CLIN. cHEM. 20/12, 1499-1506
(1974)
Calculations and Correction Factors Used in
Determination of Blood pH and Blood Gases
and Daniel C. Noonan1
Robert W. Burnett
Measurement of blood pH, P02 and Pco2 also involves
calculation of two or more derived quantities and correction of the measured values in cases where the body
temperature of the patient differs from the temperature
of measurement. References to the pertinent calculations and the temperature corrections are scattered
through the literature of several medical specialties, and
much new information has been gathered in recent
years that directly affects these calculations. This review explains each of the derived quantities and correction factors most used in this field and also provides the
best available data for the calculations, in a form that
can readily be adapted to electronic
data processing.
Keyphrases:
Po2 #{149}
Pco2 #{149}CO2 content #{149}
plasma bicarbonate concentration
#{149}base excess
#{149}oxyhemoglobin dissociation
curve
#{149}02 saturation
#{149} 02
content #{149}temperature corrections
Addftlonal
Blood pH and gas analysis usually involve the direct measurement
of blood pH, pco2, and po2. In
diagnosing,
managing,
and
monitoring
the patient,
finds it useful to have other
from these values-such
as
the physician frequently
data that can be derived
oxygen saturation,
base excess,
content.
Moreover,
normal,
the observed
ly adjusted
to take
and carbon
if the patient’s
temperature
and
is ab-
values should be mathematical-
this factor
into account.
Much of the early work in making
surements
dioxide
deriving
clinically
them has come from specialty
these basic mea-
useful
results
laboratories
from
associated
with such disciplines
as cardiology,
anesthesiology,
and respiratory
disease. As these measurements
have
proven
central
called
to be of immense
clinical
upon
value in patient
laboratory
to provide
has
these
been
measured
care, the
increasingly
and derived
literature
of physiology,
clinical
pathology,
surgery,
anesthesiology,
and respiratory
disease.
In this review, we gather together
all the relevant
mathematical
relations the clinical chemist is likely
to need in providing
comprehensive
blood-gas
service. Each of the calculations
or corrections
used in
this area of clinical chemistry
will be discussed,
and
the best available data for constants
and correctiOn
factors will be presented. This is not intended to be a
complete review of the literature
in this field, but
rather a summary of current usage. Having all the
pertinent equations in one place simplifies the task of
providing
adaptation
puter
ular
more meaningful
results;
to computer
processing,
processing
will undoubtedly
Chemistry
Conn. 06115.
I Present
address:
Laboratory,
Port
Huron
Hartford
Hospital,
Hospital,
Port
ing blood-gas analyzers
information
system.
Calculations
Hasselbaich
Received Aug.
6, 1974; accepted
Sept.
17, 1974.
on-line
Bicarbonate
may
to a larger laboratory
in Which the HendersonEquation Is Used
concentration
and CO2 content
be written
can be
pH and p co2 by use of
equation.
This equation
calculated
from a measured
the Henderson-Hasselbalch
in several
different
forms,
however,
and one must be certain of the definition of the constant or constants
involved as well as have accurate
values for these constants
before attempting
to use
the equation.
C02(gas)
between CO2 in a gas phase
may be written
+
H20
H
+
and
HC03
Mich.
and
48060.
become more pop-
future,
either
in the form of dedicated
minicomputers
in the blood-gas
laboratory
or by hay-
Hartford,
Huron,
it also facilitates
if desired.
Corn-
in the
The equilibrium
HC03
in solution
results.
Clinical
Descriptions
of the basis for the calculations
involved in blood-gas analysis and the values for the
correction factors are scattered
through
the medical
literature.
The primary
references
are found in the
we may
ous equilibrium
write
an expression
constant,
for the heterogene-
K,
CLINICALCHEMISTRY,
Vol. 20, No. 12, 1974
1499
2?
a+a
if
Is
-
HCO3
1’
=
aaoaco2
HCO
3
. aH+
pK11’
tir,,-
#{163}1#{188}J3
=
P’Z1g’
+ log S
(3)
Pco2
au2oyco2
Kig, a thermodynamic
constant,
is independent
of solution composition;
a symbolizes
activity and ‘y syrnbolizes
activity
coefficient.
We may also define
a
practical equilibrium
constant K’lg that includes the
activity
coefficients,
and is thus dependent
on solution composition.
and the value for pK’11 at 37 #{176}C
and pH 7.40 is 6.09.
Although pK’ reportedly varies among individuals,
particularly
in the presence of various diseases (4),
more recent work not only does not confirm this (5,
6)
over
but has shown
a wide range
concentrations
that pK’ is essentially
of serum protein
and
and in several different
constant
electrolyte
disease states.
In practice, calculations
involving the HendersonHasselbaich
equation
are usually done with the aid of
Kjg’
K1g22
=
a nomogram
or of a slide-rule
These may give answers that
aH+[HCOp
Pco2
VHCO3-
those
This
equation
may be rewritten
cause
pK1g’
pH
=
-
log[HC03J
(1
+ log P2
)
pK’ig in whole blood at pH 7.40 and at 37 #{176}C
can be
derived
from the recent experimental
data of Maas
(1 ) and is equal to 7.604 when bicarbonate
concentration
is expressed
in mmollliter
and p co2 in mmHg
(1 mmHg
133 Pa).
The
corresponding
value
in
plasma
is 0.01 lower because
of a systematic
difference in measured
pH between
plasma
and whole
blood (2). Maas also determined
the dependency
of
PK’lg Ofl temperature,
pH, and ionic strength.
The re-
spective
coefficients
are
pK1g’/T
APK15’/PH
pK15’/I
=
007
=
.
=
-0.
04
-0.39
In practice,
these effects are small and may be ignored unless very high accuracy
is required,
for example, if tonometered
bicarbonate
solutions
were to
be used as standards.
One must be careful to avoid confusing
=
pH -
log[HC03]
+ lO[CO2IdiSld
(2)
Quite
commonly
“[H2CO3J”
is written
instead
of
“[CO2]dissolved,” although
this is not actually correct.
Equation
2 may be rewritten
pK11
=
pH -
log[HCO3j
by using
estimate
+ log Pco,
+ log S
S is the solubility
coefficient
of C02, in milliper mmHg,
and is equal to 0.0307 for
serum at 37 #{176}C
(3 ). The relationship
between the two
constants
is
the above
of calculator.
slightly from
values,
because
a
of pK’ may have been used or be-
the 0.01 difference
between
blood
and
plasma
may not have been included.
Equation
1 allows the convenient
calculation
of
plasma bicarbonate
from a measured pH and p co2. A
related value that is also commonly
used is CO2 content, or total C02, which is defined as the sum
[CO2Ijj,o1ved + [H2co3] + [Hco3]
(1)
+
(20)
(.004)
[co3]
+
(.03)
[protein
carbamates]
(.17)
This is a useful quantity
only because it is amenable
to a simple direct measurement
that is performed
in
nearly every clinical chemistry
laboratory.
The numbers in parentheses
are the relative amounts of each
species in plasma at pH 7.4 (7, 8). It is seen that CO2
content
is numerically
quite close to [HCO3]
and
that the only other species that needs to be considered at all is [CO2]d9801j.
The working equation
for
calculating
CO2 content is thus
CO2
content
=
[HC03]
pK’ig as de-
fined above, with pK’11, which is also commonly
used.
The latter constant
is defined in terms of the concentration
of CO2 dissolved
in solution,
rather than p co2
in the gas phase,
pK1’
calculated
different
as
type
differ
+
[c02]
[Hco3-]
dissolved
+
.0307p02
(4)
Base Excess
Base excess is at present
an ambiguous
term, because it has been defined
in at least two different
ways during
the past 20 years. The differences
are
due to the fact that base excess may be defined
in
relation
to various
fluid compartments
in the body,
including
plasma,
whole blood, interstitial
fluid, or
some combination
of these.
The primary justification
for introducing
a quantity such as base excess is to obtain an index of metabolic acid-base
imbalance.
Theoretically,
in cases of
primary,
uncompensated
respiratory
imbalances
the
base excess will be zero. Conversely,
a metabolic
aci-
whether
primary
or secondary
to a
where
dosis
moles/liter
respiratory
imbalance,
should produce
either a positive (metabolic
alkalosis)
or negative
(metabolic
aci-
1500
CLINICALCHEMISTRY,Vol.
20, No. 12, 1974
dosis)
or alkalosis,
base
excess.
about
The concept
of base excess is based on the fact
that, for a given fluid, a change in p co2 will produce
a
change in pH (and bicarbonate
concentration),
which
is determined
by the buffer capacity,
fi, of the fluid.
The buffer capacity
is expressed
in mEq/liter
per pH
unit, and may be thought
of as the change in bicarbonate concentration
that would result from a change
of one unit in the pH of the fluid.
x
in vivo was less than
that
experiments
is different
because
fluid could be approximated
the
as .37
31, or 11.5 (19).
representative
in vitro value.
of physiological
conditions
than is the
The plasma
bicarbonate
concentration
that
tamed
in an acute (uncompensated)
respiratory
dosis or alkalosis
is given by
in
[HCO3jR
24 + j3(7.40
-
is obaci-
pH)
and base excess is defined
as the difference
between
the actual plasma bicarbonate
concentration
and the
concentration
that would be expected
in an uncompensated
respiratory
imbalance.
place
fluid
Base
compartment,
which is much larger than the intraspace and not nearly as well buffered
be-
vascular
cause of its low protein concentration.
The apparent
buffer capacity
of extracellular
fluid,
as determined
from these experiments,
is between
10
and 15 mEq/liter
and because
in the blood,
experiments
with whole blood; line B corresponds
to
the results of the in vivo experiments.
Although
this
subject
engendered
considerable
controversy
in the
mid-sixties,
the consensus
at present seems to be that
base excess can be a useful parameter
and that the in
vivo, or extracellular
fluid, buffer capacity
is more
equili-
bration
to the new level of CO2 actually
takes
not only in the blood, but also in the interstitial
place
The difference between the two estimations
of /3 is
graphically
in Figure
1. The buffer line
marked A corresponds
to
observed
in the in vitro
vitro. This was first demonstrated
in 1932 (13 ) and
has
since
been
confirmed
by Brackett
et al.,
Siggaard-Andersen
et al., and others
(9, 14-18)
by
measuring
the response
to acute changes
in p co2 in
dogs and in humans.
The buffer capacity
determined
from these
fluid volume
takes
shown
buffer capacity
largely depends
on the buffering
action of hemoglobin.
A commonly
used expression
for
f3 derived from such experiments
was (9.5 + 1.63 Hb)
(9 ), and various nomograms
and charts appeared
in
which values of f3 ranging from roughly 20 to 45 were
used, with an average value of 31, all at a hemoglobin
concentration
of 15 g/dl (10-12).
At the same time it was known that the buffer ca-
of whole blood
all the buffering
fi for extracellular
The early definition of base excess was based on a
value of
determined
from experiments
with whole
blood, in vitro, under which conditions the apparent
pacity
37% of extracellular
almost
excess
Referring
centration
the base
=
[HCO3j
to Figure
-
24
-
1, if the plasma
12(7.40
-
pH)
bicarbonate
(5)
con-
blood pH are located
on the graph,
of the extracellular
fluid is given by
the vertical distance between this point and line B.
The above relationship
and its derivation
have also
been quite clearly presented
by Collier et al. (20).
per pH unit. A value of 12 is sug-
gested here as being quite suitable
for routine
use. It
has been pointed out that, because blood volume is
and
excess
L40
30
-i
-i
Fig.
0
1.
Bicarbonate-pH
di-
agram, showing buffer lines
for whole blood in vitro (A ) and
for extracellular
fluid in vivo
(B)
20
10
70
7.1
7.2
7.3
7,Ll
7,5
7.6
7,7
7,8
CLINICAL
CHEMISTRY.
Vol. 20, No. 12, 1974
1501
where p is the corrected
The
following
approximations
above definition
are implicit
1. A constant
pends
somewhat
on the hemoglobin
concentration,
which is assumed
to be normal.
If the actual hemoglobin
concentration
is severely
subnormal,
f3 will
also be slightly
lower, although
this is said to be of
little clinical significance
(21).
a normal ratio
fluid volume.
In situations
where interstitial
fluid volume
is relatively high-e.g.,
neonatal
or edematous
patients-9
will be decreased
because
more fluid is available
to
dilute
the
bicarbonate
generated
by hypercapnia
It is also important
to recognize
that nomograms
or
instruments
for calculating
base excess by use of the
earlier definition,
including the widely used alignment nomogram of Siggaard-Andersen,
may also be
used to calculate
eral authors
have
tive” hemoglobin
of about 5 g/dl in
extracellular
fluid base excess. Sevpointed
out that use of an “effecconcentration
in extracellular
fluid
conjunction
with these nomograms
gives a measure of extracellular
fluid base excess (15,
19, 22 ). These values agree quite well with those calbase
from equation
chart
published
5 and the most recent
by Siggaard-Andersen
is a function
02
of hemoglobin
and follows
(A.logpo2\
Several
) also
nomograms
sigmoidal
I
-0
48
I
saturation
are available
a calculator
\
for calculating
oxy-
program
are used,
such
could
be devised
oxyhemoglobin
as those
given
dis-
by Sev-
eringhaus
(23 ), or with use of an equation
that has
been empirically
fitted to the observed curve. One
such equation
The
oxyhemoglobin
better
dissociation
as a plot of percent
oglobin/total
that
hemoglobin)
100(((p
(((p - 67.07)p
works
quite
well is2
=
-
be “shifted
67.0’7)p
+ 2396)p
+ 2121)p - 8532)p
3350)p
+ 936000
-
to the right”
1502
is usually
[(oxyhem-
and represents
a decreased
from
capillaries
to tissue
A shift to the right
in pH, as expressed
CLINICALCHEMISTRY,
communication.
Vol. 20, No. 12, 1974
ocby
concenconcenThere is
mechaone or more of these factors for
of a normal dissociation
curve; for exbeen shown that in chronic acidosis and
blood diphosphoglycerate
concentration
a direction to compensate
for the shift
the Bohr-Haldane
effect and to maindissociation curve (26 ). Nevertheless,
it
involving
maintenance
ample, it has
alkalosis
the
altered in
produced by
thin a normal
is clear that there are several
using a calculated
oxygen
assumptions
saturation
(7)
involved in
as described
above, because it considers only the effect of pH on
the dissociation curve. One very common disorder for
which this assumption
is invalid is anemia, where the
dissociation
curve is shifted
to the
because
of the increased
erythrocyte
cerate concentrations
(27).
The alternative
to calculating
to directly
measure
it in whole
(28, 29 ) and spectrophotometric
right, primarily
diphosphogly-
oxygen saturation
blood.
(30-32
is
Manometric
) techniques
Unfortunately,
oxy-
gen saturation
has been defined in different
terms for
these two methods,
and this is a potential
source of
confusion.
In the Van Slyke manometric
method,
oxygen saturation
is usually expressed
as the volume
bound
pie, as a percentage
C. R., personal
from
100] vs. oxygen tension,
X
can be delivered
of oxygen
2 Collier,
curve
saturation
are used for this determination.
02 saturation
agreement
as shown in Figure 2. If curve A represents
the dissociation curve under a standardized
set of conditions
(pH = 7.40, T = 37 #{176}C,
etc.), then curve B is said to
nisms
6,
Jconstant
in which values for the standard
curve
saturation,
equation
7 gives
30% to 100% saturation.
tration,
gen saturation
from a measured p 02 and pH. These
have been constructed
from a standardized
oxyhemoglobin dissociation
curve together with equation 6.
sociation
7 is similar
in erythrocyte
2,3-diphosphoglycerate
and is shifted to the left by increased
trations
of carbon
monoxide
in the blood.
also evidence
that there are compensatory
with oxygen
the familiar
-
nH5-
Alternatively,
in form to the version of the
given recently by Roughton and Severinghaus
(24). Although
the latter equation
gives
better agreement with experimental
data below 30%
Equation
Adair equation
equations 6 and 8.
The situation
is complicated
considerably
by the
fact that several other factors also influence oxyhemoglobin dissociation
(25 ). It is known that the curve
is shifted to the right by an increase in temperature,
an increase in Pco2 at constant pH, and by an in-
curve. In addition, it is well-known that the percent
saturation
at a given p 02 is a function of pH (BohrHaldane
effect). The Bohr-Haldane
coefficient cornmonly used (23 ) is
‘S
10t1ogp02+O.48(pH-7.4)]
crease
saturation
of p
=
cells for metabolic
utilization.
curs as a result of a decrease
Saturation
The percent
6
p
oxygen
gives base excess values that agree closely with those
calculated from equation 5.
Oxygen
by rearrang-
affinity of hemoglobin
for oxygen. In such a situation,
assuming
normal
physiologic
oxygen tensions,
more
acid-
(21
ing equation
represented
(18).
culated
obtained
02,
in the
of base excess:
value of fi ignores the fact that it de-
2. The quoted value for fi assumes
between blood volume and interstitial
p
hemoglobin
after
to hemoglobin
of the volume
equilibration
in the original
of oxygen
with
sam-
bound
to
room air. This
100
80
60
Fig. 2. A representation
of the
oxyhemoglobin
dissociation
=
I-
u-i
curve under standardized conditions (A) and “shifted to the
40
(B)
right”
u-i
0
20
10
20
30
40
50
60
70
80
Po2
definition
ignores any hemoglobin
species that does
not readily combine with oxygen, such as carboxyhemoglobin and methemoglobin.
Consequently,
a patient could have a carboxyhemoglobin
concentration
amounting
to 25% of the total
hemoglobin
while
still
showing an oxygen saturation
of, say, 95% if this definition is used. On the other hand, oxygen saturation
may be defined as oxyhemoglobin
concentration
as a
percentage of all hemoglobin species present (usually
oxyhemoglobin,
reduced hemoglobin,
and carboxyhemoglobin, although a term for methemoglobin
may
also
be added).
directly
though
by
there
This
is disagreement
of oxygen saturation
clearly
must
quantity
can also be measured
a spectrophotometric
be
about
technique.
which
definition
is the more meaningful,
well
aware
of which
Al-
the user
definition
is
being used before attempting
interpretation
of this
quantity. It is often very useful to have direct methods available for the determination
of carboxyhemoglobin and methemoglobin
in addition to oxygen saturation in order to decrease uncertainty
in establishing the oxygen transport status of the patient.
One additional
situation
in which the commonly
used oxygen saturation
nomogram fails is during the
neonatal
period. The nomograms
are based on the
dissociation
curve for adult human blood (hemoglobin
A),
and
should
not
be used
if an
appreciable
amount of hemoglobin
F is present unless the correction described below is used. The dissociation
curve
of hemoglobin F lies well to the left of that for hemoglobin A; it is believed that this is attributable
to the
affinity
of hemoglobin
F for 2,3-diphosphoglycerate(33, 34).
A careful
comparison
of published
dissociation
curves under various conditions
(35 ) shows that the
correction,
since hemoglobin
F is rapidly replaced
with hemoglobin A after birth. At about two months
postpartum
hemoglobin
F and hemoglobin
A are
present in roughly equal amounts; therefore, 0.1 unit
would be the proper pH correction before the nomogram is used.
Oxygen Content
“Oxygen content” means the total amount of oxygen contained in a given volume of whole blood, and
is usually expressed
as milliliters of oxygen per 100
ml of blood. Oxygen content may be directly measured by either the Van Slyke manometric
technique
or an electrochemical
monly is calculated
at pH 7.40 very closely approximates
the curve for adults at pH 7.60. Therefore,
when
not practical
to directly
measure
oxygen saturation
it is
in
technique,
but it more
from the oxygen saturation
com-
and
the hemoglobin concentration
of the sample.
Four moles of oxygen (22 393 ml/mol at standard
temperature
and pressure)
hemoglobin
equal to
(64 458 g/mol),
::::
02 content
grams/dl,
(ml/dl
[Hb],
and
with
so oxygen
the
whole
(02
blood)
hemoglobin
is
of Rb
as
=
saturation
02 saturation
1 mol of
capacity
gram
may thus be expressed
1.39[Hb]
where
can combine
i. 39 ml of 02 per
=
Oxygen content
lower
curve at birth
0.2 has
the age
of this
a neonate,
the nomogram
may be used after
been added to the measured
pH. Obviously,
of the infant
will determine
the magnitude
\
)
+ cpo2
concentration,
is expressed
(9)
is in
as a per-
centage. The last term gives the amount of oxygen
that is dissolved in blood arid is free, i.e., not cornbined with hemoglobin.
The value of a for whole
CLINICALCHEMISTRY, Vol. 20, No. 12, 1974
1503
blood at 37 #{176}C
is 0.00315
mmHg (24 ) (or 0.237 dIliter
It must
be remembered
ml/100
ml of blood
per
per pascal, in SI units).
when
performing
the
cal-
culation that different methods for determining
oxygen saturation
and hemoglobin
can yield different
values for these quantities.
For proper calculation of
oxygen content these two quantities
must be determined
with consistent
methods.
Specifically, if hemoglobin
is measured
as the sum of oxyhemoglobin
Table 1. Temperature-Correction Factors for
Blood pH and Gas Measurements
#{176}F
and
reduced hemoglobin,
as in the Van Slyke method,
then oxygen saturation
must be expressed as oxyhemoglobin
as a percentage
of this sum. Likewise, if
hemoglobin
is determined
spectrophotometrically,
so
that
carboxyhemoglobin
included
and
in the total,
then
(or)
oxygen
methemoglobin
saturation
is
must
pH
Patient’s temperature
#{176}C
110
109
43
42.5
108
42
107
106
9co,
(Add to observed
p01
values)
. 09
+22%
+35%
-
.08
.07
+21%
+19%
+32%
+30%
41.5
-
.07
+17%
+27%
41
-
. 06
+16%
+25%
105
40.5
-.05
+14%
+22%
104
103
40
39.5
-
.04
.04
+12%
+10%
+19%
+16%
102
101
39
38.5
-
.03
+8%
+13%
-
.02
+6%
+10%
100
38
37
-
.01
+4%
98-99
97
96
95
-
-
+7%
None
None
None
36
+.01
35.5
+.02
-4%
-6%
-7%
-10%
35
+.03
-8%
-13%
94
34.5
+.04
93
91
90
34
33
32
88
if they
are to reflect the blood gas status in vivo. The adjustment is particularly
important in monitoring patients
also
bin.
be expressed
Temperature
as a percentage
of total
hemoglo-
Corrections
are
made at a controlled temperature,
usually 37 #{176}C
in
this country.
Because
pH, p 02, and p co2 are all ternperature-dependent,
these quantities must be adjustVirtually
all blood
ed to the body
undergoing
pH
temperature
surgical
gas measurements
and
of the individual
procedures
in which
deep
hypo-
thermia
is used as an adjunct; body temperatures
of
25-28 #{176}C
are common in this circumstance.
Ideally, body temperature
should be given whenever blood pH and gases are ordered, so that the proper
correction may be applied. The corrections
given in
Table 1 are derived from measurements
on whole
blood and may not be applicable for other media.
pH. The pH of whole blood, as with most other solutions,
decreases
temperature
eral studies,
Rosenthal
as the temperature
increases.
0147 per
_#{149}
degree
Celsius
(10)
Subsequent
studies
have both confirmed
this value
and shown that the temperature
coefficient
is itself somewhat
dependent
on pH and on plasma
bicarbonate
concentration
(40 ) . At extremes
of these
)
(37-39
two quantities
-0.016
usually
p co2.
a liquid
written
the
coefficient
could
be as low as
or as high as -0.012,
but this refinement
is
ignored in practice.
For dilute solutions,
the solubility
of a gas in
is governed by Henry’s law, which may be
Mg
=
a53
where M is the concentration
the
tension
partial
1504
of gas in solution,
p is
of the gas in solution
or the equilibrium
pressure
CLINICAL
of the gas above the solution,
CHEMISTRY.
Vol. 20, No. 12, 1974
-16%
-19%
+.06
-16%
-25%
31
+.07
+.09
-19%
-22%
-30%
-35%
86
30
+.10
-26%
84
29
+.12
-39%
-43%
82
81
28
27
+.13
+.15
-29%
-32%
-34%
+.16
+.18
+ . 19
-37%
-40%
-43%
-47%
-51%
79
26
77
25
75
73
24
23
+.21
-45%
-63%
72
70
22
21
+.22
+.24
-48%
-50%
-65%
-67%
68
20
+.25
-53%
-70%
-54%
-57%
-60%
The
coefficient has been determined
in sevand the most widely used value is due to
(36 ), who found
ApH
+.04
-10%
-12%
and a
is a solubility
coefficient.
For a given concentration
of
dissolved
gas, since a is known as a function
of tern-
perature,
a partial
pressure
at one temperature
can
be converted
to any other temperature.
However,
if
the dissolved
gas is involved in an equilibrium
with
any other species in solution,
then the effect of ternperature
on the equilibrium
constant
must also be
considered
in any theoretical
approach
to the tern-
perature
dependence
of gas tensions.
For example,
the temperature
dependence
of p co2 is also a function of the temperature
dependence
of pH, discussed
above, and of the apparent
pK of carbonic
acid (41).
Experiments
have shown that the temperature
de-
pendence
is well described
by the empirical
relation-
ship
logPco2/iT
=
Icol
(11)
The commonly
accepted
experimental
value for the
constant,
fo2, is 0.0190 per degree Celsius
(23, 39,
42 ), which agrees well with a previous
indirectly
determined
value (41 ) . Assuming
that measurement
takes place at 37 #{176}C,
a p co2 corrected
to body ternperature
may be written
Pco2(at
where
T)
T is body
Pco2(37#{176}C)
100.019(T-37)
=
temperature
in degrees
(12)
Celsius.
p 02- The effect of temperature
on p 02 is also cornplex, because temperature affects not only the solubility of oxygen in the plasma
phase but also the
equilibrium
between
oxyhemoglobin
and dissolved
oxygen,
as given by the oxyhemoglobin
dissociation
curve.
When oxygen saturation is below 95%, temperature
changes in a sample of whole blood stored anaerobically do not cause a significant
change in the saturation-i.e.,
oxygen does not shift between oxyhemoglobin and dissolved oxygen. This is because the
change in p 02 is offset by the change in oxygen affiniity of hemoglobin,
as seen in the shift in the oxyhemoglobin dissociation
curve. However,
at high levels of
oxygen saturation, these factors do not balance and
the value of log p o2/T
gen saturation.
becomes a function of oxy-
An empirical relationship
of the form of equation
11 has also been useful for oxygen data.
logp02/AT
f02
=
(13)
Experimental data at both high and low saturations
have been fit with the following expression for f02
(42, 43
)
above values gives Mog po2/T
.031, which is in
good agreement
with equation 14. Equation
14 has
been used to construct
a nomogram
(43 ), which faciljtates the computation.
Derived
quantities.
Oxygen saturation:
If p 02 and
)H are known, oxygen saturation
can be estimated if
one assumes a normal oxyhernoglobin
dissociation
curve. The curve normally used in the form of a no-
mogram or slide-rule
calculation
assumes a set of
standard
conditions
including
a temperature
of 37
and a pH of 7.40. Provision is made for adjusting
this curve for other values of pH. If it is desired to es-
timate oxygen saturation in this manner, the calculation should be carrie1 out with use of the measured
02 at 37 #{176}C
and the measured
pH at 37 #{176}C.
It is not
necessary
to use temperature-corrected
values
for
‘
and pH, because
02
‘#{176}
cantly
temperature
oxygen
dependent;
saturation
is not signifi-
moreover,
corrected
values could be used only if the dissociation
curve
corresponding to the subject’s body temperature
were available.
Bicarbonate
analogous
and CO2 content: For
derived
parameters
should
concentration
reasons,
these
be calculated from the Henderson-Hasselbaich
in this case, because bicarbonate
concentration is inMoreover, the corrected values could not be used unless both the pK of
dependent
of temperature
(44
).
acid and the solubility
coefficient
were known at the temperature
of interest.
carbonic
. 032
fo2
.
-
0268 e330
fo2 should
be calculated
of CO2
(14)
where x is percent oxygen saturation. f02 may be
taken as .030 with oxygen saturations
as high as 95%
without introducing significant error, but at higher
saturation
equa-
tion by using the pH and Pco2 measured at 37 #{176}C.
It
is not necessary
to use temperature-corrected
values
from
equation
14.
References
M8.S, A. H. J., The determination
of the true equilibrium conand the practical equilibrium coefficient for the first ionizetion of carbonic acid in solutions of sodium bicarbonate, cerebrospinal fluid, plasma and serum at 25 0 and 38
Clin. Chim. Acta
stant
.
Approximately
the same result has also been obtamed indirectly
(23 ) in the following manner. p 02 is
a function of temperature, pH, and oxygen saturation; the last two quantities
are also functions
of tern-
perature. Therefore we may write,
log po2
=
tT
I
log po2’
t,
AT
log p02’
(\
\
pH
‘
1T,sat
th
log
(% sat
2. Maas, A. H. J., pH determination
of body fluids with a micro
glass electrode and a saturated KC1 bridge in the cell. Clin. Chim.
Acta 28, 373 (1970).
3. Austin, W. H., Lacombe, E., Rand, P. W., and Chatterjee,
M.,
Solubility of carbon dioxide in serum from 15 #{176}to 38 #{176}C.
J. App!.
Clin. Sci. 32, 189(1967).
5. Austin, W. H., Ferrante, V., and Anderson, C., Evaluation
whole blood pK in the acutely ill patient. J. Lab. C!in. Med.
T
p2
325 (1971).
Physiol. 18, 301 (1963).
4. Trenchard, D., Noble, M. I. M., and Guz, A., Serum carbonic
acid pK abnormalities in patients with acid-base disturbances.
‘pB,aat
(‘‘
‘
+
1o2,sat
129 (1968).
6. Austin,
sat\
1T,pH
C!in. Pathol.
()pH,po2
The first term has been experimentally
values is
laboratories
0.024 (23).
and
the
average
determined
of several
The first factor in the second
term is the Bohr-Haldane
coefficient, given by equation 6. The second factor is given by equation 10.
Again, the variation with oxygen saturation is ignored below 95% saturation.
Substitution
of the
V. V., and Ritchie,
R. F., Effect of ab-
on the pK of whole blood. Amer. J.
15, 799 (1969).
pK.J.MaineMed.Ass.
7.
Austin,
W. H.,
and Stinebaugh,
60, 10 (1969).B. J., The “not so apparent”
J., A titrimetric method for the determination
of
actual bicarbonate in cerebrospinal
fluid and plasma
or serum.
8. Mass,
in several
W. H., Ferrante,
normal plasma constituents
‘
of
72,
A. H.
Clin. Chim. Acta 29, 567 (1970).
Siggaard-Andersen,
0., Titratable
acid or base of body fluids.
Ann. N. Y Acad. Sci. 133, 41 (1966).
lO. Siggaard-Andersen,
0., and Engel, K., A new acid-base nomo,
An improved method for the calculation of the relevant
blood acid-base data. Scand. J. Clin. Lab. Invest. 12, 177 (1960).
1. Siggaard-Andersen, 0., The pH-logPco2 blood acid-base nomogram revised. Scand. J. Clin. Lab. Invest. 14, 1 (1972).
graIn.
CLINICALCHEMISTRY,
Vol. 20,
No.
12, 1974
1505
12. Siggaard-Andersen,
0., Blood acid-base
Scand. J. Clin. Lab. Invest. 15, 211 (1963).
alignment
nomogram.
13. Shaw, L. A., and Messer, A. C., The transfer of bicarbonate between the blood and tissues caused by alterations
of the carbon
dioxide concentration
in the lungs. Amer. J. Physiol. 100, 122
(1932).
14. Brackett,
N.C., Jr., et al., The carbon dioxide titration curve of
J. Med. 272, 6 (1965).
15. Siggaard-Andersen,
0., Acute experimental
acid-base disturbances in dogs. Scand. J. C!in. Lab. Invest. 14, Suppl., 66 (1962).
16. lchiyanagi, K., et al., Acid-base balance of arterial plasma during exogenous
and endogenous
hypercapnia
in man. Resp. Physiol.
normal man. New Eng!.
7. 310 (1968).
17. Engel, K., Kildeberg,
P., and Winters, R. W., Quantitative
displacement of blood acid-base status in acute hypocapnia. Scand. ,J.
C!in. Lab. Invest. 23, 5 (1969).
18. Dell, R. B., In vivo CO2 equilibration
curve. Chest 61, 3 S
(February 1972, supplement).
19. Armstrong, B. W., Mohler, J. G., and Jung, R. C., The in vivo
carbon dioxide titration curve. Lancet i, 759 (1966).
20. Collier, C. R., et a!., Use of extracellular
sis of acid-base
(February
disorders:
A conceptual
base excess in diagnoapproach. Chest 61, 6 S
1972, supplement).
A. J., et al., Regulatory
bin oxygen affinity
700 (1971).
in acidosis
27. Cropp, G. J. A., and
cerate in oxygen transport
(February
1506
mechanisms
and alkalosis.
J.
of hemoglo-
Clin. Invest.
50,
Gee, M. H., Role of 2,3-diphosphoglyin experimental
anemia. Chest 61, 16 S
1972, supplement).
CLINICAL
31. Johnson, G. W., Oxygen saturation of blood. Stand. Methods
Clin. Chem. 4, 183 (1963).
32. de la Huerga, J., and Sherrick, J. C., Measurement of oxygen
saturation of the blood. Ann. C!in. Lab. Sci. 1, 261 (1971).
33. de Verdier, C., and Garby, L., Low binding of 2,3-diphosphoglycerate to hemoglobin F. Scand. J. Clin. Lab. Invest. 23, 149
(1969).
34. Bunn, H. F., and Briehl, R. W., The interaction
phoglycerate
1088 (1970).
with
various
human
hemoglobin.
J.
of 2,3-diphosClin. Invest. 49,
35. Blood and Other Body Fluids. P. L. Altman and D. S. Dittner,
Eds. Federation
of American Societies for Experimental
Biology,
Bethesda, Md., 1961, p 151 ff.
36. Rosenthal,
T. B., The
effect of temperature
on the pH of
blood and plasma in vitro. J. Biol. Chem. 173, 25 (1948).
21. Siggaard-Andersen,
0., An acid-base chart for arterial blood
with normal and pathophysiological
reference areas. Scand. J.
Clin. Lab. Invest. 27, 239 (1971).
22. Refsum, H. E., and Kum, B. M., Relationship
between the
acid-base changes of arterial plasma during acute changes of the
CO2 tension in vivo and the hemoglobin concentration
of the
blood. Rasp. Physio!. 2, 283 (1967).
23. Severinghaus,
J. W., Blood gas calculator. J. App!. Physiol. 21,
1108(1966).
24. Roughton, F. J. W., and Severinghaus, J. W., Accurate determination
of 02 dissociation
curve of human blood above 98.7% saturation,
with data on 02 solubility in unmodified human blood
from 0 #{176}to 37 #{176}C.
J. App!. Physiol.
35, 861 (1973).
25. Siggaard-Andersen,
0., and Garby, L., The Bohr effect and the
Haldane effect. Scand. ,J. Clin. Lab. Invest. 31, 1 (1973).
26. Bellingham,
28. Van Slyke, D. D., and Neil!, J. M., The determination
of gases
in blood and other solutions by vacuum extraction and manometnc measurement. J. Bio!. Chem. 61, 523 (1924).
29. Van Slyke, D. D., and Plazen, J., Micromanometric
Ana!ysis.
Williams and Wilkins Co., Baltimore, Md. , 1961.
30. Gordy, E., and Drabkin, D. C., Spectrophotometric
studies.
XVI. Determination
of the oxygen saturation of blood by a simplifled technique applicable to standard equipment. J. Biol. Chem.
227, 285 (1957).
CHEMISTRY.
37. Graige, F. A., Lange, K., Oberman, J., and Carson, S., A simpie, accurate method of blood pH determinations
for clinical use.
Arch. Biochem. Biophys. 37, 357 (1952).
38. Austin, W. H., Lacombe,
E. H., and Rand, P. W., pH temperature conversion factors and pCO2 factors for hypothermia.
J. Appl.
Physiol. 19, 893 (1964).
.
39. Greenburg, A. G., and Moulder, P. V., Temperature
coefficients for Pco5 and pH in whole blood. Arch. Surg. 91, 867 (1965).
40. Adamsons, K., et a!., Influence of temperature
on blood pH of
the human adult and newborn.
J. AppI. Physiol. 19, 897 (1964).
41. Bradley, A. F., Stupfel, M., and Severinghaus, J. W., Effect of
temperature
on P#{248}2
and P02 of blood in vitro. J. Appi. Physiol. 9,
201 (1956).
42. Nunn, J. F., et al., Temperature
coefficients for Pco2 and Po
of blood in vitro. J. App!. Physiol. 20, 23 (1965).
43. Kelman,
G. R., and Nunn, J. F., Nomograms
for correction of
blood P02, P#{248}2,
pH and base excess for time and temperature.
J.
App!. Physiol. 21, 1484 (1966).
44. Severinghaus, J. W., Stupfel, M., and Bradley, A. F., Accuracy
of blood pH and Pco2 determination.
J. App!. Physio!.
9, 189
(1956).
Vol. 20, No. 12, 1974