Simplex Optimization of the Blue Tetrazolium Assay Procedure for α-Ketol Steroids

Simplex Optimization of the Blue Tetrazolium Assay Procedure for a-Ketol Steroids WILLIAMP. KLEEMAN'AND LEONARD C. BAILEY Received August 21, 1984, from the Department of Pharmaceutical Chemistry, Rufgers University Cofiege of Pharmacy, Piscataway, NJ 08854. Accepted for publication February 25, 1985. metric figure having (n + 1) vertices each with n coordinates; n is equal to the number of experimental variables of the system, which are to be varied during the optimization. For example, the yield of product in an organic synthesis can be a function of temperature and pressure; the simplex figure in this situation would be a triangle with each of the three vertices having different values of temperature and pressure. Even though the simplex figure cannot be given a pictorial representation when more than three variables are to be optimized, the rules which govern simplex movement to the optimum apply for a figure containing any number of variables. A simplex optimization is conducted by first determining, as described above, the variables of which the system is a function. The next step is to determine the range over which temperature and pressure are allowed to vary; criteria used to determine the range of these variables can be based on the physical limitations The blue tetrazolium react.ion' is based on the ability of blue of the experimental system. A triangle is constructed with each tetrazolium, 3,3'-(3,3'-dime:thoxy-4,4'-biphenylene)bis(Z,5-divertex described by a particular combination of temperature phenyl-2H-tetrazolium ch1o:ride) ( l ) ,to oxidize the a-ketol and pressure. At each vertex the response, defined as the yield structure of the C-17 side chain of corticosteroids in an alcoof product, is then determined. The vertices are then ranked holic solution of a strong base such as tetramethylammonium as B, best; N, next-to-the-worst; W, worst. The simplex is hydroxide ( 2 )to produce a highly colored formazan' which can BNW. Movement of the simplex begins by reflecting the worst be measured quantitatively at 525 nm. Investigations of the vertex, W, through the centroid, P, of the face remaining when kinetics of this reaction under USP assay conditions indicate the worst vertex is discarded. The new vertex is designated as pseudo-first-order kinetics with respect to the corti~osteroids"~ R. The new simplex is B N R . Generation of new vertices is and that hydrolysis of the corticosteroid ester is a prerequisite achieved simply by addition and subtraction of the appropriate for reaction with 1. A mechanism for the reduction of 1 by vector coordinates as determined by the simplex algorithm." corticosteroids has been prc~posed.~ The USP XXI/NF XV15 Product yield is now determined a t R and, as before, all vertices details the official procedure which is a modification of the of the new simplex are ranked as best, next-to-the-worst, and original Mader and Buck' method. worst. This process is repeated numerous times as the simplex Many studies have been performed in order to understand moves toward an experimental optimum. The algorithm has how certain experimental va:riables affect the sensitivity, specbuilt-in safeguards that prevent premature termination of the ificity, and reproducibility of the tetrazolium-corticosteroid optimization procedure. The simplex optimization is termireaction. Variables such as concentration of concenconcentration of 1,6.11 nated when the difference between successive experimental tration of type o F responses becomes less than a predetermined value. time,6a8,gt e m p e r a t ~ r e , ~ ~structural '~'~ features of corticosteroids,I3 and types of solvent have been st~died.'~-'' These studies used procedu res which held all but one variable Experimental Section constant while attempting to determine its optimum level. The Apparatus and Materials-A double-beam, UV-visible disadvantage of these methods is that a true optimum may light spectrophotometer (model 571, Perkin-Elmer Corp., Colenever be achieved due to lack of provision for variable interman Instruments Division, Oakbrook, IL) with 1-cm quartz action. Other statistical methods could be used which change cells, a microbalance (model AD-2, Perkin-Elmer Corp., Instruall or most of the variable levels simultaneously; this would ments Div., Norwalk, CT), and a constant-temperature bath ensure provision for variable interaction, but the number of (model K-2/RD, Lauda Instruments, Inc., Westbury, NY) were experimental observations and the time required to perform used. The solvents, methanol (J. T. Baker Chemical Co., Philthem increases exponential1,y with respect to the number of lipsburg, N J ) and anhydrous ethanol (Publicker Industries Inc., variables to be optimized. In this work, the variable size simplex Greenwich, CT), were LC and USP grade, respectively. Tetramethod of Nelder and Meadznwas used to maximize the net methylammonium hydroxide pentahydrate (Matheson, Coleabsorbance of the official blue tetrazolium r e a ~ t i o n The . ~ priman, and Bell, Norwood, OH) was stored in a tight container mary advantage of this approach is that only one experimental and used as received. Cortisone acetate, hydrocortisone acetate, observation is required for each decision concerning a particular hydrocortisone, prednisolone, and prednisone (Sigma Chemical combination of variables. Also, the algorithm" dictates the Co., St Louis, MO). were used as received. Blue tetrazolium decisions to be made, is unambiguous, and removes any bias on (Matheson, Coleman and Bell, Norwood, OH) used for assay the part of the experimenter. purposes met USP XXI/NF XVI specifications for p ~ r i t y . ~ Simplex Method, An Introduction-A simplex is a geo-

Abstract 0 Two independent, simplex procedures were employed to optimize the official blue tetrazolium reaction. The net absorbance for a fixed amount of hydrocortisone was maximized by the simultaneous variation of five factors of the pharmacopeial method, i.e.:concentrations of tetramethylammonium hydroxide, blue tetrazolium, and water, as well as temperature and time for coIIx' development. An initial simplex was used to determine an optimum response, while a second was performed to minimize the blank absorbance obtained at the optimum. A series of pharmaceutically important steroids: prednisone, prednisolone, hydrocortisone acetate, and cortison'e acetate were also analyzed by the optimized method. The results indicated improvements in sensitivity ranging from 9.27 to 22.95% for the corticosteroids studied. The optimized method also decreased the assay time in relation to the official procedure by one-sixth.

0022-3549/85/0300-0403$01.OO/O 0 7 985, American Pharmaceutical Association

Journal of Pharmaceutical Sciences / 655 Vol. 74, No. 6, June 1985

Table I-Data V

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

of First Simplex Movement' S 1 1 1 1 1 1 2 2 3 3 4 5 6 6 7 8 9 10 10 11 11 12 13 13 14 14 15 15 16 16 17 17 18 18 19 20 20 21

B 50.00 59.12 52.05 52.05 52.05 52.05 56.93 55.19 56.14 53.07 56.54 58.34 50.95 46.87 51.56 54.51 49.20 43.75 36.46 42.37 37.02 38.06 35.97 29.35 20.60 3.65 10.94 -7.03 11.15 -1.50 -1.22 28.24 -3.68 26.84 4.53 -6.51 20.39 -6.58

BT 50.00 52.05 59.12 52.05 52.05 52.05 56.93 55.19 56.14 53.07 56.54 48.44 54.07 55.08 50.88 53.55 47.87 55.74 59.39 53.63 53.92 57.04 63.72 71.65 65.27 71.13 70.17 77.72 70.18 75.58 77.78 62.23 84.23 61.49 75.63 67.79 70.69 81.63

w 27.78 29.83 29.83 36.90 29.83 29.83 34.71 32.97 33.92 30.85 24.42 29.33 29.14 28.79 24.32 25.26 30.99 26.75 25.45 23.07 19.18 27.55 19.50 13.75 20.64 18.33 12.92 4.99 11.24 4.13 2.62 21.32 11.84 17.35 8.13 13.42 13.67 8.36

Solutions-Solution I-Blue tetrazolium (0.250 g) was dissolved with 4.4 mL of methanol (0.002% water) in a 25-mL volumetric flask and diluted to volume with absolute ethanol. Solution IZ-Tetramethylammonium hydroxide pentahydrate (1.00 g) was weighed accurately into a 25-mL volumetric flask and diluted to volume with absolute ethanol. Standard solutions of the corticosteroids were prepared so that a 10.00mL aliquot contained 0.200 mg of the free steroid or steroid ester in absolute ethanol. Procedure-Since simplex optimization of this reaction would cause the volume to vary in an unpredictable way, depending upon factor movement, it was decided to set the final volume of both the official and optimized procedures to 25 mL after appropriate experimental conditions had been fixed. In this way, a comparison of both the compendia1 procedure and its optimized version could be made under conditions of equivalent concentration. A 10.00-mL aliquot of a standard corticosteroid solution, equivalent to 0.200 mg of the free steroid or steroid ester, was introduced into a 25-mL volumetric flask. The required volumes of 1, 2, and water were added in the order indicated. The solution was mixed and diluted to volume with absolute ethanol. The flask was stoppered and placed in a water bath a t the appropriate temperature for the specified length of time. The absorbance was determined against a reagent blank in which 10.00 mL of absolute ethanol was substituted for the corticosteroid standard solution and run concurrently with the sample. Simplex Method-The starting simplex for this system with five variables has six vertices, each with five coordinates: concentrations of 1, 2, and water, temperature, and time of reaction. Using the values of the pharmacopeial variable levels

656 /Journal of Pharmaceutical Sciences Vol. 74, No. 6, June 1985

Tm 30.00 32.05 32.05 32.05 39.12 32.05 36.93 35.19 36.14 33.07 36.54 38.34 40.86 45.26 41.74 38.87 42.37 42.18 44.10 51.86 61.26 51.OO 53.83 59.56 65.61 78.97 72.69 86.41 85.29 105.89 92.11 61.28 81.86 66.41 83.89 95.35 68.51 89.34

TP 31.25 33.30 33.30 33.30 33.30 40.37 38.18 36.44 27.49 37.15 36.10 37.22 38.78 41.52 37.67 42.56 42.35 43.29 46.32 47.03 51.96 52.22 51.48 56.05 56.67 63.72 66.60 79.1 1 69.90 81.69 71.07 56.93 73.31 57.30 68.49 74.34 60.62 74.42

Re

BI

0.248 0.541 0.537 0.535 0.560 0.526 0.522 0.555 0.342 0.570 0.563 0.568 0.572 0.580 0.572 0.579 0.576 0.584 0.596 0.600 0.622 0.61 1 0.624 0.646 0.648 0.661 0.700

0.010 0.018 0.028 0.028 0.020 0.030 0.025 0.023 0.013 0.018 0.013 0.020 0.020 0.032 0.025 0.039 0.035 0.039 0.039 0.052 0.095 0.072 0.092 0.160 0.101 0.054 0.225 0.387 0.124 0.147 0.134

-m

0.719 -m

-ca

0.637 -m

0.652 0.696 -m

-

0.656

0.21 6

-m

VG R1 CR1 R6 CW6" R4" R3" R2 E2" R8" R5" Rll" R12 E l 2" R10 E l0" R15" R17 E17" R16 E l 6" R14" R14 R19" E l9 R22 C,22" R21 cw21" R32C R24 CW24" R34

-

^ I

0.801

I

5

Figure 1-Absorbance

10

15 20 25 SIMPLEX NUMBER

30

35

I 40

versus simplex number for first simplex optimi-

zation. as a guide, the range for each factor was determined: solution I, 0.0-2.0 mL; solution 11, 0.0-2.0 mL; water, 0.0-5.0 mL; temperature, O-8O0C, and time, 0-100 min. In order to simplify the calculations and make the movement of the simplex easier to perceive, all factors were normalizedT2 and expressed as a percentage of their range, which could vary from 0 to 100%. The coordinates of the first vertex were chosen to be the same as those of the pharmacopeial method, except for time which was set at 30 min instead of 90 min. Using a 10% step size:' the other five vertices were constructed according to the method of Spendley et al.23 An observation of the response at each vertex was made, and the responses were ranked in order from

Table I-Continued

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

22 22 23 23 24 24 25 26 27 27 28 28 29 29 30 31 32 32 33 33 34 34 35 36 36 37 37 38 39 39 40 40 41

-0.89 15.07 20.42 28.81 6.36 0.30 6.29 17.53 13.76 11.64 13.75 15.04 14.09 15.32 2.79 15.52 3.47 14.02 17.71 9.19 8.41 12.61 9.81 6.82 12.01 3.64 12.55 20.28 17.44 11.72 19.07 11.66 4.54

70.78 70.71 70.15 69.66 76.21 81.05 74.24 68.77 73.66 91.05 74.00 75.91 74.32 75.95 76.89 73.85 81.35 71.91 72.14 75.22 77.79 73.39 76.35 76.65 74.66 77.13 74.67 73.21 72.48 75.38 73.67 74.83 76.34

12.61 13.41 5.98 -0.19 5.57 0.79 4.1 1 7.80 0.94 9.93 2.10 -2.47 0.28 -4.54 1.99 2.99 -2.62 5.19 -0.54 4.04 -0.63 3.74 0.83 1.95 2.06 0.69 2.41 1.85 3.44 1.41 -0.80 2.83 1.77

88.68 73.56 76.06 74.60 84.45 90.60 87.40 78.47 91.97 77.51 76.26 71.75 83.54 86.55 87.99 76.89 85.19 80.15 77.48 82.71 82.81 80.81 82.14 89.04 75.46 87.85 79.63 73.40 75.75 80.54 74.32 80.61 86.51

71.47 63.34 68.25 65.98 73.05 78.78 75.17 92.69 77.03 69.20 73.44 75.22 75.83 79.15 79.83 74.77 78.08 75.04 78.52 74.31 76.24 75.34 75.94 78.83 74.79 77.51 75.46 70.70 72.50 75.08 74.43 74.34 79.50

--m

-

0.677 0.724

0.213 0.713

--m

0.738 0.002 0.730 0.737 0.670 0.714 0.746

-

0.347 0.002 0.497 0.853 1.639 0.442 0.946

-m

-

0.791

1.437

-m

0.759 0.748 -m

-

0.249 1.264 -

-m

-

0.781

0.644

0.690 -m

-

0.696 0.777 0.745 0.789 0.724 0.787 0.786 0.773 0.794

1.121 1.005 0.853 1.036 0.336 1.149 1.322 1.122 1.050

-m

-

0.778 0.734

0.927 0.516

R37 CW37" R26" E26 R39" E39 R41 R35" R27 CW27' R29" E29 R49" E49 R42' R46" R47 C47" R44 CW44" R57 Cw57C R61" R50

cw50c R55 CW55" R54' R62 CW62' R59 CW59" R68

a Abbreviations used: V, vertex number; S,simplex number; B, volume of base solution as percent of range; BT, volume of blue tetrazolium solution as percent of range; W, volume of water as percent of range; Tm, time as percent of range; Tp, temperature as percent of range; Re, net reswnse of sample; 61, blank response; V13, vertex genesis. Symbols for simplex operation: R, reflection; E, expansion; C, contraction on worst side; CR, contraction on reflection side. Move accepted.

best to worst. A new vertex was generated by taking the vertex having the worst response and reflecting it through the midpoint of the remaining hyperface. If, on reevaluation of the new simplex the newly generated vertex had the worst response, the next to worst vertex was rejected. This was done to prevent regeneration of the previous simplex and premature termination of the optimization process. Whenever the simplex algorithm generated a vertex with one or more coordinates outside their predetermined ranges, that particular experiment was not performed and an unfavorable response of -w was as~igned.'~ However, that vertex was included in the calculations for the following simplex. Addition(3.loperations, such as contraction and expansion, were also included in the simplex algorithm'' to accelerate movement of the simplex figure toward the region of optimum response. The progress of the simplex was monitored by a plot of absorbance response versus simplex number and experiments were stopped when the curve approached an asymptotic maximum value of absorbance.

Results and Discussion Experimental data generated for the first simplex procedure are listed in Table I. A total of 72 moves were calculated, but only 58 experiments were required, since 14 vertices had one or more coordinates outside the variable space. Simplex movement was halted a t verteg number 72 because the system response had become asymptotic to a maximum value. Figure 1 illustrates the net absorhance of the sample versus simplex number for the first simplex procedure. The normalization equation," which was previously discussed, was used to unscale and determine the actual change occurring for each variable.

The maximum response for 0.200 mg of hydrocortisone, which occurred at vertex 69, was a net sample absorbance of 0.794 with a blank absorbance of 1.050 at 60°C after 80.5 min; the pharmacopeial method yielded a net sample absorbance of 0.562 and blank absorbance of 0.025 a t 25°C after 90 min. After examination of the data in Table I, a decision was made to use vertex 64 instead of vertex 69. This vertex was chosen because it had a net sample absorbance comparable with vertex 69, while having a slightly lower blank absorbance. The net sample and blank absorbances were 0.789 and 1.036, respectively, and they were obtained at 60°C after 75.5 rnin. Comparison of the pharmacopeial variable levels with those obtained by the optimized procedure illustrated that a definite trend in variable movement had occurred. A decrease in the concentration of water, 2 , and time for color development had taken place. In addition, there was an increase in the concentration of 1 and the temperature a t which the analysis was performed. Variable movement in this simplex procedure followed a predictable pattern based on previous st,atements made by Cheronis and Steinz5regarding the stability of tetrazolium salt solutions. They stated that the stability of a tetrazolium salt solution is a function of both the pH of the solution and the concentration of the tetrazolium salt. As the pH of the solution rose above 7, a moderate to high concentration of tetrazolium salt would result in the formation of an increasing amount of tetrazolium hydroxide, which rearranged to a colored isomer. The extent of this rearrangement reaction will vary for different tetrazolium salts. This indicated that two reactions are contributing to the color generated during the official assay with blue tetrazolium: the 1-corticosteroid reaction and the rearrangement of the 1-hydroxide. Journal of Pharmaceutical Sciences / 657 Vol. 74, No. 6, June 1985

At an elevated temperature, the 1-corticosteroid reaction and rearrangement of the 1-hydroxide were enhanced. Since the formazan and the isomer are practically insoluble in water, a decrease in water content of the system further increased the extent of formation of both species. For example, a comparison of the net sample and blank absorbances obtained in the optimization procedure (vertex 64) to those obtained by the pharmacopeial method showed increases of 40.4 and 4044.0%, respectively; the extent of the 1-hydroxide rearrangement reaction is much more dependent on temperature than the extent of the 1-corticosteroid reaction. An increase in 1 was necessary, since the 1-hydroxide rearrangement reaction reduced the amount of 1 available for reduction by the corticosteroid. Compound 2, which is a catalyst for the 1-corticosteroid reaction, showed a decrease in concentration. At elevated temperatures, a smaller quantity of 2 was needed for catalysis of the 1-corticosteroid reaction; the corresponding 1-hydroxide rearrangement reaction, which caused color in the blank, was inhibited. This situation made more 1 available for the 1corticosteroid reaction. The optimization procedure decreased the factor level for time by one-sixth in comparison with the pharmacopeial method. This was accomplished even though the extent of the 1-corticosteroid and 1-hydroxide reactions had increased, a result attributed to faster reaction kinetics a t the increased temperature. The large increase in blank absorbance obtained in the initial simplex procedure was undesirable. Therefore, a univariable simplex26optimization was performed with the concentration of 2 under investigation in order to minimize the contribution of the blank to the overall response. The initial vertex in this simplex was identical to the base coordinate in vertex 64 of the first simplex. A step size of 10.0% of the range was chosen for the variable of interest, and a simplex was constructed. The response for this simplex was calculated as follows:

Re = (R - B1) - B1 where Re is the calculated response which dictates the movement of the simplex, R is the total sample response, and B1 is the response of the blank. According to the formula, simplex movement will proceed in the direction of maximum positive deviation between the net absorbance of the sample and the absorbance of the blank. The results of this simplex procedure are shown in Table 11. The final net sample absorbance obtained by the univariable simplex was 0.691 with a blank absorbance of 0.113. In comparison with the first simplex, the net sample absorbance had been decreased by 12.4% with a corresponding decrease of 89.1% in the blank absorbance. The unscaled variable levels of the optimized procedure were: solution I, 1.49 mL; solution 11, 0.24 mL; water, 0.11 mL; temperature, 60°C; time, 75.5 min. Recommended Assay Procedure-Prepare a solution of free steroid or steroid ester by serial dilution, to contain approximately 10 g / m L in absolute ethanol. Transfer a 10.00mL aliquot of this standard solution into a glass-stoppered, 25mL volumetric flask. To this solution add 1.50 mL of solution I, 0.25 mL of solution 11, and 0.10 mL of water in the order indicated. Mix the solution and dilute to volume with absolute ethanol. Stopper the flask and place in a water bath a t 60°C for 75.5 min. Determine the absorbance against a reagent blank in which 10.00 mL of absolute ethanol is substituted for the standard solution and run concurrently with the sample. Several other glucocorticoids of pharmaceutical interest were also assayed via the optimized procedure. These were hydrocortisone acetate, cortisone acetate, prednisone, and prednisolone. Derivatives such as the acetate ester were chosen for analysis since many pharmaceutical preparations are formulated from these compounds. We also wished to determine if the optimized procedure supplied the conditions necessary for hydrolysis of the acetate ester derivatives to their free cortico658 / Journai of Pharmaceutical Sciences Vol. 74, No. 6, June 1985

steroid counterparts, since it is these species which will react with the blue tetrazolium molecule. Prednisone and prednisolone, synthetic steroids which are several times more potent in anti-inflammatory and glucocorticoid activity than the natural hormones (cortisone and hydrocortisone), were chosen because of their significant pharmaceutical importance. Table I11 lists the data obtained when the official procedure was compared with the optimized procedure. The largest percentage increase occurred with hydrocortisone, while the smallest percentage increase occurred with cortisone acetate. All other steroids studied had absorbance increases of intermediate value. In summary, the official blue tetrazolium reaction was optimized by the variable size simplex method of Nelder and Mead." This technique permitted the determination of an optimum net response for a fixed amount of hydrocortisone, while simultaneously varying five factors of the reaction. In addition, the method took into account the nonindependence of any or all of these factors; a complex optimization was accomplished with only 58 experiments. Also, a second simplex procedure required only 13 additional experiments to minimize the blank response obtained in the first simplex procedure; a grand total of 71 experiments were performed for complete optimization of the experiments1 system. The corticosteroids selected for assay by the optimized procedure had percentage Table 11-Data of Second Simplex Movement' V S B Reb 61 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 1

2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9

12.01 22.01 2.01 -7.98 -7.98 7.01 12.01 4.51 2.01 -0.49 -0.49 3.26 4.51 2.64 2.01 1.39 1.39 2.33

-0.247 -1.425 0.578 --m --m

0.241 -0.247 0.445 0.578 -m

--m

0.518 0.445 0.555 0.578 0.538 0.538 0.564

NRe

1.036 2.205 0.113

0.789 0.780 0.691

0.516 1.036 0.292 0.113

0.757 0.789 0.737 0.691

0.196 0.292 0.152 0.113 0.076 0.076 0.131

0.714 0.737 0.707 0.691 0.614 0.614 0.695

-

-

-

-

VG"

R2d E2 R1 C,ld R3 C,3d R6d E6 R8 C,8d R9 C,9d R12d El 2 R14 Cwl4d

a Abbreviations used: V, vertex number; B, volume of base solution as percent of range; 81, blank response; NRe, net response of sample; VG, vertex genesis; Re, operating response. Re calculated as follows: Re = (R - 61) - BI, where Re is the operating response, R is the overall response of the sample, and BI is the response of the blank. Symbols for simplex operation: R , reflection; E, expansion; C, contraction on the worst side. Move accepted.

Table Ill-Comparison of Data Obtained by the Optimization Procedure and Official Procedure for Selected Corticosteroids" Alb,' A2' 82 S1 S2 PI Corticosteroid Hydrocortisone 0.562 0.691 0.113 1.019 1.252 22.95 Prednisone 0.555 0.610 0.137 0.995 1.093 9.91 Prednisolone 0.566 0.680 0.140 1.020 1.225 20.14 Hydrocortisone acetate 0.510 0.590 0.140 1.031 1.193 15.69 Cortisone acetate 0.507 0.554 0.139 1.020 1.115 9.27 * Abbreviations used: A1 , absorbance recorded for official procedure; A2, absorbance recorded for optimization procedure; 92, blank absorbance recorded for optimization procedure; S1, sensitivity for official procedure in terms of absorbance units per micromole; S2, sensitivity for optimization procedure in terms of absorbance units per micromole; PI, percentage increase in sensitivity of optimization procedure over official procedure. Data based on an aliquot containing 0.200 rng of the corticosteroid or corticosteroid ester in a final volume of 25 mL. * Average of duplicates. Blank absorbances in official procedure ranged from 0.022 to 0.025.

increases in sensitivity ranging from 9.27 to 22.95% over the official procedure.

References and Notes Mader, J. W.; Buck, R. R. Anal. Chem. 1952,24,666-667. Nineham, A. W. Chem. Re&.1955,55,355-483. Smith, M. D. J . Pharm. Sci. 1980,69,960-964. Oteiza, R. M.; Wooten, R. S.; Kenner, C. T.; Graham, R. E.; Biehl, E. R. J. Pharm. Sci. 1977,66, 1385-1388. 5. “US. Pharmacopeia/National Formulary,” 21st rev./l6th ed.; U.S. Pharmacopeial Convention Rockville, MD, 1985; p. 1366. 6. Recknagel, R. 0.; Litteria, M. J. Lab. Ckn. Med. 1956, 48, 463-

1. 2. 3. 4.

468. 7. Graham, R. E.; Kenner, C. ‘7’. J. Pharm. Sci. 1973,62,103-107. 8. Izzo, A. J.; Keutmann, E. IH.;Burton, R. B. J. Clin. Endocrinol. Metab. 1 9 5 7 , 17,889-901. 9. Meyer, A. S.; Lindberg, M. (2. Anal. Chem. 1955,27, 813-817. 10. Chen, C. C.; Wheeler, J.; Tewell, H. E. J. Lab. Clin. Med. 1953, 42, 749-757. 11. Weichselbaum, T. E.; Margraf, H. W. J. Clin. Endocrinol. Metab. 1955,15,970-990.

12. Nowaczynski, W.; Goldner, M.; Genest, J. J.Lab. Clin. Med. 1955, 45, 818-821., 13. Graham, R. E.; Biehl, E. R.; Kenner, C. T.; Luttrell, G. H.; Middleton, D. L. J. Pharm. Sci. 1975,64, 226-230. 14. Manni, P. E.; Sinsheimer, J. E. Anal. Chem. 1961,33, 1900-1903. 15. Sinsheimer, J. E.; Salim, E. F. Anal. Chem. 1965,37, 566-569. 16. Johnson, C. A.; King, R.; Vickers, C. Analyst 1960,85,714-719. 17. Callahan, J. J.; Litterio, F.; Britt, E.; Rosen, B. D.; Owens, J. J. Pharm. Sci., 1962,51,333-335. 18. Graham, R. E.; Biehl, E. R.; Kenner, C. T. J. Phurm. Sci. 1976, 65, 1048-1053. 19. Graham, R. E.; Biehl, E. R.; Kenner, C. T. J. Pharm. Sci. 1978, 67, 792-795. 20. Nelder, J. A.; Mead, R. Computer J. 1 9 6 5 , 7 , 308-313. 21. Leg ett, D. J. J. Chem. Ed. 1983,60, 707-710. 22. Yarfro, L. A.; Demin , S N. Anal. Chim. Acta 1 9 7 4 , 73,,391-398. 23. Spendley, W.; Hext, R ; Himsworth, F. R. Technometrics 1962, 4,441-461. 24. Shavers, C. L.; Parsons, M. L.; Deming, S. N. J . Chem. Ed. 1979, 56,307-309. 25. Cheronis, N.; Stein, H. J. Chem. Ed. 1956,33,120-125. 26. King, P. G.; Deming, S. N. Anal. Chem. 1974,46,1476-1481.

8.

Journal of Pharmaceutical Sciences / 659 Vol. 74, No. 6, June 1985