Journal of Mathematical Biology

, Volume 63, Issue 5, pp 959–999 | Cite as

A mathematical model for breath gas analysis of volatile organic compounds with special emphasis on acetone

  • Julian King
  • Karl Unterkofler
  • Gerald Teschl
  • Susanne Teschl
  • Helin Koc
  • Hartmann Hinterhuber
  • Anton AmannEmail author


Recommended standardized procedures for determining exhaled lower respiratory nitric oxide and nasal nitric oxide (NO) have been developed by task forces of the European Respiratory Society and the American Thoracic Society. These recommendations have paved the way for the measurement of nitric oxide to become a diagnostic tool for specific clinical applications. It would be desirable to develop similar guidelines for the sampling of other trace gases in exhaled breath, especially volatile organic compounds (VOCs) which may reflect ongoing metabolism. The concentrations of water-soluble, blood-borne substances in exhaled breath are influenced by: (i) breathing patterns affecting gas exchange in the conducting airways, (ii) the concentrations in the tracheo-bronchial lining fluid, (iii) the alveolar and systemic concentrations of the compound. The classical Farhi equation takes only the alveolar concentrations into account. Real-time measurements of acetone in end-tidal breath under an ergometer challenge show characteristics which cannot be explained within the Farhi setting. Here we develop a compartment model that reliably captures these profiles and is capable of relating breath to the systemic concentrations of acetone. By comparison with experimental data it is inferred that the major part of variability in breath acetone concentrations (e.g., in response to moderate exercise or altered breathing patterns) can be attributed to airway gas exchange, with minimal changes of the underlying blood and tissue concentrations. Moreover, the model illuminates the discrepancies between observed and theoretically predicted blood-breath ratios of acetone during resting conditions, i.e., in steady state. Particularly, the current formulation includes the classical Farhi and the Scheid series inhomogeneity model as special limiting cases and thus is expected to have general relevance for a wider range of blood-borne inert gases. The chief intention of the present modeling study is to provide mechanistic relationships for further investigating the exhalation kinetics of acetone and other water-soluble species. This quantitative approach is a first step towards new guidelines for breath gas analyses of volatile organic compounds, similar to those for nitric oxide.


Breath gas analysis Volatile organic compounds Acetone Modeling 

Mathematics Subject Classification (2000)

92C45 92C35 93C10 93B07 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Julian King
    • 1
  • Karl Unterkofler
    • 1
    • 2
  • Gerald Teschl
    • 3
  • Susanne Teschl
    • 4
  • Helin Koc
    • 2
  • Hartmann Hinterhuber
    • 5
  • Anton Amann
    • 1
    • 6
    Email author
  1. 1.Breath Research Institute, Austrian Academy of SciencesDornbirnAustria
  2. 2.Vorarlberg University of Applied SciencesDornbirnAustria
  3. 3.Faculty of MathematicsUniversity of ViennaViennaAustria
  4. 4.University of Applied Sciences Technikum WienViennaAustria
  5. 5.Department of PsychiatryInnsbruck Medical UniversityInnsbruckAustria
  6. 6.University Clinic for AnesthesiaInnsbruck Medical UniversityInnsbruckAustria

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