Applications of Hadamard Transform to Gas Chromatography/Mass Spectrometry and Liquid Chromatography/Mass Spectrometry

Abstract

Successful application of the Hadamard transform (HT) technique to gas chromatography/mass spectrometry (GC/MS) and liquid chromatography/mass spectrometry (LC/MS) is described. Novel sample injection devices were developed to achieve multiple sample injections in both GC and LC instruments. Air pressure was controlled by an electromagnetic valve in GC, while a syringe pump and Tee connector were employed for the injection device in LC. Two well-known, abused drugs, 3,4-methylenedioxy-N-methylamphetamine (MDMA) and N, N-dimethyltryptamine (DMT), were employed as model samples. Both of the injection devices permitted precise successive injections, resulting in clearly modulated chromatograms encoded by Hadamard matrices. After inverse Hadamard transformation of the encoded chromatogram, the signal-to-noise (S/N) ratios of the signals were substantially improved compared with those expected from theoretical values. The S/N ratios were enhanced approximately 10-fold in HT-GC/MS and 6.8 in HT-LC/MS, using the matrices of 1023 and 511, respectively. The HT-GC/MS was successfully applied to the determination of MDMA in the urine sample of a suspect.

Fundamental Study for Increasing Multiplicity of Frequency Division Multiplex HPLC-MS

“…However, the application of this method is limited to the analysis of samples comprising known analytes. Other sequential injection methods using single columns were also developed in combination with the Hadamard transform [14,15]. However, this method is also not suitable for multiplex analyses of samples containing different components.…”

Implementation of Hadamard encoding for rapid multisample analysis in liquid chromatography

“…The first realization of this principle in chromatography was demonstrated in correlation chromatography . Multiplexing utilizing Hadamard encoding has been applied to increase S/N in many fields, including TOF–MS , CE , and GC–MS . We reported on the use of structured modulation sequences and Hadamard transform in high‐throughput multiplexing gas chromatography (htMPGC) .…”

Online High Throughput Measurements for Fast Catalytic Reactions Using Time-Division Multiplexing Gas Chromatography

“…Therefore, a superimposed (convoluted) chromatogram is recorded. As suggested by Smith, mpGC has been used for many applications to enhance the signal-to-noise ratio (SNR) by making use of the multiplex advantage. − However, the original idea was to use mpGC as a tool for process analytics . For this application, a process stream is continuously sampled according to an endlessly repeated PRBS and a deconvoluted chromatogram containing the averaged information on the components, which elute within the time duration of the last PRBS, is calculated after every time interval Δ t .…”