1 Department of Anaesthesia, and 2 Department of Intensive Care, Austin and Repatriation Medical Centre, Heidelberg, Victoria 3084, Australia
*Corresponding author. E-mail: David.Story@austin.org.au Presented in part at the Australian and New Zealand College of Anaesthetists Annual Scientific Meeting, May 12, 2002, Brisbane, Australia.
Accepted for publication: July 18, 2003
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Abstract |
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Methods. We reduced two complex equations for the sodiumchloride effect on base excess to one simple equation: sodiumchloride effect (meq litre1)=[Na+][Cl]38. We simplified the equation of the albumin effect on base excess to an equation with two constants: albumin effect (meq litre1)=0.25x(42[albumin]g litre1). Using 300 blood samples from critically ill patients, we examined the agreement between the more complex FenclStewart equations and our simplified versions with BlandAltman analyses.
Results. The estimates of the sodiumchloride effect on base excess agreed well, with no bias and limits of agreement of 0.5 to 0.5 meq litre1. The albumin effect estimates required log transformation. The simplified estimate was, on average, 90% of the FenclStewart estimate. The limits of agreement for this percentage were 8298%.
Conclusions. The simplified equations agree well with the previous, more complex equations. Our findings suggest a useful, simple way to use the FenclStewart approach to analyse acidbase disorders in clinical practice.
Br J Anaesth 2004; 92: 5460
Keywords: chemistry, analytical; complications, acidbase disorders; intensive care
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Introduction |
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Gilfix and colleagues4 used the work of Figge and colleagues7 and Fencls unpublished work8 to derive five equations to estimate the base excess effects of the strong ion difference and the total weak acid concentration. In plasma, sodium and chloride are the principal components of the extracellular strong ion difference,6 and albumin is the principal extracellular weak acid.9 While this approach is reasonably simple, most people would need a calculator to use the five equations.
We believe that these equations, used to estimate the sodiumchloride effect on base excess, can be simplified. Balasubramanyan and colleagues5 simplified the FenclStewart albumin equation. Work by Figges group9 has further modified the FenclStewart equation for the base excess effect of albumin.8 This equation can also be simplified in the same way that Balasubramanyan simplified the older equation.5 We proposed four simpler equations that require only simple mental arithmetic for clinical use.
We tested the hypothesis that the simplified estimates of the base excess effects of the plasma sodiumchloride concentration and the plasma albumin concentration have sufficiently strong agreement with the FenclStewart estimates3 4 to be used clinically. We used blood samples from critically ill adults to test this hypothesis.
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Methods |
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Arterial blood samples were collected in heparinized blood-gas syringes (Rapidlyte; Chiron Diagnostics, East Walpole, MA, USA) and analysed in the intensive care unit blood-gas analyser (Ciba Corning 865; Ciba Corning Diagnostics, Medfield, MA, USA). The analyser made measurements at 37°C. Nursing staff from the intensive care unit who had been taught to use the machine by support staff performed the analysis. Samples were not stored on ice. We collected data on the pH, partial pressure of carbon dioxide and the standard base excess.
For each data set, a further sample was drawn at the same time from the same arterial cannula using a vacuum technique with lithium heparin tubes or clot-activating tubes (Vacuette; Greiner Labortechnik, Kremsmunster, Austria). These samples were sent to the hospital core laboratory in the Division of Laboratory Medicine. Plasma and serum underwent multicomponent analysis (Hitachi 747; Roche Diagnostics, Sydney, Australia). Scientific staff from the hospital clinical chemistry department analysed the samples. Samples were not stored on ice. We collected data on the plasma or serum concentrations of sodium, chloride and albumin.
Fencl divided the effect of strong ion difference on base excess into sodium and chloride effects. This group calculated the base excess effects of changes in free water on the sodium concentration and changes in the chloride concentration:4 5 8
sodium effect (meq litre1)=0.3x([Na+]140)(1)
chloride effect (meq litre1)=102([Cl]x140/[Na+]).(2)
Sodium and chloride are the principal contributors to the strong ion difference.6 The sum of the sodium and chloride effects will give the FenclStewart estimate of the strong ion difference effect on base excess:
sodiumchloride effect (meq litre1)=0.3x([Na+]140)+102([Cl]x140/[Na+]).(3)
Separately estimating the base excess effects of changes in free water and changes in chloride provides useful information. These separate effects, however, do not need to be quantified initially to determine the effect of the sodiumchloride component of the effect of strong ion difference on base excess. Changes in the difference in sodium and chloride can be used to calculate directly the major changes in the strong ion difference. As the strong ion difference is decreased the blood becomes more acidic.6
We proposed that the calculation of the strong ion difference effect on base excess could be simplified. From the reference range in our laboratory, the median value for sodium is 140 mmol litre1 and that for chloride is 102 mmol litre1. Therefore the median difference is 38 mmol litre1. The measured sodiumchloride difference minus 38 mmol litre1 will be an estimate of the change in the strong ion difference. For sodium and chloride, 1 millimole equals 1 milliequivalent.
A change in the sodiumchloride component of the strong ion difference will change the base excess directly. Therefore our simplified version of the equation for the sodiumchloride effect on base excess is:
sodiumchloride effect (meq litre1)=[Na+][Cl]38.(4)
Albumin is the principal contributor to the plasma total weak acid concentration. The effect of albumin on the base excess is due to the anionic effect of albumin. Figge and colleagues9 developed a pH-dependent formula for the anionic effect of albumin:
albumin anionic effect (meq litre1)=(0.123xpH0.631)xalbumin (g litre1).(5)
Changes in the concentration of albumin will cause changes in the anionic effect of albumin. Changes in the anionic effect of albumin will change the base excess. As the albumin concentration is decreased the blood becomes more alkaline. We calculated the FenclStewart estimates for the base excess effects of albumin. We used the most recent estimates of the effects of albumin ionization:8
albumin effect (meq litre1)=(0.123xpH0.631)x[42albumin (g litre1)].(6)
We simplified this equation by using a single pH of 7.40:
albumin effect (meq litre1)=0.28x[42albumin (g litre1)].(7)
To facilitate calculation at the bedside we further simplified the equation by using the constant of 0.25. This allows the simple mathematics of dividing the difference in albumin concentrations by 4. Therefore the simplified equation became:
albumin effect (meq litre1)=0.25x[42albumin (g litre1)].(8)
Statistical analysis
Data were collected from patient charts and the hospital computer system. Data were stored on a computer spreadsheet (Excel, Microsoft, Seattle, WA, USA). All statistical calculations were done with Statview software (Abacus Concepts, Berkeley, CA, USA).
We used the limits of agreement method of Bland and Altman10 11 to determine the agreement between the FenclStewart and simplified estimates of the albumin and strong ion difference effects on base excess. We proposed that a bias of ±1 meq litre1 and limits of agreement of bias ±2 meq litre1 were acceptable for clinical use of the simplified equations. That is, the greatest difference between two estimates would be 3 meq litre1. Data were analysed for the overall group and three subgroups: an acidaemic group (pH <7.35), a reference range group (pH 7.357.45) and an alkalaemic group (pH >7.45). We used these groups to examine the possibility that different acidbase states may affect the agreement.
Where the difference between the estimates varied with the average of the two estimates (heterodasticity), the relationship was analysed with correlation statistics. If the correlation were statistically significant, at a P value of <0.05, the data were log-transformed. The limits of agreement statistics were reported as proportions because a log minus a log is the ratio of the antilogs.10
We analysed the relative risk of death where the standard base excess, sodiumchloride effect or unmeasured ion effect was less than 5 meq litre1. The effect of albumin was almost always alkalinizing; therefore we calculated the relative risk of death of an albumin effect on base excess greater than 5 meq litre1. We assumed the increase in mortality risk was statistically significant if the 95% confidence interval for the risk ratio did not include 1. We used Confidence Interval Analysis software (BMJ Books).
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Results |
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The agreement between the FenclStewart and simplified estimates was analysed for the entire set of 300 samples (Figs 1 and 2) and for the three subgroups: pH <7.35 (acidaemic), pH 7.357.45 (reference range) and pH >7.45 (alkalaemic) (Tables 1, 2 and 3).
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The agreement between the FenclStewart and the simplified estimates of the albumin effect varied with the average effect. This correlation had an R2 of 0.47 and a P value of <0.001. The data were log-transformed and analysed again. The log transformation removed the correlation between the difference of the estimates and the average value (Fig. 2). After log transformation there was good agreement between the Fencl and simplified estimates of the albumin effect. The simplified estimate was, on average, 90% of the Fencl estimate. The limits of agreement for this percentage were 8298%. The results were similar in the three pH subgroups, with the best agreement in the acidaemic group (Tables 2 and 3).
The relative risk of death was greater when either the standard base excess or the unmeasured ion effect was less than 5 meq litre1. A sodiumchloride effect on base excess less than 5 meq litre1 or an albumin effect greater than 5 meq litre1 was not associated with an increased risk of death (Table 4).
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Discussion |
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Balasubramanyan and colleagues5 simplified an earlier version of the equation for the albumin effect.4 These researchers, however, did not examine the agreement of the simplified equation with the more complex FenclStewart version.4 One strength of our study is that we used the most recent versions of the Fencl equations.8 Furthermore, we used a large number of samples from different patients with a wide range of acidbase disorders, including some with increased plasma lactate (another strong ion)5 or increased plasma phosphate (another important weak acid).9 Another strength is that we avoided overestimating the strength of agreement attributable to mathematical linking.13 We avoided this problem by using the limits of agreement approach of Bland and Altman.10 11
In unpublished work, Fencl8 proposed a method of combining base excess and the Stewart approach6 to acidbase physiology and disease. This approach was designed to facilitate clinical application of the Stewart approach. We suggest the following simplified version of the Fencl method.4 5
Four variables are determined (standard base excess and the base excess effects of sodiumchloride, albumin and unmeasured ions) using the following four equations:
standard base excess (mmol litre1=meq litre1) from a blood gas machine;
sodiumchloride effect (meq litre1)=[Na+][Cl]38;(4)
albumin effect (meq litre1)=0.25x[42albumin (g litre1)];(8)
unmeasured ion effect (meq litre1)=standard baseexcesssodiumchloride effectalbumin effect.(9)
These four variables, with the partial pressure of carbon dioxide, allow physicians to examine the base excess effects of the principal components of Stewarts independent factors: carbon dioxide, strong ion difference (sodiumchloride) and total weak acid concentration (albumin). The strong ion difference effect can be further analysed with the separate FenclStewart equations for sodium and chloride.4 The unmeasured ions may be strong ions, such as sulphate and acetate,14 or weak acids, such as phosphate and polygeline.15
These equations require four input variables: the base excess and the plasma concentrations of sodium, chloride and albumin. By using the plasma sodium and chloride concentrations and the simplified sodiumchloride equation we can estimate the base excess effects of electrolyte changes from i.v. fluid therapies.16 17 For example, Scheingraber and colleagues16 studied acidbase changes during major gynaecological surgery. Patients received 0.9% saline or lactated Ringers solution. The saline group had a greater metabolic acidosis, as shown by a more negative base excess. One cause of this acidosis was a decreased strong ion difference. The Scheingraber group showed that these changes in base excess and strong ion difference occurred in parallel but they did not quantify the effect. The method described in our study allows easy quantification of the effects of changes in plasma sodium and chloride (strong ion difference) on base excess (Table 5).
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Using an approach similar to ours, Balasubramanyans group5 studied critically ill children. In a subgroup of 66 children, they found that a base excess effect of unmeasured ions more negative than 5 meq litre1 was an important predictor of mortality. Our approach simplifies estimation of the unmeasured ion effect on base excess by simplifying the calculations for the effects of the strong ion difference and the total weak acid concentration. Among 300 patients, we found that an unmeasured ion effect on base excess less than 5 meq litre1 increased the risk of death by 50%. The risk of death with a standard base excess less than 5 meq litre1 was increased by 100%. There was, however, considerable overlap in the 95% confidence intervals for the relative risk of death for the unmeasured ion effect and the standard base excess. Furthermore, similar changes in the base excess effects of sodiumchloride and albumin did not increase the relative risk of death. These findings suggest that it is the unmeasured ion component of the base excess that is the important clinical marker for mortality.
We have reduced five FenclStewart equations to four simpler equations. We have maintained good agreement with the previous, more complex equations. These simple equations may allow easy, direct application of Stewarts independent factors to clinical work both inside and outside the operating room. We propose these equations as bedside clinical tools rather than as tools for detailed physiological research. Future studies should examine the importance of each of the base excess effects on patient outcome.
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Acknowledgements |
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References |
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