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Blood colour and two-wavelength oximetry

Compute the colour of blood at different saturations from the absorption spectra of oxy- and deoxyhaemoglobin, then read the saturation from the ratio of absorbances at 660 and 940 nm — the principle of the pulse oximeter.

Difficulty ●○○ ≈ 20 min

Aim Compare the colours of arterial and venous blood, establish how the ratio R = A₆₆₀/A₉₄₀ depends on oxygen saturation, and use it to work back from absorbances to saturation.
Computed from the molar absorption spectra of HbO₂ and Hb (Prahl’s compilation)

The colour of blood and the pulse oximeter

Absorption spectra (log scale)
visible 660 940 4005006007008009001000wavelength / nm10010001000010⁵10⁶ε / L mol⁻¹ cm⁻¹
  • oxyhaemoglobin HbO₂
  • deoxyhaemoglobin Hb
  • this blood
Two-wavelength oximeter
00.250.50.751oxygen saturation S0.20.5125R = A₆₆₀ / A₉₄₀

A₆₆₀ = 0.088, A₉₄₀ = 0.280, R = 0.314 → solving the two Beer–Lambert equations gives S = 98.0 %.

At 660 nm Hb absorbs 10.1 times as strongly as HbO₂: venous blood soaks up far more red light and looks darker. At 940 nm the order reverses, and near 797 nm the two are equal (the isosbestic point).

Absorption coefficients are per mole of haemoglobin (64 500 g/mol), compiled by S. A. Prahl from data of W. B. Gratzer and N. Kollias; the blood holds 150 g/L of haemoglobin, only absorption is counted (no scattering), and colours come from the transmitted spectrum with the CIE 1931 colour-matching functions. A real oximeter uses only the part of the absorbance that pulses with the heartbeat, and scattering in tissue makes the path length differ between the two wavelengths — so instruments are calibrated empirically against blood-gas measurements on volunteers rather than using the ideal equations here.

Procedure

  1. With a 1 mm layer of blood, set the saturation to 98, 90, 75 and 50 % in turn and record the colour and the ratio R.
  2. Thin the layer to 20 µm and sweep the saturation from 100 % to 0 %: is the change of colour still obvious?
  3. On the spectra, find the isosbestic point where HbO₂ and Hb cross in the near infrared, and explain why it is not used as a measuring wavelength.

What to notice

  • R changes steadily with saturation: 0.31 at 98 %, 0.53 at 90 %, 0.97 at 75 % and 1.86 at 50 %; solving the two Beer–Lambert equations reads the saturation back from R.
  • At 1 mm, blood at 98 % is bright red and at 75 % dark red, passing only about half as much light; very thin layers of both look pale red.
  • The two curves cross near 797 nm: there the absorbance does not depend on saturation, so it cannot tell oxygenated from deoxygenated blood.

In a real lab

  • A real oximeter uses only the part of the absorbance that pulses with the heart and is calibrated empirically against arterial blood gases from volunteers; nail varnish, cold fingers and movement all disturb the reading.
  • In carbon monoxide poisoning an ordinary oximeter mistakes carboxyhaemoglobin for oxyhaemoglobin and reads “normal”; a multi-wavelength CO-oximeter or a blood-gas analysis is needed.
  • Handle blood samples by biosafety rules — gloves, no sharps injuries — and dispose of waste as clinical waste.

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