Robust design multiple responses modeling and ...

Robust design multiple responses modeling and optimization for microemulsion-based hydrogel formulation Tuan-Ho Le*, Sangmun Shin*(a), Yonghee Lee**, Seong Hoon Jeong*** & Sittichai Kaewkuekool**** Department of Industrial & Management Systems Engineering, Dong-A University, Busan, 604-714, Republic of Korea E-Mail: [email protected], [email protected] ** Co-won Nuclear Engineering Center, Co-Won Co. Ltd, Busan 604-714, Republic of Korea E-Mail: [email protected] *** College of Pharmacy, Dongguk University-Seoul, Goyang, Gyeonggi 410-820, Republic of Korea E-Mail: [email protected] **** Department of Production Technology Education, King Mongkut's University of Technology Thonburi, Bangkok 10140, Thailand E-Mail: [email protected]

*

The corresponding author: Sangmun Shin*(a). Tel.:+82 51 200 7688; fax: +82 51 200 7697

Abstract- Based on the robust design (RD) principle proposed by Taguchi, the primary objective of this paper is to develop a strategy in order to obtain a safe and effective medication in the drug development program by using three sequential steps, i.e. the design of experiments, estimation, and optimization. Firstly, the extreme vertices mixture design is experimentally conducted for the formulation of microemulsion-based hydrogel. Secondly, the response surface methodology-based quartic models are proposed to estimate the multiple output responses as functions of the input factors. Finally, a new RD optimization model consisting of weighted-sum model and epsilon-constrained method is proposed to consider the trade-off between multiple responses based on the mean squared error criterion and the boundary specification on the process bias. The final results showed that a number of efficient solutions can be achieved in order to find the optimal formulation of microemulsion-based hydrogel. Keywords-Robust design; microemulsion-based hydrogel; multiple responses optimization; weighted sum model; epsilon-constrained method. Abbreviations-Robust design (RD); response surface methodology (RSM); mean squared error (MSE); design of experiments (DoE).

I. INTRODUCTION Robust design is often identified as one of the most powerful methodologies for quality improvement purposes among the design methods currently studied in the engineering community. Since introduced by Taguchi in 1986, RD consists of two basic steps based on experimental design and two steps model for analysis of the resulting data. Unfortunately, the technique proposed by Taguchi to solve the RD problem was criticized about the assumptions, experiment design and statistical analysis by Leon et al. (1987), Box et al. (1998), and Nair (1992). Based on RSM, Vining and Myers (1990)

proposed the dual responses approach where the process mean and process variance are estimated as two separate functions of input factors by using least squares method (LSM). In addition, the dual responses approach can be seen as an alternative way to achieve the optimal solutions. From this proposal, the principal procedure of RD is generated and used up to now with three sequential stages, such as experimental design, estimation, and optimization to obtain the optimal factor settings. In terms of optimization, the variance is minimized as the process mean is kept at the desired target value in the dual responses approach. However, the process bias (i.e. the absolute value of the process mean and the target value) and process variance are not minimized simultaneously in the dual responses approach. Therefore, Lin and Tu (1995) proposed the MSE model where the process bias and process variance are simultaneously minimized. Cho et al. (1996), Koksoy and Doganaksoy (2003), and Ding et al. (2004) introduced the weighted sum model to consider the trade-off between the process bias and process variance. The customers’ preference in terms of tolerance and specification of an upper boundary on bias is integrated in the bias specified model based on the ε-constraint method proposed by Shin and Cho (2005, 2006). In addition, Shin et al. (2011) attempted to customize current RD methods for a pharmaceutical experimental design problem in order to obtain optimal drug formulations. The trade-off problem as well as the specification of the boundary of the responses problem is considered in Le et al. (2014) in the pharmaceutical environment. The pharmaceutical industry is facing numerous of challenges such as the demands of competition, the strict regulation of new drugs development process as well as the careful control of the Food and Drug Administration (FDA) over the quality of these products (Peterson et al., 2009). The development of a new drug is conducted and examined closely in the laboratory experiments environment before it can be applied to animal or human subjects. However, determining the better approaches in obtaining the optimal drug formulations is still the considerable challenge to the researchers. By definition, the drug formulations are the mixture of many components. In the early stage of the drug development, the mixture design techniques determine largely the quality of the pharmaceutical products. In addition, a scientific approach is required to illustrate the output quality characteristics of the drug formulations as the functional relationships of the input proportions. Moreover, the trade-off between multiple output quality characteristics of drug formulations and the boundary specifications of responses are also the noticeable problems in order to identify the optimal formulations. Therefore, the primary objective of this paper is to develop a systematic procedure to identify the optimal solution of drug formulations based on three sequential stages, i.e., the experimental designs, model parameter estimation, and optimization. Firstly, a mixture design based on extreme vertices design is implemented to investigate the information between the control factors and the output

responses. Secondly, the multiple output responses are estimated as the full quartic functions of the input variables, instead of normal quadratic form in most researches in the literature. Thirdly, the MSE is utilized as a comparative criterion between multiple responses. An alternative RD optimization model based on the combination of the weighted sum model and the epsilon-constrained method is proposed to identify the optimal drug formulations. A pharmaceutical case study with microemulsion-based hydrogel formulation is provided and solved using MINITAB and MATLAB software packages to illustrate the purpose of the proposed optimization model. An overview of the proposed RD method is illustrated in Figure 1. DoE

Estimation

Optimization Response 1

Input variables

Optimal solutions

Response n

Figure 1: An overview of the proposed RD method

II. MODEL DEVELOPMENT 2.1. Design of experiments Design of experiments (DoE) is an efficient, structured, and planned statistical method to conduct experiments so that the input and output variables can be analyzed to yield the necessary information. The choosing the DoE methods requires careful consideration of several consideration before actually doing the experiment such as the number of factors, the levels of factors, and the relevance of interactions between factors. The proportions within the mixture, not the amount of their components, are often considered in the mixture designs. Therefore, the proportions of all ingredients in the mixture must sum to 100%, as illustrated by the equation ∑     ⋯    1, where   0 for all

 1, … , . There are three standard design techniques in the mixture designs, i.e., simplex-lattice, simplex-centroid, and extreme vertices designs. As there are both upper and lower bound constraints on the components, the extreme vertices designs are often used to conduct the experimental designs for the mixture problems. The extreme vertices for two three-component designs with both upper and lower constraints are displayed in Figure 2. The associated experimental format is shown in Table 1 in which , and  represent the vector of control variables, mean and standard deviation of replicated ,  responses, respectively.

Figure 2: The extreme vertices design for two different three-component designs with both upper and lower constraints Table 1: Experimental format Response

Control factors x Runs



…

Replications



 







s

…





s

…

…

…

…

…



…





s



…





…



… n

1 2 Design matrix

2.2. Estimation Normally, the functional relationship between the output response and the input variables is often not known, but can be modeled by some methodologies with a suitable degree of accuracy. RSM is used as the most popular approach to model the functional between the input and output factors. The main idea of RSM is to use a sequence of designed experiments to obtain optimal responses by estimating input-response functional forms when the exact functional relationships are not known or very complicated (Box and Draper (1987); Khuri and Cornell (1987); Myers and Montgomery (2002)). Based on the RSM, the functional relationship between the response  and the control factors can be represented as     

(1)

where  is a vector of control factors,  is a column vector of model parameters, and  is the random errors. The model parameters  are often estimated by LSM as  

!

"#

!

.

(2)

The model parameters of mean and standard deviation functions are estimated as follows: &%   

'

"#

&)   

*

"#+ *

'

(

(3)

.

(4)

Normally, the quadratic response surface functions are used in most RD problems. However, the full quartic polynomial functions are proposed to conduct the functional relationships between the input and output factors due to the coefficient of determination , of the data in the case study.

2.3. Optimization In pharmaceutical industry, quality characteristics of drug products such as pH, viscosity, and particle size are often considered simultaneously. The MSE is used as a comparative criterion in this study and the MSE of each quality characteristics can be calculated as follows: 

MSE0  12̂ 0 " − 50 6  780 ".

(5)

However, these output responses are often conflicted in the real situations. Therefore, the trade-off between these responses needs to be considered through the preference information from a human decision maker’s opinions. The weighted sum model is suitable to perform that problem. The weight of each response can be chosen based on their relative importance in the problems. Another issue in the pharmaceutical case study is that the environment of the reaction of the compounds in the drug (pH), viscosity, and the particle size must be in a specific limitation on the bias. Both these issues can be solved in the hybrid model to find the robust optimal solutions (i.e., the optimal factor settings, x*). Generally, the RD hybrid optimization model can be performed as follows: Minimize ∑:0 90 MSE0 " Subject to ;2̂ 0 " − 50 ; ≤ =0 for all >  1, … , ?

780 " ≤ @0 ∑:0 90  1 ∈B where

(6)

90 denotes the qth weight, =0 is the qth upper level of the qth constraint on the bias function, @0 is the qth upper level of the qth constraint on the standard deviation function, MSE0 " is the mean squared error for the qth response.

III. CASE STUDY Evaluations of the formulations are conducted whiling considering three input control factors (i.e., benzyl alcohol, polyoxyl 35, and DGM) and eight fixed factors (i.e., itraconazole, povidone K17, isoprophyl alcohol, D-Limonene, colloidal silicone, methyl paraben, propylparaben, and water). In Le et al. (21014), two output responses the pH and particle size are considered. However, three output responses, i.e., the pH, viscosity, and particle size are considered and assumed to depend only on the relative proportions of the three ingredients in the mixture design of this study. The proportions of these ingredients must be summed to 100%. In the attempt to analyze the formulations of microemulsion-based hydrogel, the environment to break up the compounds in the drug must be examined and be tested closely. Therefore, the pH values

( ) must be repeated many times (replication) and the bias as well as the standard deviation must be lie in the tight specification. In addition, the viscosity ( ) as well as the particle size of drug (C ) is a significantly important factor which is also in a stringent bound. The required specifications are:




The target value, the maximum allowable bias, and the maximum allowable response standard deviation of the pH are 6.19, 0.15, and 0.1, respectively.




The target value, the maximum allowable bias, and the maximum allowable response standard deviation of the viscosity are 1140, 70, and 2.236, respectively.




The target value and the maximum allowable bias of the particle size are 75.00 and 1.5, respectively.

The total amount of three control factors always equals 80, and the bound values for  are in the range [15, 25], while the bound values for both  and C are in the same range [25, 35]. Based on these conditions, the extreme vertices mixture design is used to conduct the experimental design. By using MINITAB software package, the extreme vertices mixture design with 19 experimental runs, the replications of the each response as well as the corresponding mean and standard deviation of each response are demonstrated in Table 2. Table 2: The extreme vertices design for the control factors Control factors

Responses





C

1

25

25

2

15

3

 (103, cp)



Runs

C





C

 

D





C

 

D

(nm)

30

6.44

6.48

6.45

6.4567

0.0208

471

557

698

575.33

114.61

28.37

35

30

6.50

6.52

6.54

6.5200

0.0200

646

775

743

721.33

67.17

128.47

20

25

35

6.68

6.69

6.70

6.6900

0.0100

356

450

432

412.67

49.89

253.41

4

15

30

35

6.50

6.51

6.52

6.5100

0.0100

451

574

521

515.33

61.70

98.22

5

20

35

25

6.49

6.44

6.45

6.4600

0.0265

370

335

361

355.33

18.18

490.93

6

25

30

25

6.64

6.64

6.63

6.6367

0.0058

367

480

400

415.67

58.11

502.00

7

15

32.5

32.5

6.42

6.41

6.43

6.4200

0.0100

382

435

403

406.67

26.69

212.41

8

22.5

25

32.5

6.52

6.51

6.52

6.5167

0.0058

692

884

890

822.00

112.62

128.60

9

22.5

32.5

25

6.43

6.44

6.47

6.4467

0.0208

453

432

401

428.67

26.16

261.73

10

25

27.5

27.5

6.63

6.63

6.65

6.6367

0.0116

403

495

525

474.33

63.57

292.69

11

17.5

35

27.5

6.57

6.59

6.58

6.5800

0.0100

854

984

1060

966.00

104.17

262.59

12

17.5

27.5

35

6.46

6.46

6.46

6.4600

0.0000

540

654

591

595.00

57.11

49.29

13

20

30

30

6.57

6.58

6.57

6.5733

0.0058

520

601

589

570.00

43.71

5.46

14

22.5

27.5

30

6.46

6.48

6.47

6.4700

0.0100

820

957

970

915.67

83.10

190.31

15

17.5

32.5

30

6.49

6.50

6.49

6.4933

0.0058

518

531

523

524.00

6.56

126.45

16

20

27.5

35.5

6.50

6.51

6.52

6.5100

0.0100

503

634

659

598.67

83.79

140.09

17

17.5

30

32.5

6.52

6.51

6.51

6.5133

0.0058

382

493

459

444.67

56.87

308.40

18

20

32.5

27.5

6.46

6.50

6.48

6.4800

0.0200

731

889

946

855.33

111.38

57.71

19

22.5

30

27.5

6.47

6.48

6.47

6.4733

0.0058

358

334

362

351.33

15.14

62.76

Based on the data in Table 2, the model parameters of the mean and standard deviation functions of responses  and  and the model parameters of the function of response C can be estimated by using Equations (2), (3), and (4). The estimated mean and standard deviations functions of responses

 and  and the estimated function of response C can be represented respectively as follows: &   "  46.8822  25.0460  10.2013C −1.7261  − 1.2891 C − 0.8542 C − 0.0026   −  " − 0.0121 C  − C " − 0.0051 C  − C "  0.0005  C  0.0006  C  0.0000  C − 0.0001   −  " − 0.0001 C  − C " − 0.0001 C  − C " ,  86.96% DN "  7.5846 − 1.1715 − 0.1005C − 0.1577  − 0.1876 C  0.0366 C − 0.0024   −  " − 0.0017 C  − C "  0.0004 C  − C "  0.0001  C − 0.0000  C  0.0000  C − 0.0000   −  " − 0.0000 C  − C "  0.0000 C  − C " ,  89.59% &   "  3219.3 − 110650 − 18042C  2837.4  − 285.7 C  3225.1 C − 19.463   −  " − 5.6002 C  − C "  25.002 C  − C " − 0.11481  C − 1.6457  C  0.25407  C  0.34162   −  " − 0.24745 C  − C "  0.49789 C  − C " ,  85.22% DN "  29443 − 12422 − 17567C − 479.31  − 325.31 C  766.61 C − 8.9221   −  " − 11.543 C  − C " − 1.7438 C  − C "  0.33437  C − 0.03873 C − 0.21295  C − 0.028766   −  " − 0.031062 C  − C "  0.1141 C  − C " ,  83.17%  P"  −59210  17742 − 1735.7C  1008.8   1464.7 C − 440.88 C C  19.705   −  "  7.5786 C  − C " − 6.6539 C  − C " − 0.42878  C  0.21437  C − 0.36503  C  0.16503   −  "  0.10482 C  − C " − 0.11853 C  − C " ,   93.36%. All coefficients of determination ,  of the estimated functions over 80 % show the reliable and efficient estimation results. The proposed RD optimization model for this study can be specified as follows: Minimize   9 MSE  9 MSE  9C MSEC

& " − 5 | ≤ RSTU Subject to |  DN " ≤ @ & " − 5 | ≤ RSTU |  DN " ≤ @ | P" − 5C | ≤ CRSTU C where 5 = 6.19, RSTU = 0.15, @ = 0.1, 5 = 1140, RSTU = 70, @ = 2.236, 5C = 75,

CRSTU = 1.5, MSE  2̂  " − 5 "  78 " , MSE  2̂  " − 5 "  78 " , and MSEC  2̂ C " − 5C "  78C ". Using MATLAB software, the proposed RD optimization model can automatically generate a number of optimal factor settings  ,  , C " based on the given weights 9 , 9 , and 9C . The efficient solutions for the pH value MSE , viscosity MSE , and particle size MSEC with different weights obtained from the RD hybrid model are shown in Table 3. The efficient Pareto solutions are drawn in the objective space with each pairs MSE values of each response, as shown in Figure 3. Table 3: The optimal solutions with different weights

9

9

9C





C

MSE

MSE

MSEC

MSE

0.97

0.01

0.02

17.039

32.996

29.972

0.047006

32585

8492.2

495.74

0.85

0.05

0.1

17.056

32.661

30.291

0.044539

56257

10635

3876.4

0.73

0.09

0.18

17.039

32.996

29.972

0.047002

32613

8491.4

4463.6

0.61

0.13

0.26

17.053

32.807

30.147

0.045932

45565

9549.9

8406.5

0.49

0.17

0.34

17.039

32.995

29.972

0.047001

32622

8491.2

8432.7

0.37

0.21

0.42

17.056

32.66

30.291

0.044538

56287

10635

16287

0.25

0.25

0.5

17.056

32.66

30.291

0.044538

56287

10635

19389

0.13

0.29

0.58

17.04

33.027

29.941

0.047469

31156

8315.1

13858

0.01

0.33

0.66

17.073

32.325

30.61

0.042512

87231

13462

37671

4

9

x 10

8

MSE2 value

7 6 5 4 3 2 0.042

0.043

0.044

0.045 0.046 MSE1 value

0.047

0.048

0.049

4

1.4

x 10

1.3

MSE3 value

1.2 1.1 1 0.9 0.8 0.7 0.042

1.4

x 10

0.043

0.044

3

4

0.045 0.046 MSE1 value

0.047

0.048

7

8

0.049

4

1.3

MSE2 value

1.2 1.1 1 0.9 0.8 0.7 2

5

6 MSE1 value

9 x 10

Figure 3: Pareto frontier using the proposed hybrid optimization model

4

The MATLAB program codes for solving the proposed RD hybrid optimization model can automatically generate a number of Pareto solutions and Pareto frontier based on the given weights 9 ,

9 , and 9C . By considering the trade-off between three responses while changing the weights from 0.0 to 1.0, the proposed method can generate all the efficient solutions in the entire region.

IV. CONCLUSION Determining the optimal settings of control factors in order to improve a product/process quality is often the challenge to the manufacturing engineering, especially the pharmaceutical industry. The problem can be solved efficiently by using the robust design principle. In this study, the extreme vertices designs are conducted because of the upper and lower constraints on the control factors. Then, the statistical tool RSM is used to perform the functional relationship between the multiple quality characteristics of the microemulsion-based hydrogel formulation and its input factors. By using MATLAB software package, the full quartic response functions are used with significant reliability. In addition, the trade-off problem between the multiple conflicted responses and the boundary specifications on the bias as well as the standard deviation can be solved efficiently by using the proposed RD hybrid model. For further extension, the correlations between multiple quality characteristics of the microemulsion-based hydrogel formulation can be investigated. Moreover, the multiple responses can be transformed into the same scale to consider the trade-off between them. Acknowledgement This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (20120683). References [1] G. Taguchi (1986), “Introduction to Quality Engineering” UNIPUB/Kraus International, White Plains, New York, USA. [2] G. E. P. Box & N. R. Draper (1987), “Empirical model-building and response surfaces (Wiley Series in Probability and Statistics)”, John Wiley & son., New York. [3] A. I. Khuri & J. A. Cornell (1987), “Response surface: Design and analyses”. Marcel Dekker, New York. [4] R. V. Leon, A. C. Shoemaker, & R. N. Kackar (1987), “Performance measures independent of adjustment: An explanation and extension of Taguchi signal-to-noise ratio”, Technometrics, Vol. 29, Pp. 253-285.

[5] G. Box, S. Bisgaard, & C. Fung (1988), “An explanation and critique of Taguchi’s contribution to quality engineering”, Quality and Reliability Engineering International, Vol. 30, Pp. 123-131. [6] G. G. Vining & R. H. Myers (1990), “Combining Taguchi and response surface philosophies: A dual response approach” Journal of Quality Technology, Vol. 22, Pp. 38-45. [7] V. N. Nair (1992), “Taguchi's parameter design: A panel discussion”, Technometrics, Vol. 34, Pp. 127-161. [8] D. K. J. Lin & W. Tu (1995), “Dual response surface optimization”, Journal of Quality Technology, Vol. 27, Pp. 34-39. [9] B. R. Cho, M. D, Philips, & K. C. Kapur (1996), “Quality improvement by RSM modeling for robust design”, The 5th Industrial Engineering Research Conference, Minneapolis, Pp. 650-655. [10] R. H, Myers & D. C. Montgomery (2002), “Response surface methodology: process and product optimization using designed experiments”, John Wiley & son.,.2nd ed., New York. [11] O. Koksoy & N. Doganaksoy (2003), “Joint optimization of mean and standard deviation using response surface methods”, Journal of Quality Technology, Vol. 35, Pp. 239-252. [12] R. Ding, D. K. J. Lin, & D. Wei, (2004), “Dual response surface optimization: A weighted MSE approach”, Quality engineering, Vol. 16, No. 3, Pp. 377-385. [13] S. Shin & B. R. Cho (2005), “Bias-specified robust design optimization and analytical solutions”, Computers & Industrial Engineering, Vol. 48, Pp. 129-148. [14] S. Shin & B. R. Cho (2006), “Robust design models for customer specified bounds on process parameters”, Journal of Systems Science and Systems Engineering, Vol. 15, No. 1, Pp. 2-18. [15] J. J. Peterson, R. D. Snee, P. R. McAllIster, T. L. Schofield, & A. J. Carella (2009), “Statistics in pharmaceutical development and manufacturing”, Journal of Quality Technology, Vol. 41, Pp. 111-132. [16] S. Shin, D. H. Choi, N. K. V. Truong, N. A. Kim, N. A. Chu, & S. H. Jeong (2011), “Time-oriented experimental design method to optimize hydrophilic matrix formulations with gelation kinetics and drug release profiles” International Journal of Pharmaceutics, Vol. 407, No. 1-2, Pp. 53-62. [17] T. H. Le, S. Shin, Y. H. Lee, S. H. Jeong & K. Sittichai (2014), “Development of a robust design hybrid optimization model for formulations of microemulsion-based hydrogel”, 2014 Bangkok International Conference on Biological Engineering & Natural Science (BBENS), BENS-1006.

Le Tuan-Ho. Le Tuan-Ho is a PhD student at the Department of Industrial & Management Systems Engineering at Dong-A University, Korea. He holds a Master of Electrical Engineering from Hanoi University of Science and Technology, Vietnam and Bachelor of Electrical Engineering from Danang

University of Technology, Vietnam. Before joining PhD program, he was a Lecturer at Quy Nhon University, Vietnam. His research interests are robust design, tolerance design, pharmaceutical quality by design, neural network, estimation, multi-objective optimization, and applied statistics. Sangmun Shin. Sangmun Shin is an Associate Professor at the Department of Industrial & Management Systems Engineering, the head of Artificial-intelligent Plant Integrated Design (APID) Institute, and the Director of the Quality Engineering Laboratory at Dong-a University, South Korea. He received his MS and PhD in Industrial Engineering from the Clemson University, USA. His research interests include quality engineering, robust and tolerance designs, multi-objective optimization and pharmaceutical process design. He received his Career Development Research Award from the Korea Research Foundation. He currently serves on the editorial board of both International Journal of Quality Engineering and Technology and International Journal of Experimental Design and Process Optimization. He is a member of IIE and Alpha Pi Mu. He has been registered by a biographical dictionary (Marquis Who's Who in the World) from 2010. Yonghee Lee. Yonghee Lee is the president of Co-won LTD. He received his MS and PhD in Industrial & Systems Engineering from Dong-a University, Republic of Korea. He had been worked in Instrument & Control Division at Korea Atomic Energy Research (KAERI) Institute for five years. His research interests include quality and safety engineering, nuclear safety review, human error, safety culture, human factors suitability, workstation design, green logistics, universal design and instrument & control human factors. Seong Hoon Jeong. Seong Hoon Jeong is an Assistant Professor at the College of Pharmacy, Dongguk University, South Korea. He received his PhD in Industrial & Physical Pharmacy from Purdue University, USA. After he worked for Pfizer Global R&D Center (previously Wyeth Research) as a Senior Research Scientist, he joined the College of Pharmacy, Pusan National University as an Assistant Professor. His research interests include design of experiment regarding the pharmaceutical development, preformulation and formulation development, and analytical method development. He currently serves on the editorial board of the Journal of Pharmaceutical Investigation. He is the member of Rho Chi Societh. Sittichai Kaewkuekool. Sittichai Kaewkuekool is Dean of Faculty of Industrial Education and Technology and Associate Professor at Department of Production Technology, King Mongkut’s University of Technology Thonburi, Bangkok Thailand. He received his MS in University of Miami, Miami, FL. MS degree in Industrial Engineering and PhD in Industrial Engineering from the Clemson University, USA. His research interests include human factors engineering, man-machine interface, and Logistics.