Local and global error models to improve uncertainty quantification

In groundwater applications, Monte Carlo methods are employed to model the uncertainty on geological parameters. However, their brute-force application becomes computationally prohibitive for highly detailed geological descriptions, complex physical processes, and a large number of realizations. The Distance Kernel Method (DKM) overcomes this issue by clustering the realizations in a multidimensional space based on the flow responses obtained by means of an approximate (computationally cheaper) model; then, the uncertainty is estimated from the exact responses that are computed only for one representative realization per cluster (the medoid). Usually, DKM is employed to decrease the size of the sample of realizations that are considered to estimate the uncertainty. We propose to use the information from the approximate responses for uncertainty quantification. The subset of exact solutions provided by DKM is then employed to construct an error model and correct the potential bias of the approximate model. Two error models are devised that both employ the difference between approximate and exact medoid solutions, but differ in the way medoid errors are interpolated to correct the whole set of realizations. The Local Error Model rests upon the clustering defined by DKM and can be seen as a natural way to account for intra-cluster variability; the Global Error Model employs a linear interpolation of all medoid errors regardless of the cluster to which the single realization belongs. These error models are evaluated for an idealized pollution problem in which the uncertainty of the breakthrough curve needs to be estimated. For this numerical test case, we demonstrate that the error models improve the uncertainty quantification provided by the DKM algorithm and are effective in correcting the bias of the estimate computed solely from the MsFV results. The framework presented here is not specific to the methods considered and can be applied to other combinations of approximate models and techniques to select a subset of realizations

Estimating biophysical variable dependences with kernels

This paper introduces a nonlinear measure of dependence between random variables in the context of remote sensing data analysis. The Hilbert-Schmidt Independence Criterion (HSIC) is a kernel method for evaluating statistical dependence. HSIC is based on computing the Hilbert-Schmidt norm of the cross-covariance operator of mapped samples in the corresponding Hilbert spaces. The HSIC empirical estimator is very easy to compute and has good theoretical and practical properties. We exploit the capabilities of HSIC to explain nonlinear dependences in two remote sensing problems: temperature estimation and chlorophyll concentration prediction from spectra. Results show that, when the relationship between random variables is nonlinear or when few data are available, the HSIC criterion outperforms other standard methods, such as the linear correlation or mutual information.

Error models in hydrogeology applications

Notre consommation en eau souterraine, en particulier comme eau potable ou pour l'irrigation, a considérablement augmenté au cours des années. De nombreux problèmes font alors leur apparition, allant de la prospection de nouvelles ressources à la remédiation des aquifères pollués. Indépendamment du problème hydrogéologique considéré, le principal défi reste la caractérisation des propriétés du sous-sol. Une approche stochastique est alors nécessaire afin de représenter cette incertitude en considérant de multiples scénarios géologiques et en générant un grand nombre de réalisations géostatistiques. Nous rencontrons alors la principale limitation de ces approches qui est le coût de calcul dû à la simulation des processus d'écoulements complexes pour chacune de ces réalisations. Dans la première partie de la thèse, ce problème est investigué dans le contexte de propagation de l'incertitude, oú un ensemble de réalisations est identifié comme représentant les propriétés du sous-sol. Afin de propager cette incertitude à la quantité d'intérêt tout en limitant le coût de calcul, les méthodes actuelles font appel à des modèles d'écoulement approximés. Cela permet l'identification d'un sous-ensemble de réalisations représentant la variabilité de l'ensemble initial. Le modèle complexe d'écoulement est alors évalué uniquement pour ce sousensemble, et, sur la base de ces réponses complexes, l'inférence est faite. Notre objectif est d'améliorer la performance de cette approche en utilisant toute l'information à disposition. Pour cela, le sous-ensemble de réponses approximées et exactes est utilisé afin de construire un modèle d'erreur, qui sert ensuite à corriger le reste des réponses approximées et prédire la réponse du modèle complexe. Cette méthode permet de maximiser l'utilisation de l'information à disposition sans augmentation perceptible du temps de calcul. La propagation de l'incertitude est alors plus précise et plus robuste. La stratégie explorée dans le premier chapitre consiste à apprendre d'un sous-ensemble de réalisations la relation entre les modèles d'écoulement approximé et complexe. Dans la seconde partie de la thèse, cette méthodologie est formalisée mathématiquement en introduisant un modèle de régression entre les réponses fonctionnelles. Comme ce problème est mal posé, il est nécessaire d'en réduire la dimensionnalité. Dans cette optique, l'innovation du travail présenté provient de l'utilisation de l'analyse en composantes principales fonctionnelles (ACPF), qui non seulement effectue la réduction de dimensionnalités tout en maximisant l'information retenue, mais permet aussi de diagnostiquer la qualité du modèle d'erreur dans cet espace fonctionnel. La méthodologie proposée est appliquée à un problème de pollution par une phase liquide nonaqueuse et les résultats obtenus montrent que le modèle d'erreur permet une forte réduction du temps de calcul tout en estimant correctement l'incertitude. De plus, pour chaque réponse approximée, une prédiction de la réponse complexe est fournie par le modèle d'erreur. Le concept de modèle d'erreur fonctionnel est donc pertinent pour la propagation de l'incertitude, mais aussi pour les problèmes d'inférence bayésienne. Les méthodes de Monte Carlo par chaîne de Markov (MCMC) sont les algorithmes les plus communément utilisés afin de générer des réalisations géostatistiques en accord avec les observations. Cependant, ces méthodes souffrent d'un taux d'acceptation très bas pour les problèmes de grande dimensionnalité, résultant en un grand nombre de simulations d'écoulement gaspillées. Une approche en deux temps, le "MCMC en deux étapes", a été introduite afin d'éviter les simulations du modèle complexe inutiles par une évaluation préliminaire de la réalisation. Dans la troisième partie de la thèse, le modèle d'écoulement approximé couplé à un modèle d'erreur sert d'évaluation préliminaire pour le "MCMC en deux étapes". Nous démontrons une augmentation du taux d'acceptation par un facteur de 1.5 à 3 en comparaison avec une implémentation classique de MCMC. Une question reste sans réponse : comment choisir la taille de l'ensemble d'entrainement et comment identifier les réalisations permettant d'optimiser la construction du modèle d'erreur. Cela requiert une stratégie itérative afin que, à chaque nouvelle simulation d'écoulement, le modèle d'erreur soit amélioré en incorporant les nouvelles informations. Ceci est développé dans la quatrième partie de la thèse, oú cette méthodologie est appliquée à un problème d'intrusion saline dans un aquifère côtier. -- Our consumption of groundwater, in particular as drinking water and for irrigation, has considerably increased over the years and groundwater is becoming an increasingly scarce and endangered resource. Nofadays, we are facing many problems ranging from water prospection to sustainable management and remediation of polluted aquifers. Independently of the hydrogeological problem, the main challenge remains dealing with the incomplete knofledge of the underground properties. Stochastic approaches have been developed to represent this uncertainty by considering multiple geological scenarios and generating a large number of realizations. The main limitation of this approach is the computational cost associated with performing complex of simulations in each realization. In the first part of the thesis, we explore this issue in the context of uncertainty propagation, where an ensemble of geostatistical realizations is identified as representative of the subsurface uncertainty. To propagate this lack of knofledge to the quantity of interest (e.g., the concentration of pollutant in extracted water), it is necessary to evaluate the of response of each realization. Due to computational constraints, state-of-the-art methods make use of approximate of simulation, to identify a subset of realizations that represents the variability of the ensemble. The complex and computationally heavy of model is then run for this subset based on which inference is made. Our objective is to increase the performance of this approach by using all of the available information and not solely the subset of exact responses. Two error models are proposed to correct the approximate responses follofing a machine learning approach. For the subset identified by a classical approach (here the distance kernel method) both the approximate and the exact responses are knofn. This information is used to construct an error model and correct the ensemble of approximate responses to predict the "expected" responses of the exact model. The proposed methodology makes use of all the available information without perceptible additional computational costs and leads to an increase in accuracy and robustness of the uncertainty propagation. The strategy explored in the first chapter consists in learning from a subset of realizations the relationship between proxy and exact curves. In the second part of this thesis, the strategy is formalized in a rigorous mathematical framework by defining a regression model between functions. As this problem is ill-posed, it is necessary to reduce its dimensionality. The novelty of the work comes from the use of functional principal component analysis (FPCA), which not only performs the dimensionality reduction while maximizing the retained information, but also allofs a diagnostic of the quality of the error model in the functional space. The proposed methodology is applied to a pollution problem by a non-aqueous phase-liquid. The error model allofs a strong reduction of the computational cost while providing a good estimate of the uncertainty. The individual correction of the proxy response by the error model leads to an excellent prediction of the exact response, opening the door to many applications. The concept of functional error model is useful not only in the context of uncertainty propagation, but also, and maybe even more so, to perform Bayesian inference. Monte Carlo Markov Chain (MCMC) algorithms are the most common choice to ensure that the generated realizations are sampled in accordance with the observations. Hofever, this approach suffers from lof acceptance rate in high dimensional problems, resulting in a large number of wasted of simulations. This led to the introduction of two-stage MCMC, where the computational cost is decreased by avoiding unnecessary simulation of the exact of thanks to a preliminary evaluation of the proposal. In the third part of the thesis, a proxy is coupled to an error model to provide an approximate response for the two-stage MCMC set-up. We demonstrate an increase in acceptance rate by a factor three with respect to one-stage MCMC results. An open question remains: hof do we choose the size of the learning set and identify the realizations to optimize the construction of the error model. This requires devising an iterative strategy to construct the error model, such that, as new of simulations are performed, the error model is iteratively improved by incorporating the new information. This is discussed in the fourth part of the thesis, in which we apply this methodology to a problem of saline intrusion in a coastal aquifer.

Kernel-based methods for change detection in remote sensing images

Nowadays, the joint exploitation of images acquired daily by remote sensing instruments and of images available from archives allows a detailed monitoring of the transitions occurring at the surface of the Earth. These modifications of the land cover generate spectral discrepancies that can be detected via the analysis of remote sensing images. Independently from the origin of the images and of type of surface change, a correct processing of such data implies the adoption of flexible, robust and possibly nonlinear method, to correctly account for the complex statistical relationships characterizing the pixels of the images. This Thesis deals with the development and the application of advanced statistical methods for multi-temporal optical remote sensing image processing tasks. Three different families of machine learning models have been explored and fundamental solutions for change detection problems are provided. In the first part, change detection with user supervision has been considered. In a first application, a nonlinear classifier has been applied with the intent of precisely delineating flooded regions from a pair of images. In a second case study, the spatial context of each pixel has been injected into another nonlinear classifier to obtain a precise mapping of new urban structures. In both cases, the user provides the classifier with examples of what he believes has changed or not. In the second part, a completely automatic and unsupervised method for precise binary detection of changes has been proposed. The technique allows a very accurate mapping without any user intervention, resulting particularly useful when readiness and reaction times of the system are a crucial constraint. In the third, the problem of statistical distributions shifting between acquisitions is studied. Two approaches to transform the couple of bi-temporal images and reduce their differences unrelated to changes in land cover are studied. The methods align the distributions of the images, so that the pixel-wise comparison could be carried out with higher accuracy. Furthermore, the second method can deal with images from different sensors, no matter the dimensionality of the data nor the spectral information content. This opens the doors to possible solutions for a crucial problem in the field: detecting changes when the images have been acquired by two different sensors.

Study of the impact of tissue density heterogeneities on 3-dimensional abdominal dosimetry: comparison between dose kernel convolution and direct monte carlo methods.

Dose kernel convolution (DK) methods have been proposed to speed up absorbed dose calculations in molecular radionuclide therapy. Our aim was to evaluate the impact of tissue density heterogeneities (TDH) on dosimetry when using a DK method and to propose a simple density-correction method. METHODS: This study has been conducted on 3 clinical cases: case 1, non-Hodgkin lymphoma treated with (131)I-tositumomab; case 2, a neuroendocrine tumor treatment simulated with (177)Lu-peptides; and case 3, hepatocellular carcinoma treated with (90)Y-microspheres. Absorbed dose calculations were performed using a direct Monte Carlo approach accounting for TDH (3D-RD), and a DK approach (VoxelDose, or VD). For each individual voxel, the VD absorbed dose, D(VD), calculated assuming uniform density, was corrected for density, giving D(VDd). The average 3D-RD absorbed dose values, D(3DRD), were compared with D(VD) and D(VDd), using the relative difference Δ(VD/3DRD). At the voxel level, density-binned Δ(VD/3DRD) and Δ(VDd/3DRD) were plotted against ρ and fitted with a linear regression. RESULTS: The D(VD) calculations showed a good agreement with D(3DRD). Δ(VD/3DRD) was less than 3.5%, except for the tumor of case 1 (5.9%) and the renal cortex of case 2 (5.6%). At the voxel level, the Δ(VD/3DRD) range was 0%-14% for cases 1 and 2, and -3% to 7% for case 3. All 3 cases showed a linear relationship between voxel bin-averaged Δ(VD/3DRD) and density, ρ: case 1 (Δ = -0.56ρ + 0.62, R(2) = 0.93), case 2 (Δ = -0.91ρ + 0.96, R(2) = 0.99), and case 3 (Δ = -0.69ρ + 0.72, R(2) = 0.91). The density correction improved the agreement of the DK method with the Monte Carlo approach (Δ(VDd/3DRD) < 1.1%), but with a lesser extent for the tumor of case 1 (3.1%). At the voxel level, the Δ(VDd/3DRD) range decreased for the 3 clinical cases (case 1, -1% to 4%; case 2, -0.5% to 1.5%, and -1.5% to 2%). No more linear regression existed for cases 2 and 3, contrary to case 1 (Δ = 0.41ρ - 0.38, R(2) = 0.88) although the slope in case 1 was less pronounced. CONCLUSION: This study shows a small influence of TDH in the abdominal region for 3 representative clinical cases. A simple density-correction method was proposed and improved the comparison in the absorbed dose calculations when using our voxel S value implementation.

Results of computer assisted navigation in Total Knee Arthroplasty (TKA): comparison with the conventional method

The aim of this retrospective study was to compare the clinical and radiographic results after TKA (PFC, DePuy), performed either by computer assisted navigation (CAS, Brainlab, Johnson&Johnson) or by conventional means. Material and methods: Between May and December 2006 we reviewed 36 conventional TKA performed between 2002 and 2003 (group A) and 37 navigated TKA performed between 2005 and 2006 (group B) by the same experienced surgeon. The mean age in group A was 74 years (range 62-90) and 73 (range 58-85) in group B with a similar age distribution. The preoperative mechanical axes in group A ranged from -13° varus to +13° valgus (mean absolute deviation 6.83°, SD 3.86), in group B from -13° to +16° (mean absolute deviation 5.35, SD 4.29). Patients with a previous tibial osteotomy or revision arthroplasty were excluded from the study. Examination was done by an experienced orthopedic resident independent of the surgeon. All patients had pre- and postoperative long standing radiographs. The IKSS and the WOMAC were utilized to determine the clinical outcome. Patient's degree of satisfaction was assessed on a visual analogous scale (VAS). Results: 32 of the 37 navigated TKAs (86,5%) showed a postoperative mechanical axis within the limits of 3 degrees of valgus or varus deviation compared to only 24 (66%) of the 36 standard TKAs. This difference was significant (p = 0.045). The mean absolute deviation from neutral axis was 3.00° (range -5° to +9°, SD: 1.75) in group A in comparison to 1.54° (range -5° to +4°, SD: 1.41) in group B with a highly significant difference (p = 0.000). Furthermore, both groups showed a significant postoperative improvement of their mean IKSS-values (group A: 89 preoperative to 169 postoperative, group B 88 to 176) without a significant difference between the two groups. Neither the WOMAC nor the patient's degree of satisfaction - as assessed by VAS - showed significant differences. Operation time was significantly higher in group B (mean 119.9 min.) than in group A (mean 99.6 min., p <0.000). Conclusion: Our study showed consistent significant improvement of postoperative frontal alignment in TKA by computer assisted navigation (CAS) compared to standard methods, even in the hands of a surgeon well experienced in standard TKA implantation. However, the follow-up time of this study was not long enough to judge differences in clinical outcome. Thus, the relevance of computer navigation for clinical outcome and survival of TKA remains to be proved in long term studies to justify the longer operation time. References 1 Stulberg SD. Clin Orth Rel Res. 2003;(416):177-84. 2 Chauhan SK. JBJS Br. 2004;86(3):372-7. 3 Bäthis H, et al. Orthopäde. 2006;35(10):1056-65.

Multi-scale support vector algorithms for hot spot detection and modelling

The algorithmic approach to data modelling has developed rapidly these last years, in particular methods based on data mining and machine learning have been used in a growing number of applications. These methods follow a data-driven methodology, aiming at providing the best possible generalization and predictive abilities instead of concentrating on the properties of the data model. One of the most successful groups of such methods is known as Support Vector algorithms. Following the fruitful developments in applying Support Vector algorithms to spatial data, this paper introduces a new extension of the traditional support vector regression (SVR) algorithm. This extension allows for the simultaneous modelling of environmental data at several spatial scales. The joint influence of environmental processes presenting different patterns at different scales is here learned automatically from data, providing the optimum mixture of short and large-scale models. The method is adaptive to the spatial scale of the data. With this advantage, it can provide efficient means to model local anomalies that may typically arise in situations at an early phase of an environmental emergency. However, the proposed approach still requires some prior knowledge on the possible existence of such short-scale patterns. This is a possible limitation of the method for its implementation in early warning systems. The purpose of this paper is to present the multi-scale SVR model and to illustrate its use with an application to the mapping of Cs137 activity given the measurements taken in the region of Briansk following the Chernobyl accident.

Validation of an analytical method for nitrous oxide (N2O) laughing gas by headspace gas chromatography coupled to mass spectrometry (HS-GC-MS): Forensic application to a lethal intoxication.

Drug abuse is a widespread problem affecting both teenagers and adults. Nitrous oxide is becoming increasingly popular as an inhalation drug, causing harmful neurological and hematological effects. Some gas chromatography-mass spectrometry (GC-MS) methods for nitrous oxide measurement have been previously described. The main drawbacks of these methods include a lack of sensitivity for forensic applications; including an inability to quantitatively determine the concentration of gas present. The following study provides a validated method using HS-GC-MS which incorporates hydrogen sulfide as a suitable internal standard allowing the quantification of nitrous oxide. Upon analysis, sample and internal standard have similar retention times and are eluted quickly from the molecular sieve 5Å PLOT capillary column and the Porabond Q column therefore providing rapid data collection whilst preserving well defined peaks. After validation, the method has been applied to a real case of N2O intoxication indicating concentrations in a mono-intoxication.

Nest distribution varies with dispersal method and familiarity-mediated aggression for two sympatric ants

Dispersal mechanisms and competition together play a key role in the spatial distribution of a population. Species that disperse via fission are likely to experience high levels of localized competitive pressure from conspecifics relative to species that disperse in other ways. Although fission dispersal occurs in many species, its ecological and behavioural effects remain unclear. We compared foraging effort, nest spatial distribution and aggression of two sympatric ant species that differ in reproductive dispersal: Streblognathus peetersi, which disperse by group fission, and Plectroctena mandibularis, which disperse by solitary wingless queens. We found that although both species share space and have similar foraging strategies, they differ in nest distribution and aggressive behaviour. The spatial distribution of S. peetersi nests was extremely aggregated, and workers were less aggressive towards conspecifics from nearby nests than towards distant conspecifics and all heterospecific workers. By contrast, the spatial distribution of P. mandibularis nests was overdispersed, and workers were equally aggressive towards conspecific and heterospecific competitors regardless of nest distance. Finally, laboratory experiments showed that familiarity led to the positive relationship between aggression and nest distance in S. peetersi. While unfamiliar individuals were initially aggressive, the level of aggression decreased within 1 h of contact, and continued to decrease over 24 h. Furthermore, individuals from near nests that were not aggressive could be induced to aggression after prolonged isolation. Overall, these results suggest that low aggression mediated by familiarity could provide benefits for a species with fission reproduction and an aggregated spatial distribution.

Urban image classification with semisupervised multiscale cluster kernels

This paper presents a semisupervised support vector machine (SVM) that integrates the information of both labeled and unlabeled pixels efficiently. Method's performance is illustrated in the relevant problem of very high resolution image classification of urban areas. The SVM is trained with the linear combination of two kernels: a base kernel working only with labeled examples is deformed by a likelihood kernel encoding similarities between labeled and unlabeled examples. Results obtained on very high resolution (VHR) multispectral and hyperspectral images show the relevance of the method in the context of urban image classification. Also, its simplicity and the few parameters involved make the method versatile and workable by unexperienced users.

Le Q-sort, un outil pour la recherche en soins le cas des représentations chez les infirmiers en psychiatrie de l'âge avancé [Q-sort, a useful research method in care in cases of psychiatric nursing of the aged]

Q-sort is a research method which allows defining profiles of attitudes toward a set of statements, ordered in relation to each other. Pertaining to the Q Methodology, the qualitative analysis of the Q-sorts is based on quantitative techniques. This method is of particular interest for research in health professions, a field in which attitudes of patients and professionals are very important. The method is presented in this article, along with an example of application in nursing in old age psychiatry.

I have faith in my thing, you know what I mean? Mixed method elements on individual investments on religious markets.

In contemporary society, religious signification and secular systems mix and influence each other. Holistic conceptions of a world in which man is integrated harmoniously with nature meet representations of a world run by an immanent God. On the market of the various systems, the individual goes from one system to another, following his immediate needs and expectations without necessarily leaving any marks in a meaningful long term system. This article presents the first results of an ongoing research in Switzerland on contemporary religion focusing on (new) paths of socialization of modern that individuals and the various (non-) belief systems that they simultaneously develop

Automatic Mallampati Classification Using Active Appearance Models

Difficult tracheal intubation assessment is an important research topic in anesthesia as failed intubations are important causes of mortality in anesthetic practice. The modified Mallampati score is widely used, alone or in conjunction with other criteria, to predict the difficulty of intubation. This work presents an automatic method to assess the modified Mallampati score from an image of a patient with the mouth wide open. For this purpose we propose an active appearance models (AAM) based method and use linear support vector machines (SVM) to select a subset of relevant features obtained using the AAM. This feature selection step proves to be essential as it improves drastically the performance of classification, which is obtained using SVM with RBF kernel and majority voting. We test our method on images of 100 patients undergoing elective surgery and achieve 97.9% accuracy in the leave-one-out crossvalidation test and provide a key element to an automatic difficult intubation assessment system.

Niche conservatism in non-native birds in Europe: niche unfilling rather than niche expansion

Aim Niche conservatism, or the extent to which niches are conserved across space and time, is of special concern for the study of non-native species as it underlies predictions of invasion risk. Based on the occurrence of 28 non-native birds in Europe, we assess to what extent Grinnellian realized niches are conserved during invasion, formulate hypotheses to explain the variation in observed niche changes and test how well species distribution models can predict non-native bird occurrence in Europe. Location Europe. Methods To quantify niche changes, a recent method that applies kernel smoothers to densities of species occurrence in a gridded environmental space was used. This corrects for differences in the availability of environments between study areas and allows discrimination between 'niche expansion' into environments new to the species and 'niche unfilling', whereby the species only partially fills its niche in the invaded range. Predictions of non-native bird distribution in Europe were generated using several distribution modelling techniques. Results Niche overlap between native and non-native bird populations is low, but niche changes are smaller for species having a higher propagule pressure and that were introduced longer ago. Non-native birds in Europe occupy a subset of the environments they inhabit in their native ranges. Niche expansion into novel environments is rare for most species, allowing species distribution models to accurately predict invasion risk. Main conclusions Because of the recent nature of most bird introductions, species occupy only part of the suitable environments available in the invaded range. This signals that apart from purely ecological factors, patterns of niche conservatism may also be contingent on population-specific historical factors. These results also suggest that many claims of niche differences may be due to a partial filling of the native niche in the invaded range and thus do not represent true niche changes.

Innovative method for carbon dioxide determination in human postmortem cardiac gas samples using headspace-gas chromatography-mass spectrometry and stable labeled isotope as internal standard.

A novel approach to measure carbon dioxide (CO2) in gaseous samples, based on a precise and accurate quantification by (13)CO2 internal standard generated in situ is presented. The main goal of this study was to provide an innovative headspace-gas chromatography-mass spectrometry (HS-GC-MS) method applicable in the routine determination of CO2. The main drawback of the GC methods discussed in the literature for CO2 measurement is the lack of a specific internal standard necessary to perform quantification. CO2 measurement is still quantified by external calibration without taking into account analytical problems which can often occur considering gaseous samples. To avoid the manipulation of a stable isotope-labeled gas, we have chosen to generate in situ an internal labeled standard gas ((13)CO2) on the basis of the stoichiometric formation of CO2 by the reaction of hydrochloric acid (HCl) with sodium hydrogen carbonate (NaH(13)CO3). This method allows a precise measurement of CO2 concentration and was validated on various human postmortem gas samples in order to study its efficiency.