Melanin- and linewidth-corrected pulse-oximetry

Current pulse oximeters tend to overestimate arterial saturation in darkly pigmented patients, increasing occult hypoxemia rates. One proposed mechanism is spectral coloring: melanin contributes to reshaping the detected spectrum of a broad-linewidth source, making the wavelength-dependent parameters behind calibration skin-tone-dependent. Diffuse optics theory allows for a melanin- and linewidth-corrected calibration equation, which to our knowledge has never been tested in vivo. In this work, we fit the empirical linear equation, the diffuse optics theoretical equation, and its corrected form to the public OpenOximetry Repository---considering 98 patients with paired arterial blood-draws, raw photoplethysmograms, and skin reflectance spectra. Accuracy is practically indistinguishable between the three approaches, yet the saturation error's dependence on melanin falls from +2.8 to +1.2 to +0.1 percentage points per unit melanin volume fraction---consistent with the spectral-coloring theory. None of these dependencies on melanin are statistically resolved here---a cohort roughly ten times larger is needed---so the correction is backed by theory and its expected direction. All three calibration approaches carry two degrees of freedom: the theoretical equation drops into existing calibration procedures, and its melanin-aware form needs a per-patient skin-tone measurement. This work demonstrates how the theoretical pulse oximetry model can be applied in calibration.