Other International Project
Project duration: 01/2013  12/2014
Principal investigator (IMS SAS): Doc. RNDr. Viktor Witkovský, CSc.
Cooperating institutions: Breath Research Institute Dornbirn, Austria
Isoprene is one of the most abundant volatile compounds in exhaled breath. It can be measured in realtime, even in breathtobreath resolution. The periphery of the human body can be depleted from isoprene by exertion of effort. Resynthesis of isoprene and complete replenishment of the isoprene stores takes about 2h. Hence the synthesis rate of isoprene can be measured noninvasively through analysis of exhaled breath.In the present project, the isoprene concentration is modeled by a 3compartment model, consisting of a richly perfused tissue compartment, a peripheral compartment and an alveolar compartment. Isoprene is produced and metabolized in the richly perfused tissue and the peripheral compartment.Two different methodologies will be employed to determine the synthesis rates of isoprene:
 Offline simulation using a “multiple shooting” technique for inverse parameter identification.
 Online simulation using, e.g., Kalman filtering.
A main focus will be on determination of the confidence intervals for the production and metabolization rate of isoprene. For the online simulation, we envisage a 7dimensional Kalman statespace, consisting of the isoprene concentrations in the three compartments. A main task will be to find optimal choices of the process noise and the measurement noise, so that the convergences of the error covariance matrices is fast (in terms of the number of time steps).The cooperation between our institutes (the Institute of Measurement Science and the Breath Research Institute) is excellent and fruitful. The Austrian partner (Breath Research Unit of the Austrian Academy of Sciences) has the expertise to perform realtime measurements of isoprene in exhaled breath and the Slovak partner (Institute of Measurement Science, Slovak Academy of Sciences Bratislava) has experience with modeling and with the tools to determine the statistical uncertainty of identified parameters.
Isoprene is a particularly interesting volatile compound, since it is a
byproduct of cholesterol metabolism. It has a relatively high
concentration in breath (around 100 partsperbillion ppb) and can be
measured in realtime, even in breathtobreath resolution. Figure 2
shows an experimental setup for such a realtime measurement developed
at the Breath Research Institute of the Austrian Academy of Sciences.
Breath is sampled from a person on a stationary bicycle through a mask
and analyzed by a protontransferreaction mass spectrometer (PTRMS,
right part of the Figure). Medical parameters such as ECG and cardiac
output are measured by a socalled "task force monitor" (CNSystems,
Graz, Austria).
The objectives of the project have been successfully achieved. In the first year of the project (2013), research and solution focused primarily on the study of problems of modeling of synthesis of isoprene in the human body and the appropriate algorithms for such an analysis in MATLAB. In the course of the project we were carried out experiments in the partner's laboratory (Breath Research Institute, Dornbirn) and obtained continuous measurements of the concentration levels of isoprene under load and when released by PTRTOFMS.
In the second year (2014) research was focused on the development of statistical methods for analysis of the dynamic synthesis of isoprene, depending on other explanatory variables (e.g. cardiac output, volume of exhaled gases, etc.) based on linear and/or nonlinear regression models, random effects model, as well as methods to analyze data using dynamic compartment models. Continued research on methods for calibration, uncertainty analysis and a computing the confidence intervals for the model parameters, as e.g. the rate of synthesis and metabolism. Great efforts was concentrated on development of the appropriate and stable algorithms for parameter estimation in the considered compartmental models (including methods and algorithms for estimating the parameters of a model based on linear combinations of exponential curves used to model the state of equilibrium).
Several PhD students and young researchers have been involved in the project, e.g.: A. Filipiak, W. Filipiak, C. Ager (D), J. King (D) T. Ludescher (D), V. Ruszanyi Chvosteková M., J. Jakubik (D).
Publications:
 JAKUBÍK, J.: Linear mixed models for genomewide association studies. In: Cocherová, E., Púčik, J., editors, YBERC 2014, Proceedings of the 6th International Young Biomedical Engineers and Researchers Conference. Bratislava, July 24, 2014, 2014, 160163. FEI STU Bratislava.
 KÖNING, R.  WIMMER, G.  WITKOVSKÝ, V.: Ellipse fitting by nonlinear constraints to demodulate quadrature homodyne interferometer signals and to determine the statistical uncertainty of the interferometric phase. Measurement Science and Technology 25(Number 11, November 2014 ), 2014, 115001 (11pp), doi:10.1088/09570233/25/11/115001.
 WITKOVSKÝ, V.: On the exact twosided tolerance intervals for univariate normal distribution and linear regression. Austrian Journal of Statistics 43(34), 2014, 279292.
 WITKOVSKÝ, V.: Poznámky o niektorých výpočtových aspektoch tradičných testov o pevných a náhodných efektoch v lineárnych zmiešaných modeloch. In: ROBUST 2014, 18. zimná škola JČMF. Jetřichovice, Česká republika, 19.1.  24.1. 2014, 2014.
 WITKOVSKÝ, V.: Statistical inferences in linear mixed models based on the Henderson's mixed model equations. In: LŠB 2014, XX. letní škola biometriky Biometrické metody a modely v současné vědě a výzkumu. Slavonice, ČR, august, 1821, 2014.
 WITKOVSKÝ, V.  ARENDACKÁ, B.: Henderson's iterative REML estimation under heteroscedasticity. In: MATHMET 2014 International Workshop on Mathematics and Statistics for Metrology, 275. PTBSeminar, PTB Berlin. Berlin, Germany, March, 2426, 2014.
 WITKOVSKÝ, V.  WIMMER, G.  AMANN, A.: Statistical methods for exhaled breath analysis based on linear mixed models. In: BREATH 2014, 8th International Conference on Breath Research & Cancer Diagnosis. Toruń, Poland, July, 69, 2014, 2014.
 WITKOVSKÝ, V.  WIMMER, G.  DUBY, T.: Logarithmic Lambert W × F random variables for the family of chisquared distributions and their applications. Statistics & Probability Letters 96, 2015, 223231.
