Biophotonics_Concepts_to_Applications

Hb spectrum decreases monotonically with increasing wavelength and eventually
intersects the HbO 2 spectrum at around 800 nm.

Example 6.4The comparison of the absorption coefficients of blood with

and without oxygen binding at two different wavelengths forms the basis of

pulse oximetry, which measures the oxygen content in blood. Consider an

aqueous solution that contains a mixture of deoxyhemoglobin and oxyhe-

moglobin. In critical clinical settings (e.g., emergency rooms, intensive care

units, and operating rooms), for such a solution theoxygen saturationSisa

characteristic of interest for determining the cardio-respiratory status of a

patient. This parameter is the percentage of hemoglobin saturated with oxy-

gen. The task of the measurement system is tofind S if the extinction

coefficients and the sample thickness d are known.

Solution: One method for measuring S is through the comparison of the

optical densities at two different wavelengths where there is a large difference

between the extinction coefficients for deoxyhemoglobin and oxyhe-

moglobin. Letεo(λi) andεd(λi) be the extinction coefficients at wavelengthλi

for HbO 2 and Hb, respectively, and let c be the total concentration of

hemoglobin molecules. If S is the oxygen saturation, then the optical densities

D(λ 1 ) and D(λ 2 ) at wavelengthsλ 1 andλ 2 , respectively, are

Hb

HbO 2

106

105

104

103

102

(^2004006008001000)
Wavelength (nm)
Molar extinction coefficient (cm
-1/M)
Fig. 6.9 Spectra of
deoxyhemoglobin and
oxyhemoglobin in terms of
the molar extinction
coefficient (The hemoglobin
data are compiled in Prahl
[ 26 ])
6.2 Absorption 159