Calibration, calibration drift and specimen interaction in autoanalyser systems

CLINICA CHIMICA ACTA

CALIBR-~TION,

161

CALIBRATION

DRIFT

XUTOANALYSER

SYSTEMS

dNNETTE

D. GARTELMANN*,

BENNET,

Biockt~istry

Drpavtmed,

(Received

March 7. 1970)

Alfred

Hospitd,

AND SPECIMEN

JANET

Melbourne

INTERACTION

IN

I. MASON AND J. A. OWEN** (-4 mtraliaj

SUMMARY

Third order poiynomials, expressing assay value as a function of peak reading on a linear chart scale, have been found to fit AutoAnalyser calibration data for 16 tests. Routine measurement of the exactness of fit is useful in detecting errors in the calibration standards or in the calibration procedure. With many procedures calibration drift in AutoAnalysers is usually small provided attention is paid to various operating conditions. With others, appreciable drift occurs as a result of changes in baseline, changes in method sensitivity or both. Full correction for calibration drift requires both factors to be taken into account which means that the calibration procedure has to be repeated. With AutoAnalysers, the influence of a specimen on the assay value of the specimen following it depends on the sampling rate but is independent of the sample/ wash period ratio, at least within the limits tested. Quantitatively, the carry over from a specimen is a constant percentage of its assay value. Correction of results for specimen interaction can be achieved by subtracting from each assay value a percentage of the assay value of the preceding specimen. Interaction between calibration standards requires difference treatment.

INTRODUCTION

In the course of devising a computer system to acquire and process data from standard AutoAnalysers (Technicon Instruments Co., Chertsey, England)192, methods of calibrating such systems and of allowing for calibration drift and specimen interaction have been investigated. Our findings are presented in three sections-calibration, calibration drift and specimen interaction. * Present address: Honeywell Pty. Ltd., Sydney (Australia). +* Present address: Department of Chemical Pathology, St. Georges Hospital Lonclon, S.W.1 (U.K.). Clin. Chim. Acta,

Medical School,

zg (1970)

161-180

I. CALIBRATIOK

Obtaining a test result in analytical chemistry usually involves establishing a calibration curve expressing the relation between an assay value and a reading from the instrument used. The test result is then obtained by some form of interpolation. The form of calibration curve obtained with AutoAnalysers varies from test to test. Many tests give calibration curves which approximate to the logarithmic curves defined by Beer’s law but some, e.g. potassium by flame photometry, give almost linear calibration curve, others, e.g. the phenolphthalein method for carbon dioxide, give S-shaped curves. Preliminary studies in this laboratory indicated that a third order polynomial curve could be fitted to most AutoAnalyser calibration data. Investigations

Our studies were carried out with standard AutoAnalyser modules grouped to provide up to five test-channels per sampler. The samplers and the flame unit were type II. The computer confi~ration and its interfacing with the AutoAnalyser samplers and recorders have been previously describedl. The computer program currently in use2 fits a third order polynomial to calibration data, expressing the assay value (A) as a function of peak reading (P), zji:. A = a+bP-/-cP2+dP3

The algorithm used is based on a procedure described by Forsythe. Peak readings are recorded on a linear scale from o-100, with the baseline end of the scale as zero. In some tests, recorder range expansion4 is used to spread calibration peaks across the recorder chart. Examples of curve fitting are shown in Fig. I. It should be noted that peak readings do not in general correspond to optical transmission readings because the baseline end of the scale is read as zero and range expansion is used in some tests. Five calibration standards are used with each test. Every time a test channel is calibrated, a calculated value is obtained for each standard from the peak reading using the polynomial. The difference between the calculated assay value of each calibration standard and its nominal value corrected for specimen interaction (see section III) is then squared and summed to provide a goodness-of-fit index; where there is a good fit, the sum of squares of these differences is small. In operation, the system prints out the sum of squares multiplied by 8, because numbers less than I are printed as zero and small values would, without this multiplication, appear as zero. Data given in this paper are as printed by the system. Some results obtained in the routine use of the computer system are given in Table I. In assessing these, four points must be noted. Firstly, in certain tests, as indicated in the column headed “mPl,oe of stazdards”, the result is expressed with one decimal point but the decimal point is ignored in calculating the sum of squares, Le. an assay value of 2.5 is taken to be 25. Secondly, differences between the nominal value of standards (corrected for interaction) and their calculated values which are less than 0.4 (0.04 in the case of results with a decimal point) are treated as zero. For example, in the case of carbon dioxide, if all five calculated values for standards are within 0.4 of the nominal values (see Table III), a zero sum of squares is obtained. This has the effect of making curves which have a very good fit appear to have a perfect fit. Thirdly, the values for sum of squares obtained for different tests are not Clin. Chin?. Acta, zg (1970)

161-180

163

AUTOANALYSERCALIBRATIONAND INTERACTIOX

IOr

t

(C)

Fig. I. Third order polynomial curves fitted to calibration data. Points represent calibration data: continuous lines represent calculated calibration curves expressing assay value (A) in terms of peak reading (P). (a) Estimation of urea: .4 = -2.423X 10+5.235% (b) Estimation

‘4 = (c)

of glucose

-2.226X

IOP-1.067X

10-eps+3.773X

10-3P3

:

10*+1.6Q5x

IoP+I.837:<

Estimation of alanine aminotransferase: -4 = 9.586- r.o73P+5.057 x ~o-sPa-+Sg+

ro-‘P*+8.g13X x

IO-*P*

rcr5P3.

In (c), readings below the baseline correspond to apparent assay values because of the shape of the calculated curve. However the computer assigns zero assay values to peaks with readings below those of the lowest standard so that erroneously low readings do not give misleading results.

strictly comparable because the nominal assay values for standards vary from test to test. Thus a difference of I”/~in assay values will contribute more to the sum of squares at an assay value of 450 (top glucose standard) than at a value of 40 (top CO, standard). Lastly, it is necessary to appreciate the sensitivity of the procedure. Taking the measurement of urea, for example, if each of the five calculated assay C&n.Claim.Acta, 29 (1970) 16x-180

BENNET et (21. TABLE

I

FIT OF THIRD

ORDER

POLYNOMIALS

TO CALIBRATION

DATA

The fit for each calibration curve is expressed as the sum of squares of deviation of data points from the calculated curve (see text\. Calibration data considered unacceptable on other grounds have been excluded. --.-__I__..__--~ -. Test Raszge of standards stm of squares* X&iOd Rattge of opti- Recodw

rcfivence

---~~_ Xlanine aminotransferase Albumin Alkaline phosphatase .Aspartate aminotransferase I .&part&e aminotransferase II Rlirubin Chloride CO, (total) Creatinine Glucose Iron Phosphate (inorganic) Potassium Protein Sodium (plasma) Sodium (urine) Urate Ikea I Urea II

tical tvansmrs- rmge

_.~~ 2 :,1 29 25 28 28

30 3r 32 33 38 3-i 36 37 39 37 37 40 Jr 41

-._. 0-80 0.0-8.0 0-80 o-400 o-200

0.o6.g 60-140 0-40 o.o--12.0 0-450 0-300 0.0-12.0 0.0-8.0 o.o--11.0 100-180 o--200 o.o--12.0 0-480 o-480

-_-.

sion values of expansion standards I” / ) factor

-.--

-

so.

_ ____“.__._.._-._._.

RF units

5a-95

1.0

g/100

P-95

I.3

29 25

1.0

23

ml

KX units/roe

ml 40-95

Xean Irango

5o--95

1.0

I_(

490

RF units mg/roo ml mmole/l mmolejl mg/roo ml mgjroo ml jdg/roo ml mg/roo ml mmole/l g/r00 ml mmole/l mmolejl mg/roo ml mgjroo ml mg/roo ml

60-95 30-95 *o-95

1.0

r9

157

I.0

26

4

40-95 60-95 30-95 45-95 O-60 * * 30-95 20-60 * * o--100** 60-9.5 20-95 jo-oS

I.0 1.0

115 I12 2-f

4

57

93 10

1.6

22

II

1.0 2.j I.0 I.-i

I.0 1.6

20-3080

2

1.4

1.0

O-87

31

1.2

2.3

O-21

I6

RF units

IO--C)0

G-20

3 4

8

“7

30 I17 I7 17 28 IO‘i

3 I5 IO IO

3 774 2.i

* Scaled x 8; see text. ** Emission values.

concentration and peak reading for those colour-producing reactions which obey Beer’s law and for which there is no recorder range expansion ; the baseline end of the peak scale is read as zero so that the optical transmission is (100-P):/,. The results are given in Table II. Use of the transformation log (100-P) improved the fit of the high-colour urea data considerably and that of the chloride and When the program was first used, the manifold used in estimating urea gave an optical transmission value of approximately ZOO/~ for the top standard (Table I, Urea I). The fit of the polynomial was relativeIy poor especially at low assay values. When the manifold was altered, however, so that the top standard gave less colour (transmission approximately 5074) the fit was better (Table I, Urea II). In the measurement of aspartate aminotransferase as initially set up, the sum of squares was larger than with any other tests (Table I, Aspartate aminotransferase I). Halving the range of standards improved the fit (Table I, Aspartate aminotransferase I I). In the case of glucose, sums of squares were larger than in most other tests though they corresponded on the average to a mean difference of less than 2 mg/roo ml. We next checked to see whether a log transformation of the peak reading (P) prior to curve fitting would improve the fit for certain tests. The analysis was carried out off-line with the aid of a CDC 3200 computer. Two log transformations were tried, log P and log (100-P). The latter transformation provides a linear function between Clin. Chinl. Acta, 29 (1970)

161-180

o-655 o-27

0-203 o-32 o-20 o-497 *-- 39 o--._II O--3’ O-80

o-87 O-35 O-IO

4-1736 o--2 18 -

AUTOANALYSER TABLE FIT

16.5

CALIBRATION AND INTERACTION

II

OF THIRD

ORDER

POLYNOMIAL

TO CALIBRATION

DATA

AFTER

LOG

TRANSFORMATIONS

Data are means and range of sum of squares. Test

No. of detns.

Albumin Aspartate aminotransferase Chloride CO, (total) Glucose Potassium Protein Sodium Urea I* Urea II*

:;*

3 3 2 2 3 2 3 2 3 3

Form of peak data p 4 ~660 56 3 I9 I I5 I2 1071 8

33 7850 2235 3 “7 228

(o-8) (1830-3080) (50-63) (o-6) (3-45) (O-I)

(11-25) (8-16) (328-1736) k-24)

log (100-P)

log P

6 3569 I9 35 I77 20

(O-10) (‘020-5330) (14-24) (x3-57) (46384) (o-39) 4 (2-7) 526 (44-1008) 52 (s-90) 49 (2r-100)

(o-82) (7830-8790) (704-3776) (3) (80-152) (6-450)

81 I (432-1500)

34 (23-45) >I04 1194 (856-1664)

curves with low transmission reading for top standards. curves with higher transmission readings (see text).

values deviated from the nominal values (see Table III) by z mg/roo ml, a sum of squares of 5 x 2%x 8 = 160 would be obtained. In general, the fit of a third order polynomial to routine AutoAnalyser calibration curves was good but data in three tests: determination of urea, aspartate aminotransferase (GOT) and glucose, require comment. protein data marginally. Transformation into the form log P either did not improve the fit or made it worse. Finally, the sensitivity of the sum of squares as a measure of curve fitting was examined by running sets of standards in which the middle one had been diluted to simulate a “bad” standard. In four of the five tests examined, the “sum of squares” was sensitive to changes in one standard (Table III). The exception was in the measurement of total CO,. This may have been due to the fact that the CO, calibration curve is S-shaped and that it TABLE EFFECT

III OF ERROR

IN

ONE

STANDARD

ON CURVE

FITTING

Data are means and range of the sum of squares. Assay values for standards were as follows: Cl CO* K Na Urea

60, 80, IOO, 120, 140 mmole/l (total) 0, 10, 20, 30. 40 mm&e/t 0.0, 2.0, 4.0, 6.0, 8.0 mmole/l Ioo, 120, 140. 160, 180 mmole/l 0, 60, 120, 240, 480 mg/Ioo ml

Test

Chloride CO, total Potassium* Sodium Urea

Evvor in middle standard

0 (O-I) 2 (o-7) IO (*33)

74 I3 2 55 60

(6*+9I) (o-40) (o-3) (21-102) (23-126)

94 2 4 35 254

f70-I3I) k-6) k-7) (20-35) (31-603)

275 I3 42 354 3I2

(211-332) (O-41) (29-59) (226-475) (271-591)

* Potassium results have one place of decimals which is ignored in calculating ** n = number of determinations.

sum of squares.

CEin. Chim. Acta, 29 (rg7o) 16r-180

was the middle standard which was diluted. In all five tests, study of the chart tracings indicated that a -2% error in one standard would not have been detected on visual inspection had it occurred in a routine run and that a --do/d error could easily have been missed. Diswssion In a number of computer-based AutoAnalyser systems, assay values have been obtained from the peak readings by linear interpolation between individual calibration pointP7. This is equivalent to joining the calibration points on a conventional chart reader by straight lines. A similar procedure has been employed in an off -line data-processing system using diode functiou generators to divide ealibration curves into five straight line segmentsa. When the calibration curve is markedly non-linear, however, or when only a few calibration data points are employed, linear interpolation between pairs of calibration points may cause error %.Fitting a curve to calibration data avoids this type of interpolation error and also makes allowance for random error in the data which is not possible with linear interpolation between data points. As an alternative method of avoiding errors due to linear interpolation between points on a curve, a method of four point interpolation was used in an earlier computer system in this laboratory’ but the algorithm proved unsatisfactory with markedly curved data plots. Another possibility is to transform readings so as to obtain a linear calibration curve. Transformation of readings in transmission units to readings in absorbance has been advocated for this purposeto but it is our experience as well as that of others5 that few calorimetric reactions follow Beer’s law over the entire working range. Yet another possibility is suggested by the finding’1 in a fluorometric AutoAnalyser procedure for measuring triglycerides, that the reciprocal of the assay value was linearly related to the reciprocal of the peak reading, viz: I

-=a+p

b

A

We became aware of this only while preparing this report and have not tested the fit of this type of curve. If it were generally applicable, there would be some advantage in having to compute two parameters instead of four. In a computer system, economy in programming and core storage requirements is achieved if the different types of calibration curve can be fitted with the same function. Our system fits a third order polynomial and data obtained from its routine use indicate that AutoAnalyser calibration curves in general can be satisfactorily described by a function of this type, Log transfo~ation of peak readings improved the fit of a high colour urea curve but made the fit with other tests worse. Another system12 also employs a high order polynomial to express calibration curves but the order of the polynomial and data on the goodness of fit are not given. Initially, the fit with urea calibration curves was relatively poor. Colour intensity in this test approximates to that defined by Beer’s law and the reason for the relatively poor fit with high colour curves was probably due to our attempt to fit a third order polynomial to data which gave a markedly curved plot at the top standard end (because of their logarithmic nature). When the colour intensity of all stanClin. Chim.

Acta,

zg (1970)

161-180

AUTOANALYSERCALIBRATIONANDINTERACTION

167

dards was reduced by altering the manifold, the plot was less curved and consequently fitted better by a third order polynomial. Similar findings were obtained in fitting third order polynomial curves to artificial data simulating calibration curves exactly obeying Beer’s law; a better fit was obtained with data corresponding to a moderate colour range than with data corresponding to a wide range. The relatively poor fit in the case of aspartate aminotransferase was due to a difference in the shape of the calibration curve from any third order polynomial curve. However, even though the fit with the initial arrangement of standards was poor, it was not completely unsatisfactory; on the average, the mean difference between calculated and nominal values for standards was 4 units and in the case of the poorest fit recorded was only 8 units. In the determination of glucose, the mean sum of squares was higher than in most other tests. This was probably more due to the high mean value of standards (viz: o, 75, 150, 300 and 450 mg/xoo ml) than to poor curve fitting The routine print-out of the sum of squares for each analytical procedure provides an early warning of certain types of analytical trouble. Our assessment (Table III) has shown that this index is particularly sensitive to errors in a single calibration standard and that, for small errors of this type, it is more sensitive than visual inspection of the chart tracing. In practice, we have found that it is sensitive also to other errors such as calibration standards run out of order or to the use of excessive range expansion causing the top standard to have a flat peak. An example of the sensitivity of the sum of squares to error arose in early stages of the routine operation of the system. Initially, the assay value of the middle standard for total protein was entered into the system as 3.6 instead of its true value 3.3 {the range of standards was o to 11.0 g/xoo ml). The mean sum of squares before the error was corrected was 170 (range 78-222) whereas after the error had been corrected the mean value became 15 (range 0-80). It must be stressed however, that obtaining a sum of squares within an allowable range does not exclude trouble with the calibration curve. For example, dilution of one standard does not affect the sum of squares in all tests (Table III). Further, dilution of all standards by a factor of 0.9 will give calibration data which are erroneous, but for which the fit is good so that the sum of squares remains within the tolerance limits. Checking that, the reading of each calibration standard peak lies within limits6 would be required to detect this type of error. II.CALIBRATION

DRIFT

Once an analytical system has been calibrated, checks have to be made during a run for calibration drift and allowance made for it if necessary. Calibration drift may result from change in the baseline reading, from change in method sensitivity (peak height above baseline produced by particular assay value) or from a combination of both processes (Fig. 2). Method sensitivity has itself two components-chemical sensitivity and colour sensitivity. Chemical sensitivity is the ratio of colour intensity to assay value; colour sensitivity is the ratio of peak reading to colour intensity. In procedures involving absorption calorimetry, a change in baseline automatically produces a change in method sensitivity (Fig. 2); the reading for zero transmission is unaffected by the change in the reagent baseline, so that the calibration Chin. &him. Acta, zg (1970) 161-180

166

BENNET

.__ a.

b.

et at.

C.

Fig. 2. Types of calibration drift. Theoretical effect of baseline change and sensitivity change on the peak readings for four standards. (a) initial state, (b) baseline change, (c) sensitivity change. In (b) and (c), the changes in the reading for the top standard are identical but the change at other assay levels differs in (b) and (c).

position position

2, in position IO and in every tenth position thereafter, including the last in the batch, for the assessment of calibration drift. The specimens imme-

diately preceding these positions are also of the same material to protect the drift specimen against being swamped by a chance high peak immediately in front of it13. In most tests, one of the calibration standards is used as the drift standard but in some tests pooled serum is used instead. The amount of calibration drift in AutoAnalyser procedures under routine operation was assessed by measuring the baseline and drift standard readings at the start and end of analytical batches. The data are summarised in Table IV which lists the change in readings and the change in assay values for the drift standards. It also lists the change in drift standard assay value which would have been predicted from the change in baseline alone causing a shift in the whole calibration curve (see Fig. 2 and APPENDIX). In half the tests for which data were collected, the mean change in assay value of the drift standard from start to finish of the batch was 1% or less, though higher values were observed in individual runs. In the other tests, the mean change in assay value of the drift standard ranged from +1.9% in the case of urea to +II% in the case of albumin. Change in the reading for the drift standard was usually in the same direction as that in the baseline reading. However in the case of total CO, and protein, the mean percentage change in the assay value was considerably greater than was predicted from change in the baseline indicating that there had been a change in method sensitivity. The cause of drift in individual runs was usually not discovered. However, a factor noted on a number of occasions to influence calibration was a change in room temperature. Data on this effect were obtained by analysing a number of specimens from a serum pool in a room at 25”, then cooling the room to 15”, waiting 40 min and analysing further specimens. Finally the room was re-warmed to 25’ and, after a further 20 min a few more specimens were run. All results were read from the calibration curve obtained at the start of the experiment and no correction for calibration drift was applied. The results (Table V) show clearly that change in room temperature had a significant effect ($ < 0.01) on the chloride and urea results. On re-warming, the mean urea result did not return to its initial value, possibly because the re-warming period was too short. A similar effect of room temperature has been noted on results in the determination of phosphate. Biochiin. Biophys. Acta, zg (1970)

161~1%

IV

DRIFTIN

ROUTINE

AIJTOANALYSER OPERATION

(-0.4 (-4.0 (-0-g (-0.9 (-0.8

to to to to to

$4.2) +3.2) +o.g) io.8) ‘ro.6) 3.0 100 20 2.0 150

$

50) 80) 70) 80) 80)

0.3 (-1.4

0.5 (-4.8 0.0 (-1.5 --“,.4 (-0.6 to +2.4)

to 4.1) to io.5) to +2.0)

2.0 4.0 7.0 I40 120

* Baseline not available because of range expansion. ** From baseline change assuming no change in sensitivity (see text). * * * Prediction not attempted.with flame emission procedures.

2.2 0.2 0.1 -0.1 0.0

? b

40 40

to to to to to

70) 80) 80) 60) 80)

Sodium Urea

(20 (30 (30 (30 (30

to to to to to

? $

39 50 52 50 50

I8 20 40

(30 (30 (30 (20 (20

8

52 50 50 43 41 2.0

0.8 -0.2 1.2 -0.1 0.3

1.2 1.3 -o.o -0.2

Nominal -Peak assay value

Dvift standard

+3_6) 1-3.2) -t&4) +1.5) +r.g)

6.0 -0.5 +5.5 -0.4 I.9

-

to 1-27)

to 5.5)

to +5)

to j-21) to i-1) to +3)

I.9 (-8

***

to 1-13)

o.=j(-770 SII)

3 (-32 ***

to to to to to

(---zz to $28) (-14 to +x0) (-6 to +3o1 (-6 to 15) (-5 to 1-13)

(-2.5 (-4.5 (-1.3 (-1.6 (-0.9

8 (-I 0(-I 0.3 (-3 -0.7 (-6 -0.3 (-7 II

(-3 to t24) I(-3 to $10) 5.8 (-8 to +24) -0.2 (-16 to +IO) -1.0 (-8 to +4)

+4.2) +9.3) f5.5) j1.2) +0.5)

(-0.6 -3.5 (-1.7 f-I.2 (-1.3

to to to to to

Change in assay value .-_.-. _________ obsevued (Oh)

change

predicted* * (%)

were recorded as positive when they occurred in the direction of a peak. see Table 1.

Albumin Chloride CO, (total) Creatinine Glucose Phosphate (inorganic) Potassium Protein

zo 40 40 32 34

Changes in baseline and peak readings (start of batch to finish) Data are expressed as mean with range. For methods and units -___ No. of Batch size Baseline change Test detns.

CALIBRATION

TABLE

170 TABLE EFFECT

BENNET

et al.

V OF CHANGE

IN

ROOM

TEMPERATURE

ON RESULTS

Results are expressed as mean & standard deviation. They were all read from a standard curve run at 25’ and are not corrected for calibration drift (see text). Test

Room temperature ;L

Chloride CO, (total) Potassium Sodium Urea

91.1

23) * f

0.51

29.0 rt 0.93 5.56 zt 0.049 135.2 & 0.85 49.4 f- 0.58

Cooled to 15’ (n = 21)

Rewarmed to 25” (n = 6)

85.9 29.2

go.8 28.3 5.60 138 46.5

zt 0.96 * 0.87

5.50 & 0.221 I37 f 0.79 45.3 f 0.66

* & & k k

0.75 0.81

0.049 0.63 0.55

* n = number of determinations.

curve expands or contracts with change in baseline. In flame emission calorimetry, however, change in baseline does not necessarily affect chart sensitivity. Investigations The computer program currently in use2 requires the same material in sample Discussion Though Farr et aLa have observed negligible drift in an AutoAnalyser system for measuring urea over a period of 5 h, we find that drift is commonly present in certain AutoAnalyser procedures. Possible factors causing drift have been discussed previousl~~~4+. Mufficient “warm-up” period, a change in enviromental temperature or a change in the speed of an overloaded pump have been found responsible, but frequently drift is unexplained. When the cause of drift is known, it can often be abolished by attention to operating conditions but unexplained drift cannot necessarily be avoided and it is thus desirable to have automatic drift correction in any computer-based AutoAnalyser system. The routine assessment of calibration drift has been achieved by having specimens of the same material throughout a batch and comparing values obtained at intervals with initial values for the material r,13y14.However, in assessing drift in this way there is a problem in distinguishing between systematic change in response of the system with time and random fluctuations in the response of the system to individual specimens. When single drift specimens are analysed at intervals, it is impossible to determine how much of the change is due to systematic drift and how much to random fluctuation and, with this arrangement, there is no alternative but to assume that all the change is due to systematic drift and to make a correction. A better assessment of systematic drift could be achieved by analysing more than one drift standard at intervals. In our experience, certain tests, e.g. albumin, total CO,, inorganic phosphate and protein (Table IV) show consistent calibration drift. Usually the change in baseline and drift standard readings were in the same direction and in most tests the change in reading for the drift standard was consistent with the change in baseline. In the case of total CO, and protein, however, the change in the result for the drift standard was greater than would have been predicted from the change in the baseline indicating Clin. Chim. Acta, zg (1970)

161-180

AUTOANALYSERCALIBRATION

AND

171

INTERACTION

that in these tests there was also a change in method sensitivity during the run. Since assessment of drift at one assay value only does not distinguish between a change in the baseline and a change in method sensitivity (Fig. 2), the appropriate correction at this assay value is not necessarily the correction required at other assay values. It can be shown (see APPENDIX) that when drift is due solely to baseline change, drift correction of assay values is independent of the assay of the result to be corrected. When drift is due to change in method sensitivity, however, the correction has to be scaled according to the assay value to be corrected. It must be concluded that complete drift correction over the whole range of assay values requires assessment of the drift at more than one assay level. Logically the minimum number of levels required depends on the calibration function used. In the case of a third order polynomial, assessment of drift at a minimum of four levels is required. In other words, full assessment and correction for drift requires the calibration curve to be repeated. It seems likely that this would be required less often than after every eight or nine test specimens, for some of the drift observed between ten specimen positions is likely to be due to random fluctuation in the drift standard reading. Most computer systems described to date have drift correction based on drift assessment at one assay leve11~6~7~10~12~‘S~1e, but manye~7~12~1a reject drift correction if it exceeds certain limits which is a safeguard against gross errors in correction at other assay values because of non-uniform drift. Accepting that drift assessment at one level is useful within limits, we have chosen to correct for drift in terms of assay value whereas othersa9139z6 have corrected for drift in terms of peak readings. We consider correction in-terms of assay value in general better than correction in terms of peak reading. In most AutoAnalyser procedures the calibration curve is not linear in terms of chart reading and reference to Fig. 2 shows that in such tests drift, uniform in terms of peak reading over the whole assay range, is a most unlikely phenomenon. In contrast, at least in the case of baseline change, drift in terms of assay value is uniform (see APPENDIX). In the case of flame photometric assays parallel drift in calibration curves has been noted”. However such assays give almost linear calibration curves so that there is little difference between correcting for drift in terms of assay value and correcting in terms of chart reading.

Fig. 3. Specimeninteraction. When two identical specimens are analysed consecutively, the peak reading for the second (P,) is greater than that of the first (PJ due to carry over. In this situation, percentage carry over is the assay value of the second peak (A,) less that of the first peak (A,) AZ---A, as a percentage of the first (A,), i.e. o/O carry over = ~ x IOO. Al

Clin. Chim. Acta,

zg (1970)

161-180

BENNET et a!.

172 III. SPECIMEN INTERACTION

In automatic analytical systems the effect of a specimen on the result for the following specimen is termed specimen interaction. In theory, at least, it occurs whenever specimens or their reaction products come in contact sequentially with a common surface. Specimen interaction is inherent in continuous flow systems. However it may also occur in discrete analytical systems, if the same pipetting system is used for sampling different specimens or if a continuous flow calorimeter is employedal. AutoAnalyser samplers are designed to introduce samples separated from one another by a period of time and, consequently, by a segment of reagent stream. In addition, the liquid stream is further segmented by air bubbles but in spite of these precautions the colour peak produced by a sample tends to run into the peak produced by the sample immediately following it. Fig. 3 shows diagramatically what happens when two identical specimens are sampled, one immediately after the other. Before the reading returns to baseline after the first peak, the next peak arrives. The second peak is higher than the first because of carry over from the first peak. The higher the concentration in a specimen, the greater the absolute effect on the next peak. Investigations

In studying carry over quantitatively, we used a sampling rate of go/h in order to make carry over more significant and thereby reduce error in its measurement. The sampling and wash periods were controlled by the computer using a specially prepared short program. The computer interface consisted of a programable relay driver operating a relay which plugged into the external timing socket of the modified Sampler III. The time intervals produced by the computer were accurate to 0.02 sec. Variation in relay action and in the movement of the sampler arm presumably caused some variation in sampling but studies with a stop watch indicated that this was less than 0.5 sec.

Fig. 4. Carry over at different concentrations. Calibration standards, separated by two cups of water to make carry over between standards negligible were run first. Three identical specimens were then run in consecutive positions. This was repeated at different concentrations. C&L Chim.

Acta, 29 (1970)

161-180

AUTOANALYSER

CALIBRATION AND INTERACTION

I73

A calibration curve was obtained for each sampling/wash ratio by analysing five standard solutions each separated by two cups of water so that carry over between standards was negligible (Fig. 4). Peak readings for standards were plotted against assay values on graph paper. We studied first the effect on carry over of the assay value of the specimen causing it. Three identical specimens were run in consecutive positions at several assay levels; each set was separated by two cups of water and each assay level was run two or three times. A sample/wash ratio of I : I was used. Assay values were read off the calibration curves. Carry over was calculated as the difference between the assay value of the second peak (A,) of each set of three and that of the first (A,) as percentage of the first assay value, i.e. A,--A, o/o carry over = -----x100 AI TABLE

VI

EFFECT OF ASSAY

VALUE

AND

SAMPLE/WASH

RATIO

ON PERCENTAGE

CARRY

OVER

Percentage carry over data are expressed as mean and range: n = number of estimations, sample period/wash period ratio. Sample rate go/h. For methods and units see Table I. Assay

Test

Albumin

Chloride

CO, (total)

carry 0veY

NO.

s/w = I:1

No.

1.2

2

12 (12)

2

17 (11-23) I7 (14-20) 23 (21-25) *

2

2.4 5.0

2

23 (23-24)

2

20

2

20 (2*21) 21 (21) 18 (17-18)

2

*

80

2 2

I7 (17)

2

IO0

‘9

(18-20)

2

IO

2

24 (20-28)

2

20

2

I8

2

2 2

:

2

5 (5-6) *

(17-19)

2

I.0

3.0 8.5

Glucose

75 150 3oo 375

(inorganic)

*

7 (53) 7 (5-9) 6

2 2

I

I.0

2

3.0 8.5

2

2.0

[#I;;

2 2

3 3 I 2 2

25 (‘7-33) 16 (‘5-17) 8 (7-11)

2

19 (19)

2

4.0

2 2

19

(18-20)

2

1.1

2

18

(17-19)

2

3.3

2 2

‘5 (“-19)

2

21

2

II0

*

*

2

120

2

2

140

2

25 (25-26) 24 (23-25)

60

2

(27-30) 27 (25-30) 24

2

Potassium Protein

8.0

Urea

Percentage

60

Creatinine

Phosphate

value*

2

120

2

360

I

s/w =

29

(21)

2

2

2 I

s/w = .3:1

(18-23)

34 (32-36) 22 (18-26) 7 (5-8) 8 (6-10) 8 (8) 6 (5-7) 7 (6-8) 6 6 (6) 15 (13-17) 16 (15-17) 9 (g-10) 23 (23-24) 18 (17-20) 18 (11-26) 22 (22-23) 21 (19-23) 2I (zo-21) 23 (23) 2r (20-22) 30 (28-32) 26 (25-26) 23

* Protein-free solution was used except in the case of albumin and proteins determination which pooled serum was used. C&z. Chim. Acta,

29 (1970)

for

161-180

BENNET

174

et al.

The results (Table VI) show that the percentage carry over was in general independent of the assay value. To study the effect of sample/wash ratio on carry over, we altered the sampling program to produce a 3 : I sample/wash ratio at the same sampling rate and repeated the experiment. The percentage carry over was essentially unaffected (Table VI). The effect on carry over of sampling standard solutions and pooled plasma was then compared. Pools of plasma were prepared with individual assay values within zoo,4 of those of standard solutions and carry over examined as previously. In most tests, the percentage carry over values with standards and plasma were the same (Table VII) but in the case of phosphate higher with standard solutions. TABLE

determination

carry over was significantly

VII

CARRY OVER WITH PLASMAAND STANDARDSOLUTIONSCOMPARED Results expressed as percentage carry over, mean and standard deviation, with number of determinations in parentheses. Sampling rate go/h. Sample/wash ratio 1 :I. For units see Table I. Test

Assay values

Chloride CO, (total) Creatinine Phosphate Potassium Sodium Urea

100 20

5.0 3.0 4.0 140 120

* P >0.4. ** Probability

Percentage

carvy oue~

p**

Standard solns.

Plasma

21.2

+ 0.7 (4)

23.4 7.4 16.4 22.0 24.9 27.9

* f + f + f

21.2 24.9 6.6 9,9 19.8 21.0 25.4

4.7 1.2 4.0 1.8 1.9 4.1

(4) (8) (5) (4) (4) (4)

f * & f & f f

3.1 3.7 1.0 0.9 2.5 2.6 5.3

* * *

(10) (10) (8) (5) (IO) (8) (10)

<0.05 *
of difference in means being due to chance alone.

Lastly we collected carry over data under day-to-day conditions. The first two specimens in each analytical batch are drift standards and the second of these normally acts as the drift datum. By modifying the AutoAnalyser program slightly, we omitted carry over correction between the first and second specimen and used the tenth peak as the drift datum. This allowed us to measure the percentage carry over in each run as described by Blaivas and Mencz lo. Some data on carry over under day-to-day conditions are given in Table VIII. TABLE

VIII

PERCENTAGECARRY OVER UNDER ROUTINEOPERATINGCONDITIONS over data are expressed as mean and range. Protein-free for units at the sampling/wash period ratio I : I.

Carry

Test Chloride CO, (total) Creatinine Glucose Iron Phosphate (inorganic) Potassium Sodium Urea Urate Clin.

Chim.

Acta,

standards were used. See Table I

Sampling vate

Assay value of carry eve? specimens

de&s.

Carvy “;I

60 60 30 40 30 30 60 60 60 30

100 20 2.0 150 100 2.0 4.0 140 120 2.0

44 44 II 23 2 44 44 44 53 6

7 8 o 1 2 5 4 II 6 3

29 (1970) 161-180

No. of

ozlw

(I-13) (o-15) (0) (o-4) (2-3) (o-11) (o-9) (6-17) (2-12) (o-10)

AUTOANALYSER

CALIBRATION

AND INTERACTION

I75

Specimen interaction is inherent in AutoAnalysersl~5~14~*8-20142. Basically it is due to longitudinal mixing in the liquid stream. Danckwert9, in a general discussion of continuous flow systems, has labelled the effect “hold-back” because some elements of liquid spend more than average time in the system. The air bubbles in the stream considerably reduce the longitudinal mixing which would otherwise occur in AutoAnalysers but a film of liquid between the bubbles and the wall of the tubing2s~27 allows some transfer to occur between inter-bubble segments. In practice it is usual to design the manifold and to select a sampling rate which reduces the carry over to such a small value that it can be ignored, except when a large peak immediately precedes a small peak; the small peak is then regarded as “swamped” and the specimen re-analysed. As the sampling rate in an AutoAnalyser system is increased, the percentage carry over increases also (compare Tables VI and VIII). With manual chart reading, routine correction for interaction is tedious but with a computer it is practicable. Routine correction for carry over allows a more rapid sampling rate and elimination of the need to re-analyse “swamped” specimens. Further, Thiers and Oglesby have shown that correction for carry over improves the reproducibility of AutoAnalyser procedures. Our investigations confirm previous reports 10~14p42 that carry over, expressed as a percentage, is independent of the assay value of the specimen causing it. This is supported by the findingzO that specimen interaction in AutoAnalysers has usually the characteristics of a constant volume contamination. On this basis, the measured response of the system to a sample is considered to be derived from a fraction (v) of the preceding sample and a fraction (1-s) of the current sample. There is, in effect, dilution and contamination. However, the dilution affects equally all samples, and like dilutions elsewhere in the system, the dilution factor can be ignored. Like others10~14~1S, we have expressed carry over as percentage of the previous result. It has been suggested19 that carry over is better expressed in terms of the ~iff~ye~~ebetween two successive results. The problem here is in deciding whether the “true” response of the system to a sample is that given by a sample run in isolation or that given by a sample run after one or more identical samples. It may be argued that the response to the first sample has been affected by the (negative) carry over effect of water preceding the first sample-the dilution effect of constant volume contamination. However in an AutoAnalyser, the absolute dilution of the sample due to mixture with reagents does not enter into the calculations of results. We feel that the dilution due to constant volume contamination should be similarly treated and consequently accept the response to an isolated sample as the “true” response of the system. Thus the carry over effect is always positive and the percentage carry over (as we accept it) equals the percentage volume contamination. If the effect of water prior to the first peak is to be taken into account, the effect of water sampled between specimens in systems using the Sampler II should also be considered. It has been reported that the carry over effect is less with standard solutions than with serum, at least with the Sampler I lsta2.Our findings with Sampler II (Table VII) indicate that, with most tests, there is little difference between plasma and standards, though there was in the case of phosphate for which we have no explanation. Ctin. Chim.

Acta,

29

(1970)

161-180

BENNET et al.

I76

Failure of an increase in the sampling/wash ratio to influence the percentage carry over was unexpected. However, carry over results from a failure of the response (i.e. colour production) to one sample to fall to zero before the response to the next sample reaches its peak. It would appear that the rate of fall of response relative to the peak height is independent of the sample/wash ratio. The transition between steady states in AutoAnalysers obeys first order kinetics to a good first approximationl*. The carry over effect thus depends mainly on the time elapsing from the moment colour intensity in the flow cell starts to diminish until the time the next peak is reached and, at any given sampling rate, this period is constant. Reducing the wash period, however, has a marked effect on the appearance of the chart tracing. Peak readings get nearer the value obtained on continuous aspiration of a specimen, but the peaks are less well defined and, with manual reading of charts, it becomes increasingly more difficult to choose the peak. This problem could be overcome by taking readings at specified points of time as in the SMA 12/60 (Technicon Corporation, Tarrytown, N.Y.)23 or in a computer system designed to do likewise. Studies on routine AutoAnalyser runs indicate that the mean percentage carry over under day-to-day conditions varies among different tests from zero to 11%. Similar variation between tests has been noted previously14. Higher values are obtained in procedures with higher sampling rates. The electronic damping applied to signals generated in the flame photometer is an additional factor producing the carry over effect in the measurement of sodium and potassium. We find, like others14t22, that the extent of carry over in a particular XutoAnalyser procedure also varies from day to day; it tends to be minimal when the tubes, especially the sample lineZ2, and coils of the manifold are clean and the dialysis membranes are fresh. Build up of a fibrin film on internal surfaces is one of the factors responsible for increasing carry over in systems analysing plasma. There would seem, therefore, to be merit in assessing the degree of interaction in each runlo. However with some tests the random error in a single result is such that the difference between two consecutive results would require to be determined several times within a run to obtain a sufficiently reliable carry over factor and this would involve a further reduction in the proportion of patients’ specimens in a batch. Our computer program allows an individual carry over correction factor in the range o-I~~/~ to be specified for each test which covers adequately the degree of carry over normally experienced. There is at present no provision for specifying a different

50

100

200

50

400

103 206 412

CONCENlllATION UNITS

Fig. 5. Diagram illustrating the effect of carry over on calibration standard assay values. standards are run under conditions giving negligible carry over (as on the left), their effective are the same as their nominal values. When there is carry over (as on the right), the effective of standards are higher than their nominal values due to carry over. In this illustration, been assumed that the carry over was 65,. Clin. Chim. Acta,

zg (1970)

161-180

When values values it has

AUTOANALYSER

CALIBRATION

I77

AND INTERACTION

correction factor for plasma and standards but it would be simple to provide this. In calculating the assay values for test specimens and for drift standards, the program subtracts from each assay value the specified percentage of the calculated assay of the preceding specimen. Since our correction for carry over is based on assay values rather than peak readings, it is clearly not possible to deal with carry over between calibration standards in the same way. However, correction for carry over is required and we have done this by adding to the nominal assay value of each calibration standard the specified percentage of the assay value of the preceding standard. This is illustrated in Fig. 5. APPENDIX

Theoretical consideration of drift correction (a) Logarithmic calibration curves. In a number of AutoAnalyser procedures, the relation between assay value of test substances and colour intensity is close to that predicted from Beer’s law. Thus if the AutoAnalyser is set up so that B is the optical transmission of the reagent blank (baseline) and T is the optical transmission given by the test peak of assay A log T = log B-kA andA=i(logB-1ogT) Usually the baseline is set to give B a value of between go and IOO; k represents method sensitivity. If during a run the baseline reading changes by an amount D, the new baseline will have an optical transmission of BfD. It is convenient to express this change in terms of the factor CI,where a = (B+D)/B. In the circumstances, a sample of assay value A will now give a peak optical transmission of T’ where log T’ = log crB-kA or A = i (log ctB - log T’) If the new peak reading T’ is read off the original calibration curve, the apparent assay A’ will be ; (log B -

log T’)

and the apparent change in assay due to the baseline drift will be log tc A’-_A, = __ k The apparent change in assay value as a result of baseline drift is thus independent of the assay value. This means that the assay correction for calibration drift computed by re-running a sample run earlier in the batch can be uniformly applied to nearby samples regardless of their assay value. When calibration drift is due solely to change in method sensitivity the situation is different. If the sensitivity changes by a factor CC,the sample of assay A will Cl&. Chim.

Acta, zg (1970) 161-180

178

BENNET

et fli.

give a new optical transmission reading T”, where log T” = Iog B-c&A or A =s

(log B - log Y’)

If the new peak value is read from the original calibration curve, the apparent assay value A” will be ; (log B -

log T”)

The apparent change in assay value due to change in chemical sensitivity is AU--A, = (a-1)A In this situation, the apparent change in assay of a sample due to calibration drift is dependent on the assay value. This means that a drift correction appropriate for one assay value has to be scaled before it can be applied to samples with other assay values. (b) Linear calibration curves. In a few AutoAnalyser procedures, e.g. determination of potassium by flame emission calorimetry, the calibration curve is essentially linearly. If E is the emission reading on a linear chart scale and B the baseline E = B+kA and A = i (E-B) If the baseline changes by an amount D, without change in sensitivity, the apparent assay value A’ becomes ; (E-B+D) and the apparent change in assay value is A’-A D k so that correction for drift is independent of assay value. If method sensitivity changes so that k becomes otk, the new peak reading E’ corresponding to an assay value A is given by the equation E’ = B+crkA and A = 2 (El-B) If the new peak value is read from the original calibration curve, the apparent assay value will be ; (El-B) zz

CXA

czin. Chim. Ada, 2g (1970) It?-IS0

AUTOANALYSER

and

CALIBRATION

AND INTERACTION

the apparent change in concentration

I79

will be

AI-A = (cc-I)A

Thus in the case of linear calibration curves, correction for change in chemical sensitivity is dependent on assay value and a computed assay drift correction must be scaled for application to samples with different assay values. (c) Other ty$es of calibratiovz curve. In many AutoAnalyser procedures, the calibration curve is neither simple logarithmic nor linear. In most cases the calibration curve can be defined empirically in terms of a low order polynomial. Applying similar arguments to those used in the case of simple logarithmic and linear curves, it can be shown that correction for baseline drift is independent of concentration whereas correction for change in method sensitivity is proportional to concentration. ACKNOWLEDGEMENTS

We are much indebted to: Dr. D. Race, Director, Computer Study Group for his support and interest. Dr. C. Bellamy, Computer Centre, Monash University for access to the CDC 3200 and to Mr. J, Buckley for assistance in analysing data with this computer. D. J. M. Owen for installation of the relay-driving interface. Numerous staff members of this department for their part in collecting and recorder data from routine operation of the system. Photographic and Medical Illustration Department, Alfred Hospital for preparation of the illustrations. REFERENCES I P. GRAY AND J. A. OWEN, Clin. Chinz. Acta, 24 (1969) 389. 2 D. GARTELMANN, P. GRAY, J. A. OWEN AND G. D. QUAN SING, Proc. 4th Australian

3 4 5 6

Computer Conference, Adelaide 1969, p. 545. G. E. FORSYTHE, J. Sot. Ind. Appl. Math., 5 (1957) 74. J. A. OWEN, Clin. Chim. Acta, 29 (1970) 89-91. IN. A. EVENSON, G. P. HICKS, J. A. KEENAN AND F. G. LARSON, Automation in Analytical Chemistry, Vol. I, Mediad Inc., New York, 1968, p. 137. L. G. WHITBY AND D. SIMPSON, J. Clin. Pathol.. zz. Suppl. (Coll. Pathol.), 3 (1969) 107. S. A. SONDOV, Dews Proceedings, Spring (1969) 303.

7 8 R. F. FARR, J. A. NEWELL, T. P. WHITEHEAD AND G. M. WIDDOWSON, in Technicon Symposium 1966, Automation in Analytical Chemistry, Vol. 2, Mediad Inc., New York, 1967, p. 225. g D. S. YOUNG AND E. COTLOVE, Clin. Chem., 12 (1966) 556, Abst. 59. IO M. A. BLAIVAS AND A, H. MENCZ, Technicon Symposium 1967, Automation in Analytical Chemistry, Vol. I, Mediad Inc., New York, 1968, p. 133. II M. E. ROYER AND H. Ko, Anal. Biochem., 29 (1969) 405. 12 H. W. JONES, J. T. LASERSOHN, G. G. NELSON, R. C. MARSHALL, I. R. ETTER AND A. M. BOULEY, The Development and Operation of a Clinical Laboratory Data Acquisition System, Mason Clinic, Seattle, Wash., 1968. 13 F. V. FLYNN, in Progress in Medical Computing, Elliot Medical Automation, London, 1965, p.46. 14 R. E. THIERS AND K. M. OGLESBY. Clin. Chem.. IO (1964) 246. 15 I. D. P. WOOTTON, J. Clin. Pathol.; 22 Suppl. (Coll.‘Fathol.)‘. 3 (1969) IOI. 16 P. D. GRIFFITHS AND N. W. CARTER, 1. Clin. Pathol.. 22 (1969) 6og. 17 P. J. SNODGRASS, K. FLJWA AND K. H-VIID, J. Lab. Clin. Med., 60 (196-z) 983. 18 R. E. THIERS, R. R. COLE AND W. J. KIRSCH, Clin. Chem., 13 (1967) 451. 19 P. M. G. BROUGHTON, Assoc. Clin. Biochem., Tech. Bull., 16, May, 1969.

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et d.

20 V. WALLACE, Anal. Biochem., 20 (1967) 517. 21 S. WESTLAKE, D. K. MCKAY, P. SURH AND D. SELIGSON, Clin. Chem., 15 (1969) 600. 22 R. M. HASLAM, Assoc. Clin. Biochem., Tech. Bull., g Nov., 1966. 23 W. J. SMYTHE, M. H. SHAMOS, S. MORGENSTERN AND L. T. SKEGGS, Technicon Symposium 1967, Automation in Analytical Chemistry, Vol. I, Mediad Inc., New York, 1968, p. 102. 24 B. E. NORTHAM, Assoc. Clin. Biochem., Tech. Bull., 7, August, 1965. 25 P. V. DANCKWERTS, Chem. Eng. Sci., 2 (1953) I. 26 A. L. CHANEY, in Technicon Symposium 1967, Automation in Clinical Chemistry, Vol. I, Mediad Inc., New York, 1968, p. 115. 27 A. HAEMERLE AND J. A. OWEN, (1969) unpublished observations. 28 H. AXELSSON, B. EKMAN AND D. KNUTTSON, in L. T. SKECGS (Ed.), Technicon Symposium, 1965, Automatiolz in Analytical Chemistry, Vol. I, Mediad Inc., New York, 1966, p. 603. 29 R. J. BARTHOLOMEW AND A. M. DELANEY, Proc. Aust. Assoc. Clin. Biochem., I (1966) 214. 30 S. R. GAMBINO AND H. SCHREIBER, Technicon Symposium, New York, 1964, paper No. 54. 31 L. T. SKEGGS, Tech&con Method File, N-5b. 32 L. T. SKEGGS, Am. J. Clin. Pathol., 33 (1960) 181. 33 A. L. CHASSON, H. J. GRADY AND M. S. STANLEY, Amer. J. Clin. Pathol., 35 (1960) 83. 34 D. S. YOUNG AND J. M. HICKS, J. C&n. Pathol., 18 (1965) 98. 35 A. L. LEVY, C. DALMASSO AND J. DALY, in L. T. SKEGGS (Ed.), Technicon Symposium, 1965. Automation in Analytical Chemistry, Vol. 2, Mediad Inc., New Y70rk, 1966, p. 551. 36 D. S. YOUNG, J. CZin. Pathol., rg (1966) 397. 37 J. ISREELI, M. PELAVIN AND G. KESSLER, Ann. N. Y., Acad. Sci., 87 (1960) 635.

38 Technicon Method File, N-2. 3g Technicoa Method File, N-140. 40 R. D. ALLAN, J. A4ed. Lab. Technol., 23 (1966) 151. 4r W. H. MARSH, B. FINGERHUT AND H. MILLER, C/in. Chem.. II (1965) 624. 42 W. H. C. WALKER, C. A. PENNOCK AND G. Ii. MCGOWAN, Clin. Chim. Acta, 27 (1970) 421.

Clin. Chim. Acta, 2g (1970) 161-180