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Supplementary File: Detection and Characterization of Ignitable Liquid Residues in Forensic Fire Debris Samples by Comprehensive Two-Dimensional Gas Chromatography

In analytical chemistry, rapid advancement in instrumentation, especially in high resolution mass-spectrometry is making a significant contribution for further developments of the field. As such, in separation science, nowadays, several hyphenated techniques have proven to be the state-of-the-art techniques for compound identification and characterization. Furthermore, these techniques have found several application areas including biomarker discovery, forensic investigation, food-health research and many others, mainly because of their high sensitivity, selectivity, and scope of analysis. As these techniques advance, the amount of data generated by the high resolution instruments has also increased tremendously, requiring a more sophisticated data analysis techniques to cope with the ‘big data’, and that can simultaneously extract and utilize the information. Taking into account the benefit of instrument coupling (i.e. LC-HRMS) for better separation and characterization of compounds has already been proven to be the most efficient approach, in the years to come, it can be speculated that even more sophisticated techniques such as liquid chromatography coupled to ion mobility spectrometry, and high resolution mass spectrometer (LC-IMS-HRMS) will be the dominating techniques, expanding the dimensionality and the complexity of the data produced. Thus, more than ever, it’s crucial for data analysis techniques to advance a lot faster to manage the computational challenges, and so as to harness the full potential of these promising analytical techniques for routine analysis. The project of this thesis was a joint effort of industry partners involved in forensic, food-safety and material science, and had a common goal and interest in the development of robust data analysis techniques for compound screening. As such, the main aim of this thesis was directed towards improving the conventional data analysis techniques in regards to peak detection, and compound identification for both targeted and untargeted screening. Given this aim, novel algorithms based on probabilistic machine learning, demonstrated to be a better alternative in comparison to conventional threshold-based approaches were developed, and validated.

Along this thesis were presented several application of Bayesian statistics in gas-chromatographic data analysis. Although complex in understanding for the public used with the frequentist data analysis, Bayesian statistics proved to be useful, robust and objective tool for chromatographic data treatment. The present work proves, in each chapter, the benefits of Bayesian statistics and encourages to use and to combine various methods from machine learning, image processing, information theory, psychometrics etc. As a successful example of such a combination of metrics is the 4th chapter of this thesis, where Jansen-Shannon divergence, coming from information theory, was combined with Bayesian hypothesis testing. The 3rd chapter can also be regarded as an image processing approach (i.e. scaling the GCxGC- FID tiles are similar to scaling tiles of images) combined with Bayesian statistics. One of the concerns in using Bayesian, is the speed of computations. This concern is rooted in the Bayes rule, more specifically in the cases where an integration of the likelihood is required to explore all space of the parameters in case of the parameter selection. One solution is the use of MCMC algorithm for sampling from the posterior distribution which can be extremely time consuming when dealing with large number of parameters (i.e. high dimensional space). However, in some cases as it was presented in the 5th chapter, an approximation – Laplace approximation – may be used to evaluate the likelihood in the optimal values of the parameters. The speed of computation presented in the discussions and conclusions of the 3rd, 4th and 5th chapters proves the efficiency of the algorithms with the objectivity of the answer provided.

Forensic examination of fire debris is a notoriously difficult analytical task due to the complexity and variability of samples encountered. The development of increasingly sophisticated analytical instrumentation facilitates greater sensitivity while drastically increasing the abundance of data produced in a single analytical run. Hybrid methods combining chemometrics and forensic statistics have been developed in order to make optimal use of the complex analytical results. This dissertation addresses the interpretation of such measurements by considering competing hypotheses and using appropriate forensic reference data. Both detection and classification tasks for ignitable liquid residue in fire debris samples are explored as valuable contributions to the investigative process and potential use in a judicial context. Assessing the evidential value of the measurements requires understanding of the analytical signal in addition to extensive comprehension of the many sources of variation within and between samples. Preliminary data processing of chromatographic samples is explored including a discussion of both common practices and an exposition of novel techniques. The statistical modelling of chemically distinctive classes of ignitable liquids and the identification of their potentially discriminative characteristics is also presented. The methods and results presented herein emphasize the importance of a deep understanding of the data produced by analytical methods and a rigorous assessment of the statistical and computational assumptions made when articulating their evidential value. Statistical interpretation of fire debris analyses is based on a general probabilistic (likelihood ratio) framework for interpretation and evaluation of evidence.

The aim of the thesis is to investigate the potential of multi-dimensional liquid chromatography (LC) and to formulate guidelines for the optimal design of spatial separation devices. Chapter 1 provides an introduction to multi-dimensional LC. In Chapter 2 a Pareto-optimization approach is applied to various types of three-dimensional systems. The efficiency is evaluated in terms of achieving the maximum peak capacity in the minimum analysis time. A peak capacity of several hundreds of thousands of peaks may be achievable within a few hours using an xLC×xLC×tLC system. In Chapter 3 microfluidic chips are considered that feature one first-dimension (1D) separation channel, 16 second-dimension (2D) channels, and 256 or 1024 third-dimension (3D) channels with specified lengths. The performance of column-based tLC×tLC systems for the separation of proteins is expected to be considerably exceeded. In Chapter 4 design aspects of two main types of flow distributors - radially interconnected (RI) and bifurcating (BF) - are discussed based on computational fluid dynamics (CFD). Guidelines are formulated for designing flow distributors and the effects of imperfections or blockages are studied. In Chapter 5 the theoretical approach described in Chapter 4 is validated in practice, using chips fabricated by micromilling. CFD simulations of the distribution of analytes in two-dimensional systems are presented. Flow confinement within the 1D channel by applying flow resistance or implementing constrictions in the segments near the outlets of the flow distributor is demonstrated by CFD and confirmed experimentally. Chapter 6 contains some reflections on the development of microfluidic devices for multi-dimensional separations.

Chromatography exists for over a hundred years and has become an important part of analytical chemistry. With the development of new instrumentations and columns that can measure more analytes at higher sensitivities simultaneously a new tool has been made possible: chromatographic profiling. Here, samples are measured untargeted and their entire profiles are then correlated to their properties, the chemical process or whatever type of research question needed to be answered. One special type of application of chromatographic profiling is the so-called -omics application such as e.g. metabolomics. In chromatographic profiling, huge quantities of data are obtained, and hypothetically, a tremendous increase in information can be obtained from profiling studies. Unfortunately, methods that can deal with the data in a timely manner are still lacking. To date, automated data pre-processing and analysis have become one of the major bottlenecks of large-scale sample analyses. In this thesis, we have tried to deal with some of the issues in a practical yet sound way. We have focused on developing new methods that either result in better data (i.e. more robust and reliable), better pre-processing or better analysis of the data, all with the aim to improve the link from samples to information.