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 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 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, it is deduced that measured end-tidal breath concentrations of acetone determined during resting conditions and free breathing will be rather poor indicators for endogenous levels. Particularly, the current formulation includes the classical Farhi and the Scheid series inhomogeneity model as special limiting cases.Comment: 38 page

Global stability of enzymatic chain of full reversible Michaelis-Menten reactions

International audienceWe consider a chain of metabolic reactions catalyzed by enzymes, of reversible Michaelis-Menten type with full dynamics, i.e. not reduced with any quasi- steady state approximations. We study the corresponding dynamical system and show its global stability if the equilibrium exists. If the system is open, the equilibrium may not exist. The main tool is monotone systems theory. Finally we study the implications of these results for the study of coupled genetic-metabolic systems

Geostatistical modeling of the spatial variability of arsenic in groundwater of southeast Michigan

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94929/1/wrcr10188.pd

The stochastic SI model with recruitment and deaths I. comparison with the closed SIS model

We compare the stochastic and deterministic version of an SI model with recuitment, background deaths, and deaths due to the disease. For the stochastic version, analysis of the mean number of susceptibles, m, and infecteds, m, and of the means of conditioned on nonextinction of the infection, m* and m*, shows that (1) if R0 [les] 1, the disease dies out monotonically for the deterministic and stochastic models, and (2) if R0 > 1, the disease dies out early with a probability close to (1/R0)a, where a is the number of infecteds introduced, or m rises to a peak and then dies out slowly. For small populations N, the peak is an obvious maximum. If N [ges] 100, the peak in m is hidden in a long, nearly stationary plateau and m* is close to the deterministic endemic level for a large range of parameter values. The analytical results are illustrated with simulations. The results for the SI model are motivated by and compared with the corresponding results for the closed SIS model.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30586/1/0000223.pd

Global, local and focused geographic clustering for case-control data with residential histories

BACKGROUND: This paper introduces a new approach for evaluating clustering in case-control data that accounts for residential histories. Although many statistics have been proposed for assessing local, focused and global clustering in health outcomes, few, if any, exist for evaluating clusters when individuals are mobile. METHODS: Local, global and focused tests for residential histories are developed based on sets of matrices of nearest neighbor relationships that reflect the changing topology of cases and controls. Exposure traces are defined that account for the latency between exposure and disease manifestation, and that use exposure windows whose duration may vary. Several of the methods so derived are applied to evaluate clustering of residential histories in a case-control study of bladder cancer in south eastern Michigan. These data are still being collected and the analysis is conducted for demonstration purposes only. RESULTS: Statistically significant clustering of residential histories of cases was found but is likely due to delayed reporting of cases by one of the hospitals participating in the study. CONCLUSION: Data with residential histories are preferable when causative exposures and disease latencies occur on a long enough time span that human mobility matters. To analyze such data, methods are needed that take residential histories into account

Modeling and analyzing HIV transmission: the effect of contact patterns

A compartmental model is presented for the spread of HIV in a homosexual population divided into subgroups by degree of sexual activity. The model includes constant recruitment rates for the susceptibles in the subgroups. It incorporates the long infectious period of HIV-infected individuals and allows one to vary infectiousness over the infectious period. A new pattern of mixing, termed preferred mixing, is defined, in which a fraction of a group's contacts can be reserved for within-group contacts, the remainder being subject to proportional mixing. The fraction reserved may differ among groups. In addition, the classic definition of reproductive number is generalized to show that for heterogeneous populations in general the endemic threshold is [beta]DcY, where cY is the mean number of contacts per infective. The most important finding is that the pattern of contacts between the different groups has a major effect on the spread of HIV, an effect inadequately recognized or studied heretofore.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27021/1/0000009.pd

Comparison of Bayesian Clustering and Edge Detection Methods for Inferring Boundaries in Landscape Genetics

Recently, techniques available for identifying clusters of individuals or boundaries between clusters using genetic data from natural populations have expanded rapidly. Consequently, there is a need to evaluate these different techniques. We used spatially-explicit simulation models to compare three spatial Bayesian clustering programs and two edge detection methods. Spatially-structured populations were simulated where a continuous population was subdivided by barriers. We evaluated the ability of each method to correctly identify boundary locations while varying: (i) time after divergence, (ii) strength of isolation by distance, (iii) level of genetic diversity, and (iv) amount of gene flow across barriers. To further evaluate the methods’ effectiveness to detect genetic clusters in natural populations, we used previously published data on North American pumas and a European shrub. Our results show that with simulated and empirical data, the Bayesian spatial clustering algorithms outperformed direct edge detection methods. All methods incorrectly detected boundaries in the presence of strong patterns of isolation by distance. Based on this finding, we support the application of Bayesian spatial clustering algorithms for boundary detection in empirical datasets, with necessary tests for the influence of isolation by distance

Unscented Kalman filter with parameter identifiability analysis for the estimation of multiple parameters in kinetic models

In systems biology, experimentally measured parameters are not always available, necessitating the use of computationally based parameter estimation. In order to rely on estimated parameters, it is critical to first determine which parameters can be estimated for a given model and measurement set. This is done with parameter identifiability analysis. A kinetic model of the sucrose accumulation in the sugar cane culm tissue developed by Rohwer et al. was taken as a test case model. What differentiates this approach is the integration of an orthogonal-based local identifiability method into the unscented Kalman filter (UKF), rather than using the more common observability-based method which has inherent limitations. It also introduces a variable step size based on the system uncertainty of the UKF during the sensitivity calculation. This method identified 10 out of 12 parameters as identifiable. These ten parameters were estimated using the UKF, which was run 97 times. Throughout the repetitions the UKF proved to be more consistent than the estimation algorithms used for comparison

Spatial variations in the incidence of breast cancer and potential risks associated with soil dioxin contamination in Midland, Saginaw, and Bay Counties, Michigan, USA

<p>Abstract</p> <p>Background</p> <p>High levels of dioxins in soil and higher-than-average body burdens of dioxins in local residents have been found in the city of Midland and the Tittabawassee River floodplain in Michigan. The objective of this study is threefold: (1) to evaluate dioxin levels in soils; (2) to evaluate the spatial variations in breast cancer incidence in Midland, Saginaw, and Bay Counties in Michigan; (3) to evaluate whether breast cancer rates are spatially associated with the dioxin contamination areas.</p> <p>Methods</p> <p>We acquired 532 published soil dioxin data samples collected from 1995 to 2003 and data pertaining to female breast cancer cases (<it>n </it>= 4,604) at ZIP code level in Midland, Saginaw, and Bay Counties for years 1985 through 2002. Descriptive statistics and self-organizing map algorithm were used to evaluate dioxin levels in soils. Geographic information systems techniques, the Kulldorff's spatial and space-time scan statistics, and genetic algorithms were used to explore the variation in the incidence of breast cancer in space and space-time. Odds ratio and their corresponding 95% confidence intervals, with adjustment for age, were used to investigate a spatial association between breast cancer incidence and soil dioxin contamination.</p> <p>Results</p> <p>High levels of dioxin in soils were observed in the city of Midland and the Tittabawassee River 100-year floodplain. After adjusting for age, we observed high breast cancer incidence rates and detected the presence of spatial clusters in the city of Midland, the confluence area of the Tittabawassee, and Saginaw Rivers. After accounting for spatiotemporal variations, we observed a spatial cluster of breast cancer incidence in Midland between 1985 and 1993. The odds ratio further suggests a statistically significant (<it>α </it>= 0.05) increased breast cancer rate as women get older, and a higher disease burden in Midland and the surrounding areas in close proximity to the dioxin contaminated areas.</p> <p>Conclusion</p> <p>These findings suggest that increased breast cancer incidences are spatially associated with soil dioxin contamination. Aging is a substantial factor in the development of breast cancer. Findings can be used for heightened surveillance and education, as well as formulating new study hypotheses for further research.</p