# Assessing breath-by-breath alveolar gas exchange: is the contiguity in time of breaths mandatory?

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## Abstract

### Purpose

A new algorithm is illustrated for the determination of breath-by-breath alveolar gas exchange that neglects the contiguity in time of breaths, i.e. it allows the breaths to be partially superimposed or disjoined in time.

### Methods

Traces of oxygen, carbon dioxide fractions, and ventilatory flow were recorded continuously over 20 min in 15 healthy subjects in resting conditions; at 5-min intervals, subjects voluntarily hyperventilated for ~ 30 s to induce abrupt changes in lung gas stores. Gas exchange data were calculated applying the new algorithm and were compared to those yielded by a reference algorithm, also providing values at the alveolar level.

### Results

Average O_{2} uptakes (*V*′O_{2}) obtained with the two algorithms were similar during quiet breathing (0.28 ± 0.06 vs. 0.29 ± 0.06 L/min; two-sided paired *t* test, *n* = 45, *p* = NS); during hyperventilation, average *V*′O_{2} was significantly lower applying the new algorithm compared to the reference algorithm (0.57 ± 0.15 vs. 0.65 ± 0.17 L/min; difference − 0.077 ± 0.048 L/min; two-sided paired *t* test, *n* = 45, *p* < 0.001). The first breath of each hyperventilation manoeuvre showed the greatest difference in *V*′O_{2} (− 0.25 ± 0.23 L/min, *z* test against zero, *n* = 45, *p* < 0.001). The volumes of O_{2} considered twice (or neglected) because of the lack of contiguity of breaths were overall small (maximum of 3 mL) and, if accounted for, had only a slight softening effect on the fluctuations of the O_{2} uptake.

### Conclusion

The new algorithm, which assumes each breath as the leading subject, was able to effectively account for changes in lung gas stores without requiring any predetermined value or off-line optimisation procedure.

## Keywords

Oxygen uptake Respiratory cycle Hyperventilation## Abbreviations

- BbB
Breath-by-breath

*b*_{f}Breath frequency

- BTPS
Body temperature pressure saturated

- ELV
End-expiratory lung volume that matched breath-by-breath changes in end-expiratory measurements so as to minimize the breath-by-breath variation, according to the approach proposed by Swanson and Sherrill (1983) and defined by the authors as “nominal effective lung volume”

- FCO
_{2}, FN_{2}, FO_{2} Instantaneous carbon dioxide, non-exchangeable gas at alveolar level (essentially nitrogen) and oxygen fractions

- IND
“Independent breath” approach, i.e. the breath-by-breath alveolar gas exchange algorithm under investigation

- MANOVA
Repeated measures multivariate analysis of variance

- STPD
Standard temperature pressure dry

- SW
“Swanson’s” approach, i.e. the breath-by-breath alveolar gas exchange algorithm taken as reference

*t*Time

*t*_{i},*t*_{e}Starting times of inspiration and expiration, respectively; defined on the flow trace where flow changes direction

*t*_{x}Time of the end-expiratory exchanged gas fraction, defined on the FO

_{2}(or FCO_{2}) trace*t*_{1},*t*_{2}Start and end times of the

*j*-th breath for the “independent breath” approach; defined on the FO_{2}/FN_{2}(or FCO_{2}/FN_{2}) trace- \(\dot {V}\)
Respiratory flow at the mouth

- \(\dot {V}E\)
Ventilation, in STPD conditions

*V*_{L}End-expiratory lung volume

- \(\dot {V}{\text{O}}_{2}^{{{\text{IND}}}}\)
Oxygen uptake calculated applying the “independent breath” approach, in STPD conditions

- \(\dot {V}{\text{O}}_{2}^{{{\text{SW}}}}\)
Oxygen uptake calculated applying the “Swanson's” approach, in STPD conditions

*V*_{T}Tidal volume, in STPD conditions

## Notes

### Acknowledgements

We thank the Cortex GmbH (Liepzig, Germany) company for having provided us with the metabolic unit. Cortex GmbH, however, was not involved in the study design, data collection, analysis or interpretation. We thank Dr. Petra Golja (University of Ljubljana) for helpful discussion and revision of the manuscript.

### Author contributions

Experimentation was carried out at the Human Exercise Physiology laboratory of the Department of Medicine, University of Udine (Italy). CV and FMP equally contributed in conception and design of the work; both performed the experiments, analysed the data and interpreted them; FMP drafted the paper. Both authors read and approved the final version of the manuscript. CV and FMP agree to be accountable for all aspects of the work. All persons designated as authors qualify for authorship, and all those who qualify for authorship are listed.

### Funding

This work was supported by funding of the Department of Medicine of the University of Udine to Dr. M.P. Francescato.

### Compliance with ethical standards

### Conflict of interest

Valentina Cettolo and Maria Pia Francescato had no competing interests.

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