Scandinav. J . Clhc. 6.Lab. Iicvestigatiorr 211-217,
15, 1963.
BLOOD ACID-BASE ALIGNMENT NOMOGRAM
SCALES FOR pH, pCO2, BASE EXCESS OF WHOLE BLOOD OF DIFFERENT HEMOGLOBIN CONCENTRATIONS, PLASMA BICARBONATE, AND PLASMA TOTAL-C02
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BY 0. SIGGAARD ANDERSEN
From the Department of Clinical Chemistry, Rigshospitalet, Copenhagen, Denmark
(Received for publication December 11, 1962)
A description of the acid-base status of
arterial blood includes three values : pH,
carbon dioxide tension (pC0,) and base
excess (BE).
pH, normally about 7.40 (7.36 to 7.42),
changes by changing pC0, as well as by
accumulation of non-volatile acid or base.
The p H value is practically always determined directly by means of the glass electrode.
pC02, normally about 40 mm Hg (33
to 47), is inversely proportional with the
alveolar ventilation. The pC0, value can be
determined directly by means of the pC0,
electrode (Severinghaus & Bradley 195S),
or indirectly by calculation from the pH and
the total-CO, of plasma, or from the p H and
the C0,-equilibration curve (Astrup 1956,
Siggaard-Andersen, Engel, Jargensen &
Astrup 1960).
Base excess, normally about zero meq/l
(fZ.3 to -2.3), indicates the accumulation
of non-volatile acid or base in the blood.
A positive value indicates a base excess (=
non-volatile acid deficit), a negative value
indicates a base deficit (= non-volatile acid
excess). The base excess value can theoretically he determined directly by titrating
with strong acid or base to a p H of 7.40 at
a pC0, of 40 mm Hg at 38" C. However,
it is difficult to carry out this titration without hemolysis, dilution of the sample, or
change in ionic strength. Therefore B E is
determined indirectly by calculation from the
pH, pC0, and hemoglobin concentration. I n
the clinical routine other values are often
used as indicators of the base excess, i. e.
buffer base, standard bicarbonate or eventually total-CO, or actual bicarbonate of the
plasma. A discussion of the base excess value
as compared to these indicators is given elsewhere (Siggaard-Andersen 1963).
It appears from this introduction that the
pC0, and the base excess values must often
be determined indirectly by calculation. A
blood acid-base nomogram for these calculations has previously been published (Siggaard-Andersen & Engel 1960, revised by
Siggaard-Andersen 1962 a, see Fig. 1).
The purpose of this paper is to present a
modified nomogram facilitating certain calculations, see Fig. 3.
CONSTRUCTION OF THE NOMOGRAM
It is necessary to distinguish between two
different types of nomograms: 1) Cartesian nomograms, or curve nomograms, using rectangular co-
211
212
0. SIGGAARD-ANDERSEN
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Fig.2. Top: The curve nomogram with pH and log
pCOe axes. Line 1 is the COs-equilibration curve
for whole blood with a hemoglobin concentration
of 15.0 g/100 ml and a base excess of -10 meq/l
blood. The pH and pCO2 coordinates to the points
A and B on the base excess and the buffer base
curves, respectively, are previously published (Siggaard-Andersen 1%2a, Tables I and 11). Bottom:
The alignment nomogram with scales for pH and
pCO2. Lines a and b represent points A and B of
the curve nomogram. Point L, or rather a fan of
straight lines through point L, represents the C02equilibration curve 1 of the curve nomogram. Thus
point L represent a base excess of -10 meq/l blood
at a hemoglobin concentration of 15 g/ ml. The
dotted curve represents the BE-scale for the hemoglobin concentration 15 g/100 ml.
\
\
\
213
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BLOOD ACID-BASE ALIGNMENT NOMOGRAM
ordinates, first described by RenC Descartes, and
2) d’Ocagne nomograms or alignment nomograms
extensively studied by d‘Ocagne (1921). The previously published nomogram (Fig. I) is a curve
nomogram using a pH, log pC02 coordinate system.
In this coordinate system the COz-equilibration
curve of plasma and whole blood (the function between pH and pCO2 at a constant base excess) is
approximately a straight line. The present nomogram is an alignment nomogram, which represents
exactly the same functions as the curve nomogram.
When the approximation is used that the CO2equilibration curve is a straight line in the curve
nomogram, the same approximation is used in the
alignment nomogram. Thus the same approximations are made and the same accuracy can be obtained from the two nomograms.
The pH, log pCOz coordinate system is represented in the alignment nomogram by two straightlined, parallel, oppositely directed scales : A linearly graded pH scale and a logarithmically graded
pCOz-scale. The same type of nomogram is used
by Van Slyke & Sendroy (1928) and by Singer &
Hastings (1948). A point (A, Fig. 2) in the curve
nomogram is represented in the alignment nomogram by a straight line (a, Fig. 2). A straight line
in the curve nomogram (1, Fig. 2) is represented
in the alignment ttmnogram by a point (L, Fig. 2),
or actually a fan of straight lines thrmgh the point.
If two points (A and B) of a straight line (I) in
the curve nomogram are given, the point (L) in
the alignment nomogram which represents the
straight line (1) can easily be constructed (see
Fig. 2).
The base excess scales were constructed by
means of the tables giving pH and pCO2 coordinates of the points on the base excess and
buffer base curves of the curve nomogram (Siggaard-Andersen 1962a, Tables I and 11). For a
given BE-value and hemoglobin concentration, two
points of the CO2-equilibration line are known.
One point is the p H and pC02 coordinates of the
BE-value (Siggaard-Andersen 1962 a, Table I).
The other point is the pH and pC02 cqordinates
of the buffer base value (Siggaard-Andersen
1962a, Table 11). The buffer base value is calculated from the B E and hemoglobin concentration :
Buffer base = 41.7 + 0.42 Hb BE. The lines
+
which correspond to these two sets of pH and pCOe
values are drawn in the alignment nomogram
(compare Fig. 2) and the intersection point represents the given BE-value and Hb-Concentration.
By means of the outlined method, points were
constructed which represent BE-values from -30
to +30 meq/l and hemoglobin concentrations of 0,
5 10, 15, 20 and 25 g/lOO ml. For B E >22, which
is not included in the above mentioned table, the
points were constructed by means of the original
experimental data (Siggaard-Andersen 1962a).
The BE-scales were drawn smoothly through the
determined points.
The bicarbonate scale. The relation between PI-€,
pCOe and HCO; of the plasma is given by the
Henderson-Hasselbalch equation :
HCOpH =pK
a pC0,
where a=0.0300 mMol/l per mm Hg pC02 for
human plasma at 38” C, according to Bartels &
Wrbitzky (1961). If pK is constant, it is possible
to construct a bicarbonate scale which is a logarithmically graded straight line, parallel to the pH and
pCO2-scales. If the pK varies linearly with the pH
(Severinghaus, Stupfel & Bradley 1956), the bicarbonate scale will simply be displaced slightly
towards the pH-scale. However, the pK of carbonic acid in plasma does not vary linearly with
the pH. At pH-values of 7.0, 7.2, 7.4 and 7.6, the
pK is found to be’ 6.113, 6.107, 6.099 and 6.089,
respectively at 38” C (Siggaard-Andersen 1962b).
It is thus impossible to construct an exact bicarbonate scale. A good approximation is obtained,
however, by means of a slightly oblique scale. The
bicarbonate concentration given by the scale is the
“apparent” bicarbonate concentration determined by
titration (see Siggaard-Andersen 1962b).
The total-COz scale. As pointed out by Van
Slyke & Sendroy (1928) and McLean (1938), it is
impossible to construct a mathematically exact
scale for total-COz of the plasma in the present
alignment nomogram. However, an approximation
can be constructed which has been found useful for
routine calculations (Van Slyke & Sendrqy 1!?28,
Singer & Hastings 1948).
-
214
0. SICCAARD-ANDERSEN
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PRACTICAL USE OF THE NOMOGRAM
Some examples of measurements and calculations under different clinical conditions
are given below. The present alignment
nomogram is easiest to use for the calculations of examples 1, 2, 3, and 4. The previously published curve nomogram (Siggaard-Andersen 1962 a) is easiest to use for
the calculations of example 5 , and the curve
nomogram also gives a better interpretation
of the principle of calcul2tions and of the
acid-base functions of the blood.
Example 1. A case of chronic pulmonary
insufficiency.
Measured values: pH = 7.34, pCOz =
82 mm Hg,hemoglobin = 17.5 g per 100 ml.
To be calculated: The base excess of the
blood.
A straight line is placed through the pH
and pCOz values on the respective scales.
The BE-value is read at the BE-scales by
interpolation between the hemoglobin concentrations 15 and 20 g per 100 ml: base
excess = +12.0 nzeq/l blood.
A hematocrit determination may substitute a
hemoglobin determination, the hemoglobin being
calculated approximately as H b = H T C X 3 3 3
g per 100 ml.
A number of values, which are often used in
place of the BE-value as indicators of the excess or
deficit of non-volatile acid or base in the blood,
can be derived from the nomogram.
The base excess of the plasma can be read on
the BE-scale corresponding to the hemoglobin concentration zero, here: B E = +18.5 meq/l plasma.
The total-COz and the actual bicarbonate concentration of the plasma can be read from the
respective scales, here : total-Cog = 44.9 mMol/l,
and HCO;= 42.5 meq/l.
The base excess of the completely oxygenated
blood is somewhat lower than the above evaluated
base excess value of the blood at the actual oxygen
saturation. This is due to formation of acid by the
oxygenation of hemoglobin. The relation between
the two values is:
B E (fully oxyg.) = BE (actual ox. sat.)
- 0.3 * H b * (100 ox.sat.)/lW. With the given
values, supposing oxygen saturation = 65 per cent :
B E (fully oxygen.) = +12.0 - 1.8 = + l o 2
meq/l blood.
Buffer base (defined by Singer & Hastings
1948) can be calculated from the B E of fully oxygenated blood and the hemoglobin concentration :
buffer base = 41.7 0.42 H b B E (fully oxygen.) = 41.7 7.4 (+10.2) = 59.3 meq/l blood.
Standard bicarbonate (J@rgensen & Astrup
1957) can be derived on the bicarbonate scale by
placing a straight h e through B E of f’ully oxygenated blood and pCO2 = 40 mm Hg, here standard bicarbonate = 33.5 meq/l plasma. The mrrected bicarbonate value of Van Slyke (Peters 8t
Van Slyke 1932 p. 937) can be derived on the bicarbonate scale by placing a straight line through
B E of fully oxygenated blood and pH = 7.40, here
“Van Slyke bicarbonate” = 38.0 meq/l plasma.
-
+
+ +
+
Example 2. A case of diabetic coma.
Measured values : pH = 7.21, plasma total-CO, = 10.0 mMol/l, hemoglobin = 15.5
g/100 ml.
To be calculated : pC0, and base excess.
A straight line is placed through the pH
and the total-CO, values on the respective
scales. On the pC0, scale is read pCOz =
24.5 nzm Hg.On the base excess scale interpolating to the appropiate hemoglobin concentration is read BE = -17.0 meq/l blood.
Other values may be calculated as outlined
in example 1.
Example 3. Immediately after severe muscular exercise.
Measured values: PH = 7.22, HCO; =
14.0 meq/l plasma and hemoglobin = 17.0
g/100 ml.
To be calculated: pC0, and base excess.
A straight line is placed through the pH
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BLOOD ACID-BASE ALIGNMENT NOMOGRAM
and the bicarbonate values on the respective
scales. O n the pC0, scale is read PCOz =
36.0 mm Hg. On the base excess scale interpolating to the appropriate hemoglobin concentration is read BE = -12.8 meq/l blood.
Example 4 , Acute pneumothorax.
Measured values: Actual PH = 7.49.
p H = 7.37 measured after equilibrating
whole blood with an 0,-C02 gas mixture of
a pC0, = 41.0 mm Hg. Hemoglobin =
14.8 g/100 ml.
To be calculated: pC0, and base excess.
A straight line is placed through p H =
7.37 and pC0, = 41.0 mm Hg on the
respective scales. O n the BE-scales interpolationg to the appropriate hemoglobin concentration is read B E = -1.7
meq/l
blood. Due to complete oxygenation of the
blood during equilibration with the gas mixture, the BE-value refers to completely oxygenated blood. Using this BE-value, the
buffer base or standard bicarbonate can be
calculated as outlined in example 1. The BEvalue at the actual oxygen saturation is calculated from B E (actual ox. sat.) = BE
0.3 Hb (lOO-ox.sat)/
(fully oxygen.)
100. If the oxygen saturation is measured to
be 86 per cent we find :
BE (actual ox.sat.) = -1.7
0.6 =
-1 .I wteq/l blood.
A straight line is placed through this BEvalue and the actual pH-value. O n the pC0,scale is read /KOz = 27.0 m m Hg. O n the
same line total-CO, or actual bicarbonate
can be read.
Example 5. A case of vomiting with impaired respiratory function.
Measured values :Actual pH = 7.54. Two
pH-values measured after equilibrating whole
blood with two different gas mixtures of
+
215
known pC0,: p H = 7.75 at pC0, = 29.3
mm Hg, and p H = 7.48 at pC0, = 64.0
mm Hg. Hemoglobin conc. = 11.8 g/
100 ml.
To be calculated: actual pC0, and base
excess.
A straight line is placed through p H =
7.75 and pC0, = 29.3 mm H g and another
straight line is placed through p H = 7.48
and pC0, = 64.0 mm Hg. A t the intersection point of these two lines is read
B E = +19.6 meq/l blood and hemoglobin = 13.5 g/100 ml. The calculated
hemoglobin concentration should agree within ~r5 g/100 ml with the directly
measured value. The calculated value refers
to fully oxygenated blood due to complete
oxygenation during equilibration with the
C0,-gas-mixture. Knowing the oxygen saturation, for instance 76 per cent, the B E of
the blood at the actual oxygen saturation can
be calculated: BE (uct.ox. sat.) = BE (fully
ox.)
0.3 H b (100--ox.sat.)/100 = 19.6
0.9 = +20.5 meq/l blood.
A straight line is placed through this B E
value and the actual p H value. On the pC0,
scale is read p C 0 2 = 56 m m H g .
+
+
+
TEMPERATURE CORRECTIONS
The nomogram refers to a temperature of
38" C. The values which are put into the
nomogram and the values derived therefrom
all refer to 38" C. However, without any
practically significant error, the nomogram
may be used for 37" C as well.
If the temperature of the patient deviates.
significantly from 38" (more than 2" C) the
pH and pC0, values measured at 38" C
must be converted to the values at the tempe-
216
0. SIGGMRD-ANDERSEN
rature of the patient, while the BE value
should not be corrected.
The pH value measured at 38" C (pH,)
is converted to the pH-value at the temperature of the patient (pH,) by means of the
formula : pHT = pH,
0.0146 ( 3 S T ) . If
the pHT is measured directly at the temperature of the patient the pH, must be calculated from the formula, because the pH, is
necessary for the calculation of BE from the
nomogram.
The temperature coefficient for whole
blood, A pH/A T = 4 . 0 1 4 6 , has beendetermined experimentaIIy (Rosenthal 1948,
Graig, Lange, Oberman & Carson 1952). It
can be shown theoreticelly that the coefficient
varies to some extent with the plasma protein concentration, the hemoglobin concentration and the pCOe level (Siggaard-Andersen 1963).
The pC,Oz value measured at 38" C
pCO,,,)
is converted to the pC0, value at
the temperature of the patient (pCO,,,) by
means of the formula :
pCO,,T = antilog (log pCO,,s - 0.021 X
(38-T)).
If the P C O ~ is
, ~measured directly at the
temperature of the patient, the pCO,,% must
be caIuIated from the formula because the
pCO,,% is necessary for the calculation of
BE from the nomogram.
The factor 0.021 varies somewhat with
the protein concentration, hemoglobin concentration and pCOe level (Siggaard-Andersen 1963).
The BE-value is defined as titratable base
when titrating to pH = 7.40 at pC0, = 40
mm Hg at 38" C. The BE-value is thus independent of the temperature of the sample.
When the BE-value is calculated from the
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+
pH and pC0, values by means of the nomogram, the pH and pCOBvalues must refer to
38" c.
The total-CO, of the plmma is determined
on anaerobically separated plasma. Theoretically, the separation should be at 38" C if
the value referring to 38" C is sought (Astrup 1956, Mfller 1959). The error committed by separating at room temperature is,
however, without practical significance.
The bicarbonute concentration of plamur
at the actual temperature can be calculated
from the pH and $0, values using the proper pK and a. The variation of the pK with
temperature is found to be A pK = -0.0035
A T (Siggaard-Andersen 1962 b). The variation of the absorption coefficient a with
temperature has been determined by Bartels
& Wrbitzky 1960.
-
SUMMARY
The blood acid-base status comprises the
pH, .pCO, and base excess values.
The alignment nomogram includes scales
for these values together with scales for bicarbonate and total-COo of plasma.
The nornogram is especially useful for calculation of base excess after direct measurement of pH, pC0, and hemoglobin concentration. The nomogram is also useful for calculation of both pCO, and base excess after
direct measurement of pH, total-CO, of
plasma and hemoglobin concentration.
The standard bicarbonate can also be calculated from the nomogram.
REFERENCES
Astrup, P.: A simple electrometric technique for
the determination of carbop dioxide tension in
blood and plasma, total content of carbon dioxide in plasma, and bicarbonate content in "se-
217
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BLOOD ACID-BASE ALIGNMENT NOMOGRAM
parated" plasma at a fixed carbon dioxide tension (40 mm Hg). S a n d J. clin. Lab. Invest.
8, 33, 1956.
Bartels, H. & Wrbitsky, R. : Bestimmung des CO2Absorptions-koeffizienten zwischen 15 und'
38" C in Wasser und Plasma. Pfliigers Arch.
ges. Physiol. 271, 162, 1960.
Graigh, F. A., Lange, K., Oberman, J. & Carson,
S.: A simple accurate method of blood pH
determinations for clinical use. Arch. Biochem.
38, 357, 1952.
J@rgensen, K. & Astrup, P.: Standard bicarbonate,
its clinical significance, and a new method for
its determination. Scand. J. clin. Lab. Invest.
9, 122, 1957.
McLean, F. C.: Application of the law of chemical
equilibrium (law of mass action) to biological
problems. Physiol. Rev. 18, 495, 1938.
MZller, B.: The hydrogen ion concentration in
arterial blood. A clinical study of patients with
diabetes mellitus and diseases of the kidneys,
lungs, and heart. Thesis, Aarhus, Denmark,
1959.
Ocagne, M. d': Trait6 de nomographie. 2. ed. Paris,
1921.
Peters, J. P. & Van Slyke, D. D.: Quantitative
clinical chemistry. I. Interpretations. London,
1932.
Rosenthal, T. B.: The effect of temperature on the
pH of blood and plasma in vitro. J. biol. Chem.
173, 25, 1948.
Severinghaus, J. W. & Bradley, A. F.: Electrodes
for blood p02 and pC02 determination. J. appl.
Physiol. 13, 515, 1958.
Siggaard-Andersen, 0. & Engel, K.: A new acidbase nomogram. An improved method for the
calculation of the relevant blood acid-base data.
Scand. J. clin. Lab. Invest. 12, 177, 1960.
- - J@rgensen,K. & Astrup, P.: A micro method for determination of pH, carbon dioxide
tension, base excess and standard bicarbonate
in capillary blood. Ibid. 12, 172, 1960.
Siggaard-Andersen, 0.: The pH, log pC02 blood
acid-base nomogram revised. Ibid. 14, 598,
1962 a.
- The first dissociation exponent of
carbonic acid
as a function of pH. Ibid. 14, 587, 1962 b.
- The acid-base status of the blood. Ibid. 15,
Suppl. 70, 1963.
Singer, R. B. & Hastings, A. B.: An improved
clinical method for the estimation of disturbances of the acid-base balance of human blood.
Medicine 27, 223, 1948.
Van Slyke, D. D. & Sendroy, J., Jr.: Line charts
for graphic calculations by the HendersonHasselbalch equation, and for calculating plasma carbon dioxide from whole blood content.
J. biol. Chem. 79, 781, 1928.
2