CUN. CHEM. 21/2, 190-194(1975)
Comparison of Methods for Calculating Serum
Osmolality from Chemical Concentrations, and
the Prognostic Value of Such Calculations
William V. Dorwart and Leslie Chalmers
Sodium,
potassium,
glucose,
blood urea nitrogen,
and
osmolality were determined for 715 hospital-patient
sera. The chemical concentrations were used to calculate osmolalities according to 13 different methods
taken from the literature. The goodness of the comparison between calculated and measured osmolality was
quite similar for several of the better methods. The
agreement was unimproved when molal chemical concentrations were used instead of molar values. The difference between measured and calculated bsmolality
was unrelated to whether a patient was discharged
from the hospital after a short or long period or ultimately died. The equation we found to yield the most accurately calculated osmolalities is
Osmolality
1.86 Na
+ (Glu/18)
+
(BUN/2.8)
For some
ing measured
+ 9
years there has been interest
in comparserum osmolality
with osmolality
calcu-
lated from chemical data on serum. The interest originated partly from a desire to “explain” serum osmolality or to account for the factors producing
it and
partly from the hope that such comparisons
might
provide some information
of clinical use. Thirteen
methods
reported
in the past for calculating
serum
osmolalities
are given in Table 1.
Osmolalities
are commonly
expressed
in terms of
total solute activity,
although
all routine
methods
of
determining
osmolality
actually
measure
some property related to solvent activity.
Solvent and solute activity may be calculated
from each other by using the
Gibbs-Duhen
equation
(14),
although
this calcula-
tion is complex when nonideal solutes are involved.
The contributions
of various solutes to osmolality are
additive
and depend on the molal activity of each solute. Nonionic
solutes such as glucose and urea have
William
Pepper
Laboratory,
Division
of Chemistry,
Hospital
the University
of Pennsylvania,
Philadelphia,
Pa. 19104.
Received
Aug. 23, 1974; accepted
Nov. 5, 1974.
190
CLINICAL
CHEMISTRY,Vol. 21, No.
2, 1975
of
activity
coefficients
close to one; hence their contribution to osmolality
is equal to their concentration.
The coefficients
1/18 and 1/2.8for the glucose
and blood
urea nitrogen
(BUN) terms in the equations
of Table
1 simply
convert
the usual
milligrams
per deciliter
values to millimolar
concentrations.
The contribution
of ionic solutes to osmolality
is more complicated
because the activities
of ions are less than their concentrations
and because
cations
and anions
contribute
separately.
Ionic contributions
are not equal to ionic
activity
because of the complex relationship
between
solute and solvent activity.
Thus, for a univalent
ion
in a typical serum of ionic strength
-‘0.15, the thermodynamic
activity
is approximately
0.6 times its#{149}
concentration,
while its contribution
to osmolality
is
of the order of 0.9 times its concentration.
The de-
pendence of serum osmolality on electrolyte concentration may be considered to be a function of sodium
alone, because total anion and cation concentration
must be equal and the cation component
is mostly
sodium. When a coefficient for sodium in the equations of Table 1 is determined
by linear regression
analysis of experimental
data, it generally is found to
be somewhat less than 2. This is often rounded off to
2-as
in equations
2, 3, 7, 8, 9, 10, 12, and 13-for
easy calculation.
The constants in some of the equations allow for materials such as P043, S042, Ca2+,
Mg2+, creatinine,
uric acid, and all the other substances that are present in the serum in low concentration. Lipid and protein are included in these constants because they are present as high-molecularweight species, in low molar concentration.
The possible range of physiological
variation
of these materials is less (in molar concentration)
than the error of
measuring
more concentrated
materials
such as sodium and urea. The inclusion
in the calculating
equation of a term for any of the minor constituents
(as in
equations
10 and 12) is unlikely
to produce
a noticeable improvement
in the agreement
of calculated
and
measured
osmolality
unless the sodium,
glucose, and
urea concentrations
can be measured
with better pre-
Table 1. Methods Taken from the Literature
Calculating
Serum Osmolality
Method
Reference
1. Osm = 2.1 Na
2. Osm=2Na
1
3.
3
Osm=2Na+7
4. Osm
=
2.63 Na
-
for
65.4
5. Osm=1.86Na+(BUN/2.8)+Glu/18
6. Osm = 1.86 Na + (BUN/2.8) +
(GlU/18)+5
7. Osm=2Na+GIu/18
8. Osm = 2 Na + (Glu/18)+ (BUN/2.8)
9. Osm=2Na+(BUN/3)+(Glu/20)
10. Osm = 1.85 Na + 1.84 K + (GIu/18)
+(BUN/2.8)+
Ca + 1.17Mg+ 1.15
11. Osm = 1.75Na + (Glu/18)
+ (BUN/2.8) + 10.1
12. Osm = 2 (Na + K) + (Glu/18)
+ (BUN/2.8)
13. Osm = 2 Na + (BUN/2.8)
died within two weeks. Assessment
of this
finding is made difficult by the omission
from the report of the method
used to calculate
osmolality.
If no term for urea was included, the calculation may simply have been picking out patients
in
terminal uremia, as a blood urea nitrogen of 140 mg/
dl will elevate measured osmolality by 50 mosmol/kg.
4
If no term
could have
5
6,
patients
dramatic
7
8
9
10
11
4
1f, 13
10
Abbreviations:
Osm, milliosmoles/kg
(in SI units,moles);
BUN, bloodurea nitrogen; glu, glucose.
for glucose was included
been identifying
patients
high glucose concentrations.
Such patients
can be
discovered by measuring BUN or glucose, so that an
osmolality measurement
would add no new prognostic information.
Edelman et al. (4) investigated
this
question
and found that the osmolal discriminate
could not be used to predict the fate of patients.
The matter was reopened by Boyd et al. (20), who
used equation 5 for his calculations.
Osmolality was
measured and calculated for samples taken from 28
patients
in hemorrhagic
shock from severe trauma.
For 16 who survived,
the osmolal discriminate
averaged 19 ± 2 mosmol/kg.
In the 12 patients
who died,
the osmolal discriminate
was 97 ± 20. In an earlier
study Boyd and Mansberger
cision than is obtainable
in a routine
clinical laboratory. The only known
abnormal
serum constituents
that can influence
those calculations
to any extent
are foreign materials
such as ethanol
and methanol.
Ethanol at a concentration
of 4.6 nil/liter (approximately a lethal concentration)
would be expected to
and does elevate measured
osmolality by 100 mosmol/kg. It has, in fact, been shown that osmometry
may be used as a rough measure of concentration
for
ethanol (15-18).
Although osmolality is related to molal rather than
molar concentrations,
the ready availability of molar
values from laboratory
data has led to their use by
most persons seeking to relate calculated
and measured osmolality. In the study of Edelman et al. (4)
that produced
equation
2, hybrid units were used
with sodium in molal concentrations
and glucose and
urea in molar units, with no explanation
of this unusual procedure.
In the present study both kinds of
units were used, to see whether anything
is to be
gained from converting
all concentrations
to molal
units.
Summarizing
thus far: there are several methods of
calculating
osmolality,
and it has not been demonstrated which of these is most effective for serum
from a variety of patients,
nor has it been shown
what concentration
units are the most appropriate
to
use in the calculations.
In 1956 Rubin et al. (19) published a very brief report on a study of 250 patients with various diseases.
In 172 patients,
all of whom recovered,
calculated
and measured osmolality agreed well. For 78 patients
measured
minus calculated
osmolality
[hereafter
measured minus calculated osmolality will be called
the “osmolal discriminate,”
the term used by Boyd et
al. (20)] was 40-125 mosmol/kg. All but two of these
the calculation
with extremely
(7) had found no differ-
ences in osmolal discriminates
when he compared
patients who died of hemorrhagic
shock with those who
survived
it. In this same paper Boyd reported a study
of dogs that
were bled until
they went into shock.
During
shock
the osmolal
discriminates
were increased
for all dogs, about 20 mosmol/kg
more for
those that died than those that recovered.
This difference was much smaller
than that reported
in the
Rubin study and the later Boyd study.
Previous literature is thus in conflict with regard to
the predictive
value
data of the present
this matter further.
of the osmolal discriminate.
The
study were used to investigate
Methods
Seven
conscious
hundred
fifteen sera were
bias during a three-month
selected
without
period from sera
submitted
to the laboratory
for testing by a SMA-6
AutoAnalyzer
(Technicon Instruments
Corp., Tarrytown, N. Y. 10591). In this system Na and K were determined with a flame photometer,
blood urea nitrogen by the diacetyl monoxime technique, and glucose
by a copper-neocuproine
reducing test. Osmolalities
were determined
cryoscopically
by use of a Model A
“Osmette” osmometer (freezing point type; Precision
Systems, Inc., Newton, Mass. 02166). For 649 of the
samples, water content was determined
via weight
loss after overnight baking at 100 #{176}C.
[Edelman
et al.
(4) used a three-day drying period, but it was determined in this study that no further weight loss occurred after the first half day.] Of the samples, 554
came from 463 different
in-patients
whose fate subsequent
to taking the samples
use of the laboratory
computer
sus records.
The patients
were
could be followed
by
and the hospital
cengrouped
according
to
whether they (a) were discharged
from the hospital
alive within two weeks of sample taking (hereafter reCLINICAL CHEMISTRY,
Vol. 21, No. 2, 1975
191
ferred to as “short-term
ill”), (b) were discharged
more than two weeks after the sample was taken
(hereafter
referred
to as “long-term
in the hospital
(hereafter
referred
Twenty-seven
patients,
accounting
appeared
in both
the long-term
ill”), or (c) died
to as “dead”).
for 89 samples,
and short-term
ill
groups because
they had samples
drawn both before
and after two weeks before their discharge.
No patients in the “dead”
group were included
in either of
the others.
By the time the final calculations
were
done no patients
had their
fates undecided;
either died or been discharged.
Molal units were calculated
to the following equation
from
molar
Molal
=
The density
1.02.
density
of serum
X
X
molar
all had
according
100
(% H20 by weight)
was assumed
to be constant
at
Results and Discussion
Osmolalities
were calculated
according
to the 13
methods
given in Table 1 and compared
with measured osmolality.
The calculations
were done with
use of both molar and molal units and the data of
Edelman
et al. (4). When we did the calculations
by
use of equation
10, the calcium and magnesium
terms
were set equal to a constant
4.0, as calcium and magnesium
were not measured
in this study. Results
of
the calculations
are set out in Table 2.
The calculation
methods
yielding
the best results
in terms of the highest
correlation
and lowest standard deviation
of difference
are those that include
glucose, blood urea nitrogen,
and sodium
(number
5,
6, 10, 11). Where the coefficients
for one or more of
these terms were rounded
off, the comparisons
were
degraded
equation
only marginally
such
or not at all, so that
as 9 is acceptable
if one wishes
an
ease of
mental calculation.
Inclusion
of a term for potassium,
as in equations
10 and 12, failed to improve
the comparision
of calculated
and measured
osmolality.
The correlations
between
measured
and calculated
osmolality
obtained
with Edelman’s
data are higher
than in the present
study. This is mainly because the
range of osmolalities
in Edelman’s
patients,
who were
specially
selected,
was greater
than in the present
study.
Edelman’s
measured
osmolalities
averaged
274.3 (SD, 22.75); those in the present study averaged
285.1 (SD, 15.06). When the range of measured
osmolality is greater, the correlations
of measured
and calculated
osmolality
improve
greatly without
affecting
the standard
deviation
of differences,
which is probably a fairer measure
of the validity
of the comparisons. It is somewhat
surprising
that the standard
deviation
of differences
for Edelman’s
data is only
slightly
smaller
than
for the present
data,
even
though
all of Edelman’s
values were the average
of
five separate
determinations
while in the present
study analytical
measurements
were done only once.
This may reflect
the increased
precision
available
from modern
automated
equipment
that has come
into use since the Edelman
study was published
in
1958.
The
standard
deviation
of differences
of -.‘6
achieved
with the best calculation
methods
is approximately
the minimum
possible,
given the present
state of routine analytical
art. The precision
of a single random
sodium determination
is about ±2 mmol/
liter and that of a single osmolality
determination
about ±2 mosmol/kg.
If the sodium is multiplied
by 2
in the calculation
the standard
deviation
of difference of ‘-.‘6 is accounted
for even without
considering
errors of measuring
glucose and blood urea nitrogen.
Therefore
the fact that a calculation
can reproduce
to
±6 mosmol/kg
a measured
osmolality
indicates
that
that calculation
is accounting
for all osmotically
active solutes.
Table 2. Comparison of Measured Osmolalities with Those Calculated from Equations in Table 1, by
Using Data from Edelman et al. (4) and Molar and Molal Data from the Present Study
et al. data (n
Edelman
Meas.
Eqn.
-
-
Corr.
1
.732
2
.732
3
4
5
6
7
8
9
10
11
12
13
.732
.732
.969
.969
.763
.967
.965
.970
.969
.969
.954
-
mean
calcd.
diff.
-17.9
-4.0
-11.0
-26.2
-6.0
-11.0
-10.5
-25.5
-23.8
-22.3
-0.8
-34.3
-19.0
=
95)
Molar units
(ii
=
Corr.
Molal units (n
X diff.
SD diff.
Corr.
X duff.
16.88
.445
-5.7
13.60
.454
-24.4
16.47
.447
16.47
20.0
6.156.15
15.42
6.88
6.83
6.01
5.85--6.72
7.80
.439
.447
.902
.901
.506
.899
.894
.905
.902
.903
.875
8.0
1.0
13.8
10.3
5.3
0.9
-9.0
-7.6
-1.4
15.5
17.7
-1.8
13.52
13.52
14.28
6.34
6.34
12.85
6.44
6.51
6.24
6.30
6.34
7.14
.454
.453
.454
.898
.898
.510
.895
.890
.900
-9.6
-16.6
-37.1
-7.2
-12.2
-17.2
-27.8
-26.3
-23.9
1.1
-37.1
-20.2
-
-
“Difference
statedas measured osmolality
minus calculated
osmolality.
192
715)
=
649)
.
SD diff.
CLINICAL CHEMISTRY, Vol. 21, No. 2, 1975
.900
.896
.875
SD duff.
13.81
13.67
13.67
14.79
6.68
6.68
13.01
6.91
6.80
6.55
6.55
6.91
7.51
Linear
regression
analysis was used to find the best
coefficients A and B (by least squares) in an equation
of the following
values
type,
using
from the present
study.
Osm
both
A Na + (Glu/18)
=
The resulting
equations
molar
and
+ (BUN/2.8)
+ B
were:
Correlation
For
molar
Osm
values
(n
1.86 Na
=
molal
Osm
=
values
+
(n
1.50 Na
(BUN/2.8)
+
SD diff.
715)
=
(Glu/18) + (BUN/2.8)
For
molal
=
+
+
9
.901
6 36
deviation
This study
of differences.
has failed
6.43
Rubin and Boyd and their coworkers
that comparison of measured
and calculated
osmolalities
is a useful indicator
of the likelihood
of patients
to survive.
These authors
found that in patients
who ultimately
647)
(Glu/18)
45
+
.900
The
above
equations
yielded
average
osmolal
discriminates
of zero.
Although
the equations
look rather different,
they
yield about the same correlations
and standard
deviation of differences.
The equation
for molar values
is identical
to that of Boyd, except for a constant
of 9
instead
of 5. Edelman’s
equation
(No. 11 in Table 1),
which was derived
by linear regression
from a mixture of molar and molal concentrations,
has a coefficient for sodium
(1.75) that is intermediate
between
those in the two equations
above.
It seems
surprising
that
molal units
do not yield
better correlations
than molar units. This anomaly
is
probably
explained
by the fact that water concentration for most of the samples was restricted
to the narrow range of 91-93%, so that molal and molar concentrations
were related by a nearly constant
factor. Had
the study
included
a number
of extremely
value in comparing
measured
with calculated
osmolalities. The data are set out in Table 3. The calculations shown were from the equations
derived
in this
study. (When the equations
of Table 1 were used, the
conclusions
were the same.) The three groups of patients
had about the same mean osmolal
discriminates and standard
deviations
of differences
between
measured
and calculated
osmolalities.
The correlations were lower for the short-term
ill patients,
but
this is because
the range of measured
osmolalities
was smaller
for this group,
illustrating
the point
made previously
that compressing
the range of data
lowers correl’ttions
without
affecting
the standard
lipemic
samples with total lipid content of (e.g.) 10%, or myeloma samples
with very high paraprotein
concentrations, the value of molal units could have been better
tested. It is apparent
that for the vast majority
of patients either system of units may be used with equal
practical
effect.
Examination
of the data in terms of eventual
fate
of the patients
showed that there was no prognostic
to confirm
the
findings
of
died, the osmolal
discriminate
was as much as 125
mosmol/kg.
In the present
study it was not outside
the range of ± 16 mosmol/kg
for any patient.
It is difficult to explain
or even examine
the discrepancies
with the Rubin
study
because
the report
of that
study was so sketchy.
The two Boyd studies
concerned patients
in hemorrhagic
shock. In the second
(20) the osmolal discriminate
seemed to have great
predictive
value and in the first (7) it did not. Reasons for this discrepancy
are not clear, but ingestion
of alcohol by some of the patients
could have been a
factor if a large proportion
of the trauma patients
appearing
at an inner-city
hospital
(as in the second
Boyd study) were inebriated
at the time of their injury. It has already been pointed
out that ethanol
can
produce very large osmolal discriminates.
In the present study it is likely that few or none of
the patients
involved
were in shock. The same was
true of the Edelman
study (4) in which the osmolal
discriminate
was found to have no predictive
value.
We conclude
that it is rare for noninebriated
patients
who are not in shock to have measured
osmolalities
that differ by more than 15 mosmol/kg
from calculated osmolalities.
The predictive
value of the osmolal
discriminate,
if any, is restricted
to patients
in shock.
It has not been determined
what might be the
extra
osmotically
active
material
in the serum
of
Table 3. Comparison of Osmotal Discriminates for Short-Term Ill, Long-Term Ill, and Dead Patients
No. samples
.lIolar
No. patients
Mean
meas. osmol.
SD
meas. osmol.
Mean osmolal
discriminate
SD diff.
Con.
values
Died
Short-term iii
Long-term iii
76
230
287
44
222
255
285.2
283.7
287.7
18.72
11.34
17.68
1.1
1.0
1.3
6.32
6.39
6.40
.941
.827
.926
76
230
287
44
222
255
285.2
283.7
287.7
18.72
11.34
17.68
1.1
1.0
1.3
7.18
6.08
6.23
.928
.843
.930
.11
olal values
Died
Short-term ill
Long-term ill
CLINICAL CHEMISTRY, Vol. 21, No. 2. 1975
193
shock
nates.
patients
that causes
large osmolal
discrimiBoyd has suggested
that at least some of this
material
is lactic acid (6). Although
does increase
greatly
in some
shock
serum lactic acid
patients,
it seems
unlikely that this would be reflected in either calculated or measured
osmolality.
At physiological
pH
lactate and other organic acids associated
with it are
almost entirely
ionized. Lactate
replaces
some of the
chloride
and bicarbonate
in serum so that the total
measurable
osmotic
concentration
is not affected
so
long as sodium concentration
is constant.
The anions
such as chloride,
bicarbonate,
and lactate
are all included in the calculation
by way of the sodium term.
Although
the ratio of small anions to small cations
changes
in acidosis because of the changing
charge of
serum proteins,
this effect is far too small to account
for the observations
reported
by Boyd. It would seem
then that any extra osmotically
active substances
in
the serum of dying shock patients
would have to be
nonionic
or they would have to include large amounts
of non-sodium
cations. A systematic
study (21) of 300
shock patients
of all types has shown that potassium
and ammonium
ions are not likely candidates
for the
extra cations.
Magnesium,
calcium,
and organic cations have apparently
not been studied
extensively
in
shock patients.
At any rate, the “extra”
osmotically
active substance(s)
in shock patients
must approach
a total concentration
of 0.1 mol/liter
if Boyd’s figures
are accurate.
Such concentrations
are well within the
limit of detection
of modern means of analysis. A systematic
search for these substances
could shed some
light on the question
of whether
they actually
exist
and could
possibly
provide
new insight
into the
mechanism
of death from shock.
References
1. Hoffman,
W. S., The Biochemistry
of Clinical
Medicine,
ed., Year Book Publishers,
Chicago, III., 1970, p 228.
2. Winters,
R. W., Disorders
of Electrolyte
olism. Pediatrics,
14th ed., H. L. Barnett,
Crofts, New York, N.Y., 1968, pp 336-368.
3. Jetter,
194
W. W., Clinical
osmometry.
4th
and Acid-Base
MetabEd., Appleton-Century-
Pa. Med. 72, 75 (1969).
CLINICAL CHEMISTRY. Vol. 21, No. 2, 1975
4. Edelman,
I. S., Leibman,
J., O’Meara,
M. P., and Birkenfeld,
W., Interrelations
between serum sodium concentration,
serum
molarity,
and total exchangeable
sodium,
total exchangeable
tassium,
and total body water. J. Clin. Invest. 37, 1236 (1958).
L.
ospo-
5. Holmes,
J. H., Measurement
of osmolality
in serum, urine and
other biologic fluids by the freezing
point determination.
In preworkshop
manual on Urinalysis
of Renal Function
Studies.
American Society
of Clinical
Pathologists,
Commission
on Continuing
Education,
Chicago, Ill., 1962.
6. Boyd, D.
ratory
Amer.
R., and Baker, R. J., Osmometry:
A new bedside laboaid for the management
of surgical
patients.
Surg. Clin. N.
51, 241 (1971).
7. Boyd, D. R., and Mansherger,
A. R., Jr., Serum water and osmolal changes
in hemorrhagic
shock, an experimental
and clinical
study. Amer. Surg. 34, 744 (1968).
S. Stevenson,
R. E., and Bowyer, F. P., Hyperglycemia
with hyperosmolal
dehydration
in nondiabetic
infants.
J. Pediat. 77, 818
(1970).
9. Mahon,
nonketotic
W. A., Holland,
J., and Urowitz,
M. B., Hyperosmolar
diabetic
coma. Can. Med. Ass. J. 99, 1090 (1968).
10. American
Association
of Clinical Pathologists
Commission
on
Continuing
Education.
Osmolality
Clinical Chemistry
Check Sampie No. CC-71 (1971), p 27.
11. Nelson, V. A., and Scheidt,
R. A., St. Luke’s Hospital,
kee, Wis., 1967, unpublished
data. Cited in ref. 10.
Milwau-
12. Gerich, J. E., Martin,
M. M., and Recant, L., Clinical
abolic characteristics
of hyperosmolar
non-ketotic
coma.
20, 228 (1971).
and met-
13. Beigelman,
coma). Diabetes
(diabetic
P. M., Severe
20, 490 (1971).
14. Moore, W. J., Physical
1962, p 120.
diabetic
Chemistry,
15. Redetzki,
H. M., Koerner,
G., Osmometry
in the evaluation
icol. 5,343 (1972).
Diabetes
ketoacidosis
3rd ed., Prentice
Hail,
Inc.,
T. A., Huges, J. R., and Smith,
A.
of alcohol intoxication.
Clin. Tox-
16. Glasser,
L., Sternglanz,
P. D., Combie,
J., and Robinson,
A.,
Serum osmolality
and its applicability
to drug overdose.
Amer. J.
Clin. Pathol. 60, 695 (1973).
17. Stern, E. L., Serum osmolality
J. Med. 290, 1026 (1974).
in cases of poisoning.
New Engi.
18. Robinson,
A. G., and Loeb, J. N., Ethanol
ingestion-Commonest cause of elevated
plasma osmolality?
New Engl. J. Med. 284,
1253 (1971).
19. Rubin, A. L., Braverman,
W. S., Dexter, R. L., et al., The relationship
between
plasma
osmolality
and concentration
in disease
states. Clin. Res. Proc. 4, 129 (1956).
20. Boyd, D. R., Folk, F. A., Condon,
R. E., et al., Predictive
of serum osmolality
in shock following
major trauma.
Surg.
21,32 (1970).
21. Cowley, R. A., Attar, S., LaBrosse,
E., Some
chemical
parameters
found in 300 shock patients.
926 (1966).
value
Forum
significant
bioJ. Trauma
9,