Patent Application: US-92110804-A

Abstract:
the invention refers to a method of resonance spectroscopy for the analysis of statistical properties of samples , comprising the following steps : a ) recording of a complex resonance frequency spectrum of each sample by means of phase sensitive quadrature detection ; b ) numerical differentiation of the recorded complex resonance frequency spectra versus frequency ; c ) determination of the absolute value of each differentiated complex resonance frequency spectrum ; d ) allocation of each fingerprint to a point of a multidimensional point set ; and e ) performing a pattern analysis of the generated points for characterizing the statistical properties of the samples . the inventive method tolerates unintended variances of measurement in the recorded resonance frequency spectra , in particular caused by phase errors , and allows reliable automated spectral analysis .

Description:
the invention offers an alternative strategy on how to deal with spectra affected by phase and base line errors as input for multivariate statistics . the quality of results of multivariate statistical analysis of nmr spectra is strongly dependent on the quality of referencing , solvent suppression , shimming , phase and baseline correction . if one or more of these aspects is / are poorly dealt with , statistical analysis may be completely spoiled providing literally unusable results . especially phase and baseline errors are notorious for hampering automated nmr screening . although automation of phasing and baseline correction has been subject of several studies , currently no perfectly reliable strategy is available . on the other hand , manual phasing and baseline correction is a tedious and time consuming procedure and can not realistically be considered in an automation context . in the following , an alternative to phasing and baseline correction will be presented which may at least give semi - quntitative multivariate statistical results . although the theoretical concept is derived based on of the assumption of lorentzian line shapes , the results should apply even if the line shape assumption does not apply in the strict sense . in the following , we consider spectra consisting of superpositions of lorentzian lines . purely mathematically speaking , the lorentzian line shape is defined by in fig1 , the real part of the lorentzian line is shown . the center is at x = 0 and its linewidth is equal to one . the absolute value of the first derivative is similar to the real part of the lorentzian line shape , i . e . repeating again : this operation ( 1 . calculation of the first derivative of the complex spectrum and 2 . determination of the absolute value , i . e . magnitude calculation ) reproduces the real part of the lorentzian line . this is illutrated in fig2 . fig2 shows the real and imaginary part of a lorentzian line a ) and their first derivatives b ). in c ) the absolute value of the complex first derivative is overlaid with the original real part line shape function . the functions are identical . note that phase errors do not affect the absolute value of the complex first derivative . as a consequence , the real part of a spectrum consisting of a number of non - overlapping lorentzian lines of similar line width is almost perfectly reproduced by the absolute value of its first derivative . no phasing is needed to obtain the real part . for experimental examples see fig1 through 13 described below . fig3 shows a phase error affected superposition of 6 lorentzian lines a ). in b ) the result of the absolute value of the first derivative of the non - phase corrected complex spectrum is plotted ( bottom ) together with the phase corrected real part spectrum ( top ). ( a ) if lines of different line width co - exist in a spectrum and / or case ( a ) shall be considered first where we start from a spectral line of half width δω s ⁡ ( ω ) = δ ⁢ ⁢ ω 2 ⁢ ⁢ π ⁢ { 1 1 + [ 2 ⁢ ( ω - ω 0 ) / δ ⁢ ⁢ ω ] 2 + i ⁢ 2 ⁢ ( ω - ω 0 ) / δ ⁢ ⁢ ω 1 + [ 2 ⁢ ( ω - ω 0 ) / δ ⁢ ⁢ ω ] 2 } which is normalized to one . then , the absolute value of the first derivative of the complex spectral line is given by : the result is proportional to the real part of the initial line , however scaled by the inverse of the line width . that means , that by the manipulation ( differentiation + absolute value calculation ) the intensity of broad lines is attenuated compared to the intensity of narrow lines : the broader the lines the stronger the attenuation . fig4 shows the effect of the line width on the result of a manipulation via differentiation and absolute value calculation . two lorentzians ( top ) are superposed . the resulting spectrum and the result of the manipulation are given in the lower part of the figure . this attenuation effect may be problematic when proper intensity ratios are needed . however , the advantage is that any distortions due to base line problems or imperfect water suppression are not transferred into the absolute value of the derivative of the spectrum , i . e . into the fingerprint . fig5 illustrates a phase error affected superposition of 6 lorentzian lines a ) added with a very broad phase twisted lorentzian back ground signal and a linear offset . in b ) the result of the absolute value of the first derivative of the non - phase corrected complex spectrum is plotted ( bottom ) together with the phase corrected real part spectrum without offset and background signal ( top ). case ( b ) mentioned above considers complications due to strongly overlapping lines . strictly speaking , intensity ratios and line shapes of two lines close to each other are modified when applying differentiation and subsequent absolute value calculation . this is illustrated in fig6 . fig6 shows the superposition of two lorentzians of equal line width ( top ). in a ) the peak - to - peak distance is 2 . 5 times the line width whereas in b ) it is one time the line width . in the lower part of the figure , the resulting spectra and the results of the manipulation are given . problems only occur in an intermediate range , where line positions are not identical on one hand and are not too far from each other on the other hand . the degree of nonlinearity after the manipulation is illustrated in the fig7 . spectra are simulated by a superposition of two lines of equal line width . the intensity of one line at frequency 0 ( the reference line ) is kept constant while the intensity of the second line is modified from zero to twice the intensity of the reference line . the change of intensity of the absolute value derivative spectrum is compiled as function of the intensity of the second line . ideally , one would expect a straight line at slope one . however , the closer the lines , the higher the degree of nonlinearity at lower intensity values of the second line . in detail , fig7 illustrates the superposition of two lorentzians of equal line width ( left ). the intensity of the right line ( indicated by an arrow ) is modified from zero to twice the intensity of the left line which is kept at a constant value . the right plot shows the intensity modification of the absolute value derivative spectrum as function of the intensity of the right line . in a second simulation shown in fig8 , the two superposed lines did not have similar line width . instead , the test line with varying intensity had twice the line width than the reference line . in detail , fig8 shows the superposition of two lorentzians of different line width ( left ). the intensity of the right line ( indicated by an arrow ) is modified from zero to twice the intensity of the left line which is kept at a constant value . the right plot shows the intensity modification of the absolute value derivative spectrum as function of the intensity of the right line . as a consequence of this non - linear behaviour , intensity fluctuations of small lines at low intensities are more affected than fluctuations of strong intensity lines . in the linear limit , fluctuation intensities are transferred into intensity fluctuations in the respective absolute value of the derivative scaled by the inverse of the line width . the non - linearity affects the results of multivariate statistics . this shall be illustrated on base of an analysis of a set of spectra from mixtures of apple and pear juice , compare fig9 . 60 samples where analyzed , wherein 10 samples were prepared for each mixing level out of 0 , 10 , 20 , 30 , 40 and 100 % pear juice percentage . bucketing was performed twice , at first using the pure real part spectra ( normal bucketing mode ) and second using the absolute value of the first derivative of the complex spectra ( special bucketing mode ). the bucketing range was 0 to 10 ppm , the bucket size was 0 . 04 ppm and the water region was excluded ( 4 . 5 to 6 ppm ). principal component analysis ( pca ) was performed on each table and the results are given in fig9 . in detail , fig9 shows a principal component analysis of bucket tables originating from a set of spectra from mixtures of apple and pear juice . the upper plots show pc 1 – pc 2 scores plots . the lower plots display the pc 1 scores value as function of the pear juice concentration c . left plots show the results related to the normal bucketing mode whereas the right plots are related to the new special bucketing mode using the absolute value of the first derivative of the complex spectra . the latter results are not dependent on phasing and base - line correction quality . clearly , the mixing levels are - well discriminated in the pc 1 – pc 2 scores plots in both cases . interestingly , the spread in pc 2 is larger in the normal bucketing mode . detailed inspection revealed that the outliers in the scores plot resulting from the normal bucketing mode are due to substantial baseline errors . those outliers do not occur in case of pca on the tables resulting from the special bucketing mode . the reason is obvious : baseline errors are suppressed in this bucketing mode due to the properties of first derivatives . when displaying the pc 1 scores values as function of the pear juice concentration , one can see a pure linear behaviour in case of the normal bucketing mode , as one would expect . in the inventive special bucketing mode there is a slight deviation from the linear relation reflecting the non - linearity discussed earlier already . however , both results ( i . e . dependencies ) are well defined and similarly suited for prediction of concentration ratios from newly incoming samples . this only depends on the quality of model building which may be optimized by sufficiently many samples as input for model building . it should be noted that the pca results arising from the special bucketing mode were not depending on the quality of phasing and base line correction as expected from the previous discussion . in conclusion , an alternative method on how to extract multivariate statistical information contained in badly phase and base line corrected spectra was introduced . in high resolution nmr , the advantages of the method more than compensate for problems arising from nonlinear effects . however , care has to be taken when shimming is not completely under control . the same resonance would result at least in a broader line if shimming was not at optimum . the resulting absolute value of the first derivative would be artificially attenuated . that means , if multiple spectra shall be used in the same statistical context , shimming quality should be similar for all of them . fig1 through 13 show experimental data illustrating the advantages of the invention . fig1 shows a manually phase corrected apple juice spectrum ( top ) and the absolute value of the first derivative of the corresponding complex spectrum ( bottom ). differences between both functions are rather minor . fig1 shows a dephased apple juice spectrum ( top ) and the absolute value of the first derivative of the corresponding complex spectrum ( bottom ). the quality of the latter is not affected by the phase error . fig1 shows a rat urine spectrum ( top ) and the absolute value of the first derivative of the corresponding complex spectrum ( bottom ). the distortions due to imperfect water suppression are not transferred into the latter function . fig1 shows similar rat urine ( top ) as in fig1 and the absolute value of the first derivative of the corresponding complex spectrum ( bottom ) which is not affected by phasing errors . / 1 / d . l . massart , b . g . m . vandeginste , l . m . c . buydens , s . de jong , p . j . lewi , and j . smeyers - 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