Beer-Lambert Law in Pulse Oximetry
Fundamental Principle
Pulse oximeters measure oxygen saturation by exploiting the Beer-Lambert law, which states that light absorbance through a medium is proportional to the concentration of absorbing substances and the path length through which light travels. 1
The Beer-Lambert law is expressed as:
A = ε × c × L
Where:
- A = absorbance of light
- ε = molar absorptivity (extinction coefficient) of the substance
- c = concentration of the absorbing substance
- L = path length through the medium 1
Application in Pulse Oximetry
Wavelength-Specific Absorption
Pulse oximeters use two specific wavelengths of light (660 nm red and 990 nm infrared) because oxygenated and deoxygenated hemoglobin absorb these wavelengths differently. 1
- Oxygenated hemoglobin (O₂Hb) absorbs more infrared light (990 nm) 1
- Deoxygenated hemoglobin absorbs more red light (660 nm) 1
Pulsatile Component Isolation
The device isolates arterial blood by detecting only the pulsatile component of blood flow, which corresponds to arterial pulsations with each heartbeat. 2 This allows the oximeter to distinguish arterial blood from venous blood and tissue, applying the Beer-Lambert law specifically to arterial hemoglobin saturation. 2
Calculation Method
By measuring differential absorbance at these two wavelengths and applying the Beer-Lambert law, the device calculates the ratio of oxygenated to deoxygenated hemoglobin. 1 The instrument transilluminates tissue with multiple wavelengths of light, measures differential absorbance at the various wavelengths, and then calculates concentrations from the known absorption spectrum of each form of hemoglobin. 1
Critical Limitations of the Beer-Lambert Law in Pulse Oximetry
Two-Wavelength Constraint
Standard pulse oximeters using only two wavelengths cannot differentiate carboxyhemoglobin (COHb) or methemoglobin (MetHb) because COHb and oxyhemoglobin have similar absorbances (extinction coefficients) at 660 nm. 1, 3 This results in pulse oximeters measuring COHb similarly to O₂Hb, yielding falsely reassuring readings in carbon monoxide poisoning—even with COHb levels of 25% or higher, the SpO₂ may still read greater than 90%. 1, 4
Perfusion Requirements
Poor peripheral perfusion from hypothermia, hypovolemia, vasoconstriction, or shock yields falsely low readings because adequate pulsatile arterial flow is essential for the device to detect signals and apply the Beer-Lambert law accurately. 2, 3 Decreased pulsatility makes it difficult for the device to isolate the arterial component needed for calculation. 2
Scattering Effects
The Beer-Lambert law assumes a homogeneous medium with constant scattering, but living tissue is highly scattering and heterogeneous. 5, 6 This requires modification of the classical Beer-Lambert law for tissue applications. 5, 6 The modified Beer-Lambert law (MBLL) accounts for scattering losses and increased photon path lengths in turbid media like tissue. 5, 6
Skin Pigmentation Interference
Dark skin pigmentation systematically overestimates oxygen saturation and interferes with signal detection, with Black patients having almost 3 times the frequency of hypoxemia missed by pulse oximetry compared to White patients. 2, 3 This represents a fundamental limitation in how the Beer-Lambert law is applied across different tissue optical properties. 2, 3
Accuracy Boundaries
Pulse oximeters have inherent accuracy limitations of ±4-5% even under optimal conditions when compared to arterial blood gas analysis. 2, 3 Accuracy is thought to be less reliable at saturations below 88%, which is further exacerbated in Black patients. 2
Pulse oximeters are good for monitoring trending phenomena but not reliable for determining absolute magnitude of change. 2 This reflects the practical limitations of applying the Beer-Lambert law in complex biological tissue rather than in controlled laboratory conditions. 2
Clinical Verification
Always verify signal quality first by checking that the heart rate displayed on the pulse oximeter matches the ECG or palpated pulse rate—if these don't match closely, the Beer-Lambert calculations are unreliable. 2 Without adequate pulsatile signal detection, the fundamental principle of isolating arterial blood for Beer-Lambert law application fails. 2