Apparatus and methods for the analytical determination of sample component concentrations that account for experimental error
First Claim
1. An improved method of determining the concentrations of one or more components of an analytical sample from an observed spectrum estimated by
wherein Yobs, is a vector whose "m" elements are the magnitudes of the observed spectrum at each value of an independent variable ω
)=P(ω
)·
C,
, C is the vector whose 37 n" elements are the estimated concentrations of "n" components that contribute to the measured spectrum, and P is a "m×
n" matrix whose elements are the magnitudes of the contribution to the spectrum of each of "n" components at each of the "m" values of the independent variable ω
, wherein the method comprises generating a sample spectrum from which the concentrations of the sample components are determined and determining the sample concentrations from the spectrum, the improvement comprising correcting for experimental error by modeling the experimental error as "r" types of errors given by the product ξ
·
K where K is a vector whose "r" elements are the magnitudes of each of the "r" types of experimental errors and ξ
is an "m×
r" matrix whose elements are the relative errors at each value of ω
for each type of experimental error, adding the product ξ
·
K to the estimated spectrum as
space="preserve" listing-type="equation">Y.sub.obs (ω
)=P(ω
)·
C+ξ
·
Kand solving for the best fit values of C and K, wherein "n" and "r" are integers each greater or equal to 1 and "m" is an integer at least "n+r".
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Abstract
The present invention provides apparatus and methods for determining the concentration of sample components of a sample by an analytical technique that yields a spectrum that can be written as Y(ω)=P(ω)·C. The apparatus and methods of the invention account for experimental errors that give rise to distortions in the observed spectrum and that consequently result in inaccurate determinations of sample component concentrations. The invention accounts for such errors by modeling the total experimental error as the sum of one or more types of errors that can be written as ξ·K. The spectrum is then modeled as Y=P·C+ξ·K. Using the observed spectrum, known values for P, and a mathematical model for ξ, this equation can be solved for the best fit value of the sample component concentrations, C, and the magnitudes of the errors, K. The method can be used for any error that can be modeled in the foregoing manner, such as a shift in the spectrum. Particular types of shift include constant shift as well as linear shift across the entire spectrum. The apparatus and methods are advantageously used in absorbance spectroscopy and chromatography.
96 Citations
18 Claims
- 1. An improved method of determining the concentrations of one or more components of an analytical sample from an observed spectrum estimated by
- space="preserve" listing-type="equation">Y.sub.obs (ω
)=P(ω
)·
C,
wherein Yobs, is a vector whose "m" elements are the magnitudes of the observed spectrum at each value of an independent variable ω
, C is the vector whose 37 n" elements are the estimated concentrations of "n" components that contribute to the measured spectrum, and P is a "m×
n" matrix whose elements are the magnitudes of the contribution to the spectrum of each of "n" components at each of the "m" values of the independent variable ω
, wherein the method comprises generating a sample spectrum from which the concentrations of the sample components are determined and determining the sample concentrations from the spectrum, the improvement comprising correcting for experimental error by modeling the experimental error as "r" types of errors given by the product ξ
·
K where K is a vector whose "r" elements are the magnitudes of each of the "r" types of experimental errors and ξ
is an "m×
r" matrix whose elements are the relative errors at each value of ω
for each type of experimental error, adding the product ξ
·
K to the estimated spectrum as
space="preserve" listing-type="equation">Y.sub.obs (ω
)=P(ω
)·
C+ξ
·
Kand solving for the best fit values of C and K, wherein "n" and "r" are integers each greater or equal to 1 and "m" is an integer at least "n+r". - View Dependent Claims (2, 3, 4, 11, 12, 13, 14, 15, 16, 17, 18)
- space="preserve" listing-type="equation">Y.sub.obs (ω
- 5. An improved method of determining the concentrations of one or more components of an analytical sample whose observed spectrum are estimated by the equation
- space="preserve" listing-type="equation">Y.sub.obs (ω
)=P(ω
)·
C
wherein Yobs is a vector whose "m" elements are the magnitudes of the observed spectrum at each value of an independent variable ω
, C is the vector whose "n" elements are the estimated concentrations of "n" components that contribute to the measured spectrum, and P is a "m×
n" matrix whose elements are the magnitudes of the contribution to the spectrum of each of "n" components at each of the "m" values of the independent variable ω
, wherein the method comprises generating a sample spectrum from which the sample component concentrations are determined and determining the sample component concentrations from the spectrum, the improvement comprising correcting for experimental error by modeling the experimental error as a shift of the spectrum by an amount dω
, estimating a shift, dω
, calculating an adjusted spectrum, Yadj, using either the equation;
##EQU28## and determining the concentrations, C, by solving either the equation;
space="preserve" listing-type="equation">Y.sub.adj =P·
Cor;
space="preserve" listing-type="equation">Y.sub.adj =P·
C+ξ
·
K.for the best fit value of C, where ξ
takes the form ξ
=Y'"'"'=(∂
Yobs)/(∂
ω
) or ξ
=P'"'"'·
C, where ##EQU29## "m" and "n" are integers, "n" is greater or equal 1 and "m" is at least "n".- View Dependent Claims (6, 7)
- space="preserve" listing-type="equation">Y.sub.obs (ω
- 8. An improved method of determining the concentrations of one or more components of an analytical sample whose observed spectrum are estimated by the equation
- space="preserve" listing-type="equation">Y.sub.obs (ω
)=P(ω
)·
C
wherein Yobs, is a vector whose "m" elements are the magnitudes of the observed spectrum at each value of an independent variable ω
, C is the vector whose "n" elements are the estimated concentrations of "n" components that contribute to the measured spectrum, and P is a "m×
n" matrix whose elements are the magnitudes of the contribution to the spectrum of each of "n" components ar each of the "m" values of the independent variable ω
, wherein the method comprises generating a sample spectrum from which the sample component concentrations are determined and determining the sample component concentrations from the spectrum, the improvement comprising correcting for experimental error by modeling the experimental error as a shift in ω
by an amount dω
, estimating a shift, dω
, calculating an adjusted P matrix, Padj, using either the equation;
space="preserve" listing-type="equation">P.sub.adj =P.sub.obs (w+dω
)or;
space="preserve" listing-type="equation">P.sub.adj =P.sub.obs +P'"'"'·
dωand determining the concentrations, C, by solving either the equation;
space="preserve" listing-type="equation">Y.sub.obs =P.sub.adj ·
Cor;
space="preserve" listing-type="equation">Y.sub.obs (ω
)=P.sub.adj (ω
)·
C+ξ
·
Kfor the best fit value of C, where ξ
takes the form ξ
=Y'"'"'=(∂
Yobs)/(∂
ω
) or ξ
=P'"'"' C, where ##EQU32## and "n" is greater or equal to 1 and "m" is at least "n".- View Dependent Claims (9, 10)
- space="preserve" listing-type="equation">Y.sub.obs (ω
Specification
-
- Resources
-
Current AssigneeCIBA Vision Corporation (Bayer AG)
-
Original AssigneeChiron Corporation (Bayer AG)
-
InventorsScharlack, Ronald S., Sodickson, Lester
-
Primary Examiner(s)Trammell, James P.
-
Assistant Examiner(s)CHOI, KYLE JAEHUN
-
Application NumberUS08/496,724Time in Patent Office978 DaysField of Search364/571.01, 364/571.02-571.06, 364/497, 364/498US Class Current702/23CPC Class CodesG01N 21/274 Calibration, base line adju...
