Multi-dimensional analysis

J. A. Apffel, T. V. Alfredson and R. E. Majors, Automated on-line multi-dimensional high performance liquid chromatographic techniques for the clean-up and analysis of water-soluble samples , J. Chromatogr. 206 43-57 (1981). 

In the analysis of complex PAH mixtures obtained from environmental samples, reversed-phase LC-FL typically provides reliable results for only 8-12 major PAHs (Wise et al. 1993a). To increase the number of PAHs determined by LC-FL, a multidimensional LC procedure is used to isolate and enrich specific isomeric PAHs that could not be measured easily in the total PAH fraction because of interferences, low concentrations, and/or low fluorescence sensitivity or selectivity. This multi-dimensional procedure, which has been described previously (Wise et al. 1977 May and Wise 1984 Wise et al. 1993a, 1993b), consists of a normal-phase LC separation of the PAHs based on the number of aromatic carbon atoms in the PAH, thereby providing fractions containing only isomeric PAHs and their alkyl-substituted isomers. These isomeric fractions are then analyzed by reversed-phase LC-FL to separate and quantify the various isomers. 

Finally, Chapter 16 provides information about the handling of U-series data, with a particular focus on the appropriate propagation of errors. Such error propagation can be complex, especially in the multi-dimensional space required for U- " U- °Th- Th chronology. All too often, short cuts are taken during data analysis which are not statistically justified and this chapter sets out some more appropriate ways of handling U-series data. 

Stone, H.L., "Iterative Solution of Implicit Approximations of Multi-Dimensional Partial Differential Equations", SIAM J. Numerical Analysis, 5, 530-558 (1968). 

Dixon, S.P., Pitfield, I.D., Perrett, D. (2006). Comprehensive multi-dimensional liquid chromatographic separation in biomedical and pharmaceutical analysis a review. Biomed. Chromatogr. 20, 508-529. 

Although is has been in use for over 50 years and has become one of the most widely used routine analysis techniques, GC research remains vibrant and challenging. There are two key areas in which dramatic advancements are being made sampling and sample introduction methods and multi-dimensional separations. A summary of sampling techniques in use with GC is shown in Table 14.9, including the basic principle of the technique and some key applications. These techniques have become critical in extending the use of GC into the diverse fields described in the Applications section. 

Recently, multi-dimensional GC has been used for highly complex separations, especially in analysis of fuels, environmental samples and flavors. Most recently, comprehensive two-dimensional GC, in which samples are continuously taken form the effluent of the (long) first... 

Jia et al. (2005) developed a two-dimensional (2-D) separation system of coupling chromatography to electrophoresis for profiling Escherichia coli metabolites. Capillary EC with a monolithic silica-octadecyl silica column (500 x 0.2 mm ID) was used as the first dimension, from which the effluent fractions were further analyzed by CE acting as the second dimension. Multi-dimensional separations have found wide applications in biomedical and pharmaceutical analysis. 

Regression equations descriptive of multi-dimensional structure/ activity relationships in quantitative terms too frequently are intellectual curiosities developed retrospectively after work in optimization of the biological properties of a series by analog or homolog synthesis has been completed. Retrospective analysis serves well to document that critical factors in the relationship between structural features/physiochemical factors and biological potency are well understood and that optimum compounds have been achieved. Structure/activity understanding developed during the course of a synthesis project, however, lends direction and efficiency to the property optimization effort. 

More recently, Yang and Thompson implemented this type of sensor in FI manifolds, which they consider ideal environments for relating the sensor s hydrodynamic response to the analyte s concentration-time profile produced by the dispersion behaviour of sample zones. Network analysis of the sensor generates multi-dimensional information on the bulk properties of the liquid sample and surface properties at the liquid/solid interface. The relationship between acoustic energy transmission and the interfacial structure, viscosity, density and dielectric constant of the analyte have been thoroughly studied by using this type of assembly [171]. 

Iwamura(51) has investigated the structure-sweetness relationship in four classes of L-aspartyl dipeptides using linear free energy descriptors and multi-dimensional regression analysis. In essence, the Hansch methodology was employed. The four classes of compounds are - ... 

Apart from all of this, multi-dimensional NMR finds considerable and still growing applications in more traditional areas of chemistry. Even if most organometallic and coordination compounds are smaller in size and exhibit simpler spectra than biopolymers, they are composed of a large pool of building blocks whose spectroscopic characteristics are less well known or unknown at all, and the bond connectivity patterns are much more diverse and intricate. Consequently, NMR spectra of organometallic and coordination compounds are less predictable, and multi-dimensional techniques are in many cases indispensable as analytical tools when structural assignments derived from the analysis of one-dimensional NMR spectra remain ambiguous or even incomplete. 

More importantly insoluble proteins, such as membrane-bound and nuclear proteins, are under-represented within 2DE analysis. However, membrane proteins can be identified by MS following a IDE separation. Unfortunately, hydrophobicity is the most common reason for poor representation of abundant proteins and seems set to be with us for quite some time (Santoni et al., 2000 Rabilloud, 2002). Emerging proteomic methods without the use of 2DE are being developed, such as isotope-coded affinity tagging (ICAT) and multi-dimensional protein identification technology (MuDPIT). 

Figure 8.2.7 Reference deconvolution applied to the methanol peak (a) original peak (b) methanol peak deconvolved to a 2 Hz Lorenzian lineshape (c) gradient-shifted methanol peak (d) gradient-shifted methanol peak deconvolved to the same 2 Hz Lorenzian lineshape (e) comparison of the sub-spectrum of the methanol sample using the subtraction algorithm with (sharp peak) and without (flattened peak) reference deconvolution. Reprinted from Hou, T., MacNamara, E. and Raftery, D., NMR analysis of multiple samples using parallel coils improved performance using reference deconvolution and multi-dimensional methods , Anal. Chem. Acta, 400, 297-305, copyright (1999), with permission of Elsevier Science...

This paper discusses SIMS as a multi-dimensional technique for the analysis of inorganic and organic materials. The paper is divided into two parts inorganic and organic (or molecular) SIMS. The inorganic SIMS part focuses on the methods of quantitative analysis and depth profiling applications. In particular, SIMS matrix effects are defined and the physical models and empirical methods used to quantify SIMS results are reviewed. 

Although samples are taken and prepared in the same way here as in the semi-quantitative analysis, in the evaluation of the complex spectra of the substances, the multi-dimensional GC technique (GCGC—MS) is employed. This consists of two series-connected GCs combined with an MS detector. As a rule, the process... 

Multi-dimensional analysis of interactivity between global ecodynamics and the Arctic Basin... 

Kondratyev K. Ya. Krapivin V. F. and Savinykh V. P. (2003a). Prospects for Civilization Development Multi-Dimensional Analysis. Logos Publ., Moscow, 575 pp. [in Russian]. 

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