A New Attempt To Solve the Scale-Up Problem for Granulation Using Response Surface Methodology

A New Attempt To Solve the Scale-Up Problem for Granulation Using Response Surface Methodology SHIGEO OGAWA',TOSHIHIKO KAMIJIMA',YOUSUKEMIYAMOTO',MASAHARUMIYAJIMA'~, HIROSHI SATO',

Kozo TAKAYAMA~, AND TSUNEJINAGAI~ Received March 12, 1993, from the 'Central Research Laboratories, Zerh pharmaceutical Co., Ltd., 25 12-1 Oshikiri, Konan-machi, Osato-gun, Saitama 360-0 1, Japan, and tDepartment of Pharmceutics, Hoshi University, Ebara 2-4-4 1, Shlnagawa-ku, Accepted for publication July 8, 1993". Tokyo 142, Japan.

Theoretical Section

Abstract 0 Scale-up from lab to production is always problematic for

the development of pharmaceuticals. In granulation, an optimal formulationof binder solution determined in a lab scale is often different than that in a production scale. A new mathematical procedure to solve this scale-up problem is assessed. Granules were prepared in the two manufacturing scales (2- and 5-kg scale) by using a highspeed mixer granulator. In the manufacturing process, the binder soiution plays an essentialrole in the formation of granules with desired physical properties, in close conformity with the manufacturing scale. A computerized optimizing technique based on a response surface methodology was developed to study the scale-up problem in the manufacturing of granules. For this purpose, a new mathematical function was introduced for the first time, which is namely an integrated optimization function. A universal optimal formulation unaffected by manufacturing scale could be obtalned by minimlzlng the integrated optimization function. Predicted values such as yield, mean granule size,and uniformity of granule size agreed well with experimental ones

on both scales. Furthermore, the optimized characteristicsmeasured at the production scalecoincided well with those obtainedat laboratory scale,suggesting that this approach could be very useful in minimizing scale-up problems. Inconsistencies in the pharmaceutical characteristics of a product between the laboratory and production scales have frequently been Such inconsistencies are mainly considered to be caused by the variability of raw materials and equipment differences. Many studies have been done so far on resolving this problem,= but due to its complexity there has been no report on a standard or simple method. Recently, a computerized optimizing technique based on a response surface methodology has been applied to obtain the optimal formulation of pharmaceuticals.'-17 For example, Shirakura et al. used this technique to select the best formulation of binder solution in the granulation process, in which physical properties such as particle size distribution is markedly affected by the binder solution.18 In overall design of pharmaceutical dosage form, the simultaneous optimization of severalproperties is indispensable. Takayama et al. introduced the generalized distance function to deal with this type optimization in the formulation of gel ointment of ketoprofen.19 However, simultaneous optimal formulation obtained on an experimental scale is likely to change on another scale, so a new approach is required to manage this type of scale-up problem in the optimization process. In the present study, an integrated optimization function was introduced in order to seek the universal optimal formulation of binder solution which is used in the granulation process and which is not affectedby manufacturing scale. Physical properties evaluated here are the yield of granules within a certain size range, mean granule size, and uniformity of granule size. _

_

_

_

_

~

Abstract published in Advance ACS Abstracts, December 15,1993.

0 1994. Americen Chemical S~C@Vand American pharmaceuticai Assoclation

The mathematical method used to investigate pharmaceutical optimization problem is described to minimize the objective function under a set of constraints. In the case of simultaneous optimization for several objectives, response variables should be incorporated into a single function such as a multiobjective function. Recently, Takayama et al.introduced the generalized distance function, S(X), so as to incorporate several objectives into a single function,'g as follows: S(X) = [Clwi(FDi(X)- FOi(X)]r]'/P g=l

where wi is the weighting coefficient, FDi(X) is the optimum value of each objective function optimized individually over the experimental region, and FOi(X) is the simultaneous optimum value of each objective function; p is a parameter relating to the impartiality among the response variables QI 1 1). The effectivenessof the introduction of this parameter on eq 1is well described in their paper. In the present study, the same type of function was used as a multiobjective function and l/FDi(X) was adopted as wi. Then, two generalized distance functions, SS(X) and SL(X) obtained in small scale (2 kg) and large scale (5 kg), respectively, were again combined into an integrated optimization function, T(X), as defined in eq 2. At this time, a penalty function defined in eq 3, PN(X), was added to T(X). This penalty function works to minimize the difference between each response value in two manufacturing scales.where FSi(X)

T(X) = SS(X) + SL(X) + PN(X)

(2)

n

PN(X) = [Elmi(FSi(X)- FLi(X))r]"P

(3)

Fl

and FLi(X) are the objective functions for small and large scale, respectively. As a weighting coefficient, wi, in eq 3, the reciprocal of the mean of FS(X) and FL(X) was employed. Thus, universal optimization not affected by manufacturing scale is completed by seeking the minimum value of T(X).

Experimental Section Material-Crystalline cellulose, marketed as Avicei PH 101, was purchased from Asahi Kasei Industries, Co., Ltd., Japan. (Hydroxypropy1)cellulose(W-P)was obtainedfromShinetau ChemicalCo., La., Japan. Ascorbic acid (J.P. grade) was purchased from Daiichi Seiyaku Co., Ltd., Japan. Lactose and cornstarch were purchased from De Melkindustrie Veghel bv, Netherlands, and Nihon Shokuhin Kako Co., Ltd., Japan, respectively. Other chemicals used were of reagent grade. Equipment-High-speed mixer granulators (VG-10,VG-25, and VG100,Powrex Co.,Ltd.) were used to prepare granules at 2-, 5-, and 20-kg scales. The 2- and 5-kg scales were regarded as small scale and large scale, respectively. VG-100 was used for the study of production scale in which the applicability of the universal optimal formulation obtained

0022-3549/94/120O-439$04.50/0

Journal of Phannsceutical Sciences / 439 Vd. 83. No. 3. March 1994

Table I-OperationaI CondHlons when Preparlng Granules High-speed Mixer Granulator Condition

VGlO

VG25

VGlOO

Amount of powder (kg) Blade rotation speed (rpm) Cross-screw rotation speed (rpm) Mixing time (minutes) Granulation time (minutes)

2 450 1450

5 300 1450

20 200 1450

3 10

3 10

3 10

Condition

Fluid-bed Dryer (FLO-5) 70 55 15

Drying air temperature ("C) Exhaust air temperature ("C) Drying time (minutes)

of Granule and Manufacturlng Scale

Table 2-Formulatlon Ingredient

W/W (%) VG10 (g) VG25 (9) VGlOO (9)

Ascorbic acid Lactose Cornstarch Crystalline cellulose (Hydroxypropyi)cellulose total

28.0 45.6 19.6 3.9 2.9

560.0 912.0 392.0 78.0 58.0

1400.0 2280.0 980.0 195.0 145.0

5600.0 9120.0 3920.0 780.0 580.0

100.0

2000.0

5000.0

20000.0

Table 4-Experhnental Detslgn and Obtalned Values of Three Response Varlables (Y,, Y,, and Y,) Formulation No.

Xf

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

1 1 -1 -1 0

d: 0 -42 0 1 1 -1 -1 0

d: 0 -d2 0

20

X2b

F

Yl*(%)

Yzd(pm)

Y3'

1 -1 1 -1 0 0 0 4 2 0 -42 1 -1 1 -1

-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1

88.3 98.0 63.6 93.0 86.2 86.5 82.9 88.5 77.3 88.7 87.1 93.0 45.7 89.9 93.3 92.5 87.0 80.8 52.7 91.5

193.8 142.9 290.8 188.6 155.8 165.2 143.1 205.7 269.0 151.9 241.5 170.2 392.2 254.4

2.4 3.7 1.9 2.3 3.3 3.1 4.2 2.5 1.9 3.3 2.1 2.7 1.7 2.0

230.2

2.2

246.5 164.2 282.4 320.0 175.7

2.1 3.5 2.0 2.2 2.8

0 0

d: 0 -42

a Volume percent of ethanol in binder solution (%). Total volume of binder solution (mL). Manufacturing scale. Yield of granule. Geometrical mean size. Geometrical standard deviation.

equipped withsieves. On the basis of the results, the cumulative residual % weight (F(d))left on the mesh size ( d )was plotted against the mesh size according to the log-normal distribution equation (eq 4):

Table 3-Level of Independent Varlables ( XI and X,) In Physlcal UnHs Level in Coded Form Independentvariable Xld (%)

XZb(2-kgscale, mL) XZb(5-kgscale,mL)

-42

-1

0

1

d 2

8 288 720

20 300 750

50 330 825

80 360 900

92 372 930

a Volume percent of ethanol in binder solution. Total volume of binder solution used in the process.

was evaluated. Operational conditions of those three machines are summarized in Table 1. The blade rotation of the three machines was adjusted to the same lap speed. Granules were dried by using a fluidbed dryer (FLO-5; Freund Industry, Ltd.) under the operational conditions shown in Table 1. A vibrating shaker (Electromag; Itoh Co., Ltd.) equipped with sieves (size 1000,500,355,250,180,150,106, and 75 pm) was used to measure the granules size distribution. Granule Preparation-All ingredients in the granule formulation shown in Table 2 were mixed for 5 min in each high-speed mixer granulator. Binder solution was then added to this powder mixture, followed by granulation for 10 min. Wet granules were then dried in a fluid-bed dryer for 15 min at 70 "C air temperature. Volume percent [ X I ;X . / ( X , + X.)] of ethanol (X,) in the binder solution [mixture of ethanol (X.)and water (X,)]used in the process and total volume (XZ; X, + X.) were selected as independent variables for the evaluation of the effect of binder solution on physical properties of granules. Those independent variables are represented as the coded form shown in Table 3. Yield of granule (Yl), geometrical mean size (Yz),and geometrical standard deviation (Y3) as an index of the uniformity of granule size were employed as response variables because they were considered the critical physical properties for granule quality. A total of 10 experiments for each scale (2 and 5 kg) were performed to obtain the regression function of each response variable according to the spherical central composite experimental design (Table 4L20 Manufacturing scale was also coded as Z = -1 for 2-kg scale and 2 = 1 for 5-kg scale. Granule Size Dietribution-The weight distribution of 20 g of granules was measured after 10 min of vibration in the vibrating shaker 440 /Journal of pharmaceutical Sciences Vol. 83. No. 3,March 1994

log2ag =

7

(Nlog d - log &I2)

(5)

c n where dg is geometrical mean size obtained as the granule size equivalent to 50% of F(d) on that plot and ug is given as the slope of the plots of F ( d )versus d and dg is geometrical standard deviation (ug) of granule size calculated from eq 6.21 a diameter of granule equivalent to 84% of F(d) (6) a diameter of granule equivalent to 50 % of F(d) Yield-Yield was determined as percent of granules in the size range of 75 to 150 pm. Prediction of Response Variables-Response variables were predicted by using the following second-order polynomial equation: ug =

Y = b,

+

$

b,Xi

+

$1

b,jXiXi

+ b,$ +

where Y is the response variable, b is the regression coefficient, and X and Z are the independent variable and scale factor in coded forms, respectively.

Results and Discussion Granule Size Distribution-The size distribution of granules could be described well by the log-normal distribution equation. As an example, the plot of granules obtained at XI = 1,Xz = -1, and 2 = -1 is shown in Figure 1. Good linearity

fE

99

1 l

Mesh size (pm)

Flgure 1-Plot of cumulative resldual % weight (40)) left on the mesh size (d) versus fhe mesh ske at Xl = 1, X, = -1, and Z = -1.

Table 5-Opttmum Regression Equation for Three Response Varlables Regression Coefficient Value

boo (constant) bol CXlO) bo2 o(27

boll (X12)

(XlX2) bo22 (x22) bio CZr, bii (XiZ) b12 (X2Z) bill (Xi2Z) biiz (XiX2Z) b122 (X22Z) P bo12

85.4 7.48 -5.85 -3.30 8.63

163 -42.2 30.6 30.5

I I

33.8 38.9

4.15 -2.30 -2.38

I I

I I 0.949 0.791 6.33 9.4ak

3 h

5J

Fd

I

-11.4 10.6 -7.85 0.978 0.896 31.4 8.8gk

2.70 0.506 -0.306

I -0.150 -0.136 -0.382 -0.138

I 0.146

I I 0.921 0.678 0.344 9.53k

Yield of granule (%). b Geometricalmean size bm). Geometrical standard deviation. Volume percent of ethanol In binder solution. Total volume of binder solution. Manufacturing scale. 0 Multiple correlation coefficient. Doubly adjusted 8 with degrees of freedom. Standard deviation. Observed F value. p < 0.01. 'This factor is not included in the optimum regression equation.

*

was observed between F(d) and d . From this figure, the values of ug and dg were calculated as 3.7 and 143 pm, respectively. Yield of this sample was found to be 87%. Experimental values of all response variables are summarized in Table 4. As is evident from Table 4, all three physical properties were significantly influenced not only by the formulation of binder solution but also by manufacturing scale. Cutt et al. have also reported that the compressibility of granules is affected by the formulation of binder s o l ~ t i o n . ~ ~ ~ ~ ~ Regression Analysis-All combinations of independent variables were investigated to find the optimal regression equation for each response variable. The coefficient of determination doubly adjusted with degrees of freedom was employed as a judgment standard for the optimal regression equation.% The regression coefficients of such equations composed of a combination of statistically significant independent variables are shown in Table 5. The values of multiple correlation coefficient,r, were high enough to predict each response variable accurately. Contour Diagram-On the basis of the optimal regression equation, the contour diagrams for yield, mean granule size, and the uniformity of granule size are illustrated in Figures 2,3, and 4 respectively,as functions of XI,Xz,and 2 under the restriction of experimental region (XI2+ X22 5 2). In order to describe the movement of the response variables accompanying the change of scale factor (Z)the , contour diagram at 2 = 0 was also added to these figures although experiments were not conducted at 2 = 0. The formulation of binder solution affected each response variable differently. The granule yield value tended to be higher with the increase in the volume of binder solution used and in the ratio of ethanol in it. The area for not less than 90% and less than 80% were extended according to the increase of manufacturing scale. On the other hand, mean granule size became larger with the decrease in the ratio of ethanol and the increase in volume. The area with large size granules in the contour diagram was reduced according to the increase of scale. The uniformity of granule size at small scale (2= -1) was raised as an increase in the ratio of water. An increase in both the volume of binder solution used and the ratio of water in it improved the uniformity at large scale (2= 1). These changes of contour diagram with manufacturing scale were considered mainly attributable to the pressure which was brought about by the increase of the weight of powders used according to the increase of scale. Mathematical Optimization-The generalized distance functions for each scale were obtained by combiningthe optimal regression equations for each response variable as an objective

Yield of granule (Y 1) n N

8

F

at Z = - 1

at Z = O

at Z = l

Volume percent of ethanol (Xi)

Flgure 2-Contour diagrams of granule yield ( Yl)as a function of XI, X,, and Z. Journal of pharmsceutlcal Sclences / 44 7 Vol. 83, No. 3, March 1994

Table 6-Optlmal Values

Formulatlon of Binder Solution at Dlfferent P SS(X)8

SL(X)b

P value

XIC

XZd

Xl

x2

2 3 4 5

-1.19 -1.20 -1.21 -1.21

-0.75 -0.67 -0.63 -0.61

0.25 0.19 0.15 0.13

0.89 0.89 0.89 0.88

* The 2-kg scale. The 5-kg scale. Volume percent of ethanol in binder solution in coded form. *Totalvolume of binder solution in coded form. function, as stated in the Theoretical Section. Figure 5 shows the contour diagram of SS(X) and SL(X) functions of X1 and X2 at P = 2. In the consequence of the minimization of generalized distance function, X1= -1.19 and Xz = -0.75 for small scale and X I= 0.25 and X2 = 0.89 for large scale were obtained as an individual optimal formulation in coded form. Further, these optimal formulations were found to be stable with the change of P value as shown in Table 6, so P = 2 was employed in this study. As seen from these results, the optimal formulation for the two scales was certainly different, so an integrated optimization function was introduced for seekingthe universal optimal formulation not affected by manufacturing scale. An integrated optimization function, T(X), was obtained

by combining the generalized distance functions for two scales and adding a penalty function, as described in the Theoretical Section. Consequently,X I= -1.11 and X2 = -0.88 at P = 2 were found to be the universal formulation of binder solution in coded form. These values were transformed into physical unit, and 16.7% as the ratio of ethanol and 304 mL and 759 mL as the volume of binder solution in small and large scales, respectively, resulted as the universal optimal formulation. This universal optimal formulation was rather close to the individual optimum for small scale. The contour diagram based on T ( X )is depicted in Figure 6. In order to compare the predicted values of each response variable at the universal optimal formulation with experimental results, granules at the 2- and 5-kg scales were newly prepared by employing the universal optimal formulation of binder solution. Results shown in Table 7 indicated that predicted values agreed well with experimental values. Furthermore, the characteristics of the granules in the universal optimal formulation were determined at the production scale (20 kg) in order to evaluate the applicability of the method introduced in this study. The results are summarizedin Table 7, as well. Although the yield was slightlylowered,the other two characteristics(mean granule size and uniformity) measured at the production scale coincided well with those obtained at laboratory scale (2- and 5-kg scale), suggesting that the universal optimal formulation obtained here was certainly stable.

Geometrical mean size (Y2) n N

at Z = - 1

?5

at Z = O

at Z = 1

!z

.9 \rz

-s: Y

1

s a c ._ D h

0

5

cd

Y

0

-fl

-\Is

0

\rz

-0

0

f2

.\rz

0

0

Volume percent of ethanol (Xi) Flguro 3-Contour diagrams of mean granule size of granules (V2)as a function of XI, X,, and Z.

Geometrical standard deviation (Y3) n N

5

at Z = - 1

0

0

Volume percent of ethanol (XI) Figure 4-Contour

diagrams of granule size uniformity ( V3) as a function of XI,X,, and Z.

442 /Journal of Pharmaceutical Sciences Vol. 83, No. 3,March 1994

at Z = 1

at Z = O

\rz

0

0

Table 7-Predlcted and Experlmental Values of Response Varlables (Y,, Y,, and Y,)

h N

5 G

.P v?

2-kg Scale

Y

1

A

+. 8

4c B r , 0

Response Variable

Y, (%)

O

Y2(pm) y3

Definition

5-kg Scale

20-6 Scale: Predic- Experi- Predic- Experi- Experited mental ted mental mental

Yield of 94.1 granule Geometrical 200 mean size Geometrical 2.4 standard deviation

90.8 218 2.1

88.4

262 2.1

91.9 236 2.1

85.9 234 2.1

Volume percent of ethanol (XI) Flgure 5-Contour diagrams of generalized distance function, SS(X) and SL(X), as a function of Xi and X2 at P = 2: 0, optimum formulation at each scale.

-s

a, 0

>

Volume percent of ethanol (XI) Flgure &-Contour diagrams of integrated optimization function, qX), as function of Xi and X, at P = 2: 0, universal optimal formulation.

This approach is based on the following assumption: independent variables selected have a large influence on the physical properties of granule in the scale-up from lab to production and optimal formulation is expected to exist within the experimental range employed for independent variables. As a consequence, selection of an independent variable and its experimental range would be important factors to obtain optimal formulation. Further, how size at the experimental scale should be employed to seek universal optimal formulation is of important issue of this approach. For example, it has to be discussed whether the universal optimal formulation determined from the results of 1and 2-kg scales would hold a consistent result at the 1000-kg scale. There is no alternative but to wait for future research. However, the application of a response surface methodology could be very useful to minimize the scale-up problem encountered in the pharmaceutical dosage development process. This approach will also be applicable to search for the cause of scaleup problem and to assume the influence of manufacturing scale on physical properties of pharmaceuticals.

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(In Japanese).

Journal of Pharmaceutical Sciences / 443 Vol. 83, No. 3, March 1994