Blood gas calculator’
JOHN W. SEVERINGHAUS
Department of Anesthesia and Cardiovascular Research Institute,
University of California Medical School, San Francisco, California
oxygen
dissociation
curve,
effects
of temperature,
pH,
COz ; hemoglobin
oxygen
affinity,
effects of temperature,
and CO2 ; blood
gases, corrections
for temperature,
pH,
PCO~ ; Bohr effect;
respiratory
calculator;
blood gas slide
SOURCES
and
pH
and
rule
(dry)*
Public
Health
SCALES
The range of normal
variation
in the position
and shape of
the oxygen
dissociation
curve for whole
blood of adult man is
not established,
since both methodologic
errors
and the influence of carbon
monoxide
may introduce
variations
comparable
to the scatter of various
authors’
data. For the present,
the best
approach
appears
to be that of collecting
data from
many
sources and constructing
an average
curve.
Figure
2 presents
such a compilation
with the resulting
new average
curve (heavy
line), and the most commonly
used standard
curve
(fine line),
calculated
by Dill and Forbes (I 6) from data provided
by Bock,
Field,
and Adair
(8). Since
the latter
curve
was primarily
determined
by the blood of one man, A. V. Bock, it is not too
surprising
that some deviation
from
the new average
normal
was seen at both ends. In particular,
Bock was a heavy smoker
and it is conceivable
that CO in samples
equilibrated
at low
oxygen
tensions
produced
a shift to the left.
The most important
source of the new curve
was a report
by Bartels
et al. (5) who published
in I 961 data from 20 to
go%
saturation
in IO normal
adults.
The
two ends of the
curve
were supplied
by the following
data.
r) Roughton
and
Kernahan
(personal
communication),
using
a special
Van
Slyke
manometric
apparatus
recently
obtained
a very
low
point in order
to obtain
a value for the reaction
constant,
Kr.
= 0.57~. 2) I prepared
At Paz = 0.9 mm Hg, Hb02
six samples with
2.3 y0 saturation
by anaerobically
mixing
known
volumes
of fully
saturated
and fully
desaturated
blood.
The
Paz, read polarographically,
was 3.8 & 0.4 mm Hg (SD). 3)
Astrup
et al. (4), investigating
a possible
shift of the dissociation curve in Buerger’s
disease (3), equilibrated
blood from 53
normal
nonsmokers
with
a POT of 6.8 mm Hg, and found
a
mean HbOz
= 4.2 %. 4) Darling
et al. (14) established
a dissociation
curve
from
I o-go%
for six normal
women.
From
HE CALCULATIONS
used in connection
with blood
gas and
expired
air analysis,
while
mathematically
simple,
involve
mu1 tiple
constants,
factors,
and equations.
For example,
if
oxygen
saturation
is to be calculated
from Pea , before insertion
into the standard
dissociation
curve,
the measured
Po2 may
require
corrections
for pH,
base excess,
and temperature.
Similarly,
the constants
pK’ and S (solubility)
to be used in the
Henderson-Hasselbalch
equation
must
be selected
for the
particular
temperature
and pH from tables giving
these values
for blood
and other
fluids
(35). The correction
of pH, PO:! ,
and Pcoz from
the temperature
of the measuring
instrument
to body
temperature
involves
linear
or logarithmic
factors,
which
for pH at least may vary
with pH range.
Expired
gas
volume
must be corrected
to body
temperature
(saturated)
and to inspired
volume
when
oxygen
consumption
is to be
calculated.
Oxygen
consumption
must be corrected
to 760 mm
Received
for publication
29 April 1965.
l This study was supported
in part by
Grant 5-K6-HE-rg,~
2.
THE
I. Standard Oxygen Dissociation Curve (Scales A, B)
T
Hg
OF
Service
1108
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Most of these calculations
have already
been simplified
by
the construction
of nomographic
solutions
such as the following: I) Siggaard-Andersen’s
(38) revision
of the Singer
Hasting nomogram,
used for pH, PcoI , HCO;r,
and base excess
(BE).
2) Line
charts for the oxygen
dissociation
curve and its
adjustments
for temperature
and pH
(34).
3) Line
charts
permitting
temperature
correction
of blood
Paz and PCO~
(I 0). 4) Consolazio’s
(I 2) nomogram
for “true
oxygen”
and
R from expired
air.
Many
of these functions
have been combined
in a slide rule
which
is herein
described.
In several
instances
revisions
in the
previous
factors,
suggested
by various
workers,
have been incorporated.
The blood
gas calculator
is illustrated
in Fig. I.
The scales and their formulas
are given in Table
I.
SEVERINGHAUS,
JOHN
W. Blood gas calculator. J. Appl.
Phys1966.-A
slide rule is described
whose
iol. 21(3):
I 108-1 I 16.
scales yield direct solutions
of the following
blood gas problems:
r) the whole blood oxygen
dissociation
curve of man with variable temperature,
pH, and base excess; 2) the effect of anaerobic temperature
change
on blood
Pea , Pcoz , and pH; 3) the
true oxygen
consumption
fraction
from mixed
expired
02 and
CO2 concentrations,
breathing
air; 4) correction
of gas volume
from
ATPS
to BTPS
or STPD;
5) Henderson-Hasselbalch
equation,
relating
pH, Pcoa , and either
HC03
or CO2 content of plasma
(range
10-40
C) or cerebrospinal
fluid
(20-40
C); 6) base excess and standard
pH and bicarbonate
(at Pcoz
= 40 mm Hg) from pH and PCO~ at 37 C. The following
modifications
of standard
blood gas relationships
are described.
The
new oxygen
dissociation
curve
deviates
maximally
from Dill’s
curve by -4.5
and + I .5 % at I 4 and 60 mm Hg PO:! , respectively.
Temperature
shifts the dissociation
curve
by A log PO:!
0.024 AT C (formerly
about 0.019).
The “Bohr
shift”
with
l;ctic
acid is about
20%
less than with
CO2 , the combined
effect being given by A log POT = -0.48
A pH + .oo13 A base.
The correction
factors for anaerobic
temperature
change diminish for PO:! at high saturation
and for pH in acidosis.
CALCULATOR
GAS
BLOOD
Downloaded from http://jap.physiology.org/ by 10.220.33.1 on June 16, 2017
J.
1110
W.
SEVERINGHAUS
TABLE I. Scales, formidas, and range of values for blood gas calculator
Scale
I.
A.
B.
C.
13.
E.
II.
F.
G.
H.
J.
k’.
III.
Oxygen
dissociation
Peg
02 saturation
pH
Temperature
Base excess
IV.
Logarithmic
Standard
A log PO?,
A log Paz
A log POT
Anaerobic
temperature
Temperature
for Pco2
Temperature
for POP
Pco2, Po2
pH
Temperature
for pH
Expired
L. co2cJo
n4. 02%
N. \~o&E
air,
true
oxygen
Expired
air, gas volume
P. Barometric
pressure
‘I’. Temperature
change,
dissociation
curve
= -0.48
A pH
= 0.024 A T
= 0.0013
BE
8-150 mm Hg
r-99%
6.6-8.0
o-45 c
-25 to +25 mEq/liter
Henderson-Hasselbalch
PI-I (vs. Cco2)
Pcoz, HCO,,
cc02
pH (vs. HCO:)
Temperature
(CSF)
pH (CSF)
Temperature
(blood)
PI-I (blood)
8.
9.
IfI.
II.
13.
13.
Base excess calculator
Hb
Pco2
(37 Ci
PH (37 c>
Base excess
Hb
Standard
HCOT
A T
=
0.265
-
0.265
FECO~ -
I
.265 Ftioz
Same
Same
ATPS
c
c
mm
8-150
Hg
6.65-7.8
o-45 c
~O&E
~O&E
from
‘5-45
‘5-45
0-107~
I I-2
I ojo
0.0-O.
to BTPS or STPD
A log V = A log P
A log I’ = A log T + log
(76 0 - P2Hz0)
Logarithmic
I
700-780
(‘760 -
P1H20)/
10-46
mm
Hg
C
Unlimited
equation
PH = 6.1
Logarithmic
pH = pK’
pK’ - log
pK’ - log
pK’ - log
pK’ - log
log [IO(PH~-~.~)
+
+
S
S
S
s
log HCOF
= f(T)
= f(pH)
= f(T)
= f(pI-I)
Empiric
Skewed
fan log grid
Linear
Empiric
Empiric
log HCO;
= pH -pK’
20
to 407~ it coincides
with
Bartels’
curve,
and at higher
saturation
lies slightly
to the left. 5) Lambertsen
et al. (24),
determining
HbOz
spectrophotometrically
and PO, by bubble
equilibration
in the Roughton-Scholander
syringe,
provided
16 points
above
go%
in normal
men.
6’) Naeraa,
StrangePetersen,
and Boye (28) recently
obtained
a large number
of
points
between
go and g8 y0 HbOn
on two subjects
using
microtonometry
and a very carefully
controlled
microspectrophotometric
technique.
POT was corrected
to pH = 7.4 using
seven samples
of known
equation
2 (below).
7) I prepared
saturation
by the above
mentioned
volumetric
mixing
technique,
correcting
for the exchange
between
dissolved
and
hemoglobin-bound
oxygen
by determining
Pas polarographically
before
and after mixing.
8) Nahas,
Morgan,
and Wood
(29) used an in vivo equilibration
technique
above
IOO mm
Hg Paz. Blood from subjects
breathing
varying
concentrations
of oxygen
flowed
through
a cuvette
oximeter.
Arterial
Paz was
determined
with the dropping
mercury
polarograph
which,
in
spite of its limitations,
did not limit the accuracy
of this method
due to the flatness
of the upper
part of the dissociation
curve.
g) Lundgren
(25), using standard
tonometry
and Van Slyke
saturation
methods,
obtained
50 points
above
IOO
mm Hg
PO,. IO) Two additional
reports
(I 3, 18) contain
confirming
data in the low range,
and no conflicting
data were found.
11) Bartels
and Harms
(6) published
additional
data at high
saturations.
-
I]
log S-
+0.088
log Pco2
6.6-7 .g
8-150
mm
6.65-T .g
20-40 C
7.0-7.6
IO-40 c
7.0-7.8
5-25
g/r00
5-150
mm
Hg,
or mEq/liter
ml
Hg
6.8-7.8
-25 to +20 mEq/liter
5-25 g/I 00 ml
6-60 mEq/liter
In order to construct
a curve from these authors’
points, the
data was plotted
on the coordinates
suggested
by Hill (22), log
PO* and log (saturation/Ioo-saturation).
This does not produce a single straight
line, but minimizes
the curvature
and
simplifies
the process of curve fitting.
In addition,
the slope of
various
parts
of the resulting
curve
reflects
the statistical
number
of simultaneous
reactions
proceeding
at that level of
saturation.
Over
the major
part of the curve,
the accepted
slope is 2.6, and increases
to about 3.0 at go% saturation
(32).
An initial
slope of I agrees acceptably
with the data at the
low end, but a final
slope of 2 is suggested
by Nahas’
and
Lundgren’s
data. This might
imply
that in the final reaction
two oxygen
molecules
combine
with Hb3(02)2
simultaneously.
Roughton
(personal
communication)
has recently
obtained
an
excellent
agreement,
using the Rand
computer,
for his values
for Kr, this new curve
(Fig. 2 and Table
2), and this assumption of a final double
oxygen
reaction.
The dissociation
curve for full-term
human
newborn
babies
at 37 C, pH = 7.4, is closely approximated
by the adult curve
at 37 c, PH = 7.6 (7).
COHb
lowers
the PO:! at any
oxygen
saturation
value,
particularly
at the lower end, such that the shape of the curve
is altered.
Normal
biological
variations
in the dissociation
curve
are believed
to be considerable
at half saturation
(5),
but minimal
at high saturation
(24), while
the contribution
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I.
2.
3.
4.
5.
6.
7.
VI.
Range
blood
Variable;
at 37 C, A log Pcoz = 0.019
A log Po2 = 0.031 A T
Logarithmic
A pH/AT
= 0.0065. (7.4’PH&-0.0146
Linear
fraction,
V. Volume
V.
Formula
curve
BLOOD
GAS
CALCULATOR
1111
rlO0
u2
DISSOCIATION
MAN,
CURVE
37; pH = 7.4
-
DILL
-
BARTELS
+
A
ROUGHTON
X
SEVERINGHAUS
ASTRUP,
BARTELS
l
LAMBERTSEN
NAERAA
v
NAHAS
II. EJects
Dissociation
to these
variations
(due
to smoking)
has not
PCO~ @on
80
100
2.
man
IlbOz,
the
These
variables
(and
others)
appear
to alter
the OsHb
affinity
uniformly
over most of the o-100
y0 saturation
range
so little change
in the shape of the curve
occurs,
except
perhaps at very
high and low saturation
(32).
For most of the
of T, pH, and Pco,,
a
curve
(5-95 %), at any combination
single factor
relates Pot values on the standard
and the nonstandard
curves.
In the case of temperature,
at constant
saturation
the expected relation
is given by the van?
Hoff isochore:
A log PO:!
where
Q is the heat of combination
of
= Q A T/2.3
RTrTz,
I mole
of O2 with Hb, R is the gas constant,
and Ti and T:!
are the two absolute
temperatures
differing
by A T. At constant Q, as temperature
falls, the factor Q/2.3
RTrTz
increases
about 0.3 %/“C.
However,
Q varies with pH, Pcoz, and buffer
base (33).
Experimentally,
A log PoJAT
is approximately
constant
between
15 and 38 C. It has not been
adequately
studied
at lower
temperatures.
Its value,
calculated
from Dill
and Forbes’
curves (I 6), ranges from 0.017
to 0.020,
depending
on the pH and temperature
range.
The line charts we prepared
(7, IO, 19, 34) both for the oxygen
dissociation
curves
and for the eflect of temperature
upon PO;? were based on these
values.
However,
recent
evidence
suggests that they are too
low. Astrup
et al. (4) determined
dissociation
curves
at 13,
23, 30, and 38 C, with pH ranging
from 7.1 to 7.7. At constant
pH and saturation,
PO:! at 13, 23, and 30 C, respectively,
was
0.251,
0.453,
and 0.63 I of the PO:! at 38 C, yielding
the relationship
A log Pox/A T = 0.024. Albers (2) obtained a value
3
Values for standard oxygen
(pH = 7.40, T = 37 C>
TABLE
in
of Temperature,
pH, and
Curue (Scales C, D, E >
85
ADULTS
80
been
DATA
I
2
4
6
IO
‘5
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
%
PO:!
I.9
3.4
5.7
7-5
10.3
13.1
‘5-4
‘7-3
19.2
21 .o
22.8
24.6
26.6
28.7
31.2
34-o
36.9
40.4
44.5
49.8
57-8
dissociation
IIbOz,
9’
92
93
94
95
95.5
96
96.5
97
97.5
98
98.5
99
99.5
99.8
99.9
99.95
curve
T!
PO2
60.0
62.7
65.7
69.4
74.2
77.3
81 .o
86.0
91.6
99-G
III
129
‘59
225
350
500
700
of 0.023 I in dogs, and Brown
and Hill
(I I) found
the value
0.0229.
Munson
and I measured
the Poq and pH of eight samples at 25 C, about
84y0 saturation,
and six samples
at 30 C,
about
67 y0 saturation.
The
shift of POT from
the standard
dissociation
curve
corrected
to observed
pH
(equation
2)
yielded
the values for A log Paz/A T of 0.0251
rt 0.0010
at
25 C and 0.0254
=t 0.0012
(SD) at 30 C, giving
a mean of 0.0252.
I determined
both Paz and pH at both 37 and 25 C on five
additional
samples with saturations
of 20-70 $?& After correcting
Downloaded from http://jap.physiology.org/ by 10.220.33.1 on June 16, 2017
DARLING
a
A
NEW
53
0
P02
of COHb
evaluated.
FIG.
2. Left
hand curves are
the new (heavy
line) and Dill
oxygen
dissociation
curves,
referred to the left ordinate.
On the
right,
the upper
25% of these
curves
is expanded,
referring
to
the right ordinate.
J. W.
SEVEKINGHAUS
02 Hb
0
/0
A log PO:! = 0.024
first
The
The effect
described
relationship
AT
(I >
of pH on the oxygen-hemoglobin
by Bohr,
Hasselbalch,
and Krogh
in common
use is
Alog
Paz
= -0.48
affinity
in r go4
A pH
was
(9).
( 2>
AlogPoz
= -0.48
A pH
+ 0.0013
BE
(3)
The changes
due to base are very small and their quantitation
requires
extreme
accuracy
of measurement
of saturation,
pH,
and gas PO, (Fig. 3).
An unresolved
discrepancy
in the magnitude
of the Bohr
shift with fixed
acid is evident
in the results
of Astrup
(4),
that value
being A log Paz/A
pH
= -0.50.
Some possible
reasons for the difference
from Naeraa’s
data may be: a) use
of multiple
subjects;
b) use of a less accurate
spectrophotometer
for some of the determinations;
c) use of HCl as the strong acid,
whereas
Naeraa
et al. used lactic acid; d) no comparison
was
made with the Bohr effect produced
by COZ.
Since the red cell to plasma
distribution
ratios for Cl- and
HC03
are similarly
altered
by CO2 and by fixed acid (17),
little, if any, of the variation
of Bohr shift can be attributed
to
altered
red cell to plasma
distribution
of Hf.
Above
85y0
saturation,
the Bohr shift decreases
and the very small changes
due to buffer
base alteration
can not be quantitated
from the
data available.
//
I
I
50
I
I
I
PO 2
1
100
1
1
FIG. 3. Oxygen
dissociation
curves for human
whole blood at
37 C showing
the difference
in the Bohr effect due to CO2 and due
to lactic acid at a plasma pH of 7.0.
III.
Effect
of A naerobic
Blood
Temperature
Change
(Scales F-K)
When
blood is cooled without
exposure
to air, pH
PCO~ and Paz fall.
PH. Rosenthal
(3 I ) reported
for whole blood the
used relationship:
A pH = -0.0147
A T. However,
et al. (I) have shown that the temperature
coefficient
as pH falls and as base rises. They found : A pH/A
T
- o-005 (7.4 - pH38 o) + 0.00005
(20 - CO,).
be transformed
approximately
to the more convenient
A pH/A
T = 0.0146
- 0.0065(7.4
-
pHs8 c) -
0.00003
rises,
and
commonly
Adamsons
decreases
= 0.0146
This may
form:
(BE)
(4)
The final
term may be ignored,
since the pH error
so introduced
is 0.006
when
correcting
over
a IO C temperature
difference
with base excess = -20.
The variation
with pH is
introduced
by an arithmetically
expanding
pH scale (J).
PO:!. As temperature
changes,
oxygen
saturation
is constant
except
at high
saturation
where
slight
exchanges
with
dissolved
oxygen
become
important.
Pea changes
both because
the dissociation
curve
changes
with
temperature
(equation
I),
and because
pH changes
with temperature
(equation
4), and
pH affects the dissociation
curve
(equation
2). Elimination
of
pH from equations 2 and 4 gives the added
effect of temperature upon Paz due to pH variation:
A log Paz = 0.007 A T
(A BE in equation 2 is o for change
of temperature).
The total
anaerobic
effect of temperature,
obtained
by adding
this to
equation I, is:
Alog
PO:! = 0.031
A T
(5)
The second-order
corrections,
due to the terms
of equation 4
for pH and base, are ignored.
Over
the range of PC02 from 10
to IOO mm Hg, for example,
it may be calculated
that A log
Po,/A
T varies from 0.030 to 0.032.
Equation
5 does not hold at high saturations,
due to change
of saturation
with
temperature,
as shown
experimentally
by
Hedley-Whyte
and Laver
(20) and by Nunn
et al. (30). The
former
group,
working
at PO? values
exceeding
250 mm Hg,
showed
that A PoJA
T may be predicted
from
the known
temperature
coefficient
of oxygen
solubility
in water,
about
I .2 %/“C.
Nunn,
at 83% saturation,
obtained
values for A log
Downloaded from http://jap.physiology.org/ by 10.220.33.1 on June 16, 2017
In the original
source (15) the value was misprinted
as -0.079,
the correction
appearing
in a later issue. Subsequent
confirming
values have ranged
from
-0.44
to -0.50
(2 I, 23). The value
may fall off at high saturation
according
to Roughton
(32).
These
values
of the relationship
of log POT to pH were
determined
with
CO2 as the acid. A portion
of the changed
oxygen
affinity
is due to molecular
CO2 rather
than the hydroby Margaria
and Green
in I 933 (26).
gen ion, as shown
Unpublished
data of Marchi
and Rossi, quoted
by Roughton
(33), showed
the Pas for half saturation
to be 29% lower
at
Pcoz
= o than at Pcoz
= 30, both at pH
= 7.4. Naeraa,
Strange-Petersen,
and Boye (28) recently
provided
extensive
quantitative
data from which
the partial
contributions
of COz
and Hf
may bc calculated.
They
and I subsequently
have
collaborated
to repeat
their measurements
at a Paz of about
30 mm Hg, the published
data having
been obtained
at 50
and 80 mm Hg. The method
of calculation
was as follows:
The Pea expected
with the observed
saturation
and pH was
computed
from
the standard
dissociation
curve
(Fig.
2) corrected
for pH (equation
2). The difference
between
the logarithms
of this Pea and of the actual tonometer
PO:! was plotted
against
the observed
PH. When
PCO~ was altered
at constant
base, the relationship
was identical
to the accepted
value
(equation 2) (See APPENDIX).
When
pH was increased
by adding
NaHC03,
or reduced
by adding
lactic acid, at constant
Pcoz, a smaller
effect was
observed,
approximating
A log PoJA
pH
= -0.40.
The
total effect of COT and Hf over the dissociation
curve
below
85% saturation
is approximated
by:
A log po2= .0013 BE. -0.40A pH
t
BLOOD
GAS
50
CALCULATOR
80
90
I I
95
97
98
99
99.5
-7
-6
-5
100 n PO,
AT
-4
P/\T
-3
-
AP
= .012S+4.63
PAT
s+66.1
-2
-1
Pol
0
50
100
m m Hg
(37
150
C pH =7,4)
200
PO,/ A T of 0.032,
approximating
the calculated
value.
At
higher
saturation,
the ratio fell.
A log PoJA
T may be calculated
at any saturation
from
the slope of the oxygen
dissociation
curve
and the water
solubility
temperature
coefficient.
The result is shown
in Fig.
4. S is the reciprocal
of the slope of the dissociation
curve;
i.e.,
A PoJA
HbO&.
It may be seen that the slide rule scales G
and Ii will overcorrect
the effect of temperature
on POT at high
saturation.
Above
go%
saturation,
one should
use Fig. 4,
rather
than the slide rule, to correct
Poft to a different
temperature.
The method
is described
in the legend of Fig. 4. This
error
at high saturation
does not apply
to the temperature
scale D of the oxygen
dissociation
curve,
or to equation I, but
only applies
during
anaerobic
temperature
change
of blood,
where
small
amounts
of dissolved
oxygen
exchange
with
hemoglobin
oxygen.
PCo2 (scales F, H). The effect on Pcoz of anaerobic
change
of temperature
in blood may be calculated
from the HendersonHasselbalch
equation,
using values of pK’
and S appropriate
for the two temperatures
(35). By subtracting
the equation
at
one temperature
from that at the other:
APH
=ApK’+AlogHCO;-AlogS-AlogPcon
(6)
Plasma
HCO3is independent
of temperature
(36).
This
calculated
temperature
effect is slightly
larger
than our previously published
corrections
(7, I o, 19) due to improved
values
confirmed
this
for pK’ and S (35). N unn et al. (30) recently
correction
experimentally.
Temperature
scale F is nonlinear
to
incorporate
the variations
in the Pcoz-temperature
relationship
A second-order
variation
of the
with
temperature
range.
Pcoz-temperature
relationship
with
pH range
is ignored
in
the slide rule. The resulting
error
approximates
a I 2 To over-
250
300
correction
of the effect of temperature
upon Pcoz if pH is 7.0.
For example,
correcting
a Pcoz of 40 mm Hg measured
at 37
C, to body temperature
of 32 C yields a PCO~ of 32 mm Hg
from the slide rule. At pH = 7.0, this 8 mm Hg correction
is
I 2 y0 too large;
the correct
PCO~ at 32 C is 33 mm Hg.
IV.
Expired
Air
True
Oxygen
Fraction,
I&/VIZ
(Scales
L,
M,
N)
CO2 excretion
is accurately
expressed
as the product
of the
volume
of air expired
per minute
and the mixed
expired
gas
CO2 concentration.
A similar
procedure,
correcting
for inspired
oxygen
concentration,
cannot
be used to compute
oxygen
consumption
since
the inspired
gas volume
from
which
the oxygen
was extracted
differs
from
the expired
gas
volume
when the respiratory
quotient
differs from I .o. Oxygen
consumption
voz in a steady
state breathing
pure air, is:
vo,
where
$9 and
PIZ
minute
and FEO~
mixed
expired
air.
are identical,l_hence
=
0.2093
Jh
~O&E
from
=
-
FEO~
X
VE
are the volumes
inspired
is the fractional
oxygen
The inspired
and expired
:
0.7907(b)
Eliminating
(VI)
=
(I
these
0.265
The equation
is solved
in which
the unit lengths
-
two
-
0.265
FEO~
-
and expired
per
concentration
in
quantities
of Nz
FECO&E
equations:
FECO~
-
1.265 FEO~
(7)
on the slide rule using linear
scales
on the CO2 and 02 scales are 0.265
Downloaded from http://jap.physiology.org/ by 10.220.33.1 on June 16, 2017
FIG.
4. Calculated
ternperature coefficient
of whole
blood
Paz as a function
of saturation.
As blood
approaches
complete
saturation,
a change of temperature results in a shift of oxygen
between
dissolved
and
hemoglobin
- bound
oxygen.
The
amount
of shift is calculated
from
the slope (inverse)
of the dissociation
curve
at that saturation
and from the temperature
coefficient
of oxygen
in the water
phase. This curve should be used
to compute
PO:! temperature
corrections
above
g5y0 saturation.
The
ordinate
value
for
A
log Paz/AT
is multiplied
by the
temperature
difference.
The antilog of this number
will be the
ratio of Po2 values at the two
temperatures.
Example.
If Poe
was 80 mm Hg at 37 C, pH =
7.4, what was Peg in the body at
30 C?
From
Fig. 4, at Po2 = 80,
A log Paz/AT
= .028
7 C X .028 = .rg6
Io.196
=
I.57 = PO&7 c)/
POQ(30 C)
= 51
PO&p C) = 80/1.57
mm Hg
whereas,
from
slide
rule
PO&O C> = 49 mm Hg.
99.75
A log PO2
I3
1114
J.
and i .265 of the true
tively.
oxygen
fraction
scale
V Volume Corrections
for Temperature,
V&or, and Pressure (Scales P, T, V>
unit
length,
respec-
Water
Gas volumes
are usually
measured
at ambient
temperature
and pressure,
saturated,
abbreviated
ATPS.
Ventilation
is
expressed
at body temperature
and pressure,
saturated
(BTPS),
while
oxygen
consumption
and CO;! production
are given
at
standard
temperature
(o C) and pressure
(760 mm Hg),
dry
(STPD).
Conversion
from ATPS
to BTPS involves
the expansion due to warming
and to the increased
water vapor
volume,
but no pressure
change.
Scale T is arranged
to add to the log
volume
scale V a distance
equal to log (T,/Ti)
(76O-PTiHzO)/
(760-P~+~0),
where
‘I’; and l’2 are ambient
and body
temOK. For conversion
to STPD,
scale P adds a distance
peratures,
equal to log (273/‘I’i)
(Pb/76o)
(76o-Piuoo)/76o.
a.
Henderson-Hasselbalch
Equation
(Scales 1-7)
(8)
be arranged:
log [I
o(pTI-pK’)
+
I]
=
log
cc02
-
log
s -
log
PC02
In order
to use the same pK’
and S scales, and the same
the new pH scale values (pHJ
scale for Pco2 and HC03,
related
to the scale 3 values (pH3)
by:
Io(~~IIr~~T~‘)
Whole
VII.
blood
Base-Excess
CO2
content
+
I
cannot
=
10(~~~3-~K
USE
OF
THE
BLOOD
GAS
Ci4LCULATOR
(9)
log
are
>
be used on these
scales.
Calculator
bicarbonate,
hemoScales 8-13 relate
base excess, standard
globin,
pH, and Pcoz at 37 C. In its construction,
the extensive
equilibration
and titration
data
of Siggaard-Andersen
(38)
was used and he suggested
the possibility
of improving
the
graphic
representation
of his data by delinearizing
the pH-log
Pcoz relationship.
To accomplish
this,
the fan-shaped
log
Pcoz grid is skewed
in such a way that the lines do not intersect at a common
point above
the grid, but along the Pcoz =
40 line. The pH-log
PCO~ relationship,
which
is read along
slanting
lines selected
for the appropriate
hemoglobin
concentration,
is thus linear
only near the normal
range,
where
A
pH/A
log Pco2 = 0.64. The purpose
of slanting
the isohemoglobin lines is to introduce
the effect of base excess on the buffer
slope, A pH/A
log Pco~. As the slide is moved,
the hemoglobin
Oxygen dissociation curve. Set the cursor arrow to the tempera(n> to which
pH and
Pop refer,
usually
the temperature
of
measurement.
Adjust
the slide
to bring
pH (C) opposite
the base
excess on cursor
scale (E). This aligns
each value
of saturation
(B)
with its appropriate
PO:! (A). The cursor
index
may be used to read
related
values
on the two scales.
The
pH
and
PO? values
must
refer
to the same
temperature.
If they
are known
at different
temperatures,
one must
be corrected
to the temperature
of the
other,
using
the anerobic
temperature
change
scales
F-K,
(see II,
below).
If POT was measured,
saturation
should
be computed
at
measurement
temperature,
regardless
of body
temperature.
If
saturation
was measured,
pH should
be corrected
to body
temperature
(see scales J, K) to permit
Pea to be read directly
at body
temperature.
To read
Pas beyond
either
end of the A scale at
extreme
conditions,
the slide
may be moved
I decade
along
the A
scale, which
is logarithmic,
and
the
PO:! readings
accordingly
multiplied
or divided
by IO.
For
full-term
newborn
babies,
the slide
rule
may
be used to
obtain
an approximate
dissociation
curve
by adding
0.2 unit
to
the measured
pH
(7). This
correction
varies
with
maturity
and
has not been established
below
I 5 or above
80 nun
Hg Pop.
II. Anaerobic temperatwe change, blood. These scales are used when
pH,
Paz, or Pco~,
known
at one blood
temperature,
is to be calculated
at a different
temperature
in the same blood.
The calculations
apply
either
in vivo
or in vitro,
provided
the temperature
change
takes
place
without
gas exchange
between
the blood
and
its environment.
The
procedure
is the same
for the three
scales.
Set the cursor
index
at the temperature
at which
the value
is
known,
on the appropriate
scale
(F, G, K) for Pco~, PO?, or pH.
Align
the known
value
of PCOB or Poft on scale H, or of pH on scale J
with
the index.
Move
the cursor
index
to the desired
temperature
and
read
the
corrected
blood
value
on the H or J scale. To
correct
POB for temperature
above
goO10 saturation,
see Fig. 4.
III. Expired air; true oxygen fraction.
These
scales
(L, M, N) are
used
when
mixed
expired
air, from
a subject
breathing
air, has
been
analyzed
for CO2 and 0~ concentration
in order
to compute
oxygen
consumption
and the respiratory
exchange
ratio,
R. Using
the cursor
index, align
the value
of CO,%
on scale L with
that of
02%
on scale 1M. The
figure
appearing
above
the arrow
labeled
“read”
is the
fraction
~o@E,
the
oxygen
consumption
per
minute
divided
by the ventilation
expired
per minute.
To obtain
oxygen
consumption,
multiply
this by VE and correct the resulting
volume
to STPD
(see IV below).
To obtain
R, divide
percent
CO2
ture
by
I oo
IV.
volumes
vOz/TjE.
Expired
from
temperature
the cursor
ture
body
air; gas volume. These
the
conditions
of
scales
are
measurement
used to correct
(ATPS)
to
gas
body
(BTPS)
or to oC, 760 mn
Hg, dry (STPD).
Using
index, align measured
volume
on scale v with
temperaof the gas when
measured,
scale 27 Move
the cursor
index
to
temperature
for BTPS volume
or to barometric
pressure at
Downloaded from http://jap.physiology.org/ by 10.220.33.1 on June 16, 2017
may
pK’ + log (s&-I)
=
A.
I.
arranged
as in equation 6 is a sum of five
The equation,
logarithmic
terms.
In order
to reduce
the slide rule solution
which
involves
four knowns,
to a single setting,
the cursor
is
used to introduce
pK’
and S (27, 35, 37) on the pH scale
(scales g-7),
identifying
the pH at which
log HC03
= log
Pcos. l‘hc
diffcrcnce
between
pH and this point
on scale 3
then equals
the difference
between
log HCOsand log PCO~
(on scale 2).
A separate
pH scale, I, is used when
pH and CO2 content
(CCO~) are the known
factors,
or when Cc02 is to be calculated
from pH and Pcoz. The equation:
pH
SEVERINGHAUS
lines cut the grid at differing
levels, corresponding
to the buffer
slope appropriate
to that hemoglobin
and buffer
base. Values
from this sliding
nomogram,
although
a closer approximation,
still differ
slightly
from
the actual
titration
data, particularly
at low hemoglobin
concentrations.
They
also differ
slightly
from values
read from
Siggaard-Andersen’s
(38) 38 C nomogram due to the I C temperature
difference
and slight difference in pK’.
The PCO~ = 40 mm Hg line was made vertical
in the grid,
permitting
its position
to indicate
both standard
bicarbonate
and standard
or “eucapneic”
pH, these being the values which
would
be observed
in the blood if its PCO~ were adjusted
to 40
mm Hg at 37 C without
change
of oxygen
saturation.
In
desaturated
blood,
these standard
values
differ
from
those
obtained
by the Astrup
equilibration
technique,
in which
the
sample
is oxygenated
before
its pH is measured
at known
Pcoz.
APPENDIX
VI.
W.
BLOOD
GAS
CALCULATOR
+.04
+.03
BASE
+.02
+.Ol
.
S6
a$0
n!? e
#
0
-.Ol
-.02
-.04
.05
FIG.
5. See APPENDIX
J
the time of volume
measurement
(not
to 760) for STPD
volume.
Since the volume
scale is logarithmic,
the decimal
place
is ignored
as in an ordinary
slide rule;
i.e., 25 is used for 2.5 or 250.
V. Henderson-Hmselbalch
equation.
Scales 1-7 are used to calculate
the relationship
between
PIT, Pco~, and plasma
or CSF HCOT,
or
between
pH,
PCOZ, and total
plasma
or CSF
CO2
(CCO~).
The
cursor
pH scale 7 (or scale 5 for CSF)
is adjusted
so the nearest
pH line crosses
the temperature
scale 6 (or scale 4 for CSF)
at the
temperature
at which
pH and/or
PCO~ arc known.
To relate
pH
Pco~,
and HCOT,
use scales 2 or 3. When
pH scale 3 is aligned
with
Pco~,
HCOT
is indicated
by the cursor
index
on scale 2. To
relate
pH,
Pcoz,
Cc02
(total
plasma
or CSF
CO2
content
in
miIlicquivalents/liter),
use scales I or 2. When
pH
on scale I is
aligned
with
Pcoz on scale 3, Cc02
is indicated
by the cursor
index
on scale 3. The
CSF scale probably
applies
to extracellular
fluid.
The term
I ICO,
is actually
total
CO2
minus
dissolved
CO2
and
includes
small
amounts
of carbamino-bound
CO?.
Do not
use
whole
blood
CO2 or HCOC
on thcsc scales.
IV. Base excess calculator.
Using
scales B-13,
buffer
base
excess
and standard
bicarbonate
ion concentrations
may
be computed
if pH and PCO~ at 37 C and hemoglobin
concentration
are known.
Set cursor
index
at pH on scale IO. Locate
the intersection
of the
index
with
the
appropriate
diagonal
hemoglobin
line
scale
8.
Slide
the grid
of PCO~ lines
to bring
the PCO~ to this intersection
point.
At PCO~ = 40, standard
bicarbonate
is indicated
above
the
window
on scale 13, and standard
pH below
the window
on scale
IO. In the small
window
at the lower
right,
read
base excess from
the grid I I underlying
the intersection
of the hemoglobin
line,
12,
with the fixed
index
line.
At this base excess
value,
the diagonal
hemoglobin
line intersects
all other
PCO~ lines
at the pH expected
in this blood
equilibrated
to that Pco~.
B.
APPENDIX
B
Recalculation
of the data
published
by Naeraa
et al. (28)
to
quantitate
the separate
p1-I and molecular
effects
of CO2 on the
dissociation
curve
was done
as follows.
For each
measured
oxygen
saturation,
a value
of PO:! was read from
the standard
oxygen
dissociation
curve
(Fig.
2). This
Paz was corrected
from
pH 7.4 to
the observed
pH by use of equation
2. The
resulting
value
of PO? is
termed
PSTD. The
ratio
of the actual
PO:! used
in equilibrating
the sample
(P,qui1)
to PSTD was plotted
against
observed
pH (Fig.
5). If equation
2 expressed
correctly
the Bohr
effect
of all samples,
whcthcr
pH
was varied
with
CO?
or fixed
acid,
then
WC should
= KOPSTD
where
K is a constant
near
1.0 expressing
find
Pcquil
the
difference
between
the dissociation
curves
of Fig.
2 and
of
Naeraa,
who
acted
as the subject.
Figure
5 suggests
that
when
CO2
was varied
with
changing
base
excess
(horizontal
dashed
lines),
the factor
-0.48
in equation
2 is appropriate.
However
when
base
excess
was
varied
at constant
PCOZ
(slanting
solid
lines),
equation
2 overcorrected
by almost
25G]0.
Above
80%
saturation
the Bohr
effect
begins
(see dashed
isopleths
for 80, 85, and go%)
to fade
-0.40
away.
A pH
The pure
and the
logarithmically
proportional
be best expressed
as the
correction
factor
(equation
base produced
by fixed
struct
Fig. 5 were
obtained
was subsequently
repeated
lationship
was
effect
pure
of ~1-1 at constant
Pcog
effect
of CO2
is neither
is A log
linearly
PO:! =
nor
to
Pco 2. Empirically
the effects
may
sum of the usual
(CO2
dcpcndent)
Bohr
2) and a factor
for the change
in buffer
acid
(equation
3). The
data
used
to conat PO:! = 52 mm Hg. The experiment
at Pop = 32 mm Hg and the same rc-
obtained.
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I. ADAMSONS,
Influence
newborn.
K. JR., S. S. DANIEL,
G. GANDY,
AND L. S. JAMES.
of temperature
on blood
pH of the human
adult
and
J. &pZ.
P/zysioZ.
I g : 897-900,
1964.
2. ALBERS,
C. Die
vcntilatorische
Gleichgewichts
in Hypothermia.
3. ASTRUP,
P. An abnormality
in
Kontrollc
des Saure-BasenAnaesthesist
I I : 43-5 I, I 962.
the oxygen-dissociation
curve
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..
-.03
1116
J.
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with non-specific
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Lancet I I 52-1 I 54, 1964.
4. ASTRUP, P., K. ENGEL, E. MUNSON, AND J. W. SEVERINGHAUS.
The influence
of temperature
and pH on the dissociation
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of human
blood. Stand.
J. Clin. Lab.
Inveht.
(in press).
BARTELS, H., K. BETKE, P. HILPERT, G. NEIMEYER, AND K.
RIEGEL.
Die sogenannte
Standard-Oz-Dissoziationskurve
des
gesunden
erwachsenen
Menschen.
Arch.
Ges. Physiol.
272: 372383, 1961.
6. BARTELS, H., AND H. HARMS. Sauerstoffdissoziationskurven
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Arch.
Ges. Physiol.
268:
334-365,
I959.
Blood
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1923.
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‘4.
‘5.
PECORA. Physio-
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York : McGraw,
I 963.
COURTICE, F. C., AND C. C. DOUGLAS. The ferricyanide
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I 05 : 345-360,
I947*
DARLING,
R. C., C. A. SMITH, E. ASMUSSEN,AND F. W. COHEN.
Some properties
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fetal and maternal
blood. J. CZin.
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DILL, D. B., A. GRAYBIEL, A. HURTADO, AND A. TAQUINI.
Der Gasaustausch
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im Alter. 2. Alternsforsch.
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20-33,
effects
possible
effects of the aggregation
of the
of haemoglobin
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London
40: iv, 1910.
23. HILPERT, P.,R. G. FLEISCHMANN,D. KEMPE,AND H. BARTELS.
The Bohr effect related
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pH. Am. J.
Physiol.
205 : 337-340,
I 963.
24. LAMBERTSEN, C. J., P. L. BUNCE, D. L. DRABKIN, AND C. F.
SCHMIDT. Relationship
of oxygen
tension
to hemoglobin
oxygen
saturation
in arterial
blood of normal
men. J. AppZ.
molecules
Physiol.
4: 473-885,
1952.
25.
LUNDGREN, C. E. C. Oxygen
19.
NAHAS, G. G., E. H. MORGAN, AND E. H. WOOD. Oxygen
dissociation
curve
of human
with high concentration
of oxygen.
&and.
J. CZin. Lab. Invest.
I 3 : 291-301,
1961.
con26. MARGARIA, R., AND A. A. GREEN. The first dissociation
stant, pK’, of carbonic
acid in hemoglobin
solutions
and its
relation
to the existence
of a combination
of hemoglobin
with carbon
dioxide.
J. BioZ. Chem.
I 02 : 61 I -634,
1933.
MIXHELL, R. A., D. A. HERBERT, AND C. T. CARMAN. Acidbase constants
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coefficients
for cerebrospinal
fluid. J. AppZ. Physiol.
20 : 27-30, I 965.
28. NAERAA, N., E. STRANGE-PETERSEN, AND E. BOYE. The influence
of simultaneous
independent
changes
of pH and
carbon
dioxide
tension on the in-vitro
oxygen
tension-saturation relationship
of human
blood. Stand.
J. CZin. Lab. Invest.
blood
15:
30.
3’0
32.
33*
‘940*
DILL, D. B., AND W. H. FORBES. Respiratory
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Am. J. Physiol.
I 32 : 685-697,
1941.
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