A scalar Riemann-Hilbert problem on the torus: applications to the KdV equation.

We take a closer look at the Riemann-Hilbert problem associated to one-gap solutions of the Korteweg-de Vries equation. To gain more insight, we reformulate it as a scalar Riemann-Hilbert problem on the torus. This enables us to derive deductively the model vector-valued and singular matrix-valued solutions in terms of Jacobi theta functions.

Modeling-based determination of physiological parameters of systemic VOCs by breath gas analysis, part 2.

In a recent paper (Unterkofler et al 2015 J. Breath Res. 9 036002) we presented a simple two compartment model which describes the influence of inhaled concentrations on exhaled breath concentrations for volatile organic compounds (VOCs) with small Henry constants.

Modeling of breath methane concentration profiles during exercise on an ergometer.

We develop a simple three compartment model based on mass balance equations which quantitatively describes the dynamics of breath methane concentration profiles during exercise on an ergometer. With the help of this model it is possible to estimate the endogenous production rate of methane in the large intestine by measuring breath gas concentrations of methane.

Modeling-based determination of physiological parameters of systemic VOCs by breath gas analysis: a pilot study.

In this paper we develop a simple two compartment model which extends the Farhi equation to the case when the inhaled concentration of a volatile organic compound (VOC) is not zero. The model connects the exhaled breath concentration of systemic VOCs with physiological parameters such as endogenous production rates and metabolic rates. Its validity is tested with data obtained for isoprene and inhaled deuterated isoprene-D5.

Measurement of endogenous acetone and isoprene in exhaled breath during sleep.

This explorative study aims at characterizing the breath behavior of two prototypic volatile organic compounds, acetone and isoprene, during normal human sleep and to possibly relate changes in the respective concentration time courses to the underlying sleep architecture. For this purpose, six normal healthy volunteers (two females, four males, age 20-29 years) were monitored over two consecutive nights (the first one being an adaption night) by combining real-time proton-transfer-reaction mass spectrometry measurements from end-tidal exhalation segments with laboratory-based polysomnographic data. Breath acetone concentrations increased overnight in all measurements, with an average relative change by a factor of up to 4 (median 2.

Breath gas analysis for estimating physiological processes using anesthetic monitoring as a prototypic example.

Analysis of exhaled trace gases is a novel methodology for gaining continuous and non-invasive information on the clinical state of an individual. This paper serves to explore some potential applications of breath gas analysis in anesthesia, describing a monitoring scheme for target site concentrations and cardiac output via physiological modeling and real-time breath profiles of the anesthetic agent. The rationale given here is mainly simulation-based, however, the underlying concepts are directly applicable to a routine clinical setting.

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

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.

Physiological modeling of isoprene dynamics in exhaled breath.

Human breath contains a myriad of endogenous volatile organic compounds (VOCs) which are reflective of ongoing metabolic or physiological processes. While research into the diagnostic potential and general medical relevance of these trace gases is conducted on a considerable scale, little focus has been given so far to a sound analysis of the quantitative relationships between breath levels and the underlying systemic concentrations. This paper is devoted to a thorough modeling study of the end-tidal breath dynamics associated with isoprene, which serves as a paradigmatic example for the class of low-soluble, blood-borne VOCs.