How do pulse oximeters distinguish between arterial and venous blood to determine SpO2?

Pulse oximeters estimate the SpO2 of arterial blood, isolated from other tissues (including venous blood), by applying the Beer-Lambert Law as arterial blood volume fluctuates throughout the cardiac cycle. The Beer-Lambert Law of absorbance demonstrates that the transmission of light is attenuated as it passes through different optical filters (tissue types).  Oxygenated hemoglobin and deoxygenated hemoglobin have unique molar extinction coefficients for different wavelengths of light. As arterial blood volume increases during systole the amount of oxygenated hemoglobin increases and ratio of red to infrared light changes (known as the modulation ratio).  

Conversely, the blood volume and therefore the amount of oxygenated hemoglobin changes very little throughout the cardiac cycle in other tissue types.  By taking the amount of change in absorbance over the change in time (pulse rate), the non-arterial tissues are effectively eliminated mathematically (see below) and the amount of oxygenated hemoglobin in arterial blood remains.

Images: Chan et al, Respiratory Medicine 2013

Mathematically (for transmittance pulse oximeters):

Light from the light-emitting diode is absorbed as it passes through various tissue types before being measured by the photodiode detector.  

Absorbance(total) = sum(Absorbance(all tissue types)) Formula 1

Absorbance(total) = Absorbance(arterial blood) + Absorbance(venous blood) + Absorbance(skin, varies by pigment type or melanin content) + Absorbance( other tissue types fat, bone, vessel walls, etc)  Formula 1a

Taking the derivative, or measuring the change in Absorbance(total) over the change in time gives the following:

dAbsorbance(total)/dt = dsum(Absorbance(all tissue types))/dt Formula 2

dAbsorbance(total)/dt = dAbsorbance(arterial blood)/dt + dAbsorbance(venous blood)/dt + dAbsorbance(skin)/dt + dAbsorbance(other tissue types)/dt  Formula 2a

As dAbsorbance for non arterial tissue types is essentially zero throughout the cardiac cycle, dAbsorbance(total)/dt reduces to:

dAbsorbance(total)/dt = dAbsorbance(arterial blood)/dt Formula 3

Absorbance = the negative log of transmission, and Formula 3 can be written as:

R = [dlog(transmission)/dt]wavelength1/[dlog(transmission)/dt]wavelength2 Formula 4

(R = Modulation Ratio, wavelength 1 and 2 are wavelengths of red light and infrared light)

or alternatively, as:

R = (AC/DC)wavelength1/(AC/DC)wavelength2  Formula 5

(AC = alternating component and DC = constant(direct) component)

Without an adequate pulse, pulse oximeters will either be unable to measure SpO2 or will report inaccurate SpO2 levels. 

References: Chan et al, Respiratory Medicine 2013 Mannheimer Anesth Analg. 2007 

Keywords: modulation, ratio