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GenHVL[W] - [W] Generalized Error, Linear Gradient ZDD

The GenHVL[W] model is offered for possible use with HPLC gradient peaks. The model was created to test whether or not a linear asymmetry across a peak would be a better match for the impact of a rapidly changing gradient across the time of elution for a given peak. The GenHVL[W] model is similar to the GenHVL[Y] model, except the asymmetric generalization varies linearly instead of logarithmically.

In most cases, the Gen2HVL or GenHVL[Y], which use a logarithmic gradient, will be the models of choice for fitting HPLC gradient peaks. If the gradient is particularly strong, however, and a peak is dramatically impacted across the span of its specific elution by a strong linear gradient, and provided there is very little intrinsic fronting or tailing arising from the a3 concentration-dependent chromatographic distortion, the peak shape may be better described by a linear rather than a logarithmic asymmetry.

You will not want to use the GenHVL[W] model for analytic non-gradient peaks. The linear gradient in the [W] density will actually work against the strongly fronted and tailed shapes arising from high intrinsic chromatographic distortions.

There is no GenNLC[W] model. Since the [W] density cannot generate a Giddings shape, the NLC cannot be reproduced.

By inserting the [W] Generalized Error with Linear Gradient ZDD for the PDF, CDF, and CDFc in GenHVL template, we produce the GenHVL[W] model:

a0 = Area

a1 = Center (as mean of underlying normal ZDD)

a2 = Width (SD of underlying normal ZDD)

a3 = HVL Chromatographic distortion ( -1 > a3 > 1 )

a4 = Power of decay (2.0=Gaussian)

a5 = ZDD asymmetry ( -1 > a5 > 1 ), adjusts skew (third moment)

Built in model: GenHVL[W]

User-defined peaks and view functions: GenHVL[W](x,a0,a1,a2,a3,a4,,a5)

Using the GenHVL[W] for Gradient Peaks

The GenHVL[W] was designed specifically for gradient peaks where the gradient is changing so rapidly the gradient strength, assumed to be linearly varying, is the main force behind the peak shape.

The following plot compares both the GenHVL[W] (linear x transform), the first set of peaks, and the GenHVL[Y] (logarithmic x transform), the second set of peaks, for a very slight a3 chromatographic distortion as might be present in a gradient chromatogram. The a0 area, a2 width, and a3 distortion parameters are identical for all of the peaks, and each set illustrates the power varying from 2.0 (a Gaussian decay) to 2.4 (a compaction much greater than a Gaussian) in .1 increments. Apart from the location, the only difference between the two sets is the .025 a5 linear asymmetry parameter in the first GenHVL[W] peaks, and the 0.025 a5 logarithmic asymmetry parameter in the second GenHVL[Y] peaks.

In both cases, you see a significant compaction in the decay. The GenHVL[W] was parameterized to produces shapes one might intuitively expect from increasing the rate of change of the gradient. The difference between the linear and logarithmic transform of the x in the model is apparent.

GenHVL[W] Considerations

The GenHVL[W] model is likely only applicable to strong gradient peak shapes and should be treated as experimental. This model should always be evaluated alongside either the Gen2HVL or GenHVL[Y] model. In our experience, the higher the a3 chromatographic distortion (the greater the intrinsic fronting or tailing), the less the asymmetry can be described linearly.

There is no NLC analog. A logarithmic asymmetry is needed to produce both the HVL and NLC shapes from a generalized model.

The [W] density borrows its ZDD settings from the [Y] density. The [W] density is not offered in the ZDD option.

Since gradient peaks can seldom be fitted with an IRF (the gradient will mask much or all of the IRF), the GenHVL[W] is not offered with built-in <irf> fitting. If you want to experiment with fitting a GenHVL[W] with an IRF, you can create a six-parameter user-defined peak with the built-in GenHVL[W] function: Y=GenHVL[W](x,a0,a1,a2,a3,a4,a5) with the starting values set to PkFnParm(GenHVL[W],n), where n=0 to 5 for the a0 through a5. User-defined peaks automatically include <e>, <e2>, and <ge> IRF fitting options.

If you wish to test a linear asymmetric variant of the GenHVL or GenHVL[Z] models, this can also be done with a similar five-parameter user-defined peak: Y=GenHVL[W](x,a0,a1,a2,a3,2.0,a4) with the starting values set to PkFnParm(GenHVL[W],n), where n=0,1,2,3,5 for a0,a1,a2,a3,a4. The 2.0 power term produces the power of 2 Gaussian tailing.

The GenHVL[W] model is part of the unique content in the product covered by its copyright.