INTRODUCTION

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FOR MANY YEARS LABORATORY exercise testing has been an important tool whereby athletes could be evaluated and their progress monitored during training. Laboratory testing also forms a vital part of basic research into the physiological responses to exercise, and the control mechanisms involved in those responses.

The traditional approach to physiological systems analysis has concentrated primarily on the linear systems approach, using deterministic exercise inputs (i.e., its values as a function of future time can be predicted with accuracy). However, it is clear from the literature that the physiological (cardiorespiratory) responses to exercise do not always conform to all the assumptions and prerequisites associated with linear systems (2, 6). The ideal profile of input stimuli for physiological systems analysis and, ultimately, the ideal exercise protocol for laboratory testing purposes, will be one that overcomes both the theoretical and practical constraints of deterministic input stimuli. It should thus not assume systems linearity, and it should test the systems over their complete natural dynamic range, in terms of both amplitude and frequency.

As a first step toward defining such a stimulus profile, we set out to discover how normal trained and untrained persons choose to exercise under "natural" or "free-range" conditions. To this end we constructed an adjustable bicycle ergometer that resembled the subjects' own bicycles as closely as possible. This individualized bicycle could be "cycled" along a high-resolution simulation of an actual mountainous cycle route. The cyclist's self-imposed work rates, with resulting heart rate, minute ventilation, and O₂ uptake (O₂) and CO₂ production (CO₂) responses, were compared with the results of each subject's own standard ramp test results.

	METHODS

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Part 1: Computer Simulation of a Competition Cycling Route

The horizontal length of the ergometer, as well as the handlebar and seat height, could be adjusted to reproduce the cyclist's posture on his own bicycle. Conventional racing equipment (chainset, saddle, pedals, and so on) was used to make the cycle as comfortable as possible. An electronic gearing system, consisting of standard shift levers and secured to rotary switches, was mounted to the handlebar stem, so that the cyclist had a selection of 10 gear ratios. The pedal cadence (rpm) was shown on a liquid crystal display fitted to the handlebars. The ergometer could produce work rates of up to 580 W; this has been shown to cover the work rates typically encountered during prolonged exercise testing (3).

Calibration of the cycle ergometer. The calibration unit consists of a 750-W series motor, which drove the pedal crankshaft of the ergometer via a reduction gearbox, a torque transducer, and an optical sensor to measure the cadence (rpm). Torque in the coupling shaft was measured by four strain gauges and amplified by an instrumentation amplifier that was mounted on, and rotated with, the shaft. Power to the amplifier, as well as the amplifier-output signal, was assessed via four carbon brushes and brass sliprings on the shaft. Torque readings were then taken at 60, 80, and 100 rpm throughout the power-output range, and the calibration curve was then constructed from the results. It is important to note that the ergometer has no flywheel, which allows for rapid changes in work rate. The ergometer was therefore linear over the specific frequency range (0-1 Hz).

Simulation of free-range cycling. When cycling is performed on the road, three major factors influence the power that must be produced by the cyclist: 1) the speed at which the cyclist is traveling; 2) the slope of the road; and 3) aerodynamic, rolling, and frictional resistance (7, 8). A bidirectional serial (RS232) communication interface between the ergometer and a personal computer was designed to monitor and simulate these three factors at a rate of 0.5 Hz.

(1)

View larger version (18K): [in this window] [in a new window]   Fig. 1.   Diagrammatic illustration of calculation of cycling speed. 1 and 2, Angular velocity of rear and front wheel (rad/s), respectively; n1 and n2, no. of teeth on wheel and crank sprockets, respectively.

(2)

View larger version (19K): [in this window] [in a new window]   Fig. 2.   Gravitational forces acting on cylist during uphill () and downhill ( and dashed line) cycling, where m is mass of bicycle (kg), M is mass of cyclist (kg), g is gravitational acceleration (9.8 m/s2), F is force component, and  is slope of road (°).

(3)

(4)

(5)

View larger version (13K): [in this window] [in a new window]   Fig. 3.   Power-speed relationship for 1° uphill (line A), flat surface (line B), and 1° downhill (line C). D, terminal speed.

Part 2: Power Distribution

During the load-incremented test, subjects were instructed to maintain a constant pedal frequency of 80 rpm. After a 3-min period of unloaded cycling (the warm-up period), the first exercise stage was performed against "zero" resistance, after which the work rate was increased by 20 W every 60 s until the subject could no longer maintain a pedaling frequency above 70 rpm despite verbal encouragement. The ventilatory threshold (VT) was derived by the V-slope method by using plots of O₂ and CO₂ (1), where VT was defined as the nonlinear breakpoint in CO₂ relative to the rise in O₂.

During the free-range exercise test, subjects were instructed to

select an intensity that you prefer, and cycle at a comfortable speed. This should be an intensity that you would choose for a 40 minute workout on the road and it should be an intensity that feels appropriate for you. You are permitted to change both the pedal cadence and gear ratio at will.

All experiments were performed indoors, under controlled, uniform environmental conditions: temperature, 21 ± 1°C; relative humidity, 54 ± 2%; and barometric pressure, 101-102 kPa. A fan provided airflow (and thus body cooling) from the front.

	RESULTS

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Dynamic Input Stimulus

View larger version (29K): [in this window] [in a new window]   Fig. 4.   Power and distance traveled during 40-min free-range exercise test in relation to slope of route for experienced (A, top and bottom, respectively) and recreational cyclist (B, top and bottom, respectively). Horizontal line, work rate at cyclist's ventilatory threshold, as determined by load-incremented exercise test.

As the work rate did not reflect the course profile in any obvious way, we determined whether the variations in the generated work rate of each subject were randomly distributed around the mean value. To this end we performed two statistical tests for randomness: 1) an even randomness test (4), in which the number of runs (sequential sets of data points) was calculated so that the work rate remained completely above or completely below the mean work rate value (calculated over a period of 40 min) for an individual subject; and 2) a Gaussian distribution test. A P < 0.05 indicated that the null hypothesis for a random distribution could not be accepted.

The P values of both the even randomness tests for the variation in work rate and those for the random Gaussian distribution tests were (for all the subjects) highly significant (P < 0.001), indicating that the distribution of work rates around the mean work rate for each cyclist was not random, or Gaussian.

To test whether the stimulus profile resembled white noise, or a possible chaotic (so-called "1/f") signal, where f is frequency, the power spectral density of the generated work rate was calculated. The spectral exponent  was calculated for each subject as the slope of the graph on a log-log plot of the power spectral density of the generated work rate (Fig. 5). The independent variable in this plot was the frequency content of the work rate signal. The dependent variable was the work rate generated by the cyclist. This indicated whether the variability of the generated work rate corresponded to band-limited Gaussian white noise (i.e., equal power at all frequencies) or whether the data had a typical 1/f distribution, indicative of chaos.

View larger version (21K): [in this window] [in a new window]   Fig. 5.   Power spectral density of generated work rate during free-range exercise test for experienced (A) and recreational cyclist (B).

The spectral exponents of the generated work rate ranged between 0.496 and 0.824 (Table 1), indicating that the generated work rate did not conform to Gaussian white noise (in which case  = 0) but tended toward 1/f  noise ( = 1). In all cases, the spectral exponents were significantly different from zero and one (P < 0.05).

Our results therefore indicate that the nature of the exercise input (the generated work rate) was neither random, nor periodic, nor steady, nor Gaussian white noise. Rather, the stimulus profile may be best described as stochastic in nature.

Frequency Distribution of the Generated Work Rate

Figure 5 shows the power spectral density of the generated work rate for the two representative subjects. Although all frequencies do not have equal power weighting, as in the case of band-limited Gaussian white noise, the stimulus profile that resulted from this study (in which each subject generated his own work rate) excited the physiological system over a wide range of frequencies (0-1 Hz). It is possible that the stimulus profile excited the system over a range wider than 0-1 Hz, but, because of the sampling frequency, input and response frequencies >1 Hz could not be analyzed in this study.

Amplitude Distribution of the Generated Work Rate

View larger version (36K): [in this window] [in a new window]   Fig. 6.   Power-output distribution during load-incremented and free-range exercise test for experienced (A, i and ii, respectively) and recreational cyclist (B, i and ii, respectively). Frequency, no. of data points.

During spontaneous free-range exercise, therefore, the physiological systems were challenged over a substantially wider range of work rates than during the forced incremental (ramp) exercise.

	DISCUSSION

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We have shown that "free" dynamic exercise can be readily simulated in the laboratory environment. If the equation relating the power, velocity, and surface gradient is known, a closed-loop configuration can be implemented to accommodate the simulation. Although we simulated a known cycling route (renowned for its mountainous profile), an entirely artificial route could also be generated and implemented.

Because an electromagnetically braked cycle ergometer was used, it was impossible to simulate downhill cycling below the terminal velocity (Fig. 3). Therefore, whenever the cycling velocity was below the terminal velocity, the work rate was set to zero. Although this might appear to be a shortcoming of the simulation, cyclists (by nature of their bicycles) are never exposed to "negative work" while cycling in a real-life situation. They can either freewheel downhill or try to exceed the terminal velocity (i.e., do positive work on the downhill stretches of the route). The only artificiality of the simulation in this respect was that the subjects were forced to do at least 60 W of positive work on the downhill stretches of the route.

When cyclists engage in noncompetitive free-range exercise, they spend a substantial proportion of time at levels that are above their VT. This finding is in accordance with those of Loftin and Warren et al. (10), who grouped cyclists by ventilatory threshold and found that, during a 16.1-km simulated time trial, both the high-VT [77 ± 4.0 (SD) % of maximal O₂ (O_{2 max})] and the low-VT (68 ± 2.8% of O_{2 max}) groups exercised at a percentage of O_{2 max} that was 12 and 14% above their respective ventilatory thresholds.

In contrast to the progressive, incremental (ramp) exercise test, which was limited to a narrower power range (60-440 W), the free-range exercise test was found to excite the physiological systems over a broader range of work rates (60-580 W), irrespective of the individual's athletic ability (competitive or recreational). The free-range exercise input thus covered both the high and low work rates in every subject. It should be noted that what is regarded as the "input signal" in this discussion is the individual's work rate, which, in the free-range exercise test, was determined by the individual himself (i.e., it was not externally imposed on the subject).

Although the subjects were instructed to cycle at "their own comfortable rate," the input signal in all cases spanned a wide frequency range (0-1 Hz) and thus would be suitable for the identification of both high- and low-frequency behavior of the physiological control systems during exercise. The input signal (the generated work rate) did not, however, comply with the strict mathematical requirements of a Gaussian white-noise signal. Thus, although the input signal covered the complete working range and frequency distribution of the physiological system during free-range exercise, the power spectral density analysis (Fig. 5) showed that all the frequencies did not have equal power weighting. Furthermore, although the work rate changed continuously and fluctuated in an apparently unpredictable manner around the mean value, statistical analysis showed that the stimulus profile was not randomly distributed. This imperfection in the mathematical characteristics of the input signal precludes the use of known nonparametric system identification techniques, such as the white-noise approach (11, 13) and the cross-correlation technique of kernel estimation (9). Future studies might be able to refine the input signal and develop an appropriate white-noise input. Alternatively, the analysis techniques could be adapted to cope with the physiological realities of exercise.

An interesting observation was the fact that the generated work rate showed power law behavior, which is generally associated with complex dynamical systems. This can be seen from the 1/f-like power spectrum, where spectral exponent  ranged from 0.496 to 0.824 (Table 1). Thus the generated work rate lies somewhere between white noise ( = 0) and 1/f noise ( = 1). In general, systems that exhibit 1/f-like power spectra are described as having a fractal or chaotic nature, which implies that, although the data look noisy and totally lack repetition, there is a definite deterministic pattern embedded within it. The cyclists' work rates under noncompetitive circumstances were thus found to have a 1/f-like power spectrum, which thus must be considered the physiological response to free-style exercise. This finding is not surprising, because it has recently been shown that normal gait is also associated with a 1/f-like spectrum, with  in the range 0.83 ± (SD) 0.23 (5).

Although it is not possible to measure work rate very easily in the field, there are published results of heart rate variations during the actual cycle race. Palmer et al. (12) have shown that these heart rate variations also appeared to be chaotic and were exactly similar to the heart rate changes when our subjects cycled the simulated route. We therefore presume that, during the simulation, the other variables (O₂, CO₂, minute ventilation, and so on), including work rate, closely mimic those that would be obtained in the field. Hence, we conclude that the simulation is a more complex stimulus than the "artificial" profiles typically used.

Although the input signal of the free-range exercise test (the generated work rate of the individual subject) has mathematical imperfections, it allows for a comprehensive analysis of many physiological responses to exercise in a relatively short-duration test. There is also no requirement to induce or coerce the subjects to exercise to exhaustion. They spontaneously exercise to produce work rates in excess of those encountered in traditional tests, without becoming "exhausted" or being unable to complete the test. We believe that this technological innovation has opened the way to a new, scientifically valid, and technically feasible method for investigating the physiological responses to exercise and their control mechanisms.