Dynamic response surface methodology using Lasso regression for organic pharmaceutical synthesis

Abstract

To study the dynamic behavior of a process, time-resolved data are collected at different time instants during each of a series of experiments, which are usually designed with the design of experiments or the design of dynamic experiments methodologies. For utilizing such time-resolved data to model the dynamic behavior, dynamic response surface methodology (DRSM), a data-driven modeling method, has been proposed. Two approaches can be adopted in the estimation of the model parameters: stepwise regression, used in several of previous publications, and Lasso regression, which is newly incorporated in this paper for the estimation of DRSM models. Here, we show that both approaches yield similarly accurate models, while the computational time of Lasso is on average two magnitude smaller. Two case studies are performed to show the advantages of the proposed method. In the first case study, where the concentrations of different species are modeled directly, DRSM method provides more accurate models compared to the models in the literature. The second case study, where the reaction extents are modeled instead of the species concentrations, illustrates the versatility of the DRSM methodology. Therefore, DRSM with Lasso regression can provide faster and more accurate data-driven models for a variety of organic synthesis datasets.

Graphical abstract

Keywords

data-driven modeling / pharmaceutical organic synthesis / Lasso regression / dynamic response surface methodology

References

[1] Coley C W, Eyke N S, Jensen K F. Autonomous discovery in the chemical sciences part I: progress. Angewandte Chemie International Edition, 2020, 59: 2–38

[2] Van de Vijver R, Vandewiele N M, Bhoorasingh P L, Slakman B L, Khanshan F S, Carstensen H H, Reyniers M F, Marin G B, West R H, Van Geem K M. Automatic mechanism and kinetic model generation for gas- and solution-phase processes: a perspective on best practices, recent advances, and future challenges. International Journal of Chemical Kinetics, 2015, 47(4): 199–231

[3] Qian F, Tao L, Sun W, Du W. Development of a free radical kinetic model for industrial oxidation of p-xylene based on artificial neural network and adaptive immune genetic algorithm. Industrial & Engineering Chemistry Research, 2012, 51(8): 3229–3237

[4] Shi H, Zhou T. Computational design of heterogeneous catalysts and gas separation materials for advanced chemical processing. Frontiers of Chemical Science and Engineering, 2021, 15(1): 49–59

[5] Selekman J A, Qiu J, Tran K, Stevens J, Rosso V, Simmons E, Xiao Y, Janey J. High-throughput automation in chemical process development. Annual Review of Chemical and Biomolecular Engineering, 2017, 8(1): 525–547

[6] Caron S, Thomson N M. Pharmaceutical process chemistry: evolution of a contemporary data-rich laboratory environment. Journal of Organic Chemistry, 2015, 80(6): 2943–2958

[7] Ulrich J, Frohberg P. Problems, potentials and future of industrial crystallization. Frontiers of Chemical Science and Engineering, 2013, 7(1): 1–8

[8] Gernaey K V, Cervera-Padrell A E, Woodley J M. A perspective on PSE in pharmaceutical process development and innovation. Computers & Chemical Engineering, 2012, 42: 15–29

[9] Yue W, Chen X, Gui W, Xie Y, Zhang H. A knowledge reasoning fuzzy-Bayesian network for root cause analysis of abnormal aluminum electrolysis cell condition. Frontiers of Chemical Science and Engineering, 2017, 11(3): 414–428

[10] Montgomery D C. Design and Analysis of Experiments. 8th edition. Hoboken: John Wiley & Sons, 2008

[11] Klebanov N, Georgakis C. Dynamic response surface models: a data-driven approach for the analysis of time-varying process outputs. Industrial & Engineering Chemistry Research, 2016, 55(14): 4022–4034

[12] Wang Z, Georgakis C. New dynamic response surface methodology for modeling nonlinear processes over semi-infinite time horizons. Industrial & Engineering Chemistry Research, 2017, 56(38): 10770–10782

[13] Dong Y, Georgakis C, Mustakis J, Hawkins J M, Han L, Wang K, McMullen J P, Grosser S T, Stone K. Constrained version of the dynamic response surface methodology for modeling pharmaceutical reactions. Industrial & Engineering Chemistry Research, 2019, 58(30): 13611–13621

[14] Domagalski N R, Mack B C, Tabora J E. Analysis of design of experiments with dynamic responses. Organic Process Research & Development, 2015, 19(11): 1667–1682

[15] Wang K, Han L, Mustakis J, Li B, Magano J, Damon D B, Dion A, Maloney M T, Post R, Li R. Kinetic and data-driven reaction analysis for pharmaceutical process development. Industrial & Engineering Chemistry Research, 2020, 59(6): 2409–2421

[16] Alpaydin E. Introduction to Machine Learning. 3rd edition. Cambridge: MIT Press, 2014

[17] Boyd S, Parikh N, Chu E, Peleato B, Eckstein J. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, 2011, 3(1): 1–122

[18] García-Muñoz S, Dolph S, Ward H W II. Handling uncertainty in the establishment of a design space for the manufacture of a pharmaceutical product. Computers & Chemical Engineering, 2010, 34(7): 1098–1107

[19] Santos-Marques J, Georgakis C, Mustakis J, Hawkins J M. From DRSM models to the identification of the reaction stoichiometry in a complex pharmaceutical case study. AIChE Journal. American Institute of Chemical Engineers, 2019, 65(4): 1173–1185

[20] Dong Y, Georgakis C, Mustakis J, Hawkins J M, Han L, Wang K, McMullen J P, Grosser S T, Stone K. Stoichiometry identification of pharmaceutical reactions using the constrained dynamic response surface methodology. AIChE Journal. American Institute of Chemical Engineers, 2019, 65(11): e16726

[21] Huri N, Feder M. In selecting the Lasso regularization parameter via Bayesian principles, 2016 IEEE International Conference on the Science of Electrical Engineering (ICSEE), 2016, 1–5

[22] Montgomery D C, Peck E A, Vining G G. Introduction to Linear Regression Analysis. 5th edition. London: Wiley, 2012

[23] Golub G H, Heath M, Wahba G. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics, 1979, 21(2): 215–223

[24] Hanrahan G, Lu K. Application of factorial and response surface methodology in modern experimental design and optimization. Critical Reviews in Analytical Chemistry, 2006, 36(3-4): 141–151

[25] Singh G, Pai R S, Devi V K. Response surface methodology and process optimization of sustained release pellets using Taguchi orthogonal array design and central composite design. Journal of Advanced Pharmaceutical Technology & Research, 2012, 3(1): 30–40

[26] Bezerra M A, Santelli R E, Oliveira E P, Villar L S, Escaleira L A. Response surface methodology (RSM) as a tool for optimization in analytical chemistry. Talanta, 2008, 76(5): 965–977

[27] Dong Y, Georgakis C, Mustakis J, Lu H, McMullen J P. Optimization of pharmaceutical reactions using the dynamic response surface methodology. Computers & Chemical Engineering, 2020, 135: 106778

Acknowledgments

Yachao Dong is grateful for the financial support of Fundamental Research Funds for the Central Universities (Grant No. DUT20RC(3)070).

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2021 Higher Education Press