Modified bi-Gaussian models to describe chromatographic peaks as a function of peak-shape parameters

Abstract

The modelling and prediction of chromatographic peak profiles have been extensively studied, with foundational contributions such as Grushka's bi-Gaussian model. In this work, this approach is extended to two modified Gaussian models: The Linear Modified Gaussian (LMG) and the Parabolic Variance Modified Gaussian (PVMG). These models enhance the traditional Gaussian framework by allowing the peak variance to change according to parabolic trends, thereby capturing deviations from ideal Gaussian peak shapes. This added flexibility enables a more accurate representation of a wide range of chromatographic peak shapes with varying degrees of asymmetry. The proposed modified bi-Gaussian models (BLMG and BVMG with six and seven parameters) use peak-shape parameters that can be expressed as functions of retention time. This makes them well suited for predicting peak shape and chromatographic resolution, which are key factors in optimising the separation of complex analyte mixtures. The BVMG model with seven parameters yields fitting errors below 1 % for most peaks and below 2 % for the peaks of all assayed probe compounds, comparable to the more sophisticated Parabolic Lorentzian Modified Gaussian (PLMG) model, while relying only on peak-shape parameters (retention time, peak height at the peak maximum, and half-widths measured at 60 and 10 % of peak height). The performance of the models is validated through the fitting and prediction of chromatographic peaks for compounds eluted using two columns with distinct retention mechanisms: Zorbax C18 and Hypercarb porous graphitic carbon columns.