## Abstract

The relationship between cardiac output (CardOut) and oxygen consumption (V̇o_{2}) during exercise has generally been assumed to be linear. To test this assumption, we studied 72 healthy subjects using a graded, 2-min cycle-ergometry exercise test to maximum while measuring gas exchange continuously and CardOut at the end of each stage, the latter using an open-circuit gas technique. Data for V̇o_{2} and CardOut at each stage were fit to a quadratic expression *y* = *a* + (*b*·V̇o_{2}) + (*c*·V̇o_{2}^{2}), and statistical significance of the quadratic *c* term was determined in each subject. Subjects were then divided into two groups: those with statistically significant negative quadratic term (“negative curvature group,” *n* = 25) and those with either nonsignificant quadratic term or *c* significantly > 0 (“non-negative curvature group,” *n* = 47, 2 with *c* significantly > 0). We found the negative curvature group had significantly higher maximal V̇o_{2}/kg (median 37.9 vs. 32.4 ml·min^{−1}·kg^{−1}; *P* = 0.03) higher resting stroke volume (SV; median 77 vs. 60 ml; *P* = 0.04), lower resting heart rate (HR; median 72 vs. 82 beats/min, *P* = 0.04), and higher tissue oxygen extraction at maximal exercise (17.1 ± 2.2 vs 15.5 ± 2.1 ml/100 ml; *P* < 0.01), with tendencies for higher maximal CardOut and SV. We also found the HR vs. V̇o_{2} relationship to be negatively curved, with negative curvature in HR associated with the negative curvature in CardOut (*P* < 0.05), suggesting the curvature in the CardOut vs. V̇o_{2} relationship was secondary to curvature in HR vs. V̇o_{2}. We conclude that the CardOut vs. V̇o_{2} relationship is not always linear, and negative curvature in the relationship is associated with higher fitness levels in normal, non-elite-athletic subjects.

- Fick equation
- oxygen extraction
- exercise capacity
- cardiac stroke volume

the fick equation expresses the mass balance between whole body O_{2} consumption (V̇o_{2}), cardiac output (CardOut), and the difference in O_{2} content between mixed venous and arterial blood (− ): The Fick equation illustrates that there are two major factors that could limit V̇o_{2} at maximal exertion, CardOut and the O_{2} extraction (− ). In young, healthy subjects, the maximal V̇o_{2} attained during exertion (V̇o_{2 max}) is determined by a combination of CardOut and maximal O_{2} extraction. If there is no pulmonary limitation (e.g., arterial desaturation), stays relatively constant up to maximal exertion, and is reduced to the point that the local Po_{2} in the capillaries becomes insufficient to drive O_{2} diffusion into the tissues. At maximal exertion, O_{2} extraction can reach values of 14–18 ml O_{2}/100 ml blood (1, 3, 6, 7).

Although it is generally assumed that CardOut increases linearly with V̇o_{2}, the pattern of variation in V̇o_{2} and CardOut as maximal O_{2} extraction is approached has not been extensively investigated and may vary among individuals. This is illustrated in Fig. 1, which shows three patterns of increase in CardOut with increasing V̇o_{2}. Dashed lines indicate isopleths of constant O_{2} extraction, with the line for O_{2} extraction of 18 ml O_{2}/100 ml blood indicated as a solid line.

In this example, all three patterns of increase in CardOut start with the same initial slope, ∼5.2 l·min^{−1}·(l/min of V̇o_{2})^{−1} and are distinguished by the amount of downward curvature. *Curve 1*, *top*, intersects a CardOut of 15 l/min at a V̇o_{2} of ∼2 l/min with O_{2} extraction of ∼14 ml O_{2}/100 ml blood. With CardOut still increasing linearly and O_{2} extraction <16 ml O_{2}/100 ml blood, this person would likely not have reached V̇o_{2 max}. By extrapolation, if this person could continue to an extraction of 18 ml O_{2}/100 ml blood, his/her V̇o_{2 max} would be well over 3.5 l/min. The second curve indicates a steadily decreasing slope in CardOut vs. V̇o_{2}, suggesting a developing CardOut limitation. At a V̇o_{2} of 2.7 l/min, O_{2} extraction is near a maximal value of 18 ml O_{2}/100 ml blood, indicating that exercise limitation is likely due to attainment of maximal O_{2} extraction, although the increase in O_{2} extraction was accelerated relative to the linear curve because of a relative reduction in CardOut at higher exercise intensities. *Curve 3* indicates a true limitation in CardOut, with the slope of CardOut vs. V̇o_{2} reaching 0 at the point of maximal O_{2} extraction.

These three illustrative examples suggest a conceptual framework for defining when CardOut is likely contributing to limitation of V̇o_{2 max}. Assume for illustrative purposes that maximal O_{2} extraction is constant at 18 ml O_{2}/100 ml blood. When the CardOut vs. V̇o_{2} relationship is purely linear, V̇o_{2 max} is defined by the V̇o_{2} at which maximal O_{2} extraction is reached, determined by the slope, with no limitation in CardOut. With increasing curvature of the CardOut vs. V̇o_{2} relationship, as CardOut falls off with increasing V̇o_{2}, the maximal O_{2} extraction is reached at a lower V̇o_{2}, and one could argue that V̇o_{2 max} is in part determined by O_{2} extraction and in part by a relative reduction in CardOut. The V̇o_{2 max} value attained will be determined by the initial slope and the degree of curvature in the CardOut vs. V̇o_{2} relationship. The extreme case is illustrated by the lower curve, where the final slope at V̇o_{2 max} is zero and CardOut reaches an upper limit that is not exceeded, even if V̇o_{2} could increase.

The degree to which the CardOut vs. V̇o_{2} relationship is nonlinear has not been rigorously investigated. In addition to knowing the relative frequency of finding a nonlinear relationship in the general population, it would be interesting to see whether nonlinearity might be associated with relative fitness (e.g., V̇o_{2 max}/kg). One could argue that, as relative fitness level increases, the ability of the heart to increase stroke volume (SV) at higher levels of exercise might become limited as filling time per unit of venous return is reduced.

The purpose of this study was to describe the relationship between CardOut and V̇o_{2} in a group of healthy individuals, not selected for athleticism but covering a range of fitness levels. We sought to answer several specific questions: *1*) in what proportion of individuals is there a statistically significant curvature in the CardOut vs. V̇o_{2} relationship? *2*) Is curvature of CardOut vs. V̇o_{2 max} related to fitness level as indicated by V̇o_{2 max}/kg or other subject characteristics? The purpose of the study focused solely on the CardOut vs. V̇o_{2} relationship and its relationship to fitness level. Although, as pointed out above, negative curvature in the CardOut vs. V̇o_{2} relationship might indicate a kind of cardiac limitation to exercise, determining the overall integrated determinants of V̇o_{2 max}, which could include limitations in any component of the O_{2} transport or utilization chain (20), is not an end point of this study. To answer these questions, we utilized an open-circuit acetylene uptake method to measure CardOut (9). Because the method does not involve altered breathing patterns or rebreathing, with inevitable buildup of CO_{2} and depletion of O_{2} during the maneuver, it does not inherently limit exercise performance, so it is well suited to the questions posed above.

## METHODS

#### Subject selection.

Healthy subjects were recruited from the population of Rochester, MN, by advertisement in the local media and within the Mayo Clinic. Subjects signed written, informed consent to participate in an exercise evaluation, which had been approved by institutional review board of Mayo Clinic. Subjects were excluded if they had clinical histories of cardiac or pulmonary diseases, including asthma and tobacco use. For all subjects, β_{2}-adrenergic receptor subtyping was performed for purposes of studying differences in exercise response based on β-receptor subtype, which is the subject of a separate report (18). Subjects were not excluded based on genotyping. Thus this group of subjects can be considered to be a sample from the general population of Rochester, MN, with weighted representation from Mayo Clinic employees.

#### Exercise evaluations.

Subjects participated in two maximal exercise protocols on separate days. For the first study, 12-lead ECG and noninvasive cuff blood pressures were monitored during a 2-min incremental protocol on a stationary exercise cycle, each increment ranging from 15 to 30 W, depending on preexercise assessment of the fitness level of the subject. Breath-by-breath gas exchange was monitored using commercial software (CPX/D, Medical Graphics, St. Paul, MN) interfaced to a respiratory mass spectrometer (15). Exercise intensity increased until volitional fatigue. The second exercise study was performed to evaluate CardOut response to exercise using a noninvasive open-circuit technique (9) following an identical protocol as the first study. CardOut measurements were made the last 30 s of every exercise intensity up to maximal exertion. At the start of the protocol, the subject was seated on the cycle ergometer with mouthpiece in place while three CardOut assessments were completed with 2–4 min between each to allow inert-gas washout from the lungs. We report here the results of the Cardout data from the second study merged with the V̇o_{2} data from the first evaluation averaged over the last 30 s of each exercise level.

#### CardOut.

During the second exercise evaluation, raw data for gas flow at the mouth and gas concentrations of acetylene (C_{2}H_{2}) and helium (He) were acquired at 100 Hz using custom data acquisition software. Data files were saved to disk for later analysis. CardOut data were analyzed using the technique described and validated previously (9). Because calculated CardOut is critically dependent on correct time alignment of gas flow and gas concentration signals, we optimized the time delay by comparing calculated inspired dead space (mass balance of He gas) with known dead space of the breathing valve. This time-delay parameter was relatively constant (±4 ms) among subjects. At each stage of exercise, the arterial to mixed venous O_{2} content difference, or O_{2} extraction, was calculated from O_{2} extraction = V̇o_{2} (ml/min)/CardOut (l/min)/10.

#### Statistical analysis.

Data for exercise intensity, heart rate (HR), V̇o_{2}, V̇co_{2}, CardOut, respiratory exchange ratio (RER = V̇co_{2}/V̇o_{2}, where V̇co_{2} is CO_{2} production), respiratory rate, minute ventilation, and tidal volume were tabulated for each exercise intensity by subject. The CardOut vs. V̇o_{2}, HR vs. V̇o_{2}, and SV vs. V̇o_{2} relationships were represented in each subject by fitting the quadratic relationship *y* = *a* + *b*·V̇o_{2} + *c*·(V̇o_{2})^{2} using multiple regression and collecting the three parameter estimates as well as the associated *t* statistics and *P* values. Subjects were then separated into two groups, those with a statistically significant (*P* < 0.05) *c* < 0 for the CardOut vs. V̇o_{2} relationship (“negative curvature group”; *n* = 25) and those with either nonsignificant or significantly positive value for *c* (“nonnegative curvature group”; *n* = 47). Only two subjects had a statistically significant *c* > 0. Differences in all parameters between these two groups were tested using the Wilcoxon's rank sum test. For all subjects, we derived initial and final slope from the first derivative of the quadratic equation using the measured resting and V̇o_{2max} for the subject, respectively: initial slope = *b* + 2·*c*·(V̇o_{2}_{rest}); final slope = *b* + 2·*c*·(V̇o_{2 max}).

To quantify curvature of the CardOut vs. V̇o_{2} relationships, we explored several parameters, including *1*) the ratio of final to initial slope (slope ratio = final slope/initial slope), *2*) the maximal difference in CardOut between that predicted by the quadratic relationship and that predicted by a linear relationship derived from the first and last observation, and *3*) the quadratic term from the fitted curve. Because there was a high degree of correlation among these parameters (*R*^{2} from 0.69 to 0.90) and because the slope ratio was dimensionless and conceptually independent of the magnitude of CardOut, we focused on slope ratio as a measure of curvature. Although only two subjects had statistically significant positive curvature to the CardOut vs. V̇o_{2} relationship, 15 subjects had a slope ratio of >1.0, which can only occur with positive curvature. To minimize the effect of these data, slope ratios of >1.0 were replaced with a value of 1.0 (Winsorized) in regression analysis. To determine whether slope ratio is related to measures of body size or exercise capacity, both univariate and multiple regression analysis were performed.

To help sort out determinants of exercise capacity, the maximal/resting ratios of the three components of the Fick equation (V̇o_{2}, CardOut, extraction) were calculated. Maximal/resting ratios of SV and HR were also analyzed.

## RESULTS

A total of 73 subjects were studied, although one subject's data were excluded from analysis because of aberrantly low CardOut values and maximal O_{2} extraction near 30 ml/100 ml. Subject characteristics for the remaining 72 subjects are listed in Table 1. Overall, subjects were of average fitness level for their age (range 20–40 yr; V̇o_{2 max}/kg ranged from 22 to 55 ml·min^{−1}·kg^{−1}). The subjects were studied on 2 separate days using identical work intensity increases; however, the maximal HRs were well matched between the 2 days [mean for all subjects on *day 1* was 184 beats/min (SD 10) and *day 2* was 183.8 beats/min (SD 10.5)]. We thus believe these two exercise tests were equivalent, so matching V̇o_{2} values from *day 1* with CardOut from *day 2* was legitimate.

Individual CardOut vs. V̇o_{2} relationships for all subjects are shown in Fig. 2, *top*, with regression curves determined from overall mean values for regression coefficients in Fig. 2, *bottom*. Figure 3 shows mean regression curves from selected previous studies, largely using dye dilution techniques or direct Fick method to measure CardOut in both athletes and normal subjects. Our data lie in the low end of the range of most previous studies, although the present data closely match our own study using the direct Fick method to validate the open-circuit method used in this study.

Our subjects were analyzed in two groups: those with significant negative curvature of the CardOut vs. V̇o_{2} curve and those whose curvature was either positive or not significantly negative. Figure 2, *bottom*, shows the mean regression curves for the two groups along with a mean regression for our Fick validation study. Differences between these groups in both physiological variables and parameters derived from these curves are shown in Tables 1 and 2. The average sum squared error of the model fit was significantly higher for the linear model compared with model with quadratic term in the negative curvature group, but not the nonnegative curvature group, confirming the model with curvature fit better in the negative curvature group. In the negative curvature group, 56% were male, whereas only 40% were male in the nonnegative curvature group, although this difference was not significant (*P* > 0.21, χ^{2} test). The negative curvature group was slightly younger (median 26 vs. 30 yr; *P* = 0.049), tended to be heavier (median 81 vs. 69 kg; *P* = 0.06), but had similar body mass index values (median 24.9 vs. 23.5 kg/m^{2}; *P* = 0.16). The V̇o_{2 max}/kg was higher (median 37.9 vs. 32.4 ml·min^{−1}·kg^{−1}; *P* = 0.03) in the negative curvature group, with a tendency for maximum CardOut to be higher (median 17.1 vs. 13.7 l/min, *P* = 0.06). The % predicted V̇o_{2 max} tended to be higher in the negative curvature group, but the difference was not significant (10). Resting HR was lower (median 72 vs. 82 beats/min; *P* = 0.04), and resting absolute SV higher (median 77 vs. 60 ml; *P* = 0.04) in the group with significant negative curvature. However, resting SV/BSA was similar in the two groups, as was maximal CardOut/BSA. Resting O_{2} extraction was similar, but maximal O_{2} extraction was higher (17.1 vs. 15.5 ml/100 ml; *P* < 0.01) in the negative curvature group. These data suggest a higher fitness level in the group with negative curvature.

To investigate whether the difference in exercise responses between groups was not simply associated with differing performance effort or possible hyperventilation that might affect the CardOut measurement in the exercise test, the average ventilatory equivalent for CO_{2} at its minimum (minute ventilation; an index of degree of hyperventilation near the ventilatory threshold) and at maximal exercise were not found to be different between the groups. Protocol duration, maximal HR, and maximal RER were also found to be not significantly different (Table 1). Furthermore, the slope of the work intensity vs. V̇o_{2} relationship averaged 10.5 ml·min^{−1}·W^{−1} (*R*^{2} = 0.96) for the negative curvature group and 10.3 ml·min^{−1}·W^{−1} (*R*^{2} = 0.97) for the non-negative curvature group.

Table 2 shows the data for ratio of maximal to resting components of the Fick equation. Consistent with higher fitness in the negative curvature group, V̇o_{2 max}/rest V̇o_{2} and maximal/rest HR are higher in the negative curvature group, with no difference in maximal/rest SV or O_{2} extraction but a tendency for higher maximal/rest CardOut.

Characteristics of the CardOut vs. V̇o_{2} relationship are also shown in Table 2. The initial slopes of the CardOut vs. V̇o_{2} curves were considerably higher in the negative curvature group. The ratio of final to initial slope was considerably lower in the negative curvature group, which is closely related to the definition of the groups. In the pooled group of subjects, V̇o_{2 max}/kg and maximal O_{2} extraction were both negatively correlated with the Winsorized version of the CardOut slope ratio (*r* = −0.29, *P* < 0.01 and *r* = −0.37, *P* < 0.01, respectively), again consistent with the negative curvature being associated with higher fitness. There was a significant relationship (*P* = 0.046 by Fisher's exact test) between the presence of significant negative curvature of HR vs. V̇o_{2} and the presence of significant negative curvature of CardOut vs. V̇o_{2}, suggesting that negative curvature in CardOut is largely related to negative curvature of HR. Ten of the 25 subjects (40%) with negative curvature of the CardOut vs. V̇o_{2} curve also had statistically significant negative curvature to the HR vs. V̇o_{2} curve, whereas only 8 (17%) of the 47 subjects in the nonsignificant curvature group had significant negative curvature in the HR vs. V̇o_{2} curve.

To identify the subject characteristics that are most associated with the CardOut slope ratio, we used multiple linear regression and an alpha of 0.10 with forward stepwise selection of parameters to optimize the final model (Proc REG, SAS Institute, Cary, NC). Independent variables considered included gender, height, weight, age, V̇o_{2 max}, rest HR, rest SV, maximal respiratory rate, and ratio of maximal to minimal values of CardOut. The final model included only a significant negative association with V̇o_{2 max} and with male gender (*P* < 0.01 and *P* = 0.099, respectively; overall *R*^{2} = 0.18).

Next we performed forward stepwise regression to explain V̇o_{2 max} in terms of subject characteristics and the ratio of final to initial slope of CardOut vs. V̇o_{2} curves (Table 3). Independent covariates considered include CardOut slope ratio as a measure of curvature, age, gender, weight, height, resting HR, and resting SV. The overall *R*^{2} was 0.84, with six statistically significant parameters at the 0.10 level remaining in the model. Because we used V̇o_{2 max} rather than V̇o_{2 max}/kg, there was a strong positive association of V̇o_{2 max} with body height and weight. There was also a strong association with male gender after controlling for height and weight. The coefficients for resting HR (*P* = 0.06) and the ratio of final to initial slope of CardOut vs. V̇o_{2} curves were both negative, indicating lower resting HR and higher degree of downward curvature of the CardOut vs. V̇o_{2} curve was associated with higher V̇o_{2 max}. Increased resting SV was associated with increased V̇o_{2 max}. Taken together, these two analyses support the conclusion that negative curvature of CardOut vs. V̇o_{2} curves is associated with indexes of higher fitness level, in particular V̇o_{2 max}.

The ratio of maximal to resting values for V̇o_{2}, CardOut, O_{2} extraction, and HR were correlated in the entire group in an effort to quantify the capacity of the subjects to expand V̇o_{2} and the components of that capacity. There was a high correlation between the V̇o_{2} ratio and O_{2} extraction ratio (*r* = 0.58, *P* < 0.01). There was a reasonable correlation between V̇o_{2} ratio and CardOut ratio (*r* = 0.46, *P* < 0.01), indicating V̇o_{2} capacity is related to a subjects' capacity for expanding CardOut. The correlation of V̇o_{2} ratio with HR ratio was not as good (*r* = 0.22, *P* = 0.06). There was poor correlation between V̇o_{2} ratio and our measure of curvature, the final/initial slope ratio of the CardOut vs. V̇o_{2} relationship (*r* = −0.11, *P* = 0.36).

## DISCUSSION

In a group of 72 healthy, relatively young subjects, we found the CardOut vs. V̇o_{2} relationship to be significantly nonlinear in 27 (38%), most (25 subjects) of whom had a negative curvature. After separating the subjects into those with significant negative curvature compared with those with nonsignificant or positive curvature, the negative curvature group was found to have higher fitness level as measured by higher V̇o_{2 max}/kg, maximal O_{2} extraction, and resting SV with lower resting HR. If negative curvature of the CardOut vs. V̇o_{2} relationship indicates an approaching mechanical limitation to cardiac pumping capacity, these results suggest that higher levels of fitness may, in some individuals, be associated with a true mechanical cardiac limitation to exercise.

#### Sources of error.

Our noninvasive method for measuring CardOut has been validated using the direct Fick method in healthy subjects (9). Nevertheless, it is worth considering whether the method was underestimating CardOut at higher levels of V̇o_{2}, causing the negative curvature. Because the open-circuit method relies on efficiency of gas exchange, it may underestimate CardOut in the presence of alveolar ventilation/perfusion mismatch. However, this group of healthy subjects was free of lung disease and were lifetime nonsmokers, and we did not observe O_{2} desaturation >4% in any subject at maximal exercise. Furthermore, we observed similar patterns of negative curvature in CardOut using the direct Fick data from our previous study and have observed evidence of negative curvature in CardOut in many of the plots of other studies using invasive measures in the literature (Fig. 3). Thus we feel this is likely a common finding, especially in athletic individuals, and not an artifact of the method.

#### Comparison with literature.

Figure 3 compares mean regressions from our data with our laboratory's previous validation study (9) as well as five other studies that provided data for all stages of exercise using more invasive techniques. Two of these (2, 5) show somewhat higher CardOut at any given V̇o_{2} compared with both our data and the other studies. Both of these studies involved elite athletes (skiers and cyclists, respectively); other groups included athletes in their studies, although not exclusively. Astrand et al. (1) found the rate of increase in CardOut per unit change in V̇o_{2} to be less above 70% of V̇o_{2 max} compared with lower V̇o_{2}, consistent with a significant negative curvature in CardOut vs. V̇o_{2} in many of their subjects. Similarly, Sullivan et al. (19) found the CardOut vs. V̇o_{2} relationship was best fit by a negatively curved power law relationship in 9 of 12 subjects. Neither study correlated this curvature in CardOut vs. V̇o_{2} in relation to subject fitness as we have in our study. Astrand et al. (1) also documented a plateau in SV above 40% maximal capacity, indicating the curvature in CardOut vs. V̇o_{2} was likely due to curvature of HR vs. V̇o_{2}, although they did not present an analysis of this.

#### Model of CardOut regulation.

We believe that these data are consistent with the following model of CardOut regulation. In a normal, healthy individual with average fitness level, the relationship between CardOut and V̇o_{2} is nearly linear. As V̇o_{2} increases proportionate with external power output, the rate of increase in CardOut will depend on the rates of increase in HR and SV with increasing V̇o_{2}. The derivative of the simple equation CardOut = SV × HR gives the two components to the rate of change in CardOut: If we eliminate the common δV̇o_{2} term in the denominator and divide both sides of this equation by SV × HR, we get the following: This last equation states that the fractional change in CardOut must equal the sum of fractional changes in HR and SV. This allows us to determine which component, change in HR vs. change in SV, contributes the most to the change in CardOut at any point in exercise. Percent changes in these components at rest, middle of the exercise protocol, and near V̇o_{2 max} are listed in Table 4. Early in exercise, the percent change in CardOut was ∼64% in the negative curvature group vs. 49% in the non-negative curvature group; increases in HR and SV contributed equally to the percent change in CardOut in both groups. The fractional change in CardOut decreased at higher exercise intensities, due largely to the increase in the denominator. At maximal exercise, the percent change in CardOut was <10% in both groups, but ∼33% lower in the negative curvature group. In the non-negative curvature group, the change in CardOut was nearly equal due to changes in HR and SV, whereas in the negative curvature group the SV component was essentially zero.

This tendency for lower percent change in SV near peak exercise in the negative curvature group, which also has higher fitness by several indexes, is in contrast to other studies that have shown a steady increase in SV up to maximal exercise in very well-trained individuals (4, 6, 12, 16, 22), although other investigators have shown SV plateau (1, 5, 7) even after training (3, 13). The existence of a plateau in SV near maximal exercise vs. athletic ability is thus still very much unsettled and needs more study to be completely resolved.

In our study the downward curvature in CardOut vs. V̇o_{2} was also significantly related to the curvature in HR vs. V̇o_{2}. Although classically the HR vs. V̇o_{2} relationship is considered to be linear (11, 21), several studies have documented some nonlinearity (8, 14). Hofmann et al. (8) found a downward deflection of the HR vs. work rate curve in 86% of normal subjects, with linear or upwardly curving relationships in the remainder. There was no difference in average maximal power output attained by curvature group, although they did not report V̇o_{2} data. By contrast, Pokan et al. (14) found positive curvature of HR vs. external work curves in patients with myocardial infarction, and the degree of upward deflection seemed to be related to a drop in cardiac ejection fraction at higher exercise intensities. Curvature in HR vs. V̇o_{2} could be related to a number of factors, including cardiac receptor densities or sensitivities, or the relative magnitudes of parasympathetic vs. sympathetic control of HR, both of which could vary with fitness. As with CardOut vs. V̇o_{2} relationship, the HR vs. V̇o_{2} relationship needs further study.

In the trained subject, maximal exercise is largely dictated by the ability of the working muscles to extract O_{2} (17, 20), and the maximal O_{2} extraction of working muscle may be higher than in the average fit individual because of changes related to training in the working muscles (3). Either as a result of training or in heart disease, the ability of the heart to maintain SV may become maximized to the point that the slope of the CardOut vs. V̇o_{2} relationship would become zero, which would define a true cardiac limitation to exercise. No change in CardOut with increasing V̇o_{2} could be related to either a plateau in both SV and HR, or a drop in SV near maximal exercise as HR continues to increase.

This model can explain the findings in the current cross-sectional study of a group of normal subjects. However, further support for this model is needed. In particular, it would be interesting to document changes in the shape of the CardOut, HR, and SV vs. V̇o_{2} relationships after training a group of unfit subjects. Would increasing maximal V̇o_{2}, maximal CardOut, and maximal SV cause a change in curvature in the relationships between CardOut, HR, or SV vs. V̇o_{2}? If negative curvature developed or became more pronounced, an approach to a mechanical cardiac limitation would be suggested. In addition, it would be worthwhile to study groups of patients with known cardiac limitations, such as heart failure due to either systolic or diastolic dysfunction. The shape of their CardOut vs. V̇o_{2} relationship would depend on how well the cardiac pump could increase SV as HR and venous return increase but filling time decreases. Patients may be characterized by both a reduced initial slope of CardOut vs. V̇o_{2} and by a tendency for CardOut to reach its limit at lower V̇o_{2}. Additional studies could lead to a definition of true central cardiac limitation to exercise, which would likely include some measure of curvature of the CardOut vs. V̇o_{2} relationship.

In conclusion, we have documented differences in the CardOut, HR. and SV vs. V̇o_{2} relationships in a group of healthy normal subjects. Our results suggest that, in contrast to commonly held assumptions about linearity of CardOut vs. V̇o_{2} and HR vs. V̇o_{2} curves, both of these relationships may have significant curvature. Furthermore, the degree of curvature may depend on fitness level of the subjects. Further work needs to be done to better define these relationships in subjects covering a range of athletic abilities and in patient groups.

## GRANTS

This work was supported by National Heart, Lung, and Blood Institute Grant HL-71478 and American Heart Association Grant 56051Z. The study was performed in the Mayo Clinic General Clinical Research Center, which is supported by US Public Health Service Grant M01-RR00585.

## Acknowledgments

The authors thank Kathy O'Malley, Angela Heydmann, and Minelle Hulsebus for technical assistance throughout this study. They also thank Renee Blumers for secretarial support and the subjects for their willingness to participate.

## Footnotes

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- Copyright © 2006 the American Physiological Society