Relationships between mechanical power, O₂ consumption, O₂ deficit and high-energy phosphates during calf exercise in humans

Abstract

Whole-body O₂ uptake (V̇O₂), O₂ deficit and the concentration of high-energy phosphates (determined by ³¹P spectroscopy) in human calf muscle were measured during moderate aerobic square-wave exercise of increasing intensity in ten volunteers. Net V̇O₂ (above resting) increased linearly with mechanical power, yielding a delta efficiency of 13.1%. "Gross" O₂ deficit increased linearly with net V̇O₂. The fraction of phosphocreatine (PC) split at steady state increased linearly with the mechanical power and with the O₂ deficit. If the [PC] in resting muscle is known, the slope of the regression between PC split and O₂ deficit (in millimoles) yields the P/O₂ ratio. To calculate this, the O₂ deficit was corrected for the amount of O₂ derived from the body stores, as obtained from literature data. The value so obtained, for a resting [PC] of 30 mM was 5.9, consistent with canonical textbook values. Furthermore, the ratio of "true" O₂ deficit to steady-state V̇O₂ is a measure of the time constant of V̇O₂ kinetics at work onset at the muscle level: assuming a monoexponential time course without time delays it amounted to about 17 s, close to the value that can be expected in mammalian muscle at 37 °C.

Appendix

As a first approximation, during aerobic exercise of moderate intensity, the O₂ uptake (V̇O₂) at the onset of exercise is a monoexponential function of time:

$$ \mathop V\limits^\cdot {\rm{O}}_{\rm{2}} \left( t \right) = \mathop V\limits^\cdot {\rm{O}}_{\rm{2}}^{\rm{r}} + \Delta \mathop V\limits^\cdot {\rm{O}}_{\rm{2}}^{\rm{s}} \cdot \left( {1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\tau _{\rm{m}} }}} \right. \kern-\nulldelimiterspace} {\tau _{\rm{m}} }}} } \right) $$

where V̇O₂ ^r and ΔV̇O₂ ^s are the resting and the net steady-state V̇O₂, respectively and τ_m is the time constant of the process, as measured at the mouth. The O₂ deficit (grossO₂ ^def) incurred at the onset of exercise can thus be calculated as:

$$ {\rm grossO}_{\rm 2}^{{\rm def}} = \int_0^\infty {\Delta \mathop V\limits^\cdot {\rm O}_{\rm 2}^{\rm s} \cdot e^{ - t/\tau _{\rm m} } {\rm }} \;{\rm d}t{\rm } = {\rm }\Delta \mathop V\limits^\cdot {\rm O}_{\rm 2}^{\rm s} \cdot \tau _{\rm m} $$

Thus, the slope of the regression of ΔV̇O₂ ^s on O₂ deficit is the time constant of O₂ uptake kinetics at the mouth. In all subjects, the individual regressions between grossO₂ ^def and ΔV̇O₂ ^s were characterized by r>0.980 (n=3) and the average τ_m was 41.8 s (see Fig. 3, solid dots). At the onset of moderate aerobic exercise below the anaerobic threshold, the grossO₂ ^def is covered by the net O₂ deficit, i.e. the amount of energy in O₂ equivalents derived from PC splitting (O₂ ^def), plus the amount of O₂ derived from the body stores (ΔO₂S), i.e.: grossO₂ ^def=O₂ ^def+ΔO₂S. Thus, a prerequisite for the calculation of the net O₂ deficit (O₂ ^def) is knowledge of ΔO₂S.

For all subjects and trials, we therefore estimated the changes of whole-body O₂ stores. These comprise mainly the amounts of O₂: i) contained in the lungs, ii) contained in the venous blood and iii) bound to muscle myoglobin [11, 12, 14]. Thus, the corresponding changes during the rest-to-work transients, or vice versa, yield the amount of O₂ consumed by the muscles at work onset, but not "seen" at the mouth, or taken up at the mouth at work offset, but not consumed by the muscle.

The changes in the pulmonary oxygen stores (ΔO₂S^p) can be estimated from the difference between the time constant of V̇O₂ measured at the mouth (τ_m) and that measured at the alveolar level (τ_p):

$$ \Delta {\rm{O}}_{\rm{2}} {\rm{S}}^{\rm{p}} {\rm{ = }}\Delta \mathop V\limits^\cdot {\rm{O}}_{\rm{2}}^{\rm{s}} \cdot {\rm{(}}\tau _{\rm{m}} - {\rm{ }}\tau _{\rm{p}} {\rm{) }} $$

According to McCreary et al. [26] the time constant of the O₂ consumption adjustment at the onset of calf exercise, calculated at the alveolar level on a breath by breath basis, is 41.9 s (ignoring the highest value reported by those authors). However, according to Cautero et al. [10] the algorithms of Beaver et al. [4], used in [26], over-estimate the time constant of the alveolar kinetics by about 10 s. Thus, we assumed that the time course of V̇O₂ at alveolar level was described by a monoexponential function with τ_p=31.9 s, a value essentially equal to the 34.3 s obtained at the alveolar level during cycloergometer exercise [10]. The individual ΔO₂S^p values were then calculated from ΔV̇O₂ ^s and the difference between the individual τ_m and τ_p=31.9 s and are reported in Table 2 for the three exercise conditions.

The changes in the venous blood stores (ΔO₂S^v) can be estimated from the product of the venous blood volume (VBV) and the change between the arterio- to mixed venous blood oxygen difference at steady state: [Δ(C _a−C _v̄)^s] and that prevailing at rest [Δ(C _a−C _v̄)^r], i.e.:

$$ \Delta {\rm{O}}_{\rm{2}} {\rm{S}}^{\rm{v}} = \left[ {\Delta (C_{\rm{a}} - C_{\overline {\rm{v}} } )^{\rm{s}} - \Delta \left( {C_{\rm{a}} - C_{\overline {\rm{v}} } } \right)^{\rm{r}} } \right] \cdot {\rm{VBV}} = \left[ {\left( {{{\mathop V\limits^\cdot {\rm{O}}_{\rm{2}}^{\rm{s}} } \over {\mathop {Q^{\rm{s}} }\limits^\cdot }}} \right) - \left( {{{\mathop V\limits^\cdot {\rm{O}}_{\rm{2}}^{\rm{r}} } \over {\mathop {Q^{\rm{r}} }\limits^\cdot }}} \right)} \right] \cdot {\rm{VBV }} $$

where Q ^̇s and Q ^̇r are the cardiac outputs at steady-state during exercise and at rest, respectively. VBV was assumed to be 65% of the total blood volume, in turn assumed to represent (in litres) 7% of body mass (in kilograms) [36]. Q ^̇ corresponding to the individual mechanical powers investigated in the present work was estimated from the data for calf exercises similar to the present ones [8]. This allowed us to determine the linear relationship between Q̇ (litres/minute) and mechanical power (W^s, watt) as: Q̇=0.40W^s+5.84 (n=5, r ²=0.945). Thus, the individual ΔO₂S^v values were obtained from the appropriate V̇O₂ and Q̇ values, the latter being derived from the corresponding mechanical power on the basis of the above equation. They are reported in Table 2 for the three exercise conditions.

The myoglobin desaturation for exercise intensities comparable to those of the present work was estimated from the data reported in [27]. These allowed us to calculate the relationship between percentage deoxymyoglobin (%deoxyMb) and mechanical power (W^s): %deoxyMb=2.09W^s+14.2 (n=4, r ²=0.968). Subsequently, knowing the individual mass of the plantar flexors (PF) and assuming a myoglobin concentration of 4.46 g/kg wet muscle [25] and a binding capacity of 1.34 mlO₂/g myoglobin, it was possible to estimate the extra amount of oxygen released by myoglobin desaturation changes from rest to exercise (ΔO₂S^m) as: ΔO₂S^m=(2.09·W^s/100)·4.46·1.34·(PF mass). The net or true oxygen deficit was finally estimated for any given work load by subtracting the three changes in oxygen stores from the whole-body oxygen deficit: O₂ ^def=grossO₂ ^def−ΔO₂S^p−ΔO₂S^v−ΔO₂S^m. The individual ΔO₂S^m and O₂ ^def values are also reported in Table 2 for the three exercise conditions.