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6 Applications and Methods in Biosignal Processing

In the next step, for Equation 6.37, the sought oxygen saturation

SpO2 =

CHbO2

CHbO2 + CHb

= ^CHbO2

Cges

(6.38)

is introduced. If Equation 6.38 is converted to CHbO2 or CHb and inserted into Equa-

tion 6.37, we obtain

α2(λ) = Cges [(εHbO2(λ) −εHb(λ)) SpO2 + εHb(λ)] .

(6.39)

Substituting Equation 6.39 into Equation 6.36, the unknown quantity Cges truncates

out, leaving an equation with the sought oxygen saturation SpO2, the four measured

values I(λ1,2, t1,2) contained in Γ and the known molar extinction coefficients εHbO2(λ)

and εHb(λ):

Γ = ^{(εHbO2(λ1) −εHb(λ1)) SpO2 + εHb(λ1)}

(εHbO2(λ2) −εHb(λ2)) SpO2 + εHb(λ2) ^.

(6.40)

Converted to SpO2 finally results in

SpO2 =

εHb(λ1) −ΓεHb(λ2)

εHb(λ1) −εHbO2(λ1) + Γ(εHbO2(λ2) −εHb(λ2)) ^.

(6.41)

From Equation 6.41 and Equation 6.35 it is immediately clear why the spectral sensit-

ivity of the photodiode is not included in the SpO2 determination. Only intensity ra-

tios measured at a specific wavelength appear in Γ. The spectral sensitivity, which

enters as a factor in the intensity, thus truncates in Γ. However, there are other causes

that affect the accuracy of the SpO2 determination. This becomes clear by looking

at the individual quantities in Equation 6.41. On the one hand, the molar extinction

coefficients of hemoglobin and oxyhemoglobin are subject to slight individual vari-

ations [79]. However, a larger error may be due to the inaccuracy in the LED wavelength

that can occur between different LEDs of the same type or within an LED due to tem-

perature variations. For commercially available LEDs the variation is in the range of

1 %, relative to the centroid of the wavelength distribution. The molar extinction coef-

ficients, which enter into Equation 6.41, depend on the wavelength (cf. Figure 6.46).

Therefore, the uncertainty in the wavelength implies an uncertainty in the molar ex-

tinction coefficients and, according to the rules of the error propagation, also an in-

accuracy in the SpO2 value. In particular, below 800 nm, the absorption spectrum

of Hemoglobin exhibits a high gradient. In this range, the wavelength uncertainty

results in a large uncertainty of the molar extinction coefficients. Therefore, in this

wavelength range, special care should be taken to use LEDs with high wavelength

stability. Another source of error is external stray light that hits the photodiode in

addition to the LED light and increases the measured intensity. High-quality sensors

therefore have housings that shade the measuring range well from external light.

At this point, the limitations of spectrometric SpO2 measurement with respect to

clinical use should be noted. The output value is expressed as a percentage and is a

measure of the saturation of the hemoglobin present with oxygen. This says nothing