Biomedical Engineering Reference
In-Depth Information
relative concentration of Hb and HbO
2
, since the characteristic color of deoxygenated blood
is blue, whereas fully oxygenated blood has a distinct bright red color.
The measurement is performed at two specific wavelengths: a red wavelength,
l
1
, where
there is a large difference in light absorbance between Hb and HbO
2
(e.g., 660 nm), and a
second wavelength,
l
2
, in the near-infrared region of the spectrum. The second wavelength
can be either isobestic (a region of the spectrum around 805 nm, where the absorbencies of
Hb and HbO
2
are equal) or around 940-960 nm, where the absorbance of Hb is slightly
smaller than that of HbO
2
. Figure 10.29 shows the optical absorption spectra of blood in
the visible and near-infrared region.
The measurement is based on Beer-Lambert's law that relates the transmitted light
power, P
t
, to the incident light power, P
0
, according to the following relationship:
P
t
10
abc
¼
P
0
ð
10
:
19
Þ
where
is a wavelength-dependent constant called the extinction coefficient (or molar
absorptivity) of the sample,
a
b
is the light path length through the sample, and
c
is the con-
centration of the sample.
Assuming for simplicity that (i)
805 nm (i.e., isobestic), (1) the
hemolyzed blood sample (blood in which the erythrocytes have been ruptured—i.e., the
hemoglobin has been released and uniformly mixed with the plasma) consists of a two-
component mixture of Hb and HbO
2
, and (2) the total light absorbance by the mixture of
these two components is additive, a simple mathematical relationship can be derived for
computing the oxygen saturation of blood:
SO
2
¼
A
B
OD
ð
l
1
¼
660 nm and
l
2
¼
l
1
Þ
ð
10
:
20
Þ
OD
ð
l
2
Þ
where
are two coefficients that are functions of the specific absorptivity of Hb and
HbO
2
, OD (or absorbance) is defined as the optical density—that is, log
10
(1/T)—where
A
and
B
Hb
Isobestic wavelength
HbO
2
600
700
800
900
1000
Wavelength [nm]
FIGURE 10.29
Optical extinction coefficients of Hb and HbO
2
.
