(17)
See e.g., V . Svoboda, R. F. Browner. and
J. D.
Winefordner,
Specbosc.. 26, 505 (1972). (18) W. H. Rodebush and T. (19) D. A . Jennings and R. A
DeVries, J. Am. Chem. SOC., 47, 2488 (1925). Keller, J. Am. Chem. Soc.. 94, 9249 (1972).
(20) C. L. Stong, Sci. Am., 222, (2), 116 (1970).
RECEIVEDfor review June 30, 1975. Accepted October 16, 1975. E. S. Yeung is an Alfred P. Sloan Research Fellow. This work was prepared for the U.S. Energy Research and Development Administration under Contract No. W-7405eng-82.
Fluorometric Determination of Erythromycin and Erythromycin Propionate in Whole Blood or Plasma and Correlation of Results with Microbiological Assay Kou-Yi Tserng and John G. Wagner*’ College of Pharmacy and Upjohn Center for Clinical Pharmacology, The University of Michigan, Ann Arbor, Mich. 48 104
A method is proposed to determine erythromycin and erythromycin propionate in 1-mi samples of whole blood or plasma, with about the same precision as the microbiological assay. When plasma spiked with erythromycin is used, results obtained with the proposed method correlate very closely with results obtained in the microbiological assay employing Sarcina lutea. Because of ease and speed of performance, the proposed method is more suitable for clinical studies than a previously described paper chromatographic method. A study of the kinetics of hydrolysis of erythromycin propionate in whole human blood revealed: a ) a short-lived enzymatic (?) hydrolysis; b) subsequent hydrolysis, which obeyed first-order kinetics and the Arrhenius relationship; and c) sufficient hydrolysis in the frozen state (-20 “C) that this must be taken Into account when estimating concentrations of erythromycin propionate which existed at the time of withdrawal of the blood, before it was stored in the freezer.
Erythromycin is administered orally in three main forms: ( a ) as erythromycin estolate [Ilosone Pulvules (Eli Lilly and Company)] (the lauryl sulfate salt of the ester, erythromycin propionate) in capsule form; ( b ) as film-coated tablets of the salt, erythromycin stearate [Erythrocin Filmtab Tablets (Abbott Laboratories)]; and ( e ) as entericcoated tablets of erythromycin base [E-Mycin Tablets (The Upjohn Company)]. When administered orally as form a , the pro-drug ( I ) , erythromycin estolate, is principally, if not entirely, absorbed as erythromycin propionate. When administered in forms b and c, the species which is absorbed and circulates in the blood is erythromycin itself. T h e controversy over the relative effectiveness of erythromycin estolate vs. erythromycin stearate or erythromycin has been discussed in several reports (2-8). It was claimed by some investigators (7, 8 ) that erythromycin estolate was superior to erythromycin on the basis of higher (apparent) serum concentrations observed following oral administration of erythromycin propionate than following oral administration of other forms of erythromycin. The microbiological assay method, employing Sarcina lutea (9, I O ) , is the commonly-used method to measure serum concentrations Address, Upjohn Center for Clinical Pharmacology, University of Michigan Medical Center, Ann Arbor, Mich. 48104. 348
following administration of different forms of erythromycin. There are several factors which must be taken into consideration in evaluating serum (plasma or whole blood) concentrations of erythromycin which have been measured by a microbiological assay method. These are as follows. (i) When samples containing erythromycin propionate are subjected to the microbiological procedure, a large, but unknown, percentage of the ester is hydrolyzed to erythromycin during the assay. (ii) Stephens et al. ( 3 ) , using a paper chromatographic method, showed that, following administration of erythromycin estolate to human volunteers, the major circulating species was erythromycin propionate. In their study, whole blood, serum, plasma, and urine contained 20-25% erythromycin and 75-80% erythromycin propionate. (iii) Erythromycin propionate is microbiologically inactive, and must be hydrolyzed to the microbiologically-active erythromycin in order to show activity. (iv) T h e investigations of Stephens et al. ( 3 ) , and the data in this report, indicate that propionyl erythromycin continues t o hydrolyze during storage of blood samples even at -20 “C. (v) The efficiency of the gastrointestinal absorption of erythromycin propionate is presumably greater than that of erythromycin. (vi) Wiegand and Chun ( 5 ) reported that about 10% of erythromycin, but only 1.5%of erythromycin propionate, in serum is free and not bound to protein. Microbiological and chemical methods of assay measure total drug (free bound). Usually, factor v, above, is given as the cause of higher (apparent) serum (plasma or whole blood) concentrations of “erythromycin” observed following oral administration of erythromycin estolate compared with those observed following oral administration of the other main forms (Le., forms b and c above). However, factors i, ii, iv, and vi also significantly contribute to the observed differences. Factors i and iv contribute to higher observed concentrations of erythromycin than those which actually existed when the blood samples were withdrawn from the subjects. Several investigators have studied or developed chemical assays for erythromycin. Ultraviolet absorption of erythromycin is far too weak to be useful ( 1 1 ) . A number of papers have been concerned with increasing ultraviolet or visible absorption via chemical reactions. Chromophores were developed by reacting with sulfuric acid ( I 2 ) , arsenomolybdate reagent ( I 3 ) , xanthydrol ( I 4 ) , methyl sulfate ( I 5 ) , tetrazolium blue ( I 6 ) , benzaldehyde (171, and by com-
ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
+
plexing with acidic dyes ( 1 8 ) . Kuzel et al. (19) developed a n ultraviolet method involving mild alkaline hydrolysis of erythromycin and reported good correlation of results with the microbiological assay method. A method based on nonaqueous titration was also reported (20). In order to measure erythromycin alone or both erythromycin and erythromycin propionate in blood, separation must precede quantitation of the two components. Anderson (21 ) employed thin layer chromatography with spot detection by means of phosphomolybdic acid-sulfuric acid reagent. Benaszek et al. (22) modified this method by use of a different solvent system and a more sensitive developer composed of cerium sulfate and molybdic acid. Radecka e t al. (23, 24) measured the compounds directly on the thin layer plate by densitometry. T h e sensitivity of these methods is insufficient to apply them to biological samples. T h e gas-liquid chromatographic method of Tsuji and Robertson (25,26) and the paper chromatographic method of Stephens et al. (3) have sufficient sensitivity and specificity, but require extensive sample manipulation and, hence, are too time-consuming. This report gives details of a simple solvent extraction method for quantitative separation of erythromycin and erythromycin propionate from whole blood or plasma (also applicable to serum). After separation, each of the compounds is quantitatively measured by the fluorometric method. Using “blind” samples of human plasma, spiked with erythromycin, the results attained with the new method correlated very closely ( r = 0.995) with results from the microbiological assay. The stability of erythromycin propionate in whole blood stored a t temperatures from -20 to 37 O C , was also investigated. This was necessary, since, if erythromycin propionate hydrolyzes during storage of samples before assay, this would contribute to apparent, but not real, increased blood levels following administration of erythromycin estolate compared with other dosage forms of erythromycin as indicated above.
EXPERIMENTAL P r e l i m i n a r y Investigations. Early attempts to couple erythromycin with a fluorescent moiety failed. I t appears that the erythromycin molecule is too unreactive towards acylating agents, such a s dansyl chloride ( 2 7 ) , under conditions that do not destroy the erythromycin itself. Use of fluorescent dyes to form complexes with a basic compound (28-30) and the use of such a dye with erythromycin ( 1 8 ) prompted us to explore this possibility. Various acidic fluorescent dyes including sodium naphthylene sulfonate, D N S (5-dimethylamino-1-naphthalenesulfonic acid), anthracene1-sulfonic acid, and Tinopal GS [sodium salt of 2-(stilbyl-4”)-(naphtho-1’,2’:4,5)-1,2,3-triazole-2”,6’-disulfonic acid] were studied. DNS does not form a n extractable dye complex with erythromycin under the conditions studied. Anthracene-1-sulfonic acid, which was reported by Borg and Westlund (30) to be superior to other fluorescent dyes, has a very low solubility in acidic aqueous media. Both sodium naphthylene sulfonate and Tinopal GS gave extractable dye complexes with erythromycin, b u t the complex made with the former dye had the disadvantage of too close fluorescence and excitation maxima. Tinopal GS was chosen as the fluorescent reagent. The extracting solvent was also studied. Chloroform was unsuitable since the dye-drug complex which was extracted into chloroform adsorbed onto glass very quickly, resulting in a marked reduction in fluorescence intensity within a few minutes. Adsorption of this type was much slower with methylene chloride, but significant loss of fluorescence was observed in several minutes. Addition of 5% n-amyl alcohol to the methylene chloride reduced this tendency. Higher proportions of n-amyl alcohol resulted in a n increase in the blank value. Finally, it was found t h a t if the organic extract was mixed with ethanol immediately after separation of the aqueous and organic phases, the resulting solution could be kept for a t least one-half hour without decrease in fluorescence intensity.
Erythromycin and erythromycin propionate have pK,’s of 8.6 and 6.9, respectively (31). Several partition coefficients have also been reported ( 3 2 ) . Diethyl ether was an attractive solvent since erythromycin has a limited solubility in it, while erythromycin propionate is quite soluble in it. Morozowich ( 3 3 ) had previously pointed out the feasibility of a separation of erythromycin and erythromycin propionate based on extraction theory. I t was found that if the p H of whole blood or plasma was adjusted to p H 6.0, then two extractions with diethyl ether removed all of the propionyl erythromycin. If erythromycin was also present in the aqueous phase (pH 6.0), it was not extracted by the diethyl ether. However, after saturation of the aqueous phase with sodium bicarbonate, and then adjustment to a high p H with saturated aqueous sodium carbonate solution, two extractions with diethyl ether completely extracted the erythromycin. Reagents. The following reagents were used: erythromycin base USP reference standard (U.S.P., Rockville, Md.), microbiological assay 982 rglmg; erythromycin propionate, microbiological assay 860 pg/mg (Eli Lilly and Co., Indianapolis, Ind.); diethyl ether, glass distilled (Burdick and Jackson Lab., Inc., Muskegon, Mich.); alcohol, dehydrated,U.S.P. (U.S. Industrial Chemical Co., New York, N.Y.); dichloromethane reagent, ACS (Matheson, Coleman and Bell, Norwood, Ohio); n-amyl alcohol, certified (Fisher Scientific Co., Fair Lawn, N.J.); sodium carbonate, reagent, ACS (Matheson, Coleman and Bell, Norwood, Ohio); sodium bicarbonate, reagent, ACS (Matheson, Coleman and Bell); citric acid monohydrate ( J . T. Baker Chemical Co., Phillipsburg, N.J.); sodium fluoride (J. T . Baker Chemical Co.); acetone (Mallinckrodt, St. Louis, Mo.). Tinopal GS solution was prepared by dissolving 100 mg of Tinopal GS (Ciba-Geigy Co., Ardsley, N.Y.) in 100 ml of 0.1 M citric acid. The resulting solution was extracted several times with methylene chloride and n-amy1 alcohol (19:l) mixture to remove some organic solvent extractable fluorescent impurities. Phosphate buffers were prepared according to Sorenson (34). All organic solvents used were pre-equilibrated with water. Methylene chloride solvent mixture was prepared by mixing methylene chloride and n -amyl alcohol in the proportion of 19:1, then equilibrating with water before use. Instrumentation. A Perkin-Elmer fluorescence spectrophotometer, model 203, equipped with a xenon power supply, model 150, was used. Instrumental response was calibrated with a dilute aqueous solution of Tinopal GS or quinine sulfate in 0.1 M sulfuric acid. Readings were made in fluorescence Superasil cells with 10-mm light paths (Lux Scientific Instrument Co., New York, N.Y.). An Adams Dynac centrifuge (Clay-Adams, Inc., Parsippany, N.J.) was used for separating organic and aqueous layers. An Eberback reciprocating shaker (Eberbach Co., Ann Arbor, Mich.) with two speeds was used for horizontal shaking during extractions. All liquids were dispensed from Repipet (Labindustries, Berkeley, Calif.) except for phosphate buffers, which were dispensed from “tilt-a-pet” repeating pipet (Tech Glass Co., Vineland, N.J.). Siliconization of Glassware. T h e centrifuge tubes used for complexing the erythromycins with the fluorescent dye were siliconized to prevent adsorption of drug-dye complex. Silicone solution was prepared by diluting 1 ml of Siliclad (Clay-Adams, Inc.) with 100 ml of warm water and adding 2 drops of concentrated a m monium hydroxide. T h e tubes were then filled with the silicone solution and allowed to stand for 3 min. T h e solution was then poured off, the tubes were rinsed several times with water, and then the coating was cured a t 120 “C for 30 min. After cooling, the tubes were immersed in nitric acid-water (1:2) and heated for 20 min a t 80 OC. T h e tubes were then rinsed with water, ethanol, and were air-dried. They were stored a t room temperature for a t least 1 day before use. All other glassware was cleaned with Calgonite (Calgon Co., S t Louis, Mo.) except for the siliconized centrifuge tubes, which were cleaned by rinsing formerly-used tubes with water and ethanol several times, then drying them. In this way, one treatment with silicone lasted for several washing cycles. When the hydrophobicity of the silicone coating deteriorated, as evidenced by wetting of t h e tube wall by water, the tubes had to be re-coated. Aqueous S t a n d a r d s . Stock solutions were prepared by dissolving erythromycin in dry acetone in the concentration range 0.1-2.8 mg/ml. Containers were sealed tightly and stored in the refrigerator. Prior to preparation of the working standards, the stock solutions were allowed to warm up to room temperature. T o prepare working standards, aliquots of 10 pl of the stock solutions were pipetted into 10-ml volumetric flasks, which were then filled u p to
ANALYTICAL CHEMISTRY, VOL. 48, NO. 2 , FEBRUARY 1976
349
1 m l W h o l e blood (or plasma)
+ 2 ml 0 . 1
Blood l a y e r
IY p h o s p h a t e . m f f e r t o pH 6 . 0
I
0.1
Ether e x t r a c t
s a t ’ d With
Isam,
f
I
Agueous
acidic layer
Ett.er l a y e r (discarded)
1
E t h e r e x t r a c t Aqueous (discarded) a c i d 1 layer 0.5 ml Tinopal G S 1 . 5 ml C H C 1 s o l v e n t rutare2 Assayed f o r e r y t h r o m y c i n
Figure 1. Scheme for whole blood or plasma
volume with 0.1 M citric acid. T h e resulting working standards were in the 0.1-2.8 bg/ml concentration range. Procedure for Aqueous Standard Curve with Erythromycin. One ml of working standard, 0.5 ml of Tinopal GS solution, and 1.5 ml of methylene chloride solvent mixture, respectively, were pipetted into a 5-ml siliconized glass-stoppered centrifuge tube. The tube was sealed tightly by dampening the glass stopper with water, then the tube was shaken horizontally a t high speed on the Eberbach shaker for 5 min. This was followed by centrifugation a t 2000 rpm for 2 min. T h e upper aqueous layer was aspirated off together with about 0.1 ml of the organic layer. Using a syringe, which was pre-moistened with ethanol to prevent adsorption of the drug-dye complex onto the syringe wall, and a 6-inch long needle, 1.0 ml of the organic layer was transferred to a culture tube (13 X 100 mm) containing 2.2 ml of absolute ethanol. T h e solution was mixed carefully, then the fluorescence was read at 430 nm with excitation at 365 nm. Procedure for Aqueous Standard Curve with Erythromycin Propionate. A standard curve for erythromycin propionate was prepared as described above for erythromycin except that erythromycin propionate was used in place of erythromycin. Whole Blood Standards. Whole blood standards were prepared by spiking pooled human whole out-dated blood (Blood Bank, University Hospital, T h e University of Michigan) with acetone stock solutions of erythromycin or erythromycin propionate or both. Procedure for Whole Blood Standard Curve with Erythromycin Propionate. Into a screw-capped (Teflon-lined) culture tube (13 X 100 mm) was pipetted 1.0 ml of blood standard, followed by 2 ml of phosphate buffer (0.1 M, usually pH 5.7) to a final pH of 6.0, then 2 ml of diethyl ether. T h e tube was shaken horizontally for 5 min a t slow speed on the Eberbach shaker. T h e tube had to be oriented on the test-tube rack on the Eberbach shaker so that the tube inclined a t an angle of about 30’ with the cap end down to avoid emulsion formation. The culture tube was transferred to the centrifuge, and was centrifuged a t 2000 rpm for 2 min. As much as possible of the upper ether layer was transferred with a syringe, equipped with a 2-inch flat-tip needle, to a 5-ml glass-stoppered centrifuge tube. None of the aqueous phase should be transferred. To the ether layer was added 1.0 ml of 0.1 M citric acid and to the blood layer was added 2 ml of fresh diethyl ether. Both were shaken for 5 min a t slow speed on the Eberbach shaker with the same tube orientation as described above, then both were 350
centrifuged for 2 min a t 2000 rpm. T h e ether layer from the citric acid solution was pipetted off and discarded. T h e ether layer from the blood was added to the citric acid solution and the tube was shaken on the Eberbach shaker as before, followed by centrifugation as before. The citric acid solution, which had to be free from any emulsion, was transferred to another clean 5-ml siliconized centrifuge tube quantitatively with a syringe; then 0.5 ml of Tinopal GS solution and 1.5 ml of methylene chloride solvent mixture were added. The same procedure was then followed as described above under “Procedure for Aqueous Standard Curve with Erythromycin”, starting with “The tube was sealed.. .”. However, if the resulting mixture, after shaking and centrifuging, gives evidence of a precipitate between the two phases, the contents of the tube should be discarded; such a precipitate indicates that some of the blood solution was accidentally transferred to the ether phase; since the protein in blood would absorb or adsorb the drug-dye complex, a rerun is necessary. Procedure for Whole Blood Standard Curve with Erythromycin. T h e 1.0-ml blood sample, spiked with erythromycin, was diluted with 2 ml of phosphate buffer to pH 6.0 as above, followed by saturation of the aqueous mixture with solid sodium bicarbonate, then addition of 3 drops of saturated sodium carbonate aqueous solution. The alkaline solution was then extracted with 2 ml of diethyl ether by shaking on the Eberbach shaker, using the same tube orientation as described above, followed by centrifugation as described above. The ether layer was transferred to a 5-ml glassstoppered centrifuge tube. The rest of the procedure was the same as described above under “Procedure for Whole Blood Standard Curve with Erythromycin Propionate” starting with “To the ether layer was added . . .”, except that 3 additional drops of saturated sodium carbonate solution was added to the blood before the second extraction with diethyl ether. Separation of Erythromycin and Erythromycin Propionate. Aqueous Solutions. T o 1.0 ml of aqueous solution which has been spiked with both erythromycin and erythromycin propionate, was added 2 ml of phosphate buffer (0.1 M , pH 6.0). The solution was then extracted twice with diethyl ether as described above under “Procedure for Whole Blood Standard Curve with Erythromycin Propionate”, starting with “The tube was shaken . . .”. The aqueous solution, after being twice extracted with diethyl ether, was saturated with solid sodium bicarbonate, then 3 drops of aqueous saturated sodium carbonate solution was added. T h e procedure described under “Procedure for Whole Blood Standard Curve with Erythromycin” starting with “The alkaline solution was extracted . . .”, was then carried out. Whole Blood or Plasma. The procedure was the same as described above for aqueous solutions, except that a spiked whole blood or plasma sample was used in place of the aqueous solution containing erythromycin and erythromycin propionate. Figure 1 summarizes the steps involved. Correlation of Results with the Microbiological Assay. Whole blood samples were spiked with erythromycin to final concentrations in the range 0.1-2.8 bg/ml. The plasma was then separated by centrifugation and aliquots were assayed both by the new extraction-fluorescent method and by the standard microbiological method. The latter assays were carried out in the Clinical Research Laboratory of The Upjohn Company with all samples being under blind label. Kinetics of Hydrolysis of Erythromycin Propionate in Whole Blood. Whole blood was pre-equilibrated a t 5, 25, 30, and 37 OC. This blood had been spiked with erythromycin propionate to a final concentration of 2.2-2.7 pg/ml. After the spike solution was mixed with the blood well, the spiked blood was maintained at the specified temperature. Aliquots of 1.0 ml of blood were withdrawn a t various times and assayed for propionyl erythromycin.
RESULTS
Standard Curves. The a q u e o u s s t a n d a r d c u r v e s , resulti n g f r o m both e r y t h r o m y c i n and e r y t h r o m y c i n p r o p i o n a t e , a r e s h o w n i n F i g u r e 2. T h e standard c u r v e s p r e p a r e d w i t h e r y t h r o m y c i n p r o p i o n a t e had g r e a t e r slopes t h a n standard c u r v e s p r e p a r e d w i t h e r y t h r o m y c i n ; thus, the ester has a g r e a t e r specific fluorescence t h a n the free base. S t a n d a r d c u r v e s p r e p a r e d f r o m whole blood and p l a s m a were i d e n t i c a l t o the a q u e o u s standard c u r v e s , i n d i c a t i n g c o m p l e t e e x t r a c t i o n of t h e t w o c o m p o u n d s f r o m w h o l e blood or p l a s m a . The recovery of both e r y t h r o m y c i n and
ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
__ Table I. Recovery of Erythromycin and Erythromycin Propionate from Blood -
Sample
Erythromycin added, a/ml
PEa
Eb
PE
E
A B C D E F G
1.94 1.94 1.36 0 0 1.36 1.36 1.36 1.36 1.36 1.36
1.53 1.53 1.53 1.53 1.53
1.80 1.84 1.43
1.56
1.07
1.36 1.40 1.30 1.36 1.32 1.30
H
1.58 1.52 1.62
...
1.07 0 0.54 0 0.27
... ... 100 103 96 100 97 96
1.07
1.07
...
0.48
...
0.30
99.0 a
PE
=
propionyl erythromycin.
b
89
...
111
101
3.6
?
6.0
Table 11. Correlation of Chemical Assay Results with Microbiological Assay Results for Erythromycin Base in Plasma Microbiological Assay of Plasma
60
Sample No. of No. detn
A B C D E F G
60
0
j
i
.".
E = erythromycin.
100
8
102 99 103 99 106 100 100
93 95 105
1.52
...
E
PE
No.
I J K
Percentage recovery
E r y t h r o m y c i n s recovered
dC
6 5 6 6 6 6 6
Av, %!ml
3.72 2.75 1.99 1.38 0.75 0.36 0.16
Chemical Assay of Plasma
Re1 s t d dev. %
N o . of detn
6.1 5.0 8.2 6.5 9.5 14.3 12.0
5
5 6 6 6 3 4
AV, i.lg/ml
3.92 2.56 1.86 1.39 0.78 0.40 0.20
Re1 s t d dev, 9
2.6 3.6 6.3 5.8 10.5 21.8 15.1
2c
drolysis of erythromycin propionate to erythromycin in 0.1
M citric acid is negligible within 2 hr. However, when the same erythromycin propionate in 0.1 M citric acid solution - 4
ce
12
6
ERY-HaOMViIh
20 MCG
i4
28
32
N
Figure 2. Typical calibration curves: ( + ) erythromycin propionate,
( 0 )erythromycin
erythromycin propionate is shown in Table I. Recovery of both compounds was essentially complete. T h e blood or plasma blank is equivalent to about 0.1 pg erythromycin per ml. The water blank is equivalent to about 0.05 pg erythromycin per ml. Effect of Time on Intensity of Fluorescence. It was found t h a t the fluorescence intensity was essentially constant for both erythromycin and erythromycin propionate from 0.5 to 2 hr after dissolving in 0.1 M citric acid solution. The p H of the citric acid solution (ca. 2.2) is the same as that reported (30) for facile conversion of an erythromycin to its corresponding anhydroerythromycin. Thus, three possibilities exist: (a) the conversion to the corresponding anhydroerythromycin is complete within the 0.5 hr under assay conditions and the anhydroerythromycin is the reactive species; (b) there is no conversion in the 2-hr period and erythromycin or erythromycin propionate is the reactive species; or (c) the conversion is partial, but conversion does not change the fluorescence intensity. No attempt was made to determine which of the three possibilities was correct. I t would be expected t h a t the anhydroerythromycins respond in the assay. Since the molar intensity of fluorescence of erythromycin propionate is higher than t h a t of erythromycin, the above result also indicated t h a t the hy-
was kept a t 25 "C for 3 days, the fluorescence intensity of the solution dropped to the value for the same concentration of erythromycin. This indicated the complete hydrolysis in 3 days. Correlation of Fluorescence Assay Results with the Microbiological Assay. Correlation of the results obtained with the extraction-fluorescence assay with those obtained by microbiological assay is shown in Table 11. T h e least squares line (Equation 1) was obtained from 7 points each of which was the average of 3-6 determinations (Table 11).
Y = 1.00 X
- 0.003
(1)
In Equation 1, Y is the average chemical assay and X is the average microbiological assay. The correlation coefficient was 0.995 ( p
