9.2 Pulse Oximetry: Theory and Instrumentation

Hemoglobin and Oxygen Saturation

Oxygen Transport in the Blood

Oxygen saturation ($SpO_2$) measures the percentage of hemoglobin binding sites occupied by oxygen molecules. It's one of the most commonly monitored vital signs because it gives you a quick, noninvasive read on how well a patient's respiratory system is working.

Hemoglobin is the protein in red blood cells that carries oxygen from the lungs to body tissues. Each hemoglobin molecule has four binding sites, so it can carry up to four oxygen molecules.

• Oxyhemoglobin ($HbO_2$): hemoglobin bound to oxygen. Higher $HbO_2$ levels mean better blood oxygenation.
• Deoxyhemoglobin ($Hb$): hemoglobin not bound to oxygen. Higher $Hb$ levels mean poorer oxygenation.

Pulse oximetry works because these two forms of hemoglobin interact with light differently.

Light Absorption Properties

The entire measurement hinges on one physical fact: $HbO_2$ and $Hb$ absorb red and infrared light by different amounts.

• Deoxyhemoglobin absorbs more red light (wavelength ~660 nm).
• Oxyhemoglobin absorbs more infrared light (wavelength ~940 nm).

A pulse oximeter shines both wavelengths through a tissue bed (typically a fingertip or earlobe) and measures how much light makes it through to a photodetector on the other side. By comparing absorption at these two wavelengths, the device can estimate the relative proportions of $HbO_2$ and $Hb$, and therefore calculate $SpO_2$.

This two-wavelength approach is why conventional pulse oximeters only distinguish between $HbO_2$ and $Hb$. They cannot detect other hemoglobin species (more on that in the Limitations section).

Pulse Oximetry Signal Processing

Ratio of Ratios Calculation

The core math behind pulse oximetry is the ratio of ratios (R). Here's how it works:

The light signal passing through tissue has two components:

• AC component: the pulsatile part, caused by arterial blood volume changing with each heartbeat. This is the signal you actually want.
• DC component: the non-pulsatile baseline, caused by absorption from venous blood, tissue, bone, and skin. This stays relatively constant.

The ratio of ratios is calculated as:

$R = \frac{AC_{red} / DC_{red}}{AC_{IR} / DC_{IR}}$

Step by step:

1. Measure the AC and DC components at the red wavelength (660 nm).
2. Measure the AC and DC components at the infrared wavelength (940 nm).
3. Compute the normalized red ratio: $AC_{red} / DC_{red}$.
4. Compute the normalized infrared ratio: $AC_{IR} / DC_{IR}$.
5. Divide the red ratio by the infrared ratio to get $R$.
6. Convert $R$ to an $SpO_2$ value using a stored calibration curve.

The normalization step (dividing AC by DC at each wavelength) is what makes the measurement independent of the total light intensity and tissue thickness. This is a key design feature.

Typical $R$ values: when $R \approx 1$, $SpO_2$ is around 85%. When $R$ is low (~0.4), saturation is near 100%. When $R$ is high (~3.4), saturation is very low.

Plethysmographic Waveform and Perfusion Index

The plethysmographic (pleth) waveform is the graphical display of pulsatile blood volume changes over time. Clinically, it's useful for more than just confirming a pulse:

• A clean, regular waveform indicates a strong, reliable signal.
• A noisy or irregular waveform warns you about motion artifacts, arrhythmias, or poor probe placement.

The perfusion index (PI) quantifies signal strength. It's calculated as:

$PI = \frac{AC_{IR}}{DC_{IR}} \times 100\%$

Higher PI values mean stronger pulsatile flow and a more trustworthy reading. A PI below ~0.5% suggests poor perfusion, and $SpO_2$ readings in that range should be interpreted with caution.

Signal Processing Techniques

Raw pulse oximetry signals are noisy. Several processing techniques improve accuracy:

• Filtering: Adaptive filters and Kalman filters remove noise from motion artifacts and electrical interference.
• Averaging: Moving averages or weighted averages smooth out beat-to-beat fluctuations for a more stable displayed value. The tradeoff is a slower response to real changes in saturation.
• Pulse validation: Algorithms identify and reject invalid or artifact-corrupted pulse segments so that only clean beats contribute to the $SpO_2$ calculation.

These techniques are why modern pulse oximeters perform reasonably well even during moderate patient movement, though no algorithm can fully compensate for severe motion.

Calibration and Limitations

Calibration Techniques

Pulse oximeters don't calculate $SpO_2$ from first principles. Instead, they map the ratio $R$ to saturation using a calibration curve stored in the device. Building that curve requires careful calibration:

1. Empirical calibration: Healthy volunteers breathe controlled low-oxygen gas mixtures to induce a range of saturation levels. At each level, the pulse oximeter's $R$ value is recorded alongside a simultaneous arterial blood gas measurement (the gold standard). This produces a lookup table of $R$ vs. true $SaO_2$.
2. Functional calibration: Mathematical models and simulated optical data are used to extend or refine the calibration curve, especially at very low saturations where it would be unethical to desaturate volunteers further.

Manufacturers typically combine both approaches. Because calibration curves are device-specific, different oximeter brands may give slightly different readings on the same patient.

Limitations and Sources of Error

Pulse oximetry is reliable in most clinical situations, but you need to know when it can fail:

• Motion artifacts: Patient movement introduces noise that can corrupt the pleth waveform and produce erroneous $SpO_2$ values.
• Low perfusion: Hypotension, hypothermia, and vasoconstriction reduce pulsatile flow. With a weak AC signal, the ratio calculation becomes unreliable.
• Dyshemoglobins: Conventional two-wavelength oximeters cannot distinguish $HbO_2$ from carboxyhemoglobin ($COHb$) or methemoglobin ($MetHb$).
  • $COHb$ (from carbon monoxide poisoning) absorbs similarly to $HbO_2$ at 660 nm, so the oximeter reads falsely high.
  • $MetHb$ absorbs equally at both wavelengths, driving $R$ toward 1 and $SpO_2$ readings toward ~85% regardless of true saturation.
• Ambient light: Bright surgical lamps or direct sunlight can reach the photodetector and contaminate the signal. Shielding the probe helps.
• Optical interference at the tissue surface: Dark nail polish (especially blue, green, or black), artificial nails, and certain intravenous dyes (e.g., methylene blue) alter light absorption and can skew readings.
• Skin pigmentation: Studies have shown that deeply pigmented skin can lead to overestimation of $SpO_2$, particularly at lower saturation levels. This is an active area of research and regulatory attention.

Proper probe placement, appropriate probe sizing, and awareness of the clinical context go a long way toward minimizing these errors. When in doubt, an arterial blood gas remains the definitive measurement.