Would you like to include PeakLab’s high-resolution peak-fitting analytics in your own instrumentation software?

#### UHPLC High-Throughput Separations

In the fast sub 1-minute separation^{1} above, only the last of the eight components can be deemed baseline resolved. The instrumental analysis above offers the apex location, the area and area percentage for each peak, and a FWHM, asymmetry, resolution, and plate count for all except the strongly overlapped peaks 3 and 4.

If the data are effectively fitted in PeakLab, each of the eight peaks are accurately separated and quantified. There is no difference between a baseline resolved peak and a non-baselined resolved peak in this type of nonlinear fitting.

##### Parametric Modeling

In the above basic analysis, you see that we have areas of 3.87 and 5.32 for peaks 3 and 4 in the conventional instrumental integration. In the PeakLab fit, we see that the actual areas are 4.77 and 4.62. The second peak is actually of lesser area!

The PeakLab values will be more accurate not only because of its management of overlapping peaks, but because the measured values above are based on the noise-free modeled peaks, not upon the raw data where noise is present. This makes it possible to compute high accuracy moments, even the higher moments, in addition to the more typical measured values.

If we look at the ratio of the area to the right of the apex to the area to the left, ApexAsym, we see values well above 1. This means the apex locations will not represent the center of mass of the elution. More importantly, the instrumental efficiencies and resolutions based on Gaussian assumptions that use apex locations and FWHM values will be significantly in error.

In the parameter table, the 8 peaks each have an a_{0} fitted area, an a_{1} center, and an a_{2} width. There are just four additional parameters, a_{3} with adds the chromatographic tailing or fronting for all eight of the peaks, a_{4} with adds a third moment skewness to all of the underlying peaks, a_{5} with adds a fourth moment ‘fatness of tails’ or kurtosis, and a_{6} with adds a first order exponential distortion or IRF. By adding just 4 crucial parameters to the 24 that would exist for fitting 8 Gaussians, the goodness of fit improves to an impressive r^{2} of 0.99995 – the fitted curve essentially overlays the data! Just 28 numeric parameters will completely reconstruct each of the 8 peaks as well as the overall data set, noise-free, and at any sampling rate desired.

##### System Suitability

For the instrumental analysis, the last peak, baseline resolved, has a FWHM based efficiency of 11925 plates. PeakLab’s FWHM plate count for this peak is very close, 11897. The instrumental estimated efficiencies are not given for the overlapped third and fourth peaks and the fifth is clearly an outlier. PeakLab’s estimates of efficiencies are much more consistent with elution time and estimated for all peaks.

PeakLab also offers a moment based efficiency estimate, Nmoment, which although noise-free, is adversely impacted by the asymmetry and the high IRF instrumental distortion. It differs mainly because the Gaussian assumption of the Ngauss plate estimate is invalid. The Ndeconv removes the IRF, has a higher plate count, and is closer to constant across the peaks. The Nmodel goes a step further and estimates the efficiency independent of the asymmetry in the core density and the chromatographic concentration-dependent tailing-fronting, mapping the performance of the column’s media independent of both concentration and packing nonidealities.

For these peaks, the instrumental analysis above does not report a resolution for three of the pairings of adjacent peaks. PeakFit furnishes both a Gaussian and a moments based resolution for every peak, including peaks 3 and 4. Because the Gaussian assumption is invalid, the moment-based resolutions Res(Stat) would best be used. Note that non-linear peak fitting easily manages resolutions well below 1.0.

With peak fitting, it is possible to integrate the differences between the fitted peaks, resulting in overlap areas. This will catch column performance issues sooner than resolution estimates if the two components will be present in the same ratio. The overlap area between peaks 3-4 is .93, 20.2% of peak 3, 19.6% of peak 4. Any increase in this overlap fraction would represent a loss of performance.

##### Statistical Modeling

Since peak fitting is a statistical procedure, each estimated parameter will have a confidence band (here 95%). The t-values are also an indicator of which parameters are most accurately estimated. This is the extract of the statistical analysis for peaks 3 and 4. The center is the most accurately estimated, the core density asymmetry the least, although as you will note each of these parameters are very strongly significant with very narrow confidence bands. In PeakLab, a value is grayed when it cannot test as significant (different from zero).

##### Deconvolution

The parameters of a chromatographic fit furnish many different levels of deconvolution. A Gaussian becomes an HVL by adding a chromatographic fronting-tailing (a_{3} in this example). A Gaussian becomes a generalized normal by adding an asymmetry term (a_{5}) and that generalized normal becomes a generalized error by adding a fourth moment power of decay term (a_{4}). A twice-generalized HVL with both a third and fourth moment term in the core probability density becomes a real world instrumental peak with one or more parameters modeling the instrumental distortions (a_{6} in this example).

This is the last of the eight peaks. The wide-tailed amber peak is the peak as sampled by the instrument. The red peak is the deconvolved peak with the IRF or instrumental distortions removed. In a PeakLab fit, there are additional levels of deconvolution where one recovers the true peak free of instrumental distortions and separation nonidealities.

#### OEM Specifics

The PeakLab numeric modeling IP consists of C++ classes which are readily converted into Windows DLLs for use in Windows-specific systems. Please contact AIST Software to discuss how this technology could be integrated into your instrument software:

Ron Brown

Phone: (541) 991-9353

Email: ron@aistsw.com

LinkedIn: https://www.linkedin.com/in/ronald-e-brown-4327a2117/

^{1}Ultrafast separation of eight test components complements of Dr. Farooq Wahab, University of Texas, Arlington (10cm x 2.1mm Agilent Poroshell 2.7um C-18 column, mobile phase 80-acetonitrile/20-water, 0.6ml/min, UVwl=220nm).