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 (<i>W</i><sub><i>h</i></sub>), at any height <i>h</i> (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 <i>W</i><sub><i>h</i></sub> = <i>p</i>(ln <i>h̅</i>)<sup><i>q</i></sup>, where <i>h̅</i> is <i>h</i><sub>max</sub>/<i>h</i>, <i>h</i><sub>max</sub> being the peak amplitude, and <i>p</i> and <i>q</i> being constants. This fits actual
chromatographic peaks well, allowing explicit expressions for <i>W</i><sub><i>h</i></sub>. We consider the optimum
height for quantitation. The width-concentration relationship is given
as ln <i>C</i> = <i>aW</i><sub><i>h</i></sub><sup><i>n</i></sup> + <i>b</i>, where <i>a</i>, <i>b</i>, and <i>n</i> are constants. WBQ ultimately performs quantitation
by projecting <i>h</i><sub>max</sub> 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
