What is the Lambert‑Beer law and how does it apply to pulse oximetry?

Lambert-Beer Law in Pulse Oximetry

Fundamental Principle

Pulse oximeters apply the Lambert-Beer law by measuring differential light absorption at two wavelengths (660 nm red and 990 nm infrared) to calculate arterial oxygen saturation, exploiting the fact that oxygenated hemoglobin absorbs more infrared light while deoxygenated hemoglobin absorbs more red light. 1, 2

How the Law Works in Pulse Oximetry

The Lambert-Beer law originally describes exponential attenuation of light passing through an absorbing medium, with attenuation proportional to the concentration of the absorber and the path length traveled. 3 In pulse oximetry, this principle is modified to account for the unique challenges of measuring through living tissue:

Core Mechanism

• The device transmits red (660 nm) and infrared (990 nm) light through tissue and analyzes the differential absorption between oxygenated versus deoxygenated hemoglobin in the pulsatile arterial component only. 1
• By isolating the pulsatile component of blood flow corresponding to arterial pulsations with each heartbeat, the oximeter distinguishes arterial blood from venous blood and surrounding tissues. 2, 4
• Oxygenated hemoglobin absorbs more infrared light (990 nm) while deoxygenated hemoglobin absorbs more red light (660 nm), allowing the device to calculate the ratio and estimate saturation. 2

Modified Beer-Lambert Law (MBLL)

Because living tissue is a turbid, scattering medium rather than a clear solution, pulse oximeters use a modified version of the Beer-Lambert law that accounts for:

• Light scattering by tissue elements, which is the primary challenge in discriminating between absorption by hemoglobin and scattering effects. 3, 5
• Variable photon path lengths through tissue due to scattering, which extends the effective distance light travels compared to a straight line. 6, 5
• Empirical calibration of the absorbance-to-saturation relationship, which imposes an inherent accuracy limitation of approximately ±4–5% even under optimal conditions. 7, 1

The modified law maintains that changes in light attenuation are proportional to changes in chromophore concentrations, but incorporates correction factors for scattering and path length variations. 8, 9

Critical Limitations of the Two-Wavelength Approach

Cannot Detect Dyshemoglobinemias

• Using only two wavelengths prevents differentiation of carboxyhemoglobin (COHb) from oxyhemoglobin because both have similar extinction coefficients at 660 nm. 1
• COHb is interpreted as oxyhemoglobin, leading to falsely elevated SpO₂ values—in patients with COHb ≥25%, pulse oximeters reported SpO₂ >90% despite substantial carboxyhemoglobin levels. 1
• Standard two-wavelength devices similarly cannot distinguish methemoglobin. 2

Scattering-Related Errors

• A 1% increase in tissue scattering increases estimated concentration changes by approximately 0.5 μM, introducing cross-talk between scattering changes and calculated saturations. 9
• The modified Beer-Lambert law assumes scattering loss is constant, but this assumption is violated when tissue perfusion or architecture changes. 9

Common Pitfalls and How to Avoid Them

Poor Perfusion States

• Inadequate peripheral perfusion (hypothermia, hypotension, vasoconstriction, severe Raynaud's phenomenon) produces falsely low SpO₂ readings because the device cannot obtain a sufficient pulsatile signal. 7, 1, 4
• Verify signal quality by confirming that the displayed pulse rate matches the ECG or palpated pulse; discordance indicates unreliable SpO₂. 1, 2
• Actively warm the measurement site before and during measurement to improve accuracy in cold peripheries. 4
• Use alternative sensor sites such as the ear lobe or forehead when peripheral perfusion is compromised. 1, 2

Skin Pigmentation Bias

• Darker skin pigmentation interferes with light detection, causing systematic overestimation of SpO₂, especially when true saturations fall below 88%. 7, 1, 2
• This creates a dangerous situation where hypoxemia may be missed in patients with darker skin. 1

Motion Artifact

• Patient movement introduces significant measurement error and data dropout; the sensor site must remain still during acquisition. 7, 1, 2
• Ensure the patient's hand is still and not gripping objects tightly. 2

Altered Tissue Architecture

• Severe finger clubbing with extensive lipodermatosclerosis changes the normal light transmission pathway and may prevent proper probe seating due to bulbous fingertip morphology. 2
• Reposition the probe and repeat measurements, or switch to an ear lobe probe after removing jewelry and rubbing the lobe to improve local perfusion. 2

Clinical Application Guidance

When to Trust Pulse Oximetry

• Pulse oximetry is valuable for monitoring trends but should not be used to quantify absolute changes in oxygenation. 1, 2
• Accuracy deteriorates at saturations <88%, which is further exacerbated in patients with darker skin pigmentation. 1, 2

When to Obtain Arterial Blood Gas

• When respiratory compromise is suspected, arterial blood gas analysis must be obtained rather than relying solely on pulse oximetry. 1, 2
• Pulse oximeters measure saturation (SaO₂) rather than partial pressure (PaO₂), and PaO₂ is more relevant for assessing pulmonary gas exchange effects in lung disease. 7, 2
• Never rely solely on pulse oximetry when clinical assessment suggests respiratory compromise, especially in patients with known perfusion issues. 2