Obligatory anaerobiosis resulting from oxygen uptake-to-blood flow ratio dispersion in skeletal muscle: a model.

We constructed a computer model whereby the dispersion of the oxygen uptake-to-blood flow ratio (VO2/Q) in working muscle could be altered around its mean level during simulated exercise. The model incorporated standard values for the cardiac output and whole-body O2 uptake responses to incremental exercise in humans. Dispersion of the VO2/Q ratio was induced by distributing Q in a Gaussian fashion around its appropriate mean value with a standard deviation (sigma). By increasing sigma, more regions of the muscle became "anaerobic" as the corresponding local muscle venous blood O2 content fell to zero; these regions thus required proportionally greater rates of lactate production to sustain the required energy transfer. The model yielded a relatively high mixed-muscle venous partial pressure of O2, suggesting that the latter may not be a sufficient indicator of whether or not there may be diffusional limitation to muscle O2 transfer during exercise or whether or not there may be anaerobic production of lactate in certain regions of exercising muscle.

Modulation of muscle and pulmonary O2 uptakes by circulatory dynamics during exercise.

The effect of cardiovascular adjustments on the coupling of cellular to pulmonary gas exchange during unsteady states of exercise remains controversial. Computer simulations were performed to assess these influences on O2 delivery and pulmonary O2 uptake (pVO2). Algorithms were developed representing muscle and "rest-of-body" compartments, connected in parallel by arterial and venous circulations to a pump-and-lungs compartment. Exercise-induced increases in VO2 and cardiac output went to the muscle compartment. Model parameters [e.g., time constants for blood flow and muscle O2 uptake (mVO2)] could be varied independently. Simulation results demonstrated that 1) the rise in pVO2 during exercise contains three phases; 2) the contribution of changes in venous O2 stores to pVO2 kinetics and the O2 deficit occur almost entirely in phase 1; 3) under a wide variety of manipulations, the kinetics of pVO2 in phase 2 were within a couple of seconds of that assigned to mVO2 (i.e., there is not an obligatory slowing of VO2 kinetics at the lungs relative to those at the muscles; 4) by use of available estimates of blood flow adjustment, O2 delivery would not limit mVO2 after exercise onset; and 5) blood flow could limit O2 delivery in recovery, if blood flow returned to base-line levels at rates similar to those during the on-transient phase.

Variables, constants, and parameters: clarifying the system structure.

This paper introduces the terminology and application of parameter estimation techniques for clarifying models of pulmonary gas-exchange control dynamics. Results are given of modeled first-order systems, and the extension of such models to higher orders is discussed with examples. It is emphasized that justification of the adequacy of a model is statistically quantifiable and must be performed before appropriate interpretation of system behavior is possible.

Model implications of gas exchange dynamics on blood gases in incremental exercise.

In humans, arterial PCO2 (PaCO2) has been demonstrated to be regulated at or near resting levels in the steady state of moderate exercise (i.e., for work rates not associated with a sustained lactic acidosis). To determine how PaCO2 might be expected to behave under the nonsteady-state conditions of incremental exercise testing, the influence of the dynamic characteristics of the primary variables that determine PaCO2 was explored by means of computer modeling. We constructed a dynamic model that utilized previously reported experimental estimates for the kinetic response parameters of ventilation (VE) and CO2 output (VCO2). In response to incremental work rate forcings, the model yielded an increase in PaCO2, which reflected the disparity between the VE and VCO2 time constants; this hypercapnic condition was maintained despite VE and VCO2 both increasing linearly with respect to the input work rate profile. The degree of hypercapnia increased with the rate of the incremental forcing, reaching 9 Torr for a 50-W/min forcing. In conclusion, therefore, sustained increases in PaCO2 during nonsteady-state incremental exercise should be interpreted with caution, because this is the predicted response even in subjects with normal ventilatory control and lung function.

Effect of interbreath fluctuations on characterizing exercise gas exchange kinetics.

Breathing has inherent irregularities that produce breath-to-breath fluctuations ("noise") in pulmonary gas exchange. These impair the precision of characterizing nonsteady-state gas exchange kinetics during exercise. We quantified the effects of this noise on the confidence of estimating kinetic parameters of the underlying physiological responses and hence of model discrimination. Five subjects each performed eight transitions from 0 to 100 W on a cycle ergometer. Ventilation, CO2 output, and O2 uptake were computed breath by breath. The eight responses were interpolated uniformly, time aligned, and averaged for each subject; and the kinetic parameters of a first-order model (i.e., the time constant and time delay) were then estimated using three methods: linear least squares, nonlinear least squares, and maximum likelihood. The breath-by-breath noise approximated an uncorrelated Gaussian stochastic process, with a standard deviation that was largely independent of metabolic rate. An expression has therefore been derived for the number of square-wave repetitions required for a specified parameter confidence using methods b and c; method a being less appropriate for parameter estimation of noisy gas exchange kinetics.

Kinetics of oxygen uptake and heart rate at onset of exercise in children.

Requirements for cellular homeostasis appear to be unchanged between childhood and maturity. We hypothesized, therefore, that the kinetics of O2 uptake (VO2) in the transition from rest to exercise would be the same in young children as in teenagers. To test this, VO2 and heart rate kinetics from rest to constant work rate (75% of the subject's anaerobic threshold) in 10 children (5 boys and 5 girls) aged 7-10 yr were compared with values found in 10 teenagers (5 boys and 5 girls) aged 15-18 yr. Gas exchange was measured breath to breath, and phases I and II of the transition and phase III (steady-state exercise) were evaluated from multiple transitions in each child. Phase I (the VO2 at 20 s of exercise expressed as percent rest-to-steady-state exercise VO2) was not significantly correlated with age or weight [mean value 42.5 +/- 8.9% (SD)] nor was the phase II time constant for VO2 [mean 27.3 +/- 4.7 (SD) s]. The older girls had significantly slower kinetics than the other children but were also found to be less fit. When the teenagers exercised at work rates well below 75% of their anaerobic threshold, phase I VO2 represented a higher proportion of the overall response, but the phase II kinetics were unchanged. The temporal coupling between the cellular production of mechanical work at the onset of exercise and the uptake of environmental O2 appears to be controlled throughout growth in children.

Does the gas exchange anaerobic threshold occur at a fixed blood lactate concentration of 2 or 4 mM?

The anaerobic threshold (theta an) is defined as the VO2 at which blood lactate concentration [lactate] begins to systematically increase (lactate "break point") during incremental exercise. Numerous studies have shown that gas exchange break points at the anaerobic threshold correlate highly (r congruent to 0.90) with the lactate break point. Recently, it has been suggested that the anaerobic threshold occurs at a fixed [lactate] of 2 mM or 4 mM. We therefore compared the gas exchange theta an to the three lactate criteria (break point, 2 mM, and 4 mM) for theta an estimation. Fourteen subjects performed an incremental cycle ergometer test. Ventilation and gas exchange were computed every 30 s. During the same 30-s intervals, venous blood was sampled for [lactate]. Four criteria were used for theta an determination: (1) systematic increase in VE/VO2, without a concomitant increase in VE/VCO2; (2) lactate break point; (3) 2 mM [lactate]; and (4) 4 mM [lactate]. Relative to the gas exchange criterion (i.e., #1), theta an was higher by 44, 280, and 1028 ml X min-1 for the three lactate criteria, respectively; the last two being significantly different (P less than 0.05). Thus, the anaerobic threshold discerned from gas exchange or the lactate break point does not correspond with a fixed, absolute [lactate] of 2 mM or 4 mM.

Parameters of ventilatory and gas exchange dynamics during exercise.

To determine the precise nonsteady-state characteristics of ventilation (VE), O2 uptake (VO2), and CO2 output (VCO2) during moderate-intensity exercise, six subjects each underwent eight repetitions of 100-W constant-load cycling. The tests were preceded either by rest or unloaded cycling ("0" W). An early component of VE, VO2, and VCO2 responses, which was obscured on any single test by the breath-to-breath fluctuations, became apparent when the several repetitions were averaged. These early responses were abrupt when the work was instituted from rest but were much slower and smaller from the 0-W base line and corresponded to the phase of cardiodynamic gas exchange. Some 20 s after the onset of the work a further monoexponential increase to steady state occurred in all three variables, the time constants of which did not differ between the two types of test. Consequently, the exponential behavior of VE, VO2, and VCO2 in response to moderate exercise is best described by a model that incorporates only the second phase of the response.

Effect of ramp slope on determination of aerobic parameters from the ramp exercise test.

The effect of ramp slope on determination of aerobic parameters from the ramp exercise test. Med. Sci. Sports Exercise, Vol. 14, No. 5, pp. 339-343, 1982. We have previously demonstrated that the four parameters of aerobic function (maximal oxygen uptake (muVO2), VO2 at the anaerobic threshold (theta an), the time constant for VO2 kinetics (tau VO2), and work efficiency (eta)) may all be determined reliably from a single test in which the work rate increases continuously at a constant rate, i.e., ramp. That study, however, utilized a single ramp slope of 50 W X min-1, which may not be appropriate for subjects with very low or very high work tolerances. We therefore studied the effect of different ramp slopes on the determination of these parameters. Ramp slopes of 20, 30, 50, and 100 W X min-1 were generated on a cycle ergometer, and each was assigned randomly to 14 healthy subjects. Ventilatory and gas exchange variables were measured breath-by-breath utilizing on-line digital computation. Ramp slopes of 20, 30, and 50 W X min-1 yielded the same values for each aerobic parameter. The 100 W X min-1 ramp yielded muVO2 and eta an values that were the same as those found for the other ramp slopes, but tau VO2 and eta could not be discerned validly from this ramp slope. We conclude that valid assessment of the four parameters of aerobic function is possible with ramp slopes between 20 and 50 W X min-1; no further information on the parameters is to be gained by prolonging the tests with ramps slower than 20 W X min-1.

Cardiac output increase and gas exchange at start of exercise.

To determine the rapidity of increased gas exchange resulting from increased cardiac output (Q) following exercise onset, subjects performed multiple rest-exercise transitions on a cycle ergometer: the early dynamics of pulmonary gas exchange were measured during 1) rhythmic breathing with ventilation kept constant at the resting level (controlled ventilation) and 2) prolonged constant airflow exhalation. With controlled ventilation, PACO2 increased and PAO2 decreased, typically beginning in the first exercise breath. After 15 s, PACO2 had increased and PAO2 decreased by 4.5-6.2 and 8.7-12.1 Torr, respectively, graded within these narrow ranges as functions of work rate (0-100 W). Exercise starting during a prolonged exhalation caused the slopes of the alveolar phases for O2 and CO2 to increase immediately or within 2-5 s following exercise onset. Work rate had little effect on the delay or the change of alveolar gas tension slope during the subsequent 10-15 s. Thus, increased gas exchange due to increasing Q occurred very rapidly following exercise onset so that it would coincide with the first or second breath of exercise in free-breathing subjects.

Breath-by-breath measurement of true alveolar gas exchange.

A method has been developed for on-line breath-by-breath calculation of alveolar gas exchange by correcting the gas exchange measured at the mouth for changes in lung gas stores. The corrections are applied to the total lung gas exchange, which is found by directly subtracting expired from inspired volume of each gas. Corrections are made for both breath-to-breath changes in lung volumes and changes in alveolar gas concentrations. The lung volume correction term has the effect of reducing the large error sensitivity of O2 exchange that has, in the past, resulted from direct determination by total lung gas exchange. Error each gas. Corrections are made for both breath-to-breath changes in lung volumes and changes in alveolar gas concentrations. The lung volume correction term has the effect of reducing the large error sensitivity of O2 exchange that has, in the past, resulted from direct determination by total lung gas exchange. Error each gas. Corrections are made for both breath-to-breath changes in lung volumes and changes in alveolar gas concentrations. The lung volume correction term has the effect of reducing the large error sensitivity of O2 exchange that has, in the past, resulted from direct determination by total lung gas exchange. Error sensitivity analysis shows that the effect of inaccuracies due to errors in measuring gas flow or gas concentrations are similar in magnitude to those in the open-circuit method that has traditionally been used. The algorithm for alveolar gas exchange has been implemented in a computer program for on-line respiratory analysis alongside the open-circuit calculation of gas exchange at the mouth that has been used in out laboratory. By use of several experimental studies, it is shown that there are very apparent breath-to-breath differences between the gas exchange measured by the two methods. During metabolic and respiratory transients, these differences often have significant influence on interpretation of the underlying physiology.