive method of sensitivity analysis used in this study is discussed which is then followed by the results obtained from the sensitivity study for different formulations and at last, the results are discussed in terms of possible impact of process deviation on the product quality at various stages of a primary drying process.
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Sensitivity Analysis
One of the most powerful techniques to relate distribution of output parameters to its input parameters is through a generalized Polynomial Chaos (gPC) method [9]. gPC utilizes polynomial expansion to relate
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input to output Probability Density Functions (PDFs). Study in [9] has identified the importance of selection of orthogonal polynomial basis function in terms of input distribution for optimum convergence. The convergence of an orthogonal polynomial basis function for a particular distribution can be studied based on the maximum error of computed output response for a function whose output to input response is known explicitly. Gaussian distribution of input PDFs demands Hermite polynomials while uniform distribution is better represented with Legendre polynomials. Convergence study of different sampling methods in [8] has shown that Smolyak gPC sparse grid method shows better convergence in predicting output response compared to Monte Carlo or Latin Hypercube sampling methods for two-dimensional Rosenbrock function. Here, the distribution of input parameters (Pch and Tsh) are assumed to be uniform with equal probability distribution between assumed intervals. This is believed to be a good approximation since there is no tendency toward a particular value of Pch or Tsh during excursion due to the randomness of such excursions. For this study, Smolyak gPC method is used to interpolate the response surfaces. Sensitivity in PUQ is calculated through the Elementary Effects method originally developed by Morris [10] and later improved by Campolongo [11].
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Elementary Effects Method
Elementary effects method facilitates effective screening of important input parameters from the pool of parameters in a mathematical model with random one-at-a-time (OAT) experiments. This method calculates number of incremental ratios for each input which are called elemental effects. These elemental effects when averaged reveal whether an input factor has (a) negligible, (b) linear and additive, (c) nonlinear or involved interactions with other input, on the output parameter of interest. For a mathematical model with K input parameters given as: = (
, …,
, ..,
)
(1) th
the elemental effect of the i input parameter for a given value of X = (X1, X2, …, XK) is: ( )=
, ….,
,
△,
△
,….,
( )
(2)
where each model input Xi is assumed to vary randomly across p selected levels in the space of the input factors uniformly distributed in the interval [0,1]. The experimental region thus consists of K*p grid and ∆
5
th
is a pre-determined multiple of 1/(p-1). The distribution for the elementary effect associated with i input factor is defined as Fi such that di(X) ~ Fi. By randomly sampling r points for each input, r elemental (1)
(2)
(r)
effects are obtained from the distribution of Fi i.e. di(X ), di(X ), …., di(X ) that are averaged to give sensitivity measure µi and standard deviation
i
of the distribution Fi. Improvement by Campolongo
replaces µ by µ* which computes the mean of distribution of the absolute value of elementary effects. Using absolute value for elementary effects eliminates the statistical error in µ that arises when the model is non-monotonic i.e. negative and positive values cancelling each other while calculating a mean. The mean µi reveals the overall influence of input parameter Xi while the standard deviation σi estimates the ensemble of the factor’s higher order effects, i.e. nonlinear and/or due to interactions with other factors. The expressions for µi and σi in elementary effects method are as follows: µ∗ = ∑#$ | =%
∑#$
(#)
(
| (#) )
(3) −µ
'
(4)
In this study, y becomes the output parameter of interest Tpr, and K = 2 for two input parameters considered: Tsh and Pch. For example, if there are only 3 grid points uniformly distributed in [0, 1] such that the grid points are at Xi = {0, 0.5, 1}, the experimental region for each parameter will have 3*2 elements and ∆ = 0.5. To demonstrate the elementary effect method, let us now consider only one input parameter, say Tsh with 3 grid points such that the first element lies between [0, 0.5] and the second lies between [0.5,1]. Let’s say the response of Tpr from sample space was found to be {0, 10 , 20} for Xi = {0, 0.5, 1}. The elementary effect for the first element becomes (10 – 0) / 0.5 = 20 and for the second element, it becomes (20 - 10) / 0.5 = 20, using Equation 2. Since the response considered here is linear, the mean of the elementary effects for Tsh will also be 20 with standard deviation of 0. This idea can be extended to both input parameters where the mean of the elementary effects method for each parameter will now consist of 6 samples. In PUQ, the sample points for elementary effects calculation are chosen from the same points that are used to interpolate the response surface using Smolyak gPC. Thus, the sensitivity is calculated at no additional cost which makes this method computationally extremely economical.
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Results and discussion
Two sucrose based and one pure mannitol-based formulation recipes were used in this study to assess the possible impact of pressure and temperature excursions on product quality during the primary drying process. Since sensitivity of these process parameters on product temperature can vary at different stages of primary drying, sensitivity is calculated at each instant in time throughout the drying process. Different parameters associated with the formulations such as heat transfer, mass transfer, and process cycle parameters are tabulated in Table 1. The process parameters considered represent a typical primary drying process for the particular formulation. The heat transfer coefficient (Kv) parameters are obtained from [12] which corresponds to a lab-scale lyophilizer referred to as LabLyo-2 with 6R SCHOTT vials in [12]. The three model recipes considered in this study are named as Presentation 1, 2, and 3 from here on where Presentation -1&2 are sucrose based formulations and Presentation-3 is a pure mannitolbased formulation. Presentation 1 and 2 are both sucrose-based formulations with only differences in fill volume and Rp parameters. The Rp parameters for pure mannitol-based formulation is obtained from [13]. The intervals for two input process parameters Pch and Tsh considered for sensitivity study are as follows: Pch = [Pch,set – 2.67, Pch,set + 6.67] Pa 0
Tsh = [Tsh,set – 5, Tsh,set + 7] C The input intervals are selected to include both the conservative and aggressive excursions possible during the primary drying process for the formulations considered in this study. Chamber pressure and shelf temperature sensitivity on the product temperature for Presentation-1 is shown in Figure 1b and the variation of product temperature throughout the primary drying at the set conditions without any excursions is shown in Figure 1a. The product temperature is more sensitive towards Pch than Tsh at the early stage of primary drying. Tsh sensitivity increases with time and exceeds Pch sensitivity towards the later stages however Pch and Tsh sensitivities are still comparable to each other in this formulation. Pch and Tsh sensitivity follow similar trends to the product temperature profile i.e. the sensitivity changes with time at early stages and reaches a steady state towards the later stages of drying. However, Pch sensitivity shows inverse relation to Tpr profile; Pch sensitivity is higher at the earlier stages which decreases towards the later stages before settling to a steady value. Later stages of primary drying
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are more significant in terms of impact on the product quality due to lower sublimation rates at these final stages. The sublimation helps maintain a cooler product temperature and when the sublimation is inadequate, the product temperature can elevate to a value greater than collapse temperature in the presence of fluctuations in the process parameters. Thus, the study on impact of process deviations at the later stages of primary drying warrants special attention. In Presentation-1, the product temperature only reaches within 4 0C of the critical temperature and has at least 4 0C of safety margin (Tsafety = Tcri - Tpr) 0
evident in Figure 1a. Pch and Tsh sensitivity obtained through elementary effects method are below 4 C for later part of the drying process, evident in Figure 1b. The Pch and Tsh sensitivity are within the temperature safety margin for Presentation-1. Based on this observation, we can predict that any type of Pch or Tsh excursion within the above considered interval during the primary drying process will probably have little to no impact on the product quality for Presentation-1. The error bars in Figure 1b, 3b, and 4b represent the standard deviation of the elementary effects of input parameters
in Equation 4. It shows that the sensitivity of Pch and Tsh is not entirely linear and the
sensitivity of one parameter has some effect on the other i.e. nonlinear interactions. These relations are consistent with the conventional knowledge about the interaction of Tsh and Pch on the product temperature. However, the standard deviation of the distribution is low, meaning less scatter around the mean for both input parameters which suggests the sensitivity can be discussed reasonably well from the mean of the distribution alone. Figure 2 shows a typical response surface for Presentation-1 at late stage (with about 90% dried product) -4
of primary drying. The response surface has root mean square error (RMSE) in the order of ~10 and -3
response surface error ~10 with the level 4 Smolyak grid. Smolyak grid level represents the order of the polynomial in gPC, meaning n-level Smolyak grid has enough sample points to fit the response surface th
with n -order polynomials. The level 4 Smolyak grid was deemed sufficient to accurately represent the output response and was used for all the three presentations. The RMSE errors in all the presentations were at the same order of magnitude. The response surface was created by computing the response of the product temperature at different chamber pressure and shelf temperature values within the prescribed interval. While the primary drying process progresses with the designed set points for Pch and Tsh, the Tpr response to varying process
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parameters was sampled at each instant in time to create a response surface. The Tpr response was then used to calculate the sensitivity by Elementary Effects method. The response surface can also be interpreted as a design space from the perspective of robustness of a product in the presence of process deviations. Study in [14] presents a similar design space created by using an expression for product temperature derived from statistical correlations. The equation for product temperature was formulated in [14] by using the statistical correlation of product temperature with different process parameters including shelf temperature and chamber pressure. The response surface can also aid in designing an optimum drying process by investigating the Tpr response at the most critical period of the primary drying, that is usually towards the later stages of drying. Evident in Figure 3a, the product temperature for Presentation-2 is the same as the critical temperature for most part of the primary drying process. Similar to in Presentation-1, Pch sensitivity is higher than Tsh sensitivity at earlier stages but the Tsh sensitivity grows to a much higher value than Pch sensitivity as 0
0
drying progresses. Pch sensitivity on Tpr is about 3 C while Tsh sensitivity is about 5 C at later stages. Since there is no temperature safety margin for majority of drying process in Presentation-2, process deviation at any stage of the primary drying can be predicted to have significant impact on the product quality. The product temperature is most likely to exceed the collapse temperature with the onset of either Pch or Tsh excursion during the primary drying process for Presentation-2. Presentation-3 however shows slightly different behavior at early stages of drying. Unlike Presentation-1 and 2, Tsh sensitivity is higher than Pch sensitivity throughout the primary drying process as can be seen in Figure 4b. Presentation-3 is a pure mannitol-based formulation where Presentation-1&2 are sucrosebased formulations. The process diagram
for Presentation-3 (Figure 4(a)) shows that there is a
considerable temperature safety margin throughout the primary drying process and the Tsh sensitivity is well within the safety margin even towards the later stage of primary drying (Figure 4(b)). The primary drying process for Presentation-3 is thus a robust process in terms of process deviations. Figure 5, 6 and 7 show process diagrams for different formulations in the presence of pressure and temperature excursions occurring at the late stage of primary drying when the cake is about 90% dried. For the excursion study at the late stage, the chamber pressure was increased by 6.67 Pa and the shelf 0
temperature was increased by 7 C for about 20 minutes and was returned to its set point then after. The
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values represent an extremely aggressive deviation study. For Presentation-1&3, both pressure and temperature excursion occur simultaneously while in Presentation- 2, only pressure excursion was studied. The product temperature for Presentation-2 at the later stage is the same as the critical temperature limit. Although Presentation-2 is a sucrose-based formulation similar to Presentation-1, the dissimilarity in product temperature variation in a primary drying process is due to the differences in fill volume and product resistance parameters. Based on the previous discussion from the sensitivity study, it was concluded that Presentation-2 will most likely exceed the critical temperature in the event of any excursion at the late stage of primary drying. Despite product temperature being more sensitive to shelf temperature, pressure excursion was chosen for Presentation-2 to demonstrate that pressure excursion alone can have significant impact on the product quality. Evident in Figure 5, the product temperature in Presentation-1 in the event of predefined pressure and 0
temperature excursion just exceeds the critical temperature by 0.5 C. As mentioned earlier, the deviation parameters studied here represent an aggressive excursion scenario and despite the occurrence of both pressure and temperature excursions simultaneously, the product temperature only exceeded the critical temperature by 0.5 0C. Presentation-2 shows robustness towards the process deviation during the primary drying process and the results are consistent with the sensitivity study. The product temperature 0
for Presentation-2 in the event of pressure excursion alone exceeded the critical temperature by 2 C, as seen in Figure 6. This can significantly compromise the quality of the product and the product temperature can reach a much higher value if both excursion scenarios occur simultaneously. Consistent with the discussion from sensitivity studies, it can be concluded that the quality of the product with Presentation-2 is most likely to be compromised in the event of any process deviation during the primary drying process. Presentation-3 still proved to be the most robust formulation considered in this study. In the event of both pressure and temperature excursion occurring simultaneously, the product temperature in Presentation-3 was still well below the critical temperature limit, evident in Figure 7. The author would like to bring the attention to the fact that the product temperature response in the event of process deviation cannot be accurately represented by quasi steady-steady state heat and mass transfer modeling. In reality, the Tpr response will be slightly different than the response represented here in Figure 5, 6, and 7 due to the thermal inertia. The Tpr will not change abruptly but will have some
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gradual response to the change in process parameters. The excursion scenarios in this study are considered purely to check the consistency with the sensitivity study. Retaining the transient terms in the heat and mass transfer modeling will provide more accurate Tpr response in the event of process deviations and can also reveal the impact of the duration of such excursions on the product quality. Based on the above discussions regarding the different formulations considered in this study, it can be concluded that the product temperature is more sensitive towards the change in shelf temperature than chamber pressure for most part of the primary drying process. In other words, excursions in shelf temperature are most likely to have significant impact on the product quality and proper shelf temperature control must be implemented to maintain a robust primary drying process. The conclusion is consistent with the conventional knowledge that a proper control should be exercised for the shelf temperature in a primary drying process. It is also worth mentioning that one can gain valuable information regarding the robustness of the process just by looking at the primary drying process cycle diagram (Figure 1a, 3a, and 4a) in terms of temperature safety margin. The process with some temperature safety margin is usually robust towards the process deviation. Also, the study of various excursion scenarios in different formulation showed consistency with the results from the sensitivity study.
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Conclusions
Sensitivity study through the elementary effects method was used in this study to asses possible impact of process deviations on the product quality during the primary drying process of two sucrose and one mannitol-based formulation. The sensitivity study was performed in an open-source PRISM uncertainty quantification tool in which the response surface for product temperature is related to its two input parameters, chamber pressure and shelf temperature, through Smolyak gPC technique. The sensitivity study revealed that the product temperature is more sensitive towards the change in shelf temperature than in chamber pressure towards the later stages of drying however, the sensitivity of process parameters varies among different formulations. Preliminary information regarding the robustness of a process can be obtained through the process cycle diagram in terms of the temperature safety margin and the sensitivity study can be used to quantify possible impact of process deviation on the product quality. Different excursion scenarios at late stages of primary drying were studied for all three
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formulations and the results were compared with the sensitivity study. The results from the deviation studies were consistent with the results of sensitivity studies. In addition, the author would like to point to the possibility of using sensitivity study to determine an optimum operating condition at each stage of the drying process that will maximize the sublimation rate and minimize the drying time without compromising the quality of the product. In overall, it can be concluded that sensitivity study can be used to assess the robustness of a primary drying process and it can be an elegant statistical technique that can aid to the designing of a more robust and optimum lyophilization process.
Acknowledgements
The authors would like to acknowledge valuable suggestions about the use of PUQ from Prof. Marisol Koslowski and graduate student Peter Kolis from Purdue University School of Mechanical Engineering. This work was supported by AbbVie Inc.
Disclosures TZ, FJ, TT, and SS are employees of AbbVie. AbbVie participated in the analysis and interpretation of data, review, writing, and approval of the publication. NA and AA are employees of Purdue University. AA serves as a scientific/technical consultant for Abbvie.
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5. Gieseler H, Kramer T, Schneid S. Quality by design in freezedrying: Cycle design and robustness testing in the laboratory using advanced process analytical technology. Pharmaceutical Technology. 10, (2008), 88-95. 6. Michael J. Pikal, Paritosh Pande, Robin Bogner, Pooja Sane, Vamsi Mudhivarthi, Puneet Sharma. Impact of natural variations in freeze-drying parameters on product temperature history: Application of quasi steady-state heat and mass transfer and simple statistics. AAPS PharmSciTech. 19 (7), (2018), 2828-2842. 7. Michael J. Pikal, M.L. Roy, S. Shah. Mass and heat transfer in vial freeze-drying of pharmaceuticals: role of the vial. Journal of Pharmaceutical Sciences. 73 (9), (1984), 1224-1237. 8. Martin Hunt, Benjamin Haley, Michael McLennan, Marisol Koslowski, Jayathi Murthy, Alejandro Strachan. PUQ: A code for non-intrusive uncertainty propagation in computer simulations. Computer Physics Communications. 194, (2015), 97-107. 9. D Xiu, G. Karniadakis. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM Journal on Scientific Computing. 24 (2), (2002), 619-644. 10. Max D. Morris. Factorial Sampling Plans for Preliminary Computational Experiments. Technometrics. 33 (2), (1991), 161-174. 11. Francesca Campolongo, Jessica Cariboni, Andrea Saltelli. An effective screening design for sensitivity analysis of large models. Environmental Modelling & Software. 22 (10), (2007), 1509-1518. 12. Tong Zhu, Ehab M. Moussa, Madeleine Witting, Deliang Zhou, Kushal Sinha, Mario Hirth, Martin Gastens, Sherwin Shang, Nandkishor Nere, Shubha Chetan Somashekar, Alina Alexeenko, Feroz Jameel. Predictive models of lyophilization process for development, scale-up/tech transfer and manufacturing. European Journal of Pharmaceutics and Biopharmaceutics. 128, (2018), 363-378. 13. Pooja Sane, Nikhil Varma, Arnab Ganguly, Michael Pikal, Alina Alexeenko, Robin H. Bogner. Spatial Variation of Pressure in the Lyophilization Product Chamber Part 2: Experimental Measurements and Implications for Scale-up and Batch Uniformity. AAPS PharmSciTech. 18 (2), (2016), 369-380. 14. Johnathan M. Goldman, Haresh T. More, Olga Yee, Elizabeth Borgeson, Brenda Remy, Jasmine Rowe, Vikram Sadineni. Optimization of Primary Drying in Lyophilization During Early-Phase Drug Development Using a Definitive Screening Design With Formulation and Process Factors. Journal of Pharmaceutical Sciences. 107, (2018), 2592-2600.
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Table 1. Summary of process parameters for different formulations considered Process Parameters
Solid Concentration Critical Temperature Chamber Pressure Shelf Temperature Fill height 6R SCHOTT Vial ∗ = + 1+ ∗ =
+
∗
1+ ∗ (lck is dried cake length)
(Csolid) (Tcri) (Pch,set) (Tsh,set) (hfill) Ap Av KC KP KD R0 A1 A2
Presentation -1 (sucrose based)
Presentation -2 (sucrose based)
9.4 % -28.0 9.332 -17.0 3.8e-3
8.8e-3 3.14e-4 3.80e-4 9.00 1.04 0.02 1.32e+5 4.57e+8 1.277e+3
3.46e+4 5.79e+8 3.214e+3
1
Presentation -3 (mannitol based)
Units
5.0 % -1.0 19.998 -5.0 6.37e-3
w/v 0 C Pa 0 C m 2 m 2 m -2 -1 Wm K -2 -1 -1 Wm K Pa -1 Pa -1 ms -1 s -1 m
2.04e+5 5.33e+7 3.0e+1
(a)
-15
(b) Tsh,set
Tsafety
6
Sensitivity Tpr (0C)
0
Temperature ( C)
-20
-25 Tcr -30
4 µ*(Pch)
-35 µ*(Tsh)
2 -40
0
2
4
6 Time (hr)
8
10
0
2
4
6 Time (hr)
8
10
(a)
-15
(b) 6
Tsh,set
µ*(Tsh)
Sensitivity Tpr (0C)
0
Temperature ( C)
-20
-25 Tcri Tp
-30
4
µ*(Pch) 2
-35 Tsafety -40
0
5
10
15 Time (hr)
20
25
30
0
0
5
10
15 Time (hr)
20
25
30
(a)
0
Tcri
Tsafety
Tsh,set Sensitivity Tpr (0C)
-5
15
0
Temperature ( C)
20
-10
10
-15
-20
-25
Tpr
0
2
4
6 Time (hr)
8
10
µ*(Tsh
5
0
µ*(Pch) 0
2
4
6 Time (hr)
8
10
100 -10 80
-15
-20
60 0
Tsh = Tsh,set + 7 C
-25
Pch = Pch,se
Tcri
40
-30 Tpr 20 -35
-40
0
2
4
6 Time (hr)
8
0 10
%dried (%)
0
Temperature ( C)
Tsh,set
-15
100
-20
80
-25
60 Tcri Tpr
-30
Pch = Pch,set
-35
-40
0
5
10
15 Time (hr)
20
40
20
25
0 30
%dried (%)
0
Temperature ( C)
Tsh,set
100 0
Tcri 80
0
Temperature ( C)
60 -10
Tsh = Tsh,set + 7 0C Pch = Pch,set + 6.
40
-15
-20
-25
Tpr
0
2
4
6 Time (hr)
8
10
20
0
%dried (%)
Tsh,set
-5
FIGURES 1. Figure 1. (a) Product temperature (Tpr) profile and (b) Chamber pressure (Pch) and shelf temperature (Tsh) sensitivity on Tpr for Presentation-1. 2. Figure 2. Tpr response surface for Presentation-1 at late stage (90% dried product at drying time ~7.95 hr) of primary drying process. 3. Figure 3. (a) Product temperature (Tpr) profile and (b) Chamber pressure (Pch) and shelf temperature (Tsh) sensitivity on Tpr for Presentation-2. 4. Figure 4. (a) Product temperature (Tpr) profile and (b) Chamber pressure (Pch) and shelf temperature (Tsh) sensitivity on Tpr for Presentation-3. 5. Figure 5. Product temperature profile in the event of pressure and temperature deviation at the late stage of primary drying for Presentation-1. 6. Figure 6. Product temperature profile in the event of pressure deviation at the late stage of primary drying for Presentation-2. 7. Figure 7. Product temperature profile in the event of pressure and temperature deviation at the late stage of primary drying for Presentation-3.
1
S0022-3549(19)30647-1
DOI:
https://doi.org/10.1016/j.xphs.2019.10.012
Reference:
XPHS 1738
To appear in:
Journal of Pharmaceutical Sciences
Received Date: 12 June 2019 Revised Date:
16 September 2019
Accepted Date: 4 October 2019
Please cite this article as: Adhikari N, Zhu T, Jameel F, Tharp T, Shang S, Alexeenko A, Sensitivity Study to Assess the Robustness of Primary Drying Process in Pharmaceutical Lyophilization, Journal of Pharmaceutical Sciences (2019), doi: https://doi.org/10.1016/j.xphs.2019.10.012. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Inc. on behalf of the American Pharmacists Association.
Sensitivity Study to Assess the Robustness of Primary Drying Process in Pharmaceutical Lyophilization 1
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Nirajan Adhikari , Tong Zhu , Feroz Jameel , Ted Tharp , Sherwin Shang , Alina Alexeenko
1,4
Affiliations: 1
School of Aeronautics and Astronautics, Purdue University, West Lafayette, Indiana, United
States 2
Drug Product Development, AbbVie Inc., North Chicago, Illinois, United States
3
Science and Technology, AbbVie Inc., North Chicago, Illinois, United States
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Corresponding Author
Corresponding Author: Alina Alexeenko, PhD School of Aeronautics and Astronautics, Purdue University Address: 701 W. Stadium Ave, West Lafayette, IN 47907 OFFICE: 765-496-1864 EMAIL: [email protected]
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Abstract The objective of this work is to apply a sensitivity study to assess the robustness of the primary drying step of pharmaceutical lyophilization with respect to deviations in process parameters. The sensitivity study can provide valuable information regarding the effect of process input parameters on the product quality that can aid in designing robust lyophilization processes. In this study, the output response is related to its inputs using Smolyak sparse grid generalized Polynomial Chaos method and the sensitivity was calculated using Elementary Effects method. Sensitivity of chamber pressure and shelf temperature on product temperature of two sucrose-based and one mannitol-based formulation was studied and the results were analyzed in terms of risk of adverse effects due to process deviations on the product quality. The study revealed that the sensitivity varies among formulations and preliminary information regarding the possible impact of process deviations can be obtained from the process cycle diagram. The product temperature showed greater sensitivity towards the change in the shelf temperature than the chamber pressure for the greater part of the primary drying stage. An aggressive process deviation scenario at the late stage of primary drying was also studied for different formulations and the results were consistent with the sensitivity study.
Keywords: Lyophilization, Freeze-drying, Mechanistic modeling, Processing, Mathematical model(s), Quality by design (QBD), Uncertainty Quantification (UQ), Sensitivity, Process deviation, Excursion study, Product robustness
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1
Introduction
Sensitivity study is a powerful statistical technique that quantifies the level of uncertainty in a mathematical model of a physical process. The study can assist in identifying a set of key factors among many variables and parameters involved in a model that can ultimately provide valuable insight to a realistic process prone to uncertainty in its input process parameters. In a lyophilization process, deviation of process parameters during primary drying can significantly compromise the quality of the end product. Most common deviations in the process parameters during a primary drying process arise from deviations in chamber pressure and shelf temperature from a set point often referred to as pressure and temperature excursions respectively. The quality of a freeze dried product is compromised when the product temperature at any point reaches above the critical temperature limit (Tcri) which is often determined using freeze drying microscopy and/or differential scanning calorimetry. Various studies in the literature [1-5] have examined the impact of elevated process temperature on the product quality. Study in [1] has shown partial collapse of the dried product even when the temperature of the product exceeded 0
the collapse temperature only by 1 C. Some of the studies have also revealed the long-term effects associated with the product stability after storage when the product temperature during the primary drying process reached above the critical temperature limit [2]. In another study in [3] with controlled pressure deviations in both experimental and theoretical models, it was revealed that the primary drying time can change by a significant amount in the presence of such deviations despite the product temperature being under the safety limit. The study also suggests extension of the design space beyond the one usually obtained through limited amount of experiments using a mechanistic process modeling. The use of such mechanistic process modeling helps to extend the experiment conditions and maximize the productivity while maintaining an acceptable product quality. The uncertainty due to the variability of chamber pressure and shelf temperature also adds up to the uncertainties of other important parameters like the heat transfer coefficient (Kv) and product resistance (Rp). Kv and Rp are direct or indirect functions of chamber pressure and shelf temperature. Kv and Rp are usually calculated as a batch average and can vary based on locations of the vials on a shelf. The study in [6] includes investigation of Kv variability in the vials inside a lyophilizer based on their positions. The variability of Kv and Rp alone can have adverse impact on the product quality. Furthermore, with added
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uncertainty due to process deviations, the impact on product quality can become even more significant. However, the study presented in this paper only includes uncertainty in process parameters that can occur in the event of pressure and temperature excursions. On a manufacturing scale, pressure and temperature excursions can compromise the quality of an entire batch of manufactured product which can add up to a significant amount of cost. Such excursions can occur randomly at any instant of a primary drying process which makes it difficult to predict the impact of excursions on the product quality. Keeping this idea in mind, the objective of this research was to aid the designing of a robust lyophilization process using sensitivity study that will provide a better understanding of the impacts of random occurrences of process deviations on the quality of a product. Presence of process deviations can have different impact on the primary drying process like elevated product temperature, lyophilizer equipment limit, extension/shortening of primary drying time, etc. Since the product temperature directly relates to the quality of the product, it has been identified as the most important parameter of interest. This study only assesses the impact of process deviation in terms of product temperature and other possible impact parameters are beyond the scope of this study. Three different formulation recipes- two sucrose-based and one pure mannitol-based- were considered in this study. The sensitivity of the product temperature (Tpr) to the chamber pressure (Pch) and the shelf temperature (Tsh) were quantified throughout the primary drying process that is mathematically modeled using quasi-steady state heat and mass transfer in vials [7], commonly referred as LyoCalc. The sensitivity study was performed using an open-source PRISM Uncertainty Quantification (PUQ) tool developed at Purdue University [8]. The organization of the remainder of the paper is as follows. First, the non-intrusive method of sensitivity analysis used in this study is discussed which is then followed by the results obtained from the sensitivity study for different formulations and at last, the results are discussed in terms of possible impact of process deviation on the product quality at various stages of a primary drying process.
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Sensitivity Analysis
One of the most powerful techniques to relate distribution of output parameters to its input parameters is through a generalized Polynomial Chaos (gPC) method [9]. gPC utilizes polynomial expansion to relate
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input to output Probability Density Functions (PDFs). Study in [9] has identified the importance of selection of orthogonal polynomial basis function in terms of input distribution for optimum convergence. The convergence of an orthogonal polynomial basis function for a particular distribution can be studied based on the maximum error of computed output response for a function whose output to input response is known explicitly. Gaussian distribution of input PDFs demands Hermite polynomials while uniform distribution is better represented with Legendre polynomials. Convergence study of different sampling methods in [8] has shown that Smolyak gPC sparse grid method shows better convergence in predicting output response compared to Monte Carlo or Latin Hypercube sampling methods for two-dimensional Rosenbrock function. Here, the distribution of input parameters (Pch and Tsh) are assumed to be uniform with equal probability distribution between assumed intervals. This is believed to be a good approximation since there is no tendency toward a particular value of Pch or Tsh during excursion due to the randomness of such excursions. For this study, Smolyak gPC method is used to interpolate the response surfaces. Sensitivity in PUQ is calculated through the Elementary Effects method originally developed by Morris [10] and later improved by Campolongo [11].
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Elementary Effects Method
Elementary effects method facilitates effective screening of important input parameters from the pool of parameters in a mathematical model with random one-at-a-time (OAT) experiments. This method calculates number of incremental ratios for each input which are called elemental effects. These elemental effects when averaged reveal whether an input factor has (a) negligible, (b) linear and additive, (c) nonlinear or involved interactions with other input, on the output parameter of interest. For a mathematical model with K input parameters given as: = (
, …,
, ..,
)
(1) th
the elemental effect of the i input parameter for a given value of X = (X1, X2, …, XK) is: ( )=
, ….,
,
△,
△
,….,
( )
(2)
where each model input Xi is assumed to vary randomly across p selected levels in the space of the input factors uniformly distributed in the interval [0,1]. The experimental region thus consists of K*p grid and ∆
5
th
is a pre-determined multiple of 1/(p-1). The distribution for the elementary effect associated with i input factor is defined as Fi such that di(X) ~ Fi. By randomly sampling r points for each input, r elemental (1)
(2)
(r)
effects are obtained from the distribution of Fi i.e. di(X ), di(X ), …., di(X ) that are averaged to give sensitivity measure µi and standard deviation
i
of the distribution Fi. Improvement by Campolongo
replaces µ by µ* which computes the mean of distribution of the absolute value of elementary effects. Using absolute value for elementary effects eliminates the statistical error in µ that arises when the model is non-monotonic i.e. negative and positive values cancelling each other while calculating a mean. The mean µi reveals the overall influence of input parameter Xi while the standard deviation σi estimates the ensemble of the factor’s higher order effects, i.e. nonlinear and/or due to interactions with other factors. The expressions for µi and σi in elementary effects method are as follows: µ∗ = ∑#$ | =%
∑#$
(#)
(
| (#) )
(3) −µ
'
(4)
In this study, y becomes the output parameter of interest Tpr, and K = 2 for two input parameters considered: Tsh and Pch. For example, if there are only 3 grid points uniformly distributed in [0, 1] such that the grid points are at Xi = {0, 0.5, 1}, the experimental region for each parameter will have 3*2 elements and ∆ = 0.5. To demonstrate the elementary effect method, let us now consider only one input parameter, say Tsh with 3 grid points such that the first element lies between [0, 0.5] and the second lies between [0.5,1]. Let’s say the response of Tpr from sample space was found to be {0, 10 , 20} for Xi = {0, 0.5, 1}. The elementary effect for the first element becomes (10 – 0) / 0.5 = 20 and for the second element, it becomes (20 - 10) / 0.5 = 20, using Equation 2. Since the response considered here is linear, the mean of the elementary effects for Tsh will also be 20 with standard deviation of 0. This idea can be extended to both input parameters where the mean of the elementary effects method for each parameter will now consist of 6 samples. In PUQ, the sample points for elementary effects calculation are chosen from the same points that are used to interpolate the response surface using Smolyak gPC. Thus, the sensitivity is calculated at no additional cost which makes this method computationally extremely economical.
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Results and discussion
Two sucrose based and one pure mannitol-based formulation recipes were used in this study to assess the possible impact of pressure and temperature excursions on product quality during the primary drying process. Since sensitivity of these process parameters on product temperature can vary at different stages of primary drying, sensitivity is calculated at each instant in time throughout the drying process. Different parameters associated with the formulations such as heat transfer, mass transfer, and process cycle parameters are tabulated in Table 1. The process parameters considered represent a typical primary drying process for the particular formulation. The heat transfer coefficient (Kv) parameters are obtained from [12] which corresponds to a lab-scale lyophilizer referred to as LabLyo-2 with 6R SCHOTT vials in [12]. The three model recipes considered in this study are named as Presentation 1, 2, and 3 from here on where Presentation -1&2 are sucrose based formulations and Presentation-3 is a pure mannitolbased formulation. Presentation 1 and 2 are both sucrose-based formulations with only differences in fill volume and Rp parameters. The Rp parameters for pure mannitol-based formulation is obtained from [13]. The intervals for two input process parameters Pch and Tsh considered for sensitivity study are as follows: Pch = [Pch,set – 2.67, Pch,set + 6.67] Pa 0
Tsh = [Tsh,set – 5, Tsh,set + 7] C The input intervals are selected to include both the conservative and aggressive excursions possible during the primary drying process for the formulations considered in this study. Chamber pressure and shelf temperature sensitivity on the product temperature for Presentation-1 is shown in Figure 1b and the variation of product temperature throughout the primary drying at the set conditions without any excursions is shown in Figure 1a. The product temperature is more sensitive towards Pch than Tsh at the early stage of primary drying. Tsh sensitivity increases with time and exceeds Pch sensitivity towards the later stages however Pch and Tsh sensitivities are still comparable to each other in this formulation. Pch and Tsh sensitivity follow similar trends to the product temperature profile i.e. the sensitivity changes with time at early stages and reaches a steady state towards the later stages of drying. However, Pch sensitivity shows inverse relation to Tpr profile; Pch sensitivity is higher at the earlier stages which decreases towards the later stages before settling to a steady value. Later stages of primary drying
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are more significant in terms of impact on the product quality due to lower sublimation rates at these final stages. The sublimation helps maintain a cooler product temperature and when the sublimation is inadequate, the product temperature can elevate to a value greater than collapse temperature in the presence of fluctuations in the process parameters. Thus, the study on impact of process deviations at the later stages of primary drying warrants special attention. In Presentation-1, the product temperature only reaches within 4 0C of the critical temperature and has at least 4 0C of safety margin (Tsafety = Tcri - Tpr) 0
evident in Figure 1a. Pch and Tsh sensitivity obtained through elementary effects method are below 4 C for later part of the drying process, evident in Figure 1b. The Pch and Tsh sensitivity are within the temperature safety margin for Presentation-1. Based on this observation, we can predict that any type of Pch or Tsh excursion within the above considered interval during the primary drying process will probably have little to no impact on the product quality for Presentation-1. The error bars in Figure 1b, 3b, and 4b represent the standard deviation of the elementary effects of input parameters
in Equation 4. It shows that the sensitivity of Pch and Tsh is not entirely linear and the
sensitivity of one parameter has some effect on the other i.e. nonlinear interactions. These relations are consistent with the conventional knowledge about the interaction of Tsh and Pch on the product temperature. However, the standard deviation of the distribution is low, meaning less scatter around the mean for both input parameters which suggests the sensitivity can be discussed reasonably well from the mean of the distribution alone. Figure 2 shows a typical response surface for Presentation-1 at late stage (with about 90% dried product) -4
of primary drying. The response surface has root mean square error (RMSE) in the order of ~10 and -3
response surface error ~10 with the level 4 Smolyak grid. Smolyak grid level represents the order of the polynomial in gPC, meaning n-level Smolyak grid has enough sample points to fit the response surface th
with n -order polynomials. The level 4 Smolyak grid was deemed sufficient to accurately represent the output response and was used for all the three presentations. The RMSE errors in all the presentations were at the same order of magnitude. The response surface was created by computing the response of the product temperature at different chamber pressure and shelf temperature values within the prescribed interval. While the primary drying process progresses with the designed set points for Pch and Tsh, the Tpr response to varying process
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parameters was sampled at each instant in time to create a response surface. The Tpr response was then used to calculate the sensitivity by Elementary Effects method. The response surface can also be interpreted as a design space from the perspective of robustness of a product in the presence of process deviations. Study in [14] presents a similar design space created by using an expression for product temperature derived from statistical correlations. The equation for product temperature was formulated in [14] by using the statistical correlation of product temperature with different process parameters including shelf temperature and chamber pressure. The response surface can also aid in designing an optimum drying process by investigating the Tpr response at the most critical period of the primary drying, that is usually towards the later stages of drying. Evident in Figure 3a, the product temperature for Presentation-2 is the same as the critical temperature for most part of the primary drying process. Similar to in Presentation-1, Pch sensitivity is higher than Tsh sensitivity at earlier stages but the Tsh sensitivity grows to a much higher value than Pch sensitivity as 0
0
drying progresses. Pch sensitivity on Tpr is about 3 C while Tsh sensitivity is about 5 C at later stages. Since there is no temperature safety margin for majority of drying process in Presentation-2, process deviation at any stage of the primary drying can be predicted to have significant impact on the product quality. The product temperature is most likely to exceed the collapse temperature with the onset of either Pch or Tsh excursion during the primary drying process for Presentation-2. Presentation-3 however shows slightly different behavior at early stages of drying. Unlike Presentation-1 and 2, Tsh sensitivity is higher than Pch sensitivity throughout the primary drying process as can be seen in Figure 4b. Presentation-3 is a pure mannitol-based formulation where Presentation-1&2 are sucrosebased formulations. The process diagram
for Presentation-3 (Figure 4(a)) shows that there is a
considerable temperature safety margin throughout the primary drying process and the Tsh sensitivity is well within the safety margin even towards the later stage of primary drying (Figure 4(b)). The primary drying process for Presentation-3 is thus a robust process in terms of process deviations. Figure 5, 6 and 7 show process diagrams for different formulations in the presence of pressure and temperature excursions occurring at the late stage of primary drying when the cake is about 90% dried. For the excursion study at the late stage, the chamber pressure was increased by 6.67 Pa and the shelf 0
temperature was increased by 7 C for about 20 minutes and was returned to its set point then after. The
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values represent an extremely aggressive deviation study. For Presentation-1&3, both pressure and temperature excursion occur simultaneously while in Presentation- 2, only pressure excursion was studied. The product temperature for Presentation-2 at the later stage is the same as the critical temperature limit. Although Presentation-2 is a sucrose-based formulation similar to Presentation-1, the dissimilarity in product temperature variation in a primary drying process is due to the differences in fill volume and product resistance parameters. Based on the previous discussion from the sensitivity study, it was concluded that Presentation-2 will most likely exceed the critical temperature in the event of any excursion at the late stage of primary drying. Despite product temperature being more sensitive to shelf temperature, pressure excursion was chosen for Presentation-2 to demonstrate that pressure excursion alone can have significant impact on the product quality. Evident in Figure 5, the product temperature in Presentation-1 in the event of predefined pressure and 0
temperature excursion just exceeds the critical temperature by 0.5 C. As mentioned earlier, the deviation parameters studied here represent an aggressive excursion scenario and despite the occurrence of both pressure and temperature excursions simultaneously, the product temperature only exceeded the critical temperature by 0.5 0C. Presentation-2 shows robustness towards the process deviation during the primary drying process and the results are consistent with the sensitivity study. The product temperature 0
for Presentation-2 in the event of pressure excursion alone exceeded the critical temperature by 2 C, as seen in Figure 6. This can significantly compromise the quality of the product and the product temperature can reach a much higher value if both excursion scenarios occur simultaneously. Consistent with the discussion from sensitivity studies, it can be concluded that the quality of the product with Presentation-2 is most likely to be compromised in the event of any process deviation during the primary drying process. Presentation-3 still proved to be the most robust formulation considered in this study. In the event of both pressure and temperature excursion occurring simultaneously, the product temperature in Presentation-3 was still well below the critical temperature limit, evident in Figure 7. The author would like to bring the attention to the fact that the product temperature response in the event of process deviation cannot be accurately represented by quasi steady-steady state heat and mass transfer modeling. In reality, the Tpr response will be slightly different than the response represented here in Figure 5, 6, and 7 due to the thermal inertia. The Tpr will not change abruptly but will have some
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gradual response to the change in process parameters. The excursion scenarios in this study are considered purely to check the consistency with the sensitivity study. Retaining the transient terms in the heat and mass transfer modeling will provide more accurate Tpr response in the event of process deviations and can also reveal the impact of the duration of such excursions on the product quality. Based on the above discussions regarding the different formulations considered in this study, it can be concluded that the product temperature is more sensitive towards the change in shelf temperature than chamber pressure for most part of the primary drying process. In other words, excursions in shelf temperature are most likely to have significant impact on the product quality and proper shelf temperature control must be implemented to maintain a robust primary drying process. The conclusion is consistent with the conventional knowledge that a proper control should be exercised for the shelf temperature in a primary drying process. It is also worth mentioning that one can gain valuable information regarding the robustness of the process just by looking at the primary drying process cycle diagram (Figure 1a, 3a, and 4a) in terms of temperature safety margin. The process with some temperature safety margin is usually robust towards the process deviation. Also, the study of various excursion scenarios in different formulation showed consistency with the results from the sensitivity study.
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Conclusions
Sensitivity study through the elementary effects method was used in this study to asses possible impact of process deviations on the product quality during the primary drying process of two sucrose and one mannitol-based formulation. The sensitivity study was performed in an open-source PRISM uncertainty quantification tool in which the response surface for product temperature is related to its two input parameters, chamber pressure and shelf temperature, through Smolyak gPC technique. The sensitivity study revealed that the product temperature is more sensitive towards the change in shelf temperature than in chamber pressure towards the later stages of drying however, the sensitivity of process parameters varies among different formulations. Preliminary information regarding the robustness of a process can be obtained through the process cycle diagram in terms of the temperature safety margin and the sensitivity study can be used to quantify possible impact of process deviation on the product quality. Different excursion scenarios at late stages of primary drying were studied for all three
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formulations and the results were compared with the sensitivity study. The results from the deviation studies were consistent with the results of sensitivity studies. In addition, the author would like to point to the possibility of using sensitivity study to determine an optimum operating condition at each stage of the drying process that will maximize the sublimation rate and minimize the drying time without compromising the quality of the product. In overall, it can be concluded that sensitivity study can be used to assess the robustness of a primary drying process and it can be an elegant statistical technique that can aid to the designing of a more robust and optimum lyophilization process.
Acknowledgements
The authors would like to acknowledge valuable suggestions about the use of PUQ from Prof. Marisol Koslowski and graduate student Peter Kolis from Purdue University School of Mechanical Engineering. This work was supported by AbbVie Inc.
Disclosures TZ, FJ, TT, and SS are employees of AbbVie. AbbVie participated in the analysis and interpretation of data, review, writing, and approval of the publication. NA and AA are employees of Purdue University. AA serves as a scientific/technical consultant for Abbvie.
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5. Gieseler H, Kramer T, Schneid S. Quality by design in freezedrying: Cycle design and robustness testing in the laboratory using advanced process analytical technology. Pharmaceutical Technology. 10, (2008), 88-95. 6. Michael J. Pikal, Paritosh Pande, Robin Bogner, Pooja Sane, Vamsi Mudhivarthi, Puneet Sharma. Impact of natural variations in freeze-drying parameters on product temperature history: Application of quasi steady-state heat and mass transfer and simple statistics. AAPS PharmSciTech. 19 (7), (2018), 2828-2842. 7. Michael J. Pikal, M.L. Roy, S. Shah. Mass and heat transfer in vial freeze-drying of pharmaceuticals: role of the vial. Journal of Pharmaceutical Sciences. 73 (9), (1984), 1224-1237. 8. Martin Hunt, Benjamin Haley, Michael McLennan, Marisol Koslowski, Jayathi Murthy, Alejandro Strachan. PUQ: A code for non-intrusive uncertainty propagation in computer simulations. Computer Physics Communications. 194, (2015), 97-107. 9. D Xiu, G. Karniadakis. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM Journal on Scientific Computing. 24 (2), (2002), 619-644. 10. Max D. Morris. Factorial Sampling Plans for Preliminary Computational Experiments. Technometrics. 33 (2), (1991), 161-174. 11. Francesca Campolongo, Jessica Cariboni, Andrea Saltelli. An effective screening design for sensitivity analysis of large models. Environmental Modelling & Software. 22 (10), (2007), 1509-1518. 12. Tong Zhu, Ehab M. Moussa, Madeleine Witting, Deliang Zhou, Kushal Sinha, Mario Hirth, Martin Gastens, Sherwin Shang, Nandkishor Nere, Shubha Chetan Somashekar, Alina Alexeenko, Feroz Jameel. Predictive models of lyophilization process for development, scale-up/tech transfer and manufacturing. European Journal of Pharmaceutics and Biopharmaceutics. 128, (2018), 363-378. 13. Pooja Sane, Nikhil Varma, Arnab Ganguly, Michael Pikal, Alina Alexeenko, Robin H. Bogner. Spatial Variation of Pressure in the Lyophilization Product Chamber Part 2: Experimental Measurements and Implications for Scale-up and Batch Uniformity. AAPS PharmSciTech. 18 (2), (2016), 369-380. 14. Johnathan M. Goldman, Haresh T. More, Olga Yee, Elizabeth Borgeson, Brenda Remy, Jasmine Rowe, Vikram Sadineni. Optimization of Primary Drying in Lyophilization During Early-Phase Drug Development Using a Definitive Screening Design With Formulation and Process Factors. Journal of Pharmaceutical Sciences. 107, (2018), 2592-2600.
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Table 1. Summary of process parameters for different formulations considered Process Parameters
Solid Concentration Critical Temperature Chamber Pressure Shelf Temperature Fill height 6R SCHOTT Vial ∗ = + 1+ ∗ =
+
∗
1+ ∗ (lck is dried cake length)
(Csolid) (Tcri) (Pch,set) (Tsh,set) (hfill) Ap Av KC KP KD R0 A1 A2
Presentation -1 (sucrose based)
Presentation -2 (sucrose based)
9.4 % -28.0 9.332 -17.0 3.8e-3
8.8e-3 3.14e-4 3.80e-4 9.00 1.04 0.02 1.32e+5 4.57e+8 1.277e+3
3.46e+4 5.79e+8 3.214e+3
1
Presentation -3 (mannitol based)
Units
5.0 % -1.0 19.998 -5.0 6.37e-3
w/v 0 C Pa 0 C m 2 m 2 m -2 -1 Wm K -2 -1 -1 Wm K Pa -1 Pa -1 ms -1 s -1 m
2.04e+5 5.33e+7 3.0e+1
(a)
-15
(b) Tsh,set
Tsafety
6
Sensitivity Tpr (0C)
0
Temperature ( C)
-20
-25 Tcr -30
4 µ*(Pch)
-35 µ*(Tsh)
2 -40
0
2
4
6 Time (hr)
8
10
0
2
4
6 Time (hr)
8
10
(a)
-15
(b) 6
Tsh,set
µ*(Tsh)
Sensitivity Tpr (0C)
0
Temperature ( C)
-20
-25 Tcri Tp
-30
4
µ*(Pch) 2
-35 Tsafety -40
0
5
10
15 Time (hr)
20
25
30
0
0
5
10
15 Time (hr)
20
25
30
(a)
0
Tcri
Tsafety
Tsh,set Sensitivity Tpr (0C)
-5
15
0
Temperature ( C)
20
-10
10
-15
-20
-25
Tpr
0
2
4
6 Time (hr)
8
10
µ*(Tsh
5
0
µ*(Pch) 0
2
4
6 Time (hr)
8
10
100 -10 80
-15
-20
60 0
Tsh = Tsh,set + 7 C
-25
Pch = Pch,se
Tcri
40
-30 Tpr 20 -35
-40
0
2
4
6 Time (hr)
8
0 10
%dried (%)
0
Temperature ( C)
Tsh,set
-15
100
-20
80
-25
60 Tcri Tpr
-30
Pch = Pch,set
-35
-40
0
5
10
15 Time (hr)
20
40
20
25
0 30
%dried (%)
0
Temperature ( C)
Tsh,set
100 0
Tcri 80
0
Temperature ( C)
60 -10
Tsh = Tsh,set + 7 0C Pch = Pch,set + 6.
40
-15
-20
-25
Tpr
0
2
4
6 Time (hr)
8
10
20
0
%dried (%)
Tsh,set
-5
FIGURES 1. Figure 1. (a) Product temperature (Tpr) profile and (b) Chamber pressure (Pch) and shelf temperature (Tsh) sensitivity on Tpr for Presentation-1. 2. Figure 2. Tpr response surface for Presentation-1 at late stage (90% dried product at drying time ~7.95 hr) of primary drying process. 3. Figure 3. (a) Product temperature (Tpr) profile and (b) Chamber pressure (Pch) and shelf temperature (Tsh) sensitivity on Tpr for Presentation-2. 4. Figure 4. (a) Product temperature (Tpr) profile and (b) Chamber pressure (Pch) and shelf temperature (Tsh) sensitivity on Tpr for Presentation-3. 5. Figure 5. Product temperature profile in the event of pressure and temperature deviation at the late stage of primary drying for Presentation-1. 6. Figure 6. Product temperature profile in the event of pressure deviation at the late stage of primary drying for Presentation-2. 7. Figure 7. Product temperature profile in the event of pressure and temperature deviation at the late stage of primary drying for Presentation-3.
1