Transferability of results obtained for sodium, potassium and chloride ions with different analysers

Transferability of results obtained for sodium, potassium and chloride ions with different analysers

Clinica Chimica Acta 275 (1998) 151–162 Transferability of results obtained for sodium, potassium and chloride ions with different analysers Javier R...

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Clinica Chimica Acta 275 (1998) 151–162

Transferability of results obtained for sodium, potassium and chloride ions with different analysers Javier Rodriguez-Garcia*, Teresa Sogo, Santiago Otero, Juan M. Paz Laboratorio Central, Hospital Xeral de Galicia, Universidad de Santiago de Compostela, 15706 Santiago de Compostela, Spain Received 5 January 1998; received in revised form 20 April 1998; accepted 21 April 1998

Abstract In this study we have assessed transferability in seven different analysers commonly used in clinical chemistry laboratories to measure sodium, potassium and chloride ions. The inaccuracy and linearity of the techniques were satisfactory in most cases, and therefore all the equipment may be used in both pathological and normal ranges of the electrolytes evaluated. In most cases it was possible to correct the inaccuracy. The equipment which gave the best performance when analysing the three ions assessed after considering the Process Capability Index (CPI) and Performance Index (PI) was Nova-5. According to Hyltoft-Petersen’s criteria, the results obtained for the three ions with the different analysers cannot be used indiscriminately, apart from potassium. However, after comparison of the results obtained by indirect potentiometry with those obtained by other techniques, we can conclude that the transferability of results is possible in almost every case, as standard deviation from regression (S y.x ) was lower than the permissible analytical error.  1998 Elsevier Science B.V. All rights reserved. Keywords: Transferability; Ions; Indirect potentiometry; Direct potentiometry

1. Introduction Frequently different instruments and measurement methods for a particular Abbreviations: ISE, Ion-Selective Electrode; AAE, Allowable Analitical Error; CPI, Process Capacity Index; PI, Performance Index. *Corresponding author. Fax: 1 34 81 570102. 0009-8981 / 98 / $19.00  1998 Elsevier Science B.V. All rights reserved. PII: S0009-8981( 98 )00081-3

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analyte are used in the same laboratory or in laboratories belonging to the same clinical area, thus making the study of the possible transferability of results very important [1,2]. If transferability is possible it allows the laboratories to give the results obtained by different methods in terms of the same rank of reference. This is particularly important in the case of serum electrolytes, as they are one of the most frequently requested tests in Clinical Laboratories (in routine as well as in emergency situations) and there is a great variety of instruments and measurement methods for analysing these ions. Accordingly, the discrepancies in the results for sodium and potassium between the direct ion-selective electrode (ISE) methods and those needing predilution of the sample (indirect ISE and flame photometry) are well known [3,4]. Moreover, we can usually show that sodium determinations made with direct ISE systems from different manufacturers do not give the same results for the same samples [5]. In the present study we have evaluated transferability of results for sodium, potassium and chloride ions in serum, evaluated by seven different analysers, four using potentiometry without sample dilution, one by atomic emission spectrometry, one using potentiometry with sample dilution, and one based on an enzymatic method.

2. Material and methods

2.1. Instrumentation We used Nova-5 (Nova Biochemical, Newton, MA),Cobas Mira (F. Hoffmann-La Roche, Basle, Switzerland), and Ion 150 AC (Jookoo Company Ltd., Tokyo, Japan) as analysers using potentiometry without sample dilution and based on wet chemistry, and Ektachem 700 (Eastman Kodak, Rochester, NY) as an analyser based on dry chemistry. For those assays involving emission spectrometry we used the flame photometer Corning 435 (Ciba-Corning Diagnostics, Halstead, England). We used a Hitachi 747 analyser (Boehringer Mannheim GmbH, Mannheim, Germany) which measures sodium, potassium and chloride ions by indirect potentiometry techniques, and we used a Hitachi 717 analyser (Boehringer Mannheim GmbH, Mannheim, Germany) to perform enzymatic assays.

2.2. Samples The samples used were those normally obtained in the laboratory after collection in Vacutainer tubes (Becton Dickinson Co., Rutherford, NJ) free of anticoagulant. After collection, tubes were centrifuged (4000 rpm) at 48C after

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the coagulum retraction was observed. Those samples with abnormal protein and / or triglyceride values were eliminated because this causes a known bias with direct potentiometry. Normal ranges for these analytes in our laboratory are: total protein 65–83 g / l; triglycerides 0.28–1.69 mmol / l. In order to study the within- and between-day variation a pool of normal sera was prepared and divided into three fractions: one of these aliquots was used as an average level for sodium, potassium and chloride; sodium chloride and potassium chloride were added to the second aliquot, used as a high level, and the third was diluted with albumin at 7% in order to achieve a low level of ion concentration. The serum pools were aliquoted and preserved at 2 208C until analysis.

2.3. Calibration solutions All analysers were calibrated according to the manufacturer’s instructions. Nova-5 was calibrated automatically using two different levels of aqueous standards provided for use with the instrument. Cobas Mira was calibrated with 2 aqueous standards from F. Hoffmann-La Roche of 150 and 100 mmol / l for sodium, 7.04 and 3.04 mmol / l for potassium, and 138 and 92 mmol / l for chloride. Jookoo-Ion 150 AC was automatically calibrated in two levels with programmable time intervals; the standard solutions supplied for use with the instrument were 140 and 160 mmol / l for the sodium, 4.0 and 6.0 mmol / l for potassium and 100 and 120 mmol / l in the case of chloride. The flame photometer has a dilutor on line model 800, which dilutes samples and standards with water 1:200, and adds a 1.5 mmol / l lithium solution, as an internal standard. The standard solutions supplied for use with the instrument were 140, 120 and 160 mmol / l for sodium, and 5.2, 2.0 and 8.0 mmol / l for potassium. The Hitachi 747 was calibrated with aqueous standards supplied with the instrument using two concentrations 160 and 120 mmol / l for sodium, 7.04 and 3.04 mmol / l for potassium, and 120 and 80 mmol / l for chloride. A compensation for the levels of the different ions assessed was made in the analyser using a second standard with an albumin matrix with concentrations of 146 mmol / l for sodium, 4.7 mmol / l for potassium, and 100 mmol / l for chloride. Calibration of the Hitachi 717 was made on only one level using an aqueous standard supplied for use with the instrument, of 123 mmo / l of sodium, 4.4 mmol / l of potassium and 100 mmol / l of chloride. It is difficult to study the inaccuracy of analytical instruments equipped with selective electrodes, as there is no consensus regarding calibration and reference standards of ionic activity, and there are also limitations in the control materials suggested by the manufacturers [6,7]. We therefore prepared a reference solution

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of sodium and potassium chloride from which, using serial dilutions, 14 working solutions were prepared, including decision levels for the different ions.

2.4. Reagents The reagents provided in the commercial kits were used in all analysers, and methods were adapted to the manufacturer’s instructions. The sodium, potassium and chloride enzymatic assays were based on electrolyte-dependent beta-galactosidase, pyruvate kinase and alpha-amylase respectively (reagent kits supplied by Boehringer Mannheim). The water (free from metals), had a resistivity of 18.2 Mohm 3 cm at 258C and was obtained through a Milli-Q Plus system (Millipore Corporation, Bedford, MA). The sodium chloride (Art. 6404) and potassium chloride (Art. 4936) were from Merck (Darmstadt, F.R.G.). The albumin solution was prepared from 20% albumin (Hoechst-Behring, Marburg, F.R.G.).

2.5. Statistical analyses The study of within-day and between-day imprecision was made according to the selective electrode evaluating protocol proposed by the Spanish Society of Clinical Chemistry [8]. The estimate of total analytical error in the decision levels for the study of reliability was made according to the protocol of the Commission of Techniques Validation from the Societe´ Franc¸aise de Biologie Clinique [9]. The study of the interval of linearity was made according to the protocol of NCCLS [10]. The Westgard criterion [11] was used to evaluate inaccuracy. To determine which equipment was best suited to avoid imprecision, we used the Process Capacity Index (CPI) [12,13] and Campbell’s Performance Index (PI) [14]. Regression studies between the different analysers were made following the Haeckel-Feldman method [15,16]. Regression line equations were obtained after having eliminated the aberrant data, according to Burnett’s criterion [17]. We used Kafka’s less restrictive criterion [18], calculated according to the reference rank of each method, as a medically acceptable error (AAE), as the reference ranges for the different ions were narrow. The results were considered as transferable if no medically significant differences were found, either in the level of precision or inaccuracy, according to Hyltoft Petersen’s criteria [19]. If this did not occur, it had to be verified whether, depending on the regression equation, the values of one method could be predicted through the other, bearing this equation in mind and the standard deviation from regression (Sy? x ) related to the medically acceptable deviation.

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3. Results and discussion Tables 1 and 2 summarise the within-run and between-run precision studies. The within-run CVs measured for 3 levels ranged from 0.09% to 1.19% for sodium, from 0.27% to 2.79% for potassium, and from 0.18% to 1.09 for chloride. The medically acceptable CV (CVa) was exceeded only for the low and medium levels of sodium analysed in the Hitachi 717, although these values were not significantly different. The between-run CVs, measured over a 20 day period for 3 levels, ranged from 0.52% to 1.49% for sodium, from 0.66% to 4.50% for potassium, and from Table 1 Within-day imprecision Sodium

Potassium

Chloride

Mean (mmol / l)

CV%

Mean (mmol / l)

CV%

Mean (mmol / l)

CV%

Low level Cobas mira Jookoo Kodak E700 Nova 5 Corning 435 Hitachi 747 Hitachi 717

108.1 109.4 104.7 106.3 105.8 105.7 98.8

0.40 0.62 0.56 0.41 0.84 0.83 1.19 a

2.20 2.14 2.17 2.16 2.09 2.21 2.18

0.76 0.77 1.01 0.34 0.31 1.16 2.79

81.9 81.7 78.6 84.5

1.07 0.50 0.62 0.63

80.7 76.9

0.53 1.02

Medium level Cobas mira Jookoo Kodak E700 Nova 5 Corning 435 Hitachi 747 Hitachi 717

149.6 143.0 142.3 149.3 144.3 144.5 151.1

0.20 0.28 0.51 0.44 0.62 0.68 1.14 a

4.49 4.54 4.62 4.79 4.72 4.75 4.79

0.27 0.38 1.11 0.40 1.23 0.95 1.53

110.6 108.1 109.2 111.8

0.41 0.37 0.44 0.49

106.3 102.8

0.69 1.03

High level Cobas mira Jookoo Kodak E700 Nova 5 Corning 435 Hitachi 747 Hitachi 717

162.4 152.6 156.8 162.2 159.8 159.2 164.8

0.09 0.22 0.49 0.22 0.59 0.69 0.88

7.49 6.95 7.30 7.45 7.36 7.30 7.30

0.35 0.43 0.62 0.24 1.04 0.80 1.05

127.3 121.9 126.6 127.1

0.23 0.48 0.48 0.18

122.4 118.1

0.72 1.09

Maximum allowable Coefficient of Variation (CVa): Sodium 0.97%, Potassium 3.82%, Chloride 1.50%, [18]. a Not significantly different from CVa [9].

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Table 2 Between-day imprecision Sodium

Potassium

Chloride

Mean (mmol / l)

CV%

Mean (mmol / l)

CV%

Mean (mmol / l)

CV%

Low level Cobas mira Jookoo Kodak E700 Nova 5 Corning 435 Hitachi 747 Hitachi 717

105.3 107.0 103.8 105.9 104.3 105.1 99.2

0.93 1.12 a 0.59 0.73 0.96 0.88 1.49 b

2.13 2.10 2.15 2.14 2.19 2.19 2.27

1.76 1.16 2.38 2.06 4.50 a 3.37 3.30

79.2 79.8 78.0 83.7

1.49 1.22 1.08 0.95

77.2 77.4

1.30 1.22

Medium level Cobas mira Jookoo Kodak E700 Nova 5 Corning 435 Hitachi 747 Hitachi 717

147.3 142.2 141.6 147.7 144.7 144.1 151.5

0.67 0.66 0.53 0.52 0.79 0.61 0.96

4.74 4.52 4.61 4.74 4.73 4.76 4.81

1.00 0.95 1.24 0.82 1.87 1.27 1.82

108.2 107.4 109.6 110.3

1.30 0.95 0.77 0.52

105.2 104.7

0.81 0.95

High level Cobas mira Jookoo Kodak E700 Nova 5 Corning 435 Hitachi 747 Hitachi 717

160.4 153.5 155.4 161.2 158.8 156.8 163.7

0.70 0.71 0.61 0.54 0.63 0.71 0.76

7.39 6.99 7.18 7.43 7.33 7.46 7.33

1.51 1.14 1.22 0.66 1.58 1.28 1.19

125.1 122.5 126.2 126.5

1.13 1.44 0.56 0.54

121.3 117.9

1.01 1.10

Maximum allowable Coefficient of Variation (CVa): Sodium 0.97%, Potassium 3.82%, Chloride 1.50% [18]. a Not significantly different from CVa. b Significantly different from CVa.

0.52% to 1.49% for chloride. The CV exceeded those which are medically acceptable in the case of sodium with Jookoo (1,12%) and Hitachi 717 (1.49%), and in the case of potassium (at low levels, though not at medium and high levels) with the flame photometer Corning 435 (4.50%). The chloride ion was within acceptable limits for all of the levels and instruments tested. Table 3 shows data from the study of inaccuracy with protein free solutions. Inaccuracy was clinically significant for sodium analysed in the Kodak E700 and chloride analysed in the Jookoo 150 AC, Kodak and Hitachi 717, as in every case the difference of averages is higher than the medically acceptable error

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Table 3 Study of inaccuracy n

Mean (mmol/l)

Significance

Theoretical

Observed

AAE

Regression

r

Sy?x

Sodium Cobas mira

14

120.0

121.0

N.S.

1.4

y 5 1.00x 2 2.0

0.999

0.34

Jookoo

12

120.0

122.0

N.S.

1.3

y 5 1.01x 2 3.6

0.999

1.70

Kodak E700

11

121.2

127.9

. 0.05

1.4

y 5 0.94x 1 0.2

0.999

0.11

Nova 5

14

120.0

120.9

N.S.

1.5

y 5 0.99x 1 0.3

0.999

0.53

Corning 435

14

120.0

120.7

N.S.

1.4

y 5 0.98x 2 1.2

0.999

0.97

Hitachi 747

14

120.0

122.0

N.S.

1.4

y 5 0.99x 2 0.8

0.999

0.51

Hitachi 717

12

110.0

107.2

N.S.

1.9

y 5 1.02x 1 0.1

0.999

0.04

Potassium Cobas mira

14

5.00

5.08

N.S.

0.2

y 5 1.01x 2 0.14

0.999

0.047

Jookoo

14

5.00

5.00

N.S.

0.2

y 5 1.01x 2 0.07

0.999

0.018

Kodak E700

14

5.00

5.12

N.S.

0.2

y 5 0.98x 2 0.02

0.999

0.044

Nova 5

14

5.00

5.04

N.S.

0.2

y 5 1.00x 2 0.08

0.999

0.015

Corning 435

14

5.00

5.03

N.S.

0.2

y 5 1.00x 2 0.05

0.999

0.067

Hitachi 747

14

5.00

5.07

N.S.

0.2

y 5 0.99x 2 0.01

0.999

0.030

Hitachi 717

14

5.00

4.90

N.S.

0.2

y 5 1.02x 1 0.02

0.999

0.003

Chloride Cobas mira

14

125.0

124.9

N.S.

1.6

y 5 1.00x 2 0.2

0.999

0.32

Jookoo

12

114.6

106.6

. 0.05

1.5

y 5 1.11x 2 3.6

0.999

0.32

Kodak E700

12

120.4

116.4

. 0.05

1.6

y 5 1.04x 2 0.8

0.999

0.21

Nova 5

14

125.0

124.2

N.S.

1.5

y 5 0.99x 1 1.2

0.999

0.36

Hitachi 747

14

125.0

123.9

N.S.

1.6

y 5 0.96x 1 6.4

0.999

0.71

Hitachi 717

11

110.5

103.5

. 0.05

1.5

y 5 1.05x 1 1.1

0.999

0.13

N.S., Not significantly different.

(AAE). However, this inaccuracy may be mathematically corrected in all of the cases as the standard deviation from regression is lower than the medically acceptable level. The potassium ion is the only ion which has proved to be the most reliable in all of the equipment studied (Table 4), as the medically acceptable error was not exceeded in any of the instruments by the high estimate limit of the total analytical error (at a confidence level of 95%). According to these criteria, the highest reliability for the different ions was that provided by Nova-5 and the Cobas Mira, and the lowest was that provided by the Ektachem 700 and Hitachi 717. The linearity study summarised in Table 5 shows that linearity was acceptable for every ion assessed and with every piece of equipment, as the normal and pathological rank of values was largely covered in all of the cases. For sodium

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Table 4 Study of reliability

Cobas mira Jookoo Kodak E700 Nova 5 Corning 435 Hitachi 747 Hitachi 717

Sodium

AAE

Potassium

AAE

Chloride

AAE

2.060.59 2.460.82 7.061.40 0.960.60 3.660.60 2.061.20 2.562.90

1.4 1.3 1.4 1.5 1.4 1.4 1.9

0.0960.02 0.0260.03 0.1260.08 0.0860.04 0.0560.11 0.0660.09 0.1260.08

0.2 0.2 0.2 0.2 0.2 0.2 0.2

0.260.91 7.460.82 3.260.97 0.261.09

1.6 1.5 1.6 1.5

2.461.50 6.162.80

1.6 1.5

(82–172 mmol / l) and chloride (60–175 mmol / l) ions, the Ektachem 700 presents the shortest linearity interval from the lowest extreme, and the Hitachi 717 for sodium (48–168 mmol / l) and chloride (50–150 mmol / l) in the highest extreme. In the case of potassium the linearity is practically the same with every piece of equipment tested. The Process Capacity Index [12,13] and Performance Index [14] for the different equipment studied are shown in Table 6. According to these criteria, the Nova-5 is the equipment with the best performance for the three ions. The worst results for sodium were obtained through the enzymatic method of the Hitachi 717, whereas for potassium and chloride the worst results were obtained using the Corning 435 flame photometer and the Cobas Mira, respectively. To evaluate the transferability of results between different equipment, and using the indirect potentiometry as a reference, we have used Hyltoft Petersen’s criteria [19] for imprecision as well as for the inaccuracy condition (Table 7). This method establishes that if one of the methods is highly imprecise, then the other must have a low degree of imprecision. When both have a low degree of imprecision, then a certain bias may be tolerated. When both are highly imprecise, only a small bias is tolerable between the methods. According to these criteria, the results obtained for the potassium ion can be used indiscriminately with the different equipment as all of the equipment Table 5 Study of linearity Linearity range (mmol / l)

Cobas mira Jookoo Kodak E700 Nova 5 Corning 435 Hitachi 747 Hitachi 717

Sodium

Potassium

Chloride

48–192 48–192 82–172 48–192 48–192 48–192 48–168

2–8 2–8 2–8 2–8 2–8 2–8 2–8

50–200 50–160 60–175 50–200 50–200 50–150

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Table 6 Process Capacity Index (CPI) and Performance Index (PI) for sodium, potassium and chloride in the analysers evaluated CPI

Cobas mira Jookoo Kodak E700 Nova 5 Corning 435 Hitachi 747 Hitachi 717

PI

Sodium

Potassium

Chloride

Sodium

Potassium

Chloride

4.053 4.262 5.330 5.208 3.499 4.551 2.750

10.549 11.644 8.747 12.864 5.653 8.271 5.712

3.846 5.263 6.494 9.615

2.838 2.881 3.587 3.656 2.406 3.116 1.271

7.487 7.881 6.038 9.131 4.004 5.895 4.114

2.262 3.095 3.818 5.654

6.173 5.263

3.630 3.095

Performance Standard: Sodium 4 mmol / l, Potassium 0.5 mmol / l, Chloride 5 mmol / l.

Table 7 Transferability of results between the Hitachi 747 (x) and other analyzers ( y) (Hyltoft Petersen’s criterion) A

B

C

D

Sodium Cobas mira Jookoo Kodak E700 Nova 5 Corning 435 Hitachi 717

0.821 0.808 0.653 0.642 0.996 1.294

0.08 1.73 2 1.07 2 0.06 2 0.32 2 1.52

1.0 0.0 5.6 1.1 1.3 5.0

0.580 0.588 0.682 0.688 0.477 0.310

Potassium Cobas mira Jookoo Kodak E700 Nova 5 Corning 435 Hitachi 717

2.613 2.515 3.151 2.285 5.110 4.925

26.77 26.32 26.47 26.62 26.55 25.58

0.01 0.07 0.05 0.03 0.04 0.17

3.919 3.935 3.935 3.076 3.493 3.524

Chloride Cobas mira Jookoo Kodak E700 Nova 5 Hitachi 717

2.346 1.559 1.249 0.926 1.559

1.45 2 4.20 2 2.28 3.28 2 4.49

1.0 6.9 2.9 0.3 6.0

0.752 1.056 1.180 1.314 1.056

Interrelationships between allowable DBias, and the imprecision of two methods. The condition of imprecision is achieved when A # B and that of bias when C # D [19]. A 5 CV 2x 1 CV 2y B 5 0.25 (3.92 CVI 2 uDb u)2 2 2 CV I2 ; CVI 5 within-subject biological variation. C 5 uDb u xy 5 ubias x 2 bias y u D 5 3.92 CVI 2 1.96(Cv x2 1 Cv y2 1 2CV I2 )1 / 2 .

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complies with the conditions of imprecision and bias. Conversely, only the Jookoo fits these conditions for sodium, while the Nova 5 fits for chloride. The comparison of the results obtained by indirect pontentiometry and by other methods studied is shown in Table 8. There are statistically significant differences for all the ions and equipment tested (except those obtained from Corning 435) when they were compared with data obtained through indirect potentiometry in the Hitachi 747. These differences are not medically significant for the potassium ion in any of the equipment studied, whereas they were significant using Jookoo and the Hitachi 717 enzymatic method for sodium and chloride ions, respectively. However, the interconvertibility of results between pairs of apparatus was possible in most cases due the fact that the different regression equations can be used to predict the value on another instrument (Table 8), since the standard deviation from regression was lower than the medically acceptable level. The exceptions were those of sodium in the Ektachem and Hitachi 717, which

Table 8 Correlation for the Hitachi 747 (x) analyser against the other analysers ( y) n

Sodium Cobas mira Jookoo Kodak E700 Nova 5 Corning 435 Hitachi 717

257 290 255 267 281 199

Potassium Cobas mira Jookoo Kodak E700 Nova 5 Corning 435 Hitachi 717

329 326 317 330 333 301

Chloride Cobas mira Jookoo Kodak E700 Nova 5 Hitachi 717

263 254 217 296 202

Mean (mmol/l) X

Y

140.9 140.9 141.1 140.9 140.7 141.5

144.9 140.2 139.5 145.4 140.9 148.4

4.55 4.54 4.52 4.55 4.55 4.54

103.2 103.0 103.3 103.5 103.1

N.S. Not Significantly different.

4.56 4.36 4.42 4.57 4.54 4.45

105.7 104.5 106.0 107.7 102.3

Significance

Regression equation

r

Sy?x

AAE

, 0.001 , 0.001 , 0.001 , 0.001 N.S. , 0.001

y 5 1.20x 1 0.60 y 5 0.90x 1 13.5 y 5 0.99x 1 0.15 y 5 1.07x 2 6.19 y 5 1.00x 2 0.45 y 5 1.36x 2 43.8

0.911 0.908 0.806 0.920 0.909 0.830

1.065 0.985 1.421 1.034 1.059 1.449

1.4 1.4 1.4 1.4 1.4 1.4

, 0.05 , 0.001 , 0.001 , 0.001 N.S. , 0.001

y 5 1.03x 2 0.12 y 5 0.96x 1 0.02 y 5 0.98x 2 0.04 y 5 1.01x 2 0.05 y 5 0.96x 1 0.19 y 5 0.97x 1 0.05

0.982 0.985 0.964 0.985 0.963 0.945

0.060 0.060 0.080 0.050 0.084 0.100

0.2 0.2 0.2 0.2 0.2 0.2

, 0.001 , 0.001 , 0.001 , 0.001 , 0.001

y 5 0.98x 1 5.02 y 5 0.90x 1 11.7 y 5 0.99x 1 3.27 y 5 0.91x 1 13.2 y 5 0.91x 1 8.85

0.936 0.947 0.922 0.943 0.874

0.945 0.838 1.035 0.866 1.401

1.5 1.5 1.5 1.5 1.5

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showed standard deviation from regression slightly higher than the medically acceptable level. In conclusion, the results obtained in the present study allow us to suggest that the transferability of results for the different ions is always possible. All the different equipment may be used indiscriminately to analyse potassium. Conversely, this was not possible for analysing sodium and chloride ions in most cases. However, the interconvertibility of results obtained from almost any analyser may be achieved through appropriate regression equations.

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