Width Based Quantitation of Chromatographic Peaks: Principles and Principal Characteristics

Height- and area-based quantitation reduce two-dimensional data to a single value. For a calibration set, there is a single height- or area-based quantitation equation. High-speed high-resolution data acquisition now permits rapid measurement of the width of a peak (W_h), at any height h (a fixed height, not a fixed fraction of the peak maximum) leading to any number of calibration curves. We propose a width-based quantitation (WBQ) paradigm complementing height or area based approaches. When the analyte response across the measurement range is not strictly linear, WBQ can offer superior overall performance (lower root-mean-square relative error over the entire range) compared to area- or height-based linear regression methods, rivaling weighted linear regression, provided that response is uniform near the height used for width measurement. To express concentration as an explicit function of width, chromatographic peaks are modeled as two different independent generalized Gaussian distribution functions, representing, respectively, the leading/trailing halves of the peak. The simple generalized equation can be expressed as W_h = p(ln h̅)^q, where h̅ is h_max/h, h_max being the peak amplitude, and p and q being constants. This fits actual chromatographic peaks well, allowing explicit expressions for W_h. We consider the optimum height for quantitation. The width-concentration relationship is given as ln C = aW_hⁿ + b, where a, b, and n are constants. WBQ ultimately performs quantitation by projecting h_max from the width, provided that width is measured at a fixed height in the linear response domain. A companion paper discusses several other utilitarian attributes of width measurement.