Robust bayesian estimation of kinetics for the polymorphic transformation of L-glutamic acid crystals

AIChE Journal

Volumn 54, Issue 12, 2008, Pages 3248-3259

  Hermanto, Martin Wijaya ^a   Kee, Nicholas C ^a,b   Tan, Reginald B H ^a,c   Chiu, Min Sen ^a   Braatz, Richard D ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^c INSTITUTE OF CHEMICAL AND ENGINEERING SCIENCES   (Singapore)

Author keywords

Bayesian inference; Markov chain monte carlo; Pharmaceutical crystallization modeling; Polymorphism

Indexed keywords

BAYESIAN INFERENCE; BAYESIAN INFERENCES; CONTROL STRATEGIES; CRYSTAL FORMS; CRYSTAL QUALITIES; CRYSTAL SIZES; ESTIMATED PARAMETERS; EXPERIMENTAL DATUMS; FTIR SPECTROSCOPIES; GLUTAMIC ACIDS; IN-SITU; KINETIC MODELS; MARKOV CHAIN MONTE CARLO; MARKOV CHAIN MONTE CARLO SIMULATIONS; MODEL PREDICTIONS; OPERATING CONDITIONS; PHARMACEUTICAL CRYSTALLIZATION MODELING; PHARMACEUTICAL MANUFACTURING; POINT ESTIMATES; POLYMORPHIC CRYSTALLIZATIONS; POLYMORPHIC TRANSFORMATIONS; ROBUST BAYESIAN ESTIMATIONS; SOLUTE CONCENTRATIONS;

BAYESIAN NETWORKS; CONTROL THEORY; CRYSTALLIZATION; CRYSTALLOGRAPHY; FOURIER TRANSFORM INFRARED SPECTROSCOPY; IMAGE SEGMENTATION; INFERENCE ENGINES; KINETIC PARAMETERS; KINETIC THEORY; MARKOV PROCESSES; MONTE CARLO METHODS; NANOCRYSTALLINE ALLOYS; PARAMETER ESTIMATION; POLYMORPHISM; PROBABILITY; ROBUST CONTROL; UNCERTAIN SYSTEMS;

PROBABILITY DISTRIBUTIONS;

EID: 57049102903     PISSN: 00011541     EISSN: 15475905     Source Type: Journal    
DOI: 10.1002/aic.11623     Document Type: Article

References (56)

1. De Anda JC, Wang XZ, Lai X, Roberts KJ. Classifying organic crystals via in-process image analysis and the use of monitoring charts to follow polymorphic and morphological changes, J Process Control. 2005; 15:785-797.
2. Blagden N, Davey R. Polymorphs take shape. Chem Britain, 1999;35:44-47,
3. Fujiwara M, Nagy ZK, Chew JW, Braatz RD. First-principles and direct design approaches for the control of pharmaceutical crystallization. J Process Control. 2005;15:493-504.
4. Rohani S, Home S, Murthy K. Control of product quality in batch crystallization of pharmaceuticals and fine chemicals, Part 1: Design of the crystallization process and the effect of solvent. Org Process Res Dev. 2005;9:858-872.
5. Yu LX, Lionberger RA, Raw AS, D'Costa R, Wu HQ, Hussain AS. Applications of process analytical technology to crystallization processes. Adv Drug Delivery Rev. 2004;56:349-369.
6. Cardew PT, Davey RJ. The kinetics of solvent-mediated phase transformations. Proc R Soc Land A. 1985;398:415-428.
7. Sakai H, Hosogai H, Kawakita T, Onuma K, Tsukamoto K. Transformation of α-glycine to γ-glycine. J Cryst Growth. 1992; 116:421-426.
8. Saranteas K, Bakale R, Hong YP, Luong H, Foroughi R, Wald S. Process design and scale-up elements for solvent mediated polymorphic controlled tecastemizole crystallization. Org Process Res Dev. 2005:9:911-922.
9. Yu L. Survival of the fittest polymorph: how fast nucleater can lose to fast grower. CrystEngComm. 2007;9:841-851.
10. Bard Y. Nonlinear Parameter Estimation. New York: Academic Press. 1974.
11. Bates DM, Watts DG. Nonlinear Regression Analysis and Its Applications. New York: Wiley, 1988.
12. Mendes P, Kell DB. Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics. 1998;14:869-883.
13. Ono T, Kramer HJM, Ter Horst JH, Jansens PJ. Process modeling of the polymorphic transformation of L-glutamic acid. Cryst Growth Des. 2004;4:1161-1167.
14. Scholl J, Bonalumi D, Vicum L, Mazzotti M. In situ monitoring and modeling of the solvent-mediated polymorphic transformation of L-Glutamic acid. Cryst Growth Des. 2006;6:881-891.
15. Caillet A. Sheibat-Othman N, Fevotte G. Crystallization of monohy-drate citric acid. II. Modeling through population balance equations. Cryst Growth Des. 2007;7:2088-2095.
16. Fevotte G, Alexandre C. Nida SO. A population balance model of the solution-mediated phase transition of citric acid. AlChE J. 2007;53:2578-2589.
17. Box GEP, Draper NR. The Bayesian estimation of common parameters from several responses. Biometrika. 1965;52:355-365.
18. Duran MA, White BS. Bayesian estimation applied to effective heat transfer coefficients in a packed bed. Chem Eng Sci. 1995;50:495-510.
19. Bois FY, Fahmy T, Block JC, Gatel D. Dynamic modeling of bacteria in a pilot drinking-water distribution svstem. Water Res. 1997; 31:3146-3456.
20. Coleman MC, Block DE. Bayesian parameter estimation with informative priors for nonlinear systems. AIChE J. 2006;52:651-667.
21. Pouillot R, Albert I, Cornu M, Denis JB. Estimation of uncertainty and variability in bacterial growth using Bayesian inference. Application to listeria monocytogenes, Int J Food Microbiol. 2003:81:87-104,
22. Gunawan R, Jung MY, Seebauer EG, Braatz RD. Maximum a posteriori estimation of transient enhanced diffusion energetics. AIChE J. 2003;49:2114-2122.
23. Miller SM, Rawlings JB. Model identification and control strategies for batch cooling crystallizers. AIChE J. 1994:40:1312-1327.
24. Nagy ZK, Braatz RD. Worst-case and distributional robustness analysis of finite-time control trajectories for nonlinear distributed parameter systems. IEEE Trans Control Syst Technol. 2003:11:694-704.
25. Beck JV, Arnold KJ. Parameter Estimation in Engineering and science. New York: Wiley, 1977.
26. Tierney L. Markov Chains for exploring posterior distributions. Ann Stat. 1994;22:1701-1728.
27. Liu JS. Monte Carlo Strategies in Scientific Computing. New York: Springer, 2001.
28. Gelman A, Carlin JB, Stern HS. Rubin DB. Bayesian Data Analysis. New York: Chapman & Hall/CRC, 2004.
29. Chen WS, Bakshi BR, Goel PK, Ungarala S. Bayesian estimation via sequential Monte Carlo sampling: unconstrained nonlinear dynamic systems. Ind Eng Chem Res. 2004;43:4012-4025.
30. Lang L, Chen WS, Bakshi BR, Goel PK, Ungarala S. Bayesian estimation via sequential Monte Carlo sampling - constrained dynamic systems. Automatica. 2007;43:1615-1622.
31. Fujiwara M, Chow PS, Ma DL, Braatz RD. Paracetamol crystallization using laser backscattering and ATR-FTIR spectroscopy: metastability, agglomeration and control. Cryst Growth Des. 2002;2:363-370.
32. Togkalidou T, Fujiwara M, Patel S, Braatz RD. Solute concentration prediction using chemometrics and ATR-FTIR spectroscopy. J Crist Growth. 2001:231:534-543.
33. Xie YL, Kalivas JH. Evaluation of principal component selection methods to form a global prediction model by principal component regression. Anal Chirn Acta. 1997;348:19-27.
34. Bretthorst GL. An introduction to parameter estimation using Bayesian probability theory. In: Fougere PF, editor. Maximum Entropy and Basesian Methods. Dordrecht: Kluwer Academic Publishers, 1990:53-79.
35. Carlin BP, Louis TA. Bayes and Empirical Bayes Methods for Data Analysis. Boca Raton: Chapman & Hall/CRC, 2000.
36. Box GEP, Tiao GC, Bayesian Inference in Statistical Analysis. Reading, Mass: Addison-Wesley, 1973.
37. Metropolis N, Rosenbiuth AW, Rosenbluth MN, Teller AH. Equation of state calculations by fast computing machines, J Chem Phys. 1953;21:1087-1092.
38. Haario H, Saksman E, Tamminen J. An adaptive Metropolis algorithm. Bernoulli. 2001;7:223-242.
39. Liang FM, Wong WH. Real-parameter evolutionary Monte Carlo with applications to Bayesian mixture models. J Am Stat Assoc. 2001;96:653-666.
40. Liang F. Dynamically weighted importance sampling in Monte Carlo computation. J Am Stat Assoc. 2002;97:807-821.
41. Laskey KB. Myers JW, Population Markov Chain Monte Carlo, Machine Learn. 2003;50:175-196.
42. Braak CJ. A Markov Chain Monte Carlo version of the genetic algorithm differential evolution: easy Bayesian computing for real parameter spaces. Slat Comput. 2006;16:239-249.
43. Clontz NA, McCabe WL. Contact nucleation of magnesium sulfate heptahydrate. AIChE Symp Ser. 1971;67:6-17.
44. Hulburt HM, Katz S. Some problems in particle technology: a statistical mechanical formulation. Chem Eng Sci. 1964;19:555-574.
45. Mersmann A. Crystallization Technology Handbook, 2nd ed. Boca Raton: CRC Press, 2001.
46. Kitamura M, Ishizu T. Growth kinetics and morphological change of polymorphs of L-glutamic acid. J Cryst Growth. 2000;209:138-145.
47. Togkalidou T, Braatz RD, Johnson B, Davidson O, Andrews A. Experimental design and inferential modeling in pharmaceutical crystallization. AIChE J. 2001;47:160-168.
48. Togkalidou T, Tung HH, Sun Y, Andrews A, Braatz RD. Solution concentration prediction for pharmaceutical crystallization processes using robust chemometries and ATR FT1R spectroscopy. Org Process Res Dev. 2002;6:317-322.
49. Tadayyon A, Rohani S. Determination of particle size distribution by Par-Tec 100: modeling and experimental results. Part Part Syst Charact. 1998;15:127-135.
50. Simmons M, Langston P, Burbidge A. Particle and droplet size analysis from chord distributions. Powder Technol. 1999;102:75-83.
51. Ruf A, Worlitschek J, Mazzotti M, Modeling and experimental analysis of PSD measurements through FBRM. Part Part Syst Charact. 2000;17:167-179.
52. Hukkanen EJ, Braatz RD. Measurement of particle size distribution in suspension polymerization using in situ laser backscattering. Sens Actuators B. 2003;96:451-459.
53. Heath AR, Fawell PD, Bahri PA, Swift JD. Estimating average particle size by focused beam reflectance measurement (FBRM). Part Part Syst Charact. 2002;19:84-95.
54. Togkalidou T, Tung HH, Sun Y, Andrews AT, Braatz RD. Parameter estimation and optimization of a loosely-bound aggregating pharmaceutical crystallization using in-situ infrared and laser backscattering measurements. Ind Eng Chem Res. 2004;43:6168-6181.
55. Gunawan R, Ma DL, Fujiwara M, Braatz RD. Identification of kinetic parameters in a multidimensional crystallization process. Int J Mod Phys B. 2002;16:367-374.
56. Starbuck C, Spartalis A, Wai L, Wang J, Fernandez P, Lindemann CM, Zhou GX, Ge ZH. Process optimization of a complex pharmaceutical polymorphic system via in situ Raman spectroscopy. Cryst Growth Des. 2002;2:515-522.