Chapter 21, Problem 54P

Operation of the pulse oximeter (see previous problem). The transmission of light energy as it passes through a solution of light-absorbing molecules is described by the Beer-Lambert law

$\begin{array}{ccc}I=I_0{10}^{-\in CL}& \text{or}& {\log }_{10}\left(\frac{I}{I_0}\right)=-\in CL\end{array}$

which gives the decrease in intensity I in terms of the distance L the light has traveled through a fluid with a concentration C of the light-absorbing molecule. The quantity ∈ is called the extinction coefficient, and its value depends on the frequency of the light. (It has units of m²/mol.) Assume the extinction coefficient for 660-nm light passing through a solution of oxygenated hemoglobin is identical to the coefficient for 940-nm light passing through deoxygenated hemoglobin. Also assume 940-nm light has zero absorption (∈ = 0) in oxygenated hemoglobin and 660-nm light has zero absorption in deoxygenated hemoglobin. If 33% of the energy of the red source and 76% of the infrared energy is transmitted through the blood, what is the fraction of hemoglobin that is oxygenated?