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Department of Physiology, St. George's Hospital Medical School, London SW17 0RE, United Kingdom; Division of Cardiology, Department of Medicine, Duke Medical Center, Durham 27710; and Durham Veterans Affairs Medical Center, Durham, North Carolina 27705
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
FOOTNOTES
REFERENCES
ABSTRACT 
Whipp, Brian J., Michael B. Higgenbotham, and Frederick C. Cobb. Estimating exercise stroke volume from asymptotic oxygen
pulse in humans. J. Appl. Physiol.
81(6): 2674-2679, 1996.
Noninvasive techniques have been devised
to estimate cardiac output (
) during exercise to
obviate vascular cannulation. However, although these techniques are
noninvasive, they are commonly not nonintrusive to subjects'
spontaneous ventilation and gas-exchange responses. We hypothesized
that the exercise stroke volume (SV) and, hence,
might be accurately estimated simply from the response pattern of two
standardly determined variables:
O2 uptake
(
O2) and heart rate (HR).
Central to the theory is the demonstration that the product of
and mixed venous
O2 content is virtually constant (k) during steady-state exercise. Thus from the Fick
equation, O2 = · CaCO2 
k, where
CaCO2 is the arterial
CO2 content, the
O2 pulse
(O2-P) equals
SV · CaCO2 (k/HR). Because the arterial O2 content
(CaO2) is usually relatively constant in
normal subjects during exercise,
O2-P should change hyperbolically
with HR, asymptoting at
SV · CaO2. In
addition, because the asymptotic
O2-P equals the slope (S) of the
linear O2-HR relationship,
exercise SV may be predicted as S/CaO2.
We tested this prediction in 23 normal subjects who underwent a 3-min
incremental cycle-ergometer test with direct determination of
CaO2 and mixed venous O2
content from indwelling catheters. The predicted SV closely reflected the measured value (r = 0.80). We
therefore conclude that, in normal subjects, exercise SV may be
estimated simply as five times S of the linear
O2-HR
relationship (where 5 is approximately 1/CaO2).
cardiac output; oxygen uptake; heart rate
INTRODUCTION THE EXERCISE STROKE VOLUME
(SVex) is one of the most
important indexes of both the functional state of the heart and the
propensity for achieving a high level of physical activity.
Consequently, several noninvasive estimators have been developed that
obviate the requirements for intravascular catheterization. Noninvasive methods such as Doppler (5) and impedance (23) techniques require
technical acumen for accurate determination and also are not commonly
available to most laboratories. Estimation procedures such as
CO2 rebreathing (12) or acetylene
uptake (10), on the other hand, temporarily disrupt the determination
of other ventilatory and gas-exchange variables that may also be of
interest during the exercise test. They do, however, all
allow the stroke volume (SV) profile to be estimated.
We describe in this paper a method of estimating a single average value
for SVex in normal subjects that
uses only standardly computed variables and, consequently, does not
disrupt the temporal profile of any other variable of interest during
the investigation.
METHODS Theory. We hypothesize that a single
average value for SVex can be
accurately estimated from the response profiles of
O2 uptake (
O2) and heart rate (HR) in
normal healthy subjects. The ratio of
O2 and HR
represents the O2
pulse (O2-P); this simply is derived from the Fick equation
or
(1)
where
CaO2 and
(2)
O2
are the arterial and mixed venous
O2 contents, respectively, and
is cardiac output.
Central to this theory is the demonstration (6) that the product of
and
O2
is virtually constant over a wide range of steady-state work rates.
Therefore, Eq. 2 can be rewritten as
|
(3) |
Because CaO2 is normally
relatively constant during exercise,
O2-P should therefore change
hyperbolically with respect to HR (as shown in Fig.
1A),
with an asymptote on the O2-P axis
at a value of SVex × CaO2. That is, as shown in
Eq. 3, as HR becomes large,
k/HR tends at zero, at which time
O2-P equals
SVex × CaO2. Therefore, when
O2-P is plotted as a function of
1/HR, it results in a linear relationship (Fig
1B) that extrapolates to the
asymptotic O2-P. In the region in
which O2 changes as a
linear function of HR, the asymptotic
O2-P is nothing more than the
slope of the O2-HR
relationship, i.e.,
O2/HR,
as shown in Fig. 1C. Hence
|
(4) |
|
(5) |
O2) and HR for progressively increasing exercise. Note that linear
O2-HR relationship results in
progressive increase in O2-P,
such that in the limit slope (S) of
O2 as function of HR is equivalent
to asymptotic O2-P (i.e., O2-Plim).
By using a somewhat different approach, Cole and Miller (4) have also theorized that this relationship should hold true.1 That is, if CaO2 has been determined before or during the exercise (the exercise-induced hemoconcentration produces only a small error term), then SV may be calculated. If not, it may be closely estimated, i.e., as CaO2 (in l/l) approximately equals 0.2 in normal subjects, then
|
(6) |
Experiments. We tested this prediction in 23 healthy men aged between 20 and 50 yr who had a normal medical history and physical examination and were not receiving medications. The subjects' heights ranged from 173 to 185 cm, weights from 63 to 103 kg, and hemoglobin concentrations from 13.2 to 16.7 g/100 ml. The subjects gave informed consent for the study, which was approved by the Institutional Ethical Review Board.
The subjects each performed an incremental exercise test on an
electromagnetically braked cycle ergometer (Fitron, Lumes) with the
work rate increased in 25-W steps, each lasting 3 min, up to 125 W. The
pedaling frequency was maintained between 60 and 70 revolutions/min.
This profile is widely used in exercise testing, since in normal
subjects it allows steady states of and
O2 to be
attained. One hour before the test, a 2-in. cannula was
inserted percutaneously into the brachial artery, and a 7-Fr Swan-Ganz
catheter was positioned in the pulmonary artery via an antecubital
vein. At rest, and in the last 30 s of each work rate, arterial and
mixed venous blood (2-3 ml) was drawn for measurement of
O2 content (model 282, Instrumentation Laboratory). HR was monitored by standard
electrocardiographic leads.
Expired volume was measured with a turbine volume sensor (Alpha
Technologies) calibrated with known volumes of room air at mean flows
and flow profiles spanning the exercise range. Respired air was sampled
continuously at the mouthpiece for continuous measurement of
PO2 (Fuel Cell analyzer) and
PCO2 (Infrared analyzer).
Precision-analyzed mixtures were used for calibration. The time delay
between the volume and gas-concentration signals was measured by
passing a bolus of gas through the system (2). Electrical signals from
these devices underwent analog-to-digital conversion and were processed
(model 2000, Sensormedics) for breath-to-breath determination of
pulmonary gas-exchange variables but with particular reference to
O2
(O2
STPD).
RESULTS
The typical response profiles for the gas-exchange and cardiovascular
variables of interest are shown in Figs. 2
and 3.
O2 increased as a linear
function of work rate with a slope of ~10 ml · min
1 · W1,
as previously demonstrated (9, 21), and increased
linearly with respect to O2
with a slope of ~5. The mean slope of this relationship (Fig. 3) was
actually 5.6, with an SE of estimate of 0.29 and an intercept on the
axis of 5.2 l/min with an SE of 0.41. The dashed
lines in Fig. 3 represent a 95% confidence interval, ranging from 5.00 to 6.17 for the slope and from 4.38 to 6.02 for the intercept on the
axis. This resulted in an r of 0.87 and an
r2 of 0.76.
, cardiac output;
O2,
mixed venous O2 content; SV,
stroke volume; W, work rate.
, determined by direct Fick measurements as function
of O2 in 23 normal subjects
performing incremental exercise. Solid line through data points,
regression line; dashed lines, 95% confidence limits on slope.
The product of and
O2
(the returning O2 delivery to the
lung), however, was not constant in our studies but increased initially
before becoming stable over the higher work-rate range. This was a
consistent pattern in all of our subjects. However, the increase of
O2 as a function of
HR was linear over this work-rate range. The linearity of this response
predicts that O2-P as a function
of 1/HR will consequently be linear. This is depicted in Fig. 2,
bottom right. SV, estimated
noninvasively from the slope of the
O2-HR relationship, was shown
to be 140 ml in this subject. This compares well with the measured SV
of 133 ml. It is important to point out that the actual SV was not constant over this work-rate range; rather, it increased from an
average of 108 ± 17 (SD) ml at 25 W to 115 ± 16 ml at 125 W.
Figure 4 depicts the relationship between
the SV estimated, as described in
METHODS, as a function of the SV
determined from the direct Fick computation of and
the measured HR and also the difference between the measured and
estimated value as a function of the average of the two values, as
proposed by Bland and Altman (3). This demonstrated a good relationship
between the variables. The estimated SV correlated highly with the
directly measured SV (r = 0.78, r2 = 0.61). The
slope of this relationship was 0.77, with 95% confidence limits from
0.49 to 1.05. The SV intercept was 24.1 ml; this was not significantly
different from zero, since the 95% confidence limited extended from
7.4 to 57.0 ml. The mean difference between the measured and the
estimated SV values, however, was only 0.9 ml (±2 SD = 18 ml)
(i.e., there was no significant difference between them), and only
three of the points were not within 10% of the measured value.
In Fig. 5, the SV was estimated by using
the inverse of the measured CaO2 as the
multiplier of the O2-HR
slope. This differs from the method used in Fig. 4, in which we
used the value 0.2 as the
CaO2. This changed the
relationship somewhat but not statistically significantly. The slope
increased to 0.85, with 95% confidence limits from 0.60 to 1.09 and an
SV intercept of 12.5 ml, which again was not significantly different
from zero (the 95% confidence intervals extend from 14.5 to
39.6 ml). Similarly, the correlation coefficient for this relationship
increased somewhat to an r of 0.85 and
an r2 of 0.73. The difference between these two values averages 3 ml (±2 SD = 19 ml). The use of the directly measured
CaO2 in the estimation algorithm
corrected one of the two noticeably errant points in Fig. 4. The other
point, however, remained noticeably low even with this correction.
Consequently, although it does not allow the profile of SV change to be determined, the simple algorithm for estimating the exercise SV noninvasively, as described in METHODS, may be considered to have resulted in acceptable estimations (Fig. 4) with respect to the values actually measured for 21 of the 23 subjects.
DISCUSSION
The value of a noninvasive estimator of a cardiovascular variable such
as SV depends on the constructs that underlie the estimation procedure
having a sound basis in physiology and on it providing useful
information with an appropriate degree of accuracy. The physiological
basis of this estimation lies in the implication of the widely reported
linear relationship between
O2 and HR during exercise in
healthy subjects. This relationship has, as a necessary consequence, a
hyperbolic increase in O2-P in
this range. It is important to recognize, however, that although our technique for estimating SV depends on the asymptotic
O2-P, it is not necessary that
O2-P actually attains, or even
closely approaches, this asymptotic value. It is only necessary that,
over the range in which it is measured, it changes as though it would
attain this asymptotic value were the response to
continue. This means that even if nonlinearities in the
O2-HR rate relationships were
to occur at very high work rates (i.e., resulting in distortions in the
hyperbolic increase in O2-P), the
projection derived from the appropriate regions remains valid. That is,
the variables of interest must have an appropriate pattern of response
to meet the criteria for the estimation; without this, the estimation should not be attempted. Because the pattern of the
O2-HR response was typically
linear, the simple estimation procedure of multiplying the
slope of the O2-HR
relationship by five (i.e., the inverse of the
CaO2) consequently provided a highly
acceptable estimation of the directly measured SV, as shown in Fig. 4.
In fact, the difference between the measured and estimated values was
not significantly different.
We also tested our estimation algorithm on data available in the
literature (1, 7-9, 11, 16-20) that
1) allowed the asymptotic O2-P to be determined from an
adequate number of data points and 2) provided SV measurements or
both and HR. Data included subjects of
varying fitness levels and included effects of physical training. However, the tests were all sufficiently long that steady states of
O2 and
would have likely been attained. As shown in Fig. 6, the results cohered well with our
experimental findings despite the fact that the
values in these studies were determined by a variety of techniques,
including CO2 and acetylene
rebreathing, dye dilution, and direct Fick.
In 2 of the 23 subjects in our study, the values were
noticeably and unacceptably low. In one subject, this
proved to be a consequence of an unexpectedly low
CaO2 of 175 ml/l rather than the 200 ml/l that forms the basis of the simple estimation technique. When the
correct value for the CaO2 was included
in the estimation, this increased the estimated SV from 115 to 131 ml
compared with a measured value of 145 ml. This disparity,
however, was not the cause of the other errantly low value. It may be a
consequence of the assumption that a steady state of
O2 is attained in all normal
subjects within 3 min. If the time constant or mean response time (14,
22) for O2 were ~45 s, then
O2 for the
exponential increase would only be just attaining 98% of the expected
steady-state value at 3 min. In addition, as our sample for
O2 was averaged over the
last 30 s of the work rate, the average would be appreciably less than
this value. Of course, when sampling over the last 30 s of a 3-min
increment, a subject with an even longer time constant for
O2 would be even further from
the presumed steady-state value.
, however, has been consistently demonstrated to
increase with a time constant that is appreciably faster than that for O2 (5, 15). It is possible,
therefore, that a subject may attain a steady state for
with O2
still being in its transient phase of response. We do not know whether
this is the case, since we did not establish the kinetics of the
O2 response in these studies.
This does, however, point to the fact that, although 3 min is a popular
duration for work-rate increments, it will not be of sufficient
duration for some subjects to attain a steady state of
O2; a 4-min increment would
be much more inclusive. However, 6 min may be necessary for such
steady-state requirements if other gas-exchange indexes such as
ventilation or CO2 output are
required, since their response time constants are appreciable longer
(22).
It is especially important that care is taken to ensure high confidence
on the O2-HR regression in
highly fit subjects, since the slope increases tangentially toward
infinity at high values. Small errors in the slope can therefore
produce large errors in SV estimation. This is of less concern at low
slope values. By the same token, a group mean response of a range of individual slopes is also prone to error and should be avoided.
There is another important caveat, however. Although we have
demonstrated that the estimation procedure appears to provide an
adequate characterization for such a steady-state incremental test, we
do not know whether the same relationship will hold true for the
now-popular non-steady-state (ramp-type) incremental exercise tests.
The main concern is the disparity of the time constants of
and O2.
If, however, it can be demonstrated that the slope of the
O2-HR relationship during a
rapid incremental test is the same as that for the steady-state test
(after the appropriate number of time constants have elapsed), then the
consequent parallel displacement of the
O2-HR relationship will not
affect the value for the asymptotic
O2-P, although it will affect the
rate at which this is achieved.
In conclusion, we have demonstrated that an acceptably linear
relationship between O2 and
HR during steady-state incremental exercise can be used to estimate a
value for the exercise SV in normal subjects. Naturally, if SV changes
during the exercise, the estimator can only provide a single
value reflective of the average SV over that work-rate interval. In
normal subjects, therefore, the exercise SV may be estimated simply as
|
(7) |
|
(8) |
This relationship is not valid, however, in patients with lung disease, anemia, or hyperemia; normal subjects at high altitude or breathing hypoxic inspirates; or subjects who desaturate during exercise, such as some highly trained athletes. Further studies are needed, however, to determine to what extent the relationship holds for the now-popular non-steady-state incremental exercise testing in normal subjects.
FOOTNOTES
Address for reprint requests: B. J. Whipp, Dept. of Physiology, St. George's Hospital Medical School, Cranmer Terrace, London SW17 0RE, United Kingdom.
Received 11 August 1995; accepted in final form 15 July 1996.
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| 4. | Cole, T. J., and G. J. Miller. Interpretation of the parameters relating oxygen uptake to heart rate and cardiac output during submaximal exercise. J. Physiol. Lond. 231: 12P, 1973. |
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| 6. | Durand, J. Circulatory responses to exercise. In: Lactate: Physiologic, Methodologic and Pathologic Approaches, edited by P. R. Moret, J. Weber, J.-L. Haissly, and H. Denolin. Berlin: Springer-Verlag, 1980, p. 25-34. |
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