Yuri Kalambet, Ampersand Ltd., Moscow, Russia www.ampersand.ru Implementation of chemometric techniques in chromatographic data station software Yuri Kalambet, Ampersand Ltd., Moscow, Russia www.ampersand.ru

Data processing Noise level estimation Noise filtration and/or data bunching Peak search Peak quantification (area, height, asymmetry, etc.) Table of components (qualitative analysis) Calibration graph (quantitative analysis) Peak shape analysis and deconvolution Periodic noise filtration Multichannel (spectral) data analysis

Noise High-frequency noise estimation using the whole time series data set Noise filtration could cause questions from GLP rules Bunching never causes questions from GLP, but can significantly reduce observed noise Noise is taken into account while: peak detection; approximation quality evaluation multichannel/spectral analysis

Peak Quantification Baseline Y position using weighted Savitsky-Goley approximation with evaluation of approximation quality Primary peak parameters using adaptive polynomial approximation, where parameters of polynomial depend on target peak width and asymmetry Criterion for algorithm selection: Peak parameters should be resistant to bunching operation

Noise definition 1st derivative point DOES NOT belong to “noise pool of points” if both of the neighboring derivative points have the same sign 1st derivative point DOES NOT belong to “noise pool of points” if its absolute value is outside 5 sigma of absolute values distribution (iterative procedure)

Calibration Predictive relationship between input and detector response Input: calibration samples – concentrations of components Output: peak area or height Prediction: Predict unknown input looking at response

ESTD Calibration Response (Area or Height) versus Quantity Quantity is provided without error - false Response is measured with random normally distributed error – sometimes true

Calibration Curve Axes: Q – Quantity (NOT Concentration), R – Response (Area or Height) Independent variable: Typically Q, sometimes R Calibration curve: polynomial interpolation Prediction: either solution of polynomial equation (independent Q) or value of polynomial (independent R) – we denote either of them W(R)

Quantification Absolute Concentration Quantity of injected substance Qx = W(Rx) Concentration of initial sample Cx = Qx/V = W(Rx)/(Vinj*A/D) Vinj – injection volume A – amount D – dilution

ISTD Targets Reason Axis Sample-size variations Q Effect of sample preparations Q Instrument drift R All reasons are acting always together

ISTD tricks Add component with known concentration to sample Add component with known concentration to calibration samples Usually it’s done together, but who told that you can’t do it separately?

ISTD with ESTD calibration = Relative Concentration Accounts for systematic error due to sample-size error and sample losses while preparation. Assumption: volume is unknown and is calculated using known concentration of the internal standard V = Qxistd/Cxistd = Wistd(Rxistd)/Cxistd, Qxistd is calculated using calibration curve of Internal standard from Rxistd, Cxistd – declared concentration of standard in sample Relative Concentration C = Qx/V = Cxistd×Wx(Rx)/ Wistd(Rxistd)

“Universal” ISTD Calibration If calibration is nonlinear, we must measure this nonlinearity, i.e. we MUST know ESTD calibration curve of the Internal Standard component In the case we learned this curve somehow, we can use this curve to change positions of calibration points of other components using the same trick as was used while calculating Relative Concentration: Qn = Cn×V = Cn×Wistd(Ristd)/Cistd So, for Internal Standard predefined curve is in use, all other components get curves constructed conditionally, condition being known calibration curve of the Internal Standard component

Pro et Contra Advantages: Only one type of axes Calibration curves are suitable for calculation of both Absolute and Relative concentrations Disadvantages: ESTD Calibration curve of Internal Standard is required

Qn = Cn×V = Cn×Wistd(Ristd)/Cistd Multiplication of Q axis of Internal Standard to any number will multiply Q coordinates of all corrected points of all components to the same number, hence causing “affinity” change of all calibration curves. Calibration curve will change, absolute concentration also, but not Relative Concentration C = Cxistd×Wx(Rx)/ Wistd(Rxistd) If all calibration dependencies are linear through origin Q = K×R, it is possible to select multiplication factor so, that Kistd = 1 and we will get relative response factors for all other components.

“Classic” ISTD Calibration dependence in coordinates Response Ratio vs. Concentration ratio Calibration curve: polynomial, typically straight line through origin Prediction: from Response Ratio predict Concentration Ratio Peculiarities: no calibration curve for Internal Standard component

Example of “Classic” ISTD failure Response A Response B (Standard) Concentration Area Ratio Concentration Ratio 18.1269247 9.516258 1 1.904837 32.9679954 18.12692 2 1.818731 55.0671036 32.968 4 1.67032 79.8103482 55.0671 8 1.449329 95.9237796 79.81035 16 1.201897

ESTD/”Universal” ISTD Calibration

“Classic” ISTD calibration curve

Device Drift Drift model: R = K×F(Q) Drift can be compensated completely, if exists such k, that K×F(Q)=F(k×Q) Particular case: linear through origin calibration; K = k

Example

Conclusions ISTD is split in two parts: ISTD quantification (Relative Concentration) and ISTD Calibration. Parts can be applied separately Relative Concentration is applicable for both ESTD and “Universal” ISTD calibrations Full “Universal” ISTD calibration can be used for both ESTD and ISTD calculations Simplified “Universal” ISTD calibration can be used in the case of linear through origin calibrations instead of “Classic” ISTD calibration including imitation of user interface Full “Universal” ISTD solution still works where “Classic” already fails, i.e. it allows to get into account wide concentration range of Internal Standard in the case of nonlinear calibrations

Difficulties User mind. The more users are used to “Classic” ISTD method, the more difficult it is to change their minds. Typical argument: -“Old approach works. We typically use linear through origin calibrations. Why should we change the way how we work?”.

Peak deconvolution by shape Peak shape Gaussian Exponentially modified Gaussian Corresponds to reference peak Tuning, specific to chromatography Peak width individual for every peak; the same for all peaks proportional to retention time asymmetry of the same sign (2) Optimization criterion quadratic (sum of squares of residuals) weighted quadratic (weight = response)

Gaussian peak shape analysis

Gaussian peak shape analysis

Gaussian peak shape analysis

EMG peak shape analysis Problems: product of zero to infinity for some range of parameters Solution: or “standard” Gaussian function, depending on parameter values

Fourier-domain periodic noise filtration Median filter in Fourier space

Periodic noise filtration – mains frequency

Periodic noise filtration – pump pulsations

Multichannel chromatogram questions Which channel is better? How to detect peaks? How to identify peaks? How to access substance purity?

Multichannel chromatogram answers Calculated channels Using weighted PCR: Noise-normalized detector response space for spectra comparison Measure of difference for spectra: angle “Local” spectrum quality: angle with neighbors Factor analysis with missing (overloaded) points allowed Qualitative and quantitative spectra comparison

Weighted PCA Channel weighting Point weighting

Calculated channels Summary. Types of Calculated channels: Total Average Difference Integral Derivative - up to 3-rd order Angle «Response/Time» channel Spectral ratio channel

Spectral chromatogram with angle profile.

Best purity spectrum advantage

Spectrum identification Step 1: Spectrum calculation.

Step 2: Performing recognition.

Step 3: Conflicts resolving.

Step 4: View and print report.

Calculated channels in “Chrom&Spec”. Summary. Types of Calculated channels: Total Average Difference Integral Derivative - up to 3-rd order Angle «Response/Time» channel Spectral ratio channel

Main spectral window.

3D multi-channel chromatogram view.

2D multi-channel chromatogram view.

Factor analysis example. Picture shows the “sum of s/n” channel of multi-channel chromatogram. Usual peak-detection procedure failed to resolve peaks. What about factor analysis?

Factor analysis. Step 1. Software makes PCR of the region selected and suggests number of components in the analyzed region (Rank). Overlapping only 2 peaks means that software does not look for overlapping of 1st and 3rd components, only 1st and 2nd and then 2nd and 3rd.

Factor analysis. Step 2 On the left panel we can choose any channel to view peak deconvolution results. Rotation is selected using “local purity” attribute, resulting in “Pure component” approach

Factor analysis. Step 3 The resolved peaks are displayed together with the original channel. The chromatogram with additional newly generated channels can be saved into separate file. Each generated channel represents the detector response, corresponded to particular component. When user finishes the wizard, the original peak is split in the proportions, corresponding to component’s fractions.