Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Chemical analysis
Reexamination Certificate
1997-03-05
2002-05-21
Kemper, M. (Department: 2165)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Chemical analysis
C073S061520
Reexamination Certificate
active
06393368
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates generally to chromatographic techniques such as high speed liquid chromatography and gas chromatography, and more particularly to methods and apparatuses for analyzing a multichannel chromatogram which is detected by a diode array detector or the like.
A large number of approaches have been proposed for separating or resolving overlapping peaks on a multichannel chromatogram. The multichannel chromatogram refers to a type of a chromatogram having three-dimensional information composed of an absorbance component, a time component, and a wavelength component. Representatives of such approaches include factor analysis and principal component analysis which are techniques of multivariate analysis (see, for example, U.S. Pat. No. 4,807,148 issued to J. K. Strasters et al.; H. R. Keller et at, Journal of Liquid Chromatography, No. 12, pp. 3-22 (1988); J. Craig Hamilton et al., Chemometrics and Intelligent Laboratory Systems, No. 12, pp. 209-224 (1992); Journal of Chemometrics, No. 4, pp. 1-13 (1990), and so on).
A non-linear least-squares analysis has also been proposed as another approach for analyzing a multichannel chromatogram (see, for example, Itoh et al, Abstracts of Seventh Liquid Chromatography Conference, pp. 5 (1986); Itoh et al, Abstracts of 22th Applied Spectrometry Tokyo Conference, pp. 141 (1987); and Itoh et at, Abstracts of 19th HPLC Research Conversation, pp. 30 (1988)). This approach has been developed from a method for fitting overlapping peaks on a multichannel chromatogram obtained from GS/MS using the Gaussian (normal distribution function), which was proposed by F. J. Knorr, by substituting EMG (Exponentially Modified Gaussian) as a more realistic model function for the former Gaussian. This approach will be explained here in detail since it will facilitate the understanding of later descriptions.
Multichannel chromatogram data gathered from a diode array detector is given by the following matrix Dij (1):
D=R·A·S=R·X
(1)
where i represents a time index, j a wavelength index, k a component index, Dij the absorbance, Rik a normalized retention waveform (chromatogram magnitude), Akk a quantitative factor relative to the concentration of a k-component, Skj a normalized spectral intensity, and Xkj a quantitative spectral intensity multiplied with the factor Akk relative to the concentration of a k-component. It should be noted that the wavelength index j is used as a n index of the m/z value when a mass spectrometer is used.
Here, a trial matrix R′ik is introduced in place of the chromatogram intensity matrix Rik. From the equation (1), a trial spectral intensity matrix X′jk can be computed from the trial matrix R′kl and the matrix Dij containing the measured data. Consequently, a trial data matrix D′ij can be obtained as expressed by the following equation (2):
D′=R′·
(
R′
T
·R
′)
−1
·R′·
T
D
(2)
where T in R′
T
means a transpose matrix, and −1 in (R′
T
·R′)
−1
means that the associated matrix is an inverse matrix.
The least-squares method determines parameters so as to minimize Dij-D′ij and provides the best-fit R′ik for each component. In this way, the respective component matrices R′ik and X′ik can be separated or resolved from the matrix Dij including data on overlapping peaks.
This approach utilizes EMG which can also represent a asymmetric tailing peak as the R′ik matrix (the following equation (3)).
R′
ik
=1/(&tgr;
k
&sgr;
k
(2&pgr;)
½)
∫
o
t1
exp[−(
t
i
−t
RK
−t
′)
2
]/2&sgr;
k
2
−t
′/&tgr;
k
)]
dt′
(3)
where t
RK
is retention time for a k-component, &sgr;
K
standard deviation for the k-component, and &tgr;
K
the time constant for the k-component.
JP-A-60-2447 describes a chromatographic quantitative analyzing method and apparatus which detect temporal changes in absorbance at multiple wavelengths as three-dimensional information to perform quantitative analysis. The chromatographic quantitative analyzing method and apparatus employ functions f
1
(&lgr;) and f
2
(&lgr;) which represent two previously measured two-dimensional standard spectra. Then, an equation is obtained for a two-dimensional synthesized component function fs(&lgr;) of a measured sample having overlapping peaks using the above-mentioned functions f
1
(&lgr;) and f
2
(&lgr;). The overlapping peaks are resolved by the obtained equation.
Other approaches utilizing deconvolution have also been proposed as a method for analyzing an ordinary chromatogram, i.e., a chromatogram having two-dimensional information (composed of an absorbance component and a time component). See, for example, U.S. Pat. No. 4,941,101 issued to Paul Benjamine Crilly; Paul Benjamine Crilly, IEEE Transaction on Instrumentation and Measurement, No. 40, pp. 558-562 (1991); and Journal of Chemometrics, No. 5, pp. 85-95 (1991).
Here, the convolution is defined. Original data is detected by a detector, and dispersed by an inherent device function h(t) (dispersion function(instrument function)) which represents the detection characteristics of the detector. The deconvolution is determined to be the processing for removing a dispersion portion of the data by the device function h(t) from the dispersion data. An equation defining the deconvolution is given in the following equation (4):
D
(
t
)=∫
−∞
∞
h
(
t
′)
d
(
t−t
′)
dt′=h
(
t
)*
d
(
t
) (4)
where D(t) is a detected waveform, d(t) an original waveform, and h(t) a dispersion function.
For the convolution applied to analysis on a chromatogram having two-dimensional information, several approaches have been proposed for promoting the convergence. Specifically, these approaches have been proposed principally relying on iteration methods, and include the Gaussian elimination which performs an inverse matrix operation, as well as Jacobi's method, Gauss-Seidel's method, Fourier Transform method, Van Cittert's method, Constrained Iterative method, Jansson's method, Gold's ratio method, and so on. For details of these methods, see “Waveform Data Processing for Scientific Measurements”, edited by Shigeo Minami, published by CQ Editorial, pp. 122-139 (1986); and P. A. Jansson, “Deconvolution with Applications in Spectroscopy, New York, Academic (1984).
Also, a method based on factor analysis for separating or resolving overlapping peaks on a multichannel chromatogram is introduced in detail, for example, by Edmund R. Malinowski, “Factor Analysis in Chemistry”, John Wiley & Sons, Inc. (1991).
This factor analysis based method is multivariate analysis, and its basic thinking is that a data matrix D is modeled as a product of a spectral matrix X and an elution profile matrix Y, as represented by the following equations (5) and (6). It should be noted however that the equation (6) defines that each component k is normalized to a peak area of one. However, since the data matrix D cannot be uniformly resolved from a mathematical point of view, several rational constraints are provided to solve the problem.
D=XY
(5)
∑
j
Y
kj
=
Y
k
-
=
1
(
6
)
where
Dij: Signal Magnitude;
Xik: Spectral Intensity;
Ykj: Elution Profile;
i: Channel Index;
k: Component Index;
j; Time Index.
Generally, an elgenvalue problem is solved for the data matrix D, the number n of components is determined by principal component analysis, an abstract elution profile matrix V having a characteristic vector as its element is transformed by a matrix T, and thus a physically meaningful elution profile matrix Y is obtained. As the matrix Y is determined, the spectral matrix X can be computed from the data matrix D by the following equations (7)-(15).
More specifically, solving the eigenvalue problem, the data matrix D is represented by a product of an abstract spectral matrix U and the abst
Deguchi Kisaburo
Ito Masahito
Kemper M.
Kenyon & Kenyon
LandOfFree
Method and apparatus for analyzing multi-channel chromatogram does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Method and apparatus for analyzing multi-channel chromatogram, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Method and apparatus for analyzing multi-channel chromatogram will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-2877052