68
J. Kumar V. and K. A. Reddy
3.9 Alternate Method for Computation of SpO 2
The pulsatile component v 0λ of the PPG signal after applying natural logarithm to a
PPG obtained from equation is:
v 0λ = ln(v 0 ACλ )| pulse = −
(ε Hbλ Hb + ε HbOλ HbO 2 )x
2
2 ˆ
x
x= ˆ
x
x= 0
(3.28)
Applying Eq. (3.28) for the outputs of the red and IR photo detectors, we get the
pulsatile portions v 0R and v 0I R as
v 0R = −
(ε HbR Hb + ε HbO R HbO 2 )x
2
2 ˆ
x
x= ˆ
x
x= 0
v 0I R = −
(ε HbI R Hb + ε HbO I R HbO 2 )x
2
2 ˆ
x
x= ˆ
x
x= 0
The peak-to-peak values V pR and V pI R of v 0R and v 0I R respectively are:
V pR =
(ε HbR Hb + ε HbO R HbO 2 ) ˆ
x
2
(3.29)
V pI R =
(ε HbI R Hb + ε HbO I R HbO 2 ) ˆ
x
2
(3.30)
Dividing Eq. (3.29) by (3.30) results in.
V pR
V pI R
=
(ε HbR Hb + ε HbO R HbO 2 )
(ε HbI R Hb + ε HbO I R HbO 2 )
=
(ε HbR + ε HbO R Q)
(ε HbI R + ε HbO I R Q)
,
where Q =
HbO 2
Hb . Rearranging the above equation, we get:
Q =
V pI R ε HbR − V pR ε HbI R
V pR ε HbO I R − V pI R ε HbO R
(3.31)
Substituting Q from Eq. (3.31) in Eq. (3.3) we get:
SpO 2 =
V pI R ε HbR − V pR ε HbI R
(V pR ε HbO I R − V pI R ε HbO R ) + (V pI R ε HbR − V pR ε HbI R )
100 %
(3.32)
Once again it is easily seen that Eq. (3.32) is devoid of not only patient dependent
parameters but also independent of the red and IR source intensities and detector