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

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

Environmental Determinants of Infectious Disease: A Framework for Tracking Causal Links and Guiding Public Health Research

BACKGROUND: Discoveries that emerging and re-emerging pathogens have their origin in environmental change has created an urgent need to understand how these environmental changes impact disease burden. In this article we present a framework that provides a context from which to examine the relationship between environmental changes and disease transmission and a structure from which to unite disparate pieces of information from a variety of disciplines. METHODS: The framework integrates three interrelated characteristics of environment–disease relationships: a) Environmental change manifests in a complex web of ecologic and social factors that may ultimately impact disease; these factors are represented as those more distally related and those more proximally related to disease. b) Transmission dynamics of infectious pathogens mediate the effects that environmental changes have on disease. c) Disease burden is the outcome of the interplay between environmental change and the transmission cycle of a pathogen. RESULTS: To put this framework into operation, we present a matrix formulation as a means to define important elements of this system and to summarize what is known and unknown about the these elements and their relationships. The framework explicitly expresses the problem at a systems level that goes beyond the traditional risk factor analysis used in public health, and the matrix provide

Nonrandom Mixing Models of HIV Transmission

Models of HIV transmission and the AIDS epidemic generally assume random mixing among those infected with HIV and those who are not. For sexually transmitted HIV, this implies that individuals select sex partners without regard to attributes such as familiarity, attractiveness, or risk of infection. This paper formulates a model for examining the impact of nonrandom mixing on HIV transmission. We present threshold conditions that determine when HIV epidemics can occur within the framework of this model. Nonrandom mixing is introduced by assuming that sexually active individuals select sex partners to minimize the risk of infection. In addition to variability in risky sex rates, some versions of our model allow for error (or noise) in information exchanged between prospective partners. We investigate several models including random partner selection (or proportionate mixing), segregation of the population by risky sex rates, a probabilistic combination of segregation and random selection induced by imperfect information (or preferred mixing), and a model of costly search with perfect information. We develop examples which show that nonrandom mixing can lead to epidemics that are more severe or less severe than random mixing. For reasonable parameter choices describing the AIDS epidemic, however, the results suggest that random mixing models overstate the number of HIV infections that will occur

HIV Treatment as Prevention: Debate and Commentary-Will Early Infection Compromise Treatment-as-Prevention Strategies?

Universal HIV testing and immediate antiretroviral therapy for infected individuals has been proposed as a way of reducing the transmission of HIV and thereby bringing the HIV epidemic under control. It is unclear whether transmission during early HIV infection—before individuals are likely to have been diagnosed with HIV and started on antiretroviral therapy—will compromise the effectiveness of treatment as prevention. This article presents two opposing viewpoints by Powers, Miller, and Cohen, and Williams and Dye, followed by a commentary by Fraser

Phenotypic Signatures Arising from Unbalanced Bacterial Growth

Fluctuations in the growth rate of a bacterial culture during unbalanced growth are generally considered undesirable in quantitative studies of bacterial physiology. Under well-controlled experimental conditions, however, these fluctuations are not random but instead reflect the interplay between intra-cellular networks underlying bacterial growth and the growth environment. Therefore, these fluctuations could be considered quantitative phenotypes of the bacteria under a specific growth condition. Here, we present a method to identify “phenotypic signatures” by time-frequency analysis of unbalanced growth curves measured with high temporal resolution. The signatures are then applied to differentiate amongst different bacterial strains or the same strain under different growth conditions, and to identify the essential architecture of the gene network underlying the observed growth dynamics. Our method has implications for both basic understanding of bacterial physiology and for the classification of bacterial strains

Using Dynamic Stochastic Modelling to Estimate Population Risk Factors in Infectious Disease: The Example of FIV in 15 Cat Populations

BACKGROUND:In natural cat populations, Feline Immunodeficiency Virus (FIV) is transmitted through bites between individuals. Factors such as the density of cats within the population or the sex-ratio can have potentially strong effects on the frequency of fight between individuals and hence appear as important population risk factors for FIV. METHODOLOGY/PRINCIPAL FINDINGS:To study such population risk factors, we present data on FIV prevalence in 15 cat populations in northeastern France. We investigate five key social factors of cat populations; the density of cats, the sex-ratio, the number of males and the mean age of males and females within the population. We overcome the problem of dependence in the infective status data using sexually-structured dynamic stochastic models. Only the age of males and females had an effect (p = 0.043 and p = 0.02, respectively) on the male-to-female transmission rate. Due to multiple tests, it is even likely that these effects are, in reality, not significant. Finally we show that, in our study area, the data can be explained by a very simple model that does not invoke any risk factor. CONCLUSION:Our conclusion is that, in host-parasite systems in general, fluctuations due to stochasticity in the transmission process are naturally very large and may alone explain a larger part of the variability in observed disease prevalence between populations than previously expected. Finally, we determined confidence intervals for the simple model parameters that can be used to further aid in management of the disease

Recent HIV-1 Infection Contributes to the Viral Diffusion over the French Territory with a Recent Increasing Frequency

To analyse the contribution of primary human immunodeficiency virus type 1 (HIV-1) infection (PHI) to the French viral epidemic. sequences included 987 PHI from the French ANRS PRIMO cohort between 1999 and 2010 and were analysed using a population-based phylogenetic approach. Clinical features, risk factors, sexual behaviour and drug resistance for clustered and nonclustered transmission events were ascertained.Viruses from 125 (12.7%) of PHI cosegregated into 56 transmission chains, with increasing frequency during the last years (10.2% before 2006 versus 15.2% of clusters in 2006–2010, p = 0.02). The mean number of patients per cluster was 2.44. Compared to unique PHI, clusters involved more often men, infected through homosexual intercourse, of young age, with a high number of casual sexual partnerships and frequent previous HIV serological tests. Resistant strains were found in 16.0% and 11.1% of clusters and unique PHI, respectively (p = 0.11). Overall, 34% (n = 19) clusters included patients followed in French regions far apart, involving 13 clusters with at least one Parisian patient.PHIs are a significant source of onward transmission, especially in the MSM population. Recently infected people contribute to the spread of the viral epidemic throughout the French territory. Survey of transmitted drug resistance and behavioural characteristics of patients involved into clustered PHI may help to guide prevention and treatment interventions

A rationale for continuing mass antibiotic distributions for trachoma

BACKGROUND: The World Health Organization recommends periodic mass antibiotic distributions to reduce the ocular strains of chlamydia that cause trachoma, the world's leading cause of infectious blindness. Their stated goal is to control infection, not to completely eliminate it. A single mass distribution can dramatically reduce the prevalence of infection. However, if infection is not eliminated in every individual in the community, it may gradually return back into the community, so often repeated treatments are necessary. Since public health groups are reluctant to distribute antibiotics indefinitely, we are still in need of a proven long-term rationale. Here we use mathematical models to demonstrate that repeated antibiotic distributions can eliminate infection in a reasonable time period. METHODS: We fit parameters of a stochastic epidemiological transmission model to data collected before and 6 months after a mass antibiotic distribution in a region of Ethiopia that is one of the most severely affected areas in the world. We validate the model by comparing our predicted results to Ethiopian data which was collected biannually for two years past the initial mass antibiotic distribution. We use the model to simulate the effect of different treatment programs in terms of local elimination of infection. RESULTS: Simulations show that the average prevalence of infection across all villages progressively decreases after each treatment, as long as the frequency and coverage of antibiotics are high enough. Infection can be eliminated in more villages with each round of treatment. However, in the communities where infection is not eliminated, it returns to the same average level, forming the same stationary distribution. This phenomenon is also seen in subsequent epidemiological data from Ethiopia. Simulations suggest that a biannual treatment plan implemented for 5 years will lead to elimination in 95% of all villages. CONCLUSION: Local elimination from a community is theoretically possible, even in the most severely infected communities. However, elimination from larger areas may require repeated biannual treatments and prevention of re-introduction from outside to treated areas