Simple photon diffusion analysis of the effects of multiple scattering on pulse oximetry

Photon diffusion theory is used to derive analytical expressions that relate the ac-dc intensity ratios measured by transmission-mode and reflectance-mode pulse oximeters to arterial oxygen saturation (SaO2). The effects of multiple scattering are examined by comparing the results of the photon diffusion analysis with those obtained using an analysis based on the Beer-Lambert law which neglects scattering. We show that the difference between the average lengths of the paths travelled by red and infrared photons makes the calibration curve of oximeters sensitive to the total attenuation coefficients of the tissue in the two wavelength bands, as well as to absorption by the pulsating arterial blood. Therefore, the shape of the calibration curve is affected by tissue blood volume, source-detector placement, and other variables that change the wavelength dependence of the attenuation coefficient of the tissue. After evaluating the relationship between SaO2 and the red/IR ac-dc ratio (R) under a variety of physiological conditions, we conclude that, for oximeters utilizing fixed calibration curves based on measurements obtained from normal subjects, errors introduced by interfering variables should be less than a few percent when SaO2 exceeds 70%. Predicted errors at lower oxygen saturation values are substantially greater because R is much more sensitive to interfering variables in this measurement range.