L7 - Pulse Oximetry

Properties

• Non-invasive
• Measures arterial oxygen saturation

Applications

• For patients at risk of respiratory failure
• Monitor the efficiency of gas exchange
• Continuous information

$O_2$ Saturation

$<80\%$	$<90\%$	$90\%-95\%$	$>95\%$
Severe hypoxemia	Hypoxemia	Good to use pulse oximetry	Normal

Hemoglobin

Hemoglobin	Oxyhemoglobin	Deoxyhemoglobin
Iron-containing oxygen-transport protein in the red blood cells	Formed during respiration when $O_2$ binds to hemoglobin	Without the bound $O_2$

Optical Absorption

Why does arteries look red?

Because $Hb{O}_2$ absorbs less red color wavelength regime compared to $Hb$. The unabsorbed red color will be reflected back to the eyes. The opposite applies for why veins look bluish-red.

Colors of Different Hemoglobins

Deoxyhemoglobin $Hb$	Oxyhemoglobin $Hb{O}_2$	Methemoglobin $MetHb$	Carboxyhemoglobin $COHb$
Bluish-red	Red	Dark chocolate-brown	Bright cherry

Ratio of Oxyhemoglobin over All Types of Hemoglobin

$$Sp{O}_2=\frac{Hb{O}_2}{Hb+Hb{O}_2+MetHb+COHb}\cdot 100\%$$

Ratio of Oxyhemoglobin over the Concentration of Oxyhemoglobin and Deoxyhemoglobin

$$Sa{O}_2=\frac{Hb{O}_2}{Hb+Hb{O}_2}$$

Normally, $MetHb$ and $COHb$ are close to zero, so $Sp{O}_2$ should be similar to $Sa{O}_2$.

Spectrophotometry

600$nm$ ~ 1000$nm$ light is used, as red light is absorbed the least for our body and it has high penetration.

Beer-Lambert Law

$$\begin{array}{rl}& I=I_{0}10^{-\alpha cL}\\ & A=log\left(\frac{I_0}{I}\right)=\alpha cL\\ & A_{total}=A_{Hb{O}_2}+A_{Hb}+A_{venous}+A_{others}\end{array}$$

$I$	Output intensity
$I_0$	Input intensity
$\alpha$	Absorptivity of the sample (extinction coefficient)
$c$	Concentration of the absorbing substance
$L$	Length of the path through the sample
$A$	Absorbance

Measuring $Sa{O}_2$

1. Measuring the absorbance of $Hb{O}_2$ and $Hb$ at two different wavelengths
2. Apply high-pass filtering to remove (DC) components
3. Solving both equations with $R=\frac{A_1}{A_2}=\frac{{\alpha }_{Hb}^{(1)}{c}_{Hb}L+{\alpha }_{Hb{O}_2}^{(1)}{c}_{Hb{O}_2}L}{{\alpha }_{Hb}^{(2)}{c}_{Hb}L+{\alpha }_{Hb{O}_2}^{(2)}{c}_{Hb{O}_2}L}$

The two wavelengths should have a big difference in extinction coefficient, so to minimize noise.

$$\begin{array}{rl}Sa{O}_2& =\frac{c_{Hb{O}_2}}{c_{Hb{O}_2+c_{Hb}}}\\ & =\frac{{\alpha }_{Hb}^{(1)}-{\alpha }_{Hb}^{(2)}R}{({\alpha }_{Hb}^{(1)}-{\alpha }_{Hb{O}_2}^{(1)})-({\alpha }_{Hb}^{(2)}-{\alpha }_{Hb{O}_2}^{(2)})R}\end{array}$$

In Reality

LEDs are not monochromatic, scattering will also occur, so the above modal is only approximately true.

So, the relationship between oxygen saturation and ratio is determined empirically by fitting the clinical data to the above function.

Then, calibration can be done for different sensor designs.

Optical Plethysmography