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

2. 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

3. 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

4. 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

5. 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)

6. 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

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

8. 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)

9. 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

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

11. 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?

12. 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)

13. “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

14. 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

15. 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.

16. “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

17. Example of “Classic” ISTD failure
Response A
Response B
(Standard)
Concentration
Area Ratio
Concentration Ratio 1 2
32.968 4 8 16

18. ESTD/”Universal” ISTD Calibration

19. “Classic” ISTD calibration curve

20. 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

21. Example

23. 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

24. 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?”.

25. 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)

26. Gaussian peak shape analysis

27. Gaussian peak shape analysis

28. Gaussian peak shape analysis

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

30. Fourier-domain periodic noise filtration
Median filter in Fourier space

31. Periodic noise filtration – mains frequency

32. Periodic noise filtration – pump pulsations

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

34. 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

35. Weighted PCA
Channel weighting
Point weighting

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

37. Spectral chromatogram with angle profile.

38. Best purity spectrum advantage

39. Spectrum identification
Step 1:
Spectrum calculation.

40. Step 2:
Performing recognition.

41. Step 3:
Conflicts resolving.

42. Step 4:
View and print report.

43. 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

44. Main spectral window.

45. 3D multi-channel chromatogram view.

46. 2D multi-channel chromatogram view.

47. 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?

48. 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.

49. 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

50. 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.