European Journal of Applied Physiology

, Volume 119, Issue 2, pp 495–508 | Cite as

The “independent breath” algorithm: assessment of oxygen uptake during exercise

  • Maria Pia FrancescatoEmail author
  • Valentina Cettolo
Original Article



Reduction of noise of breath-by-breath gas-exchange data is crucial to improve measurements. A recently described algorithm (“independent breath”), that neglects the contiguity in time of breaths, was tested.


Oxygen, carbon dioxide fractions, and ventilatory flow were recorded continuously over 26 min in 20 healthy volunteers at rest, during unloaded and moderate intensity cycling and subsequent recovery; oxygen uptake (\(\dot {V}{{\text{O}}_{\text{2}}}\)) was calculated with the “independent breath” algorithm (IND) and, for comparison, with three other “classical” algorithms. Average \(\dot {V}{{\text{O}}_{\text{2}}}\) and standard deviations were calculated for steady-state conditions; non-linear regression was run throughout the \(\dot {V}{{\text{O}}_{\text{2}}}\) data of the transient phases (ON and OFF), using a mono-exponential function.


Comparisons of the different algorithms showed that they yielded similar average \(\dot {V}{{\text{O}}_{\text{2}}}\) at steady state (p = NS). The standard deviations were significantly lower for IND (post hoc contrasts, p < 0.001), with the slope of the relationship with the corresponding data obtained from “classical” algorithms being < 0.69. For both transients, the overall kinetics (evaluated as time delay + time constant) was significantly faster for IND (post hoc contrasts, p < 0.001). For the ON transient, the asymptotic standard errors of the kinetic parameters were significantly lower for IND, with the slope of the regression line with the corresponding values obtained from the “classical” algorithms being < 0.60.


The “independent breath” algorithm provided consistent average O2 uptake values while reducing the overall noise of about 30%, which might result in the halving of the required number of repeated trials needed to assess the kinetic parameters of the ON transient.


Gas exchange Signal-to-noise ratio Mean response time 



Asymptotic standard error


“Auchincloss” approach, i.e., the breath-by-breath alveolar gas-exchange algorithm according to Auchincloss et al. (1966)


Body temperature pressure saturated


“expiration-only” approach, i.e., the breath-by-breath gas-exchange algorithm that uses information obtained during expiration and the Haldane transformation (Roecker et al. 2005; Ward 2018)

FCO2, FN2, FO2

Instantaneous carbon dioxide, non-exchangeable gas at alveolar level (essentially nitrogen) and oxygen fractions


Inspired oxygen and nitrogen ambient fractions


“independent breath” approach, i.e., the breath-by-breath alveolar gas-exchange algorithm under investigation (Cettolo and Francescato 2018b)


Repeated measures multivariate analysis of variance


Mean response time of the ON and OFF kinetics, respectively


Residual sum of squares


Standard temperature pressure dry




t student value for a determined degree of freedom at a certain probability level


Time delay of the start of the ON and OFF kinetics, respectively

ti, te

Starting times of inspiration and expiration, respectively; defined on the flow trace, where flow changes direction


Start time of signal change of the ON and OFF transients, respectively, as obtained by the non-linear regression procedure


Time of the end-expiratory exchanged gas fraction, defined on the FO2 trace

t1, t2

Start and end times of the jth breath for the “independent breath” approach; defined on the FO2/FN2 trace

\(\dot {V}\)

Respiratory flow at the mouth


End-expiratory lung volume

\(\dot {V}{{\text{O}}_2}^{{{\text{IND}}}}\), \(\dot {V}{{\text{O}}_2}^{{{\text{WES}}}}\), \(\dot {V}{{\text{O}}_2}^{{{\text{AUC}}}}\), and \(\dot {V}{{\text{O}}_2}^{{{\text{EXP}}}}\)

Oxygen uptake calculated applying the “independent breath”, the “Wessel”, the “Auchincloss”, and the “expiration-only” approaches, respectively; all the data are expressed in STPD conditions

\(\dot {V}{{\text{O}}_2}^{{\text{r}}}\)

Baseline O2 uptake for the ON kinetic analysis

\(\dot {V}{{\text{O}}_2}^{{{\text{ss}}}}\)

Average steady-state O2 uptake for the OFF kinetic analysis


“Wessel” approach, i.e., the breath-by-breath alveolar gas-exchange algorithm according to Wessel et al. (1979)

\(\Delta \dot {V}{{\text{O}}_2}^{{{\text{rec}}}}\)

Fall of oxygen uptake at the end of recovery

\(\Delta \dot {V}{{\text{O}}_2}^{{{\text{ss}}}}\)

Increase in oxygen uptake at steady state


Time constant of the ON and OFF responses, respectively, as obtained by the non-linear regression procedure



Funding was provided by Università degli Studi di Udine—Dpt. of Medicine (2017).

Author contributions

CV and FMP equally contributed in conception and design of the experiments; both performed the experiments, analysed the data, and wrote the paper. Both authors read and approved the final version of the manuscript.

Supplementary material

421_2018_4046_MOESM1_ESM.doc (33 kb)
Supplementary material 1 (DOC 33 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MedicineUniversity of UdineUdineItaly

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