Deconvolving chromatographic peaks
AssigneeHewlett-Packard Company
InventorRichard F. Lacey
Life of this patent
Estimating the term…
Abstract
Deconvolution of up to three overlapping chromatographic peaks is provided in which pure spectral components are extrapolated from a Euclidean-normalized expression of chromatographic data in the space of the three principal factors. A coordinate transformation to planar coordinates after expansion in factor space and before extrapolation yields the simplicity of linear extrapolation in combination with the inherent accuracy of Euclidean, as opposed to standard, normalization. The estimation of the pure component spectra permits the constructions of a concentration matrix. Improved estimates and an error bound are provided by applying assumptions of non-negativity and limited deviation from the means to the concentration matrix.
Claims13
A method comprising the steps of:
- obtaining a mixture including plural components;
- chromatographically processing said mixture to obtain an elution in which said components are at least partially separated chronologically;
- spectrally analyzing said elution to obtain a series of data spectra;
- constructing a chromatogram from said series of data spectra;
- factor analyzing said chromatogram so as to determine three principal factors;
- expressing each data spectrum as a Euclidean-normalized linear sum of said three principal factors so that each data spectrum can be represented as a point on the surface of a sphere with unit radius;
- performing a coordinate transformation on said data spectra, said coordinate transformation being selected to map great circles onto straight lines in a plane;
- and
- deriving component spectra for said components of said mixture from said data spectra as expressed in said plane.
The method of estimating component spectra of an interval of a chromatogram, said method comprising the steps of:
- selecting an interval of a chromatogram, said interval comprising a series of data arrays, each data array representing values of a dependent variable at a respective value of an independent variable;
- expressing each data array as a Euclidean-normalized linear sum of the three principal factors of said chromatogram so that each data array is represented by a point on a sphere of unit radius;
- expressing said data arrays as points on a plane by means of a coordinate transformation which maps great circles of a sphere onto straight lines in a plane;
- determining from said planar representation of said data arrays a series of vertices, at least some of said vertices being determined through linear extrapolation;
- and
- estimating the component spectra from the expression of said data arrays as points on a plane.
A system for estimating the component spectra of an interval of a chromatogram, said system comprising:
- first means for obtaining a chromatogram and identifying an interval of interest thereof, said interval comprising a series of data arrays, each data array representing values of a dependent variable at a respective value of an independent variable;
- second means for expressing each data array as a Euclidean-normalized linear sum of the three principal factors of said chromatogram so that each data array represents a point on a sphere of unit radius;
- third means for expressing said data arrays as points on a plane by means of a coordinate transformation which maps great circles of a sphere onto straight lines in a plane;
- and
- fourth means for determining from said planar representation of said data arrays a series of vertices, at least some of said vertices being determined through linear extrapolation;
- and
- fifth means for estimating the component spectra from the expression of said data arrays as points on a plane.
A computer program comprising:
- first means for factor analyzing a data matrix to determine three principal factors;
- second means for expressing each data array as a Euclidean-normalized linear sum of the three principal factors of said chromatogram so that each data array represents a point on a sphere of unit radius;
- third means for expressing said data arrays as points on a plane by means of a coordinate transformation which maps great circles of a sphere onto straight lines in a plane;
- and
- fourth means for determining from said planar representation of said data arrays a series of vertices, at least some of said vertices being determined through linear extrapolation;
- and
- fifth means for estimating the component spectra from the expression of said data arrays as points on a plane.
Dependencies are inferred from the claim text.