Mathematical models of the process of submlimationand optimization of lyophilization modes
https://doi.org/10.17650/1726-9784-2018-17-3-20-28
Abstract
The purpose of this study is to analyze methods of mathematical modeling for calculating the stage of primary sublimation, as the most important stage in lyophilization technology. Presented are mathematical formulas, equations for the calculation of heat and mass transfer processes, during the removal of 90 % of all frozen ice. A model is considered that takes into account the contribution of all thermal effects, including the transient energy balance, taking into account the heat transfer through the side wall of the vial and radiation, even if they are present in a small amount. The mathematical model can be used to optimize the lyophilization cycle, and also as tools for technological monitoring (using sensors based on models). The model considered in the article is a one-dimensional nonstationary state model in which the correct comprehensive transient energy balance has been introduced to describe the heat transfer through the glass of the vial, and the results are estimated using experimental data. The equations used in the simulation describe the mass and energy balances in the dried layer, taking into account the rate of adsorption/desorption of water at the interface, mass and heat transfer at the sublimation interface, as well as the energy balance of heat transfer in the wall of vials, shelf and other factors affecting the process of sublimation. Conclusions are made on the presented mathematical models and the characteristic of the direction of the process of optimization of primary sublimation in lyophilization technology is given.
About the Authors
E. V. Blynskaya
V.V. Zakusov Institute of Pharmacology
Russian Federation
Russian Federation
8 Baltiyskaya St., Moscow 125315
S. V. Tishkov
V.V. Zakusov Institute of Pharmacology
Russian Federation
Russian Federation
8 Baltiyskaya St., Moscow 125315
K. V. Alekseyev
Moscow medical university “REAVIZ”
Russian Federation
Bldg. 2, 2 Krasnobogatyrskaya St., Moscow 107564
Russian Federation
Bldg. 2, 2 Krasnobogatyrskaya St., Moscow 107564
S. V. Minaev
V.V. Zakusov Institute of Pharmacology
Russian Federation
Russian Federation
8 Baltiyskaya St., Moscow 125315
References
1. Gulyakin I.D., Hashem A., Nikolaeva L.L. et al. Development of a new technology for the preparation of a dosage form for the intravenous administration of an indole carbazole derivative, LHS-1208. Rossiysky Bioterapevtichesky Zhurnal = RussianJournal of Biotherapy 2016;15(2):55–60 (In Russ.)
2. LantsovaA.V., KotovaE.A., SanarovaE.V. et al. Development of a lyophilized liposomal drug form of cipheline. Rossiysky Bioterapevtichesky Zhurnal = Russian Journal of Biotherapy 2015;14(2):79–84 (In Russ.)
3. Arshinova O.Yu., Oborotova N.A., Sanarova E.V. Auxiliary substances in the technology of lyophilization of drugs. Razrabotka i registratsiya lekarstvennykh sredstv = Development and registration of medicines 2013;2:20–5. (In Russ.)
4. Blynskaya E.V., Tishkov S.V., Alekseev K.V. Technological approaches to improving the process of lyophilization of protein and peptide drugs. Rossiysky Bioterapevtichesky Zhurnal = Russian Journal of Biotherapy 2017;16(1):6–11 (In Russ.)
5. Blynskaya E.V., Tishkov S.V., Alekseev K.V., Marakhova A.I. Auxiliary substances in the technology of lyophilization of peptides and proteins. Farmatsya = Pharmacy 2017;66(1):14–8 (In Russ.)
6. Barresi A.A., Pisano R., Fissore D. et al. Monitoring of the primary drying of a lyophilization process in vials. Chem Eng Proc: Process Intensification 2009;48(1):408–23. DOI:10.1016/j.cep.2008.05.004.
7. Genin N., Rene F., Corrieu G. A method for on-line determination of residual water content and sublimation end-point during freeze-drying. Chemical Engineering and Processing: Process Intensification 1996;35(4):255–63. DOI:10.1016/0255-2701(95)04131-1.
8. Pikal M.J. Use of laboratory data in freeze-drying process design: heat and mass transfer coefficients and the computer simulation of freezedrying. J Parenter Sci Technol 1985;39:115–39. DOI:10.1208/pt050458.
9. Millman M.J., Liapis A.I., Marchello J.M. An analysis of the lyophilisation process using a sorption sublimation model and various operational policies. AIChE J 1985;31(10):1594–604. DOI:10.1002/aic.690311003.
10. Pisano R., Fissore D., Velardi S.A., Barresi A.A. In-line optimization and control of an industrial freeze-drying process for pharmaceuticals. Journal of Pharmaceutical Sciences 2010;99(11): 4691–709. DOI:10.1002/jps.22166.
11. Ybema H., Kolkman-Roodbeen L., te Booy M.P., Vromans H. Vial lyophilization: calculations on rate limiting during primary drying. Pharm Res 1995;12(9):1260–3. DOI:10.1023/A:1016248918285.
12. Brülls M., Rasmuson A. Heat transfer in vial lyophilization. Int J Pharm 2002;246(1): 1–16. DOI:10.1016/S0378-5173(02)00353-8. PMID: 12270604.
13. Hottot A., Peczalski R., Vessot S., Andrieu J. Freeze drying of pharmaceutical proteins in vials: modeling of freezing and sublimation steps. Drying Technol 2006;24:561–70. DOI:10.1080/07373930600626388.
14. Zhai S., Su H., Taylor R., Slater K.H. Pure ice sublimation within vials in a laboratory lyophiliser; comparison of theory with experiments. Chem Eng Sci 2005;60:1167–76. DOI:10.1016/j.ces.2004.09.078.
15. Trelea I.C., Passot S., Fonseca F. et al. An interactive tool for the optimization of freeze-drying cycles based on quality criteria. Drying Tech 2007;25(5):741–51. DOI:10.1080/07373930701370100.
16. Sheehan P., Liapis A.I. Modeling of the primary and secondary drying stages of the freeze-drying of pharmaceutical product in vials: numerical results obtained from the solution of a dynamic and spatially multidimensional lyophilisation model for different operational policies. Biotechnol Bioeng 1998;60(3):712–28. DOI:10.1002/(SICI)1097-0290(19981220)60:6<712::AID-BIT8>3.0.CO;2–4.
17. Mason E.A., Malinauskas A.P., Evans R.B. Flow and diffusion of gases in porous media. J Chem Phys 1967; 46(8):3199–216. DOI:10.1063/1.1841191.
18. Kast W., Hohenthanner C.R. Mass transfer within the gas-phase of porous media. Int J Heat Mass Transfer 2000;43(5):807–23. DOI:10.1016/S0017-9310(99)00158-1.
19. Liapis A.I., Bruttini R. Freeze-drying of pharmaceutical crystalline and amorphous solutes in vials: Dynamic multi-dimensional models of the primary and secondary drying stages and qualitative features of the moving interface. Drying Tech 1995;13(1–2):43–72. DOI:10.1080/07373939508916942.
20. Sadikoglu H., Liapis A.L., Crasser O.K., Bruttini R. Estimation of the effect of product shrinkage on the drying times, heat input and condenser load of the primary and secondary drying stages of the lyophilization process in vials. Drying Tech 1999;17(10):2013–35. DOI:10.1080/07373939908917670.
21. Canuto C., Hussaini M.Y., Quarteroni A. et al. Spectral methods in fluid dynamics. New York: Springer Science & Business Media, 2012. 551 р. DOI:10.1007/978-3-540-52205-8.
22. Fornberg B. A practical guide to pseudospectral methods. Cambridge: Cambridge university press, 1998; 1. 231р. DOI:10.1017/S002211209722848X.
23. Funaro D. Polynomial approximation of differential equations. Berlin: Springer Science & Business Media, 2008; 8. 305 р.
24. Hamdami N., Monteau J.Y., Le Bail A. Effective thermal conductivity of a high porosity model food at above and sub-freezing temperatures. Int J Refrig 2003;26(7):809–16. DOI:10.1016/S0140-7007(03)00051-3.
25. Velardi S.A., Barresi A.A. Development of simplified models for the freezedrying process and investigation of the optimal operating conditions. Chem Eng Res Design 2008;86:9–22. DOI:10.1016/j.cherd.2007.10.007.
26. Sandall O.C., King C.J., Wilke C.R. The relationship between transport properties and rates of freeze-drying of poultry meat. AIChE Journal 1967;13(3):428–38. DOI:10.1002/aic.690130309.
27. Hill J.E., Sunderland J.E. Sublimation-dehydrationin the continuum, transition and free-molecule flow regimes. Int J Heat Mass Transfer. 1971;14(4):625–38. DOI:10.1016/0017-9310(71)90011-1.
Review
For citations:
Blynskaya E.V., Tishkov S.V., Alekseyev K.V., Minaev S.V. Mathematical models of the process of submlimationand optimization of lyophilization modes. Russian Journal of Biotherapy. 2018;17(3):20-28. (In Russ.) https://doi.org/10.17650/1726-9784-2018-17-3-20-28
Views:
471
Email this article 
