Mathematical modeling of trace gas exhalation kinetics

Due to its broad scope and applicability, breath gas analysis holds great promise as a versatile framework for general bio-monitoring applications and diagnostics. While sufficiently accurate and fast instrumental techniques are vital for fully exploiting this huge potential, also several methodological issues need to be addressed before breath gas analysis can become the ``new blood test``. Specifically, a crucial yet underestimated aspect of breath gas analysis concerns the blood-gas kinetics of the VOCs under scrutiny as well as their systemic distribution and physiological flow within the human body. The concentrations of blood-borne VOCs in exhaled breath are primarily influenced by: breathing patterns and pulmonary blood flow, affecting gas exchange in the alveolar space diffusion mechanisms in the conducting airways the systemic concentrations of the compound, governed by endogenous production, metabolism, and distribution. In two recent papers1,2 we have developed two mathematical models for the breath behavior of two specific VOCs, i.e., acetone and isoprene. Due to the fact that these substances reflect a relatively wide spectrum of distinct physico-chemical characteristics, the results we have obtained so far are an excellent starting point for extending the quantitative knowledge of VOC exhalation kinetics to a wider range of experimental scenarios as well as to other classes of endogenous and exogenously administered trace gases. Within the proposed project we suggest to extend the 3-compartment model for isoprene into a more detailed pharmacokinetic compartment model including, e.g., the lungs, liver, fat, richly perfused tissue, resting muscles, and working muscles. Together with the accompanying experimental investigations this is expected to provide further insights into the novel hypothesis that a peripheral (muscle) tissue group acts as an explicit extrahepatic production site of isoprene in the body, thus indicating a new metabolic pathway for this most abundant hydrocarbon in human breath. Finally, this model will be combined with our existing acetone model yielding a unified model which is intended to serve as a general mechanistic basis for quantitative VOC analyses (e.g., the estimation of endogenous production and metabolism rates or the reconstruction of blood and tissue concentrations from observable breath levels). Particularly, as a prototypic test case within a realistic clinical setting we shall apply the proposed model for real- time assessments of the anesthetic state on the basis of exhaled breath measurements. The work packages embrace several theoretical and experimental investigations for achieving this goal. Our mathematical simulation models are based on the causal physical laws of mass balance differential equations. The mathematical methods employed for that purpose include, e.g., identifiability/observability, Hermann-Krener rank criterion, multiple shooting, and sensitivity analysis. J. King, H. Koc, K. Unterkofler, P. Mochalski, A. Kupferthaler, G. Teschl, S. Teschl, H. Hinterhuber, and A. Amann: Physiological modeling of isoprene dynamics in exhaled breath, J. Theoret. Biol. 267 (2010) 626-637. J. King, K. Unterkofler, G. Teschl, S. Teschl, H. Koc, H. Hinterhuber, and A. Amann, A mathematical model for breath gas analysis of volatile organic compounds with special emphasis on acetone, J. Math. Biol 63 (2011), 959- 999.

Endogenous volatile organic compounds (VOCs) are released within the human organism either as a result of normal metabolic activity or due to pathological disorders. They enter the blood stream and are eventually metabolized or excreted via exhalation, skin emission, urine, etc. Breath sampling presents a golden opportunity for a non-invasive means of extracting information on these topics. Other advantages lie in the possibility to extract breath samples as often as desired, and in the fact that exhalation can be measured in real time, even in breath-to-breath resolution. All together, these factors render breath analysis to be an ideal choice for the purpose of obtaining ongoing information on the current metabolic and physiological state of an individual.In that process, the identification and quantification of potential disease biomarkers serve as the driving force in that analysis of exhaled breath. Moreover, future applications for medical diagnosis and therapy control with dynamic assessments of normal physiological function or pharmacodynamics are intended. Exogenous VOCs, substances that penetrate the body as a result of environmental exposure, furthermore, can be ultimately utilized to quantify body burden. Finally, breath tests are often based on the ingestion of isotopically labeled precursors, producing isotopically labeled carbon dioxide as well as the possibility of many other labeled metabolites.Yet, due to a whole host of confounding factors biasing the concentrations of volatiles in the breath, breath sampling currently stands far-removed from the ranks of standardized procedure. These factors are related to both the breath sampling protocols as well as to the complex physiological mechanisms underlying pulmonary gas exchange. Even under resting conditions, exhaled breath concentrations of VOCs can strongly be influenced by specific physiological parameters such as cardiac output and breathing patterns, depending on the physico-chemical properties of the compound under study. Understanding the influence of all these factors and harnessing their control are therefore central to achieving an accurate standardization of breath sample collection and for the correct deduction of the corresponding blood concentration levels, and ultimately paving the way for the routinization of breath sampling.In this project we developed new and extended our previously developed models and verified them experimentally. These models allow the determination of blood concentrations from their breath concentration. In addition they enable to calculate production rates and metabolic rates from breath concentration.Furthermore, in a series of investigations the knowledge on the human volatilome was extended:(i) An investigation of blood and breath volatiles quantified altogether 74 compounds occurring in both types of samples.(ii) By measuring emissions of volatile organic compounds from skin we created a databank of human-borne volatiles having a high potential as markers of human presence, which could be used for early location of entrapped victims in rescue operations during earthquakes.(iii) Finally, assessment, origin, and implementation of breath volatile cancer markers were investigated.A total of 25 articles were published in journals with high impact factors.