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. We compare our results with those obtained in recent literature.

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. In this paper we extend this investigation concerning the influence of inhaled concentrations on exhaled breath concentrations for VOCs with higher Henry constants. To this end we extend our model with an additional compartment which takes into account the influence of the upper airways on exhaled breath VOC concentrations.

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 2.5). Nighttime concentration maxima were usually recorded 2-3 h before lights on. For breath isoprene, a nocturnal increase in baseline concentrations of about 74% was observed, with individual changes ranging from 36-110%. Isoprene profiles exhibited pronounced concentration peaks, which were highly specific for leg movements as scored by tibial electromyography. Furthermore, relative to a linear trend, baseline isoprene concentrations decreased during the transition from the NREM to the REM phase of a complete sleep cycle.

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. 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 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.

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. Real-time measurements of exhaled breath under an ergometer challenge reveal characteristic changes of isoprene output in response to variations in ventilation and perfusion. Here, a valid compartmental description of these profiles is developed. By comparison with experimental data it is inferred that the major part of breath isoprene variability during exercise conditions can be attributed to an increased fractional perfusion of potential storage and production sites, leading to higher levels of mixed venous blood concentrations at the onset of physical activity. In this context, various lines of supportive evidence for an extrahepatic tissue source of isoprene are presented. Our model is a first step towards new guidelines for the breath gas analysis of isoprene and is expected to aid further investigations regarding the exhalation, storage, transport and biotransformation processes associated with this important compound.