Critical analysis of the relationship between arterial saturation and the ratio-of-ratios used in pulse oximetry

Pulse oximetry is a well-established technique for the assessment of arterial oxygen Saturation ( ${\mathrm{SaO}}_2$ ). A quantitative analysis of its basic measurements may benefit its further development.

We aim to derive and discuss the quantitative relationship between ${\mathrm{SaO}}_2$ and the measured quantity in pulse oximetry and the ratio-of-ratios ( $R$ ) of pulsatile intensities at red and infrared wavelengths.

The source of the pulsatile optical signal is the systolic and diastolic pulsation of the arterial compartment within the probed tissue. From a diffuse optics point of view, this is associated with an absorption change in the region that arterial blood expands into and a mean partial optical path length through that expanded arterial volume. This observation is the basis for a modified Beer-Lambert law analysis of the relationship between ${\mathrm{SaO}}_2$ and $R$ .

The equation that relates ${\mathrm{SaO}}_2$ and $R$ contains parameters that include the molar extinction coefficients of oxy- and deoxy-hemoglobin and the ratio of the mean partial optical path lengths in the arterial pulsatile expansion volume at the two wavelengths.

The analysis reported here clarifies the source of the calibration equations used in pulse oximetry and provides guidance to assess the impact of various key optical parameters on the accuracy of pulse oximetry.