Biomedical Engineering Reference
In-Depth Information
of thickness less than 1.4 mm or 42 mean free paths. Most ballistic imaging techniques
reported in the literature have achieved approximately 30 mfp. Therefore, this approach
is suitable for thin tissue samples but suffers loss of signal and resolution for thick tissues
as a result of the strong scattering of light by the tissue.
EXAMPLE PROBLEM 17.10
Calculate the decay of ballistic light after penetrating a biological tissue 30 mean free paths
thick. If the scattering coefficient of the tissue is 100 cm
1
, calculate the corresponding thickness
in cm.
Solution
Based on Beer's law, the decay is exp(-30)
10
-14
. The thickness is 30/100
¼
9.4
¼
0.3 cm.
For tissue of clinically useful thickness (5 to 10 cm), scattered light must be used to image
breast cancers. It has been shown that for a 5-cm-thick breast tissue with an assumed absorp-
tion coefficient of 0.1 cm
1
, and reduced scattering coefficient of 10 cm
1
, the detector must
collect transmitted light that has experienced at least 1,100 scattering events in the tissue to
yield enough signal. Therefore, ballistic light or even quasi-ballistic light does not exist for
practical purposes. However, if a 10 mW visible or near-infrared laser is incident on one side
of the 5-cm-thick breast tissue, it has been estimated, using diffusion theory, that the diffuse
transmittance is on the order of 10 nW/cm
2
or 1,010 photons/(s cm
2
), which is detectable
using a photomultiplier tube. Similarly, the diffuse transmittance through a 10-cm-thick
breast tissue would be on the order of 1 pW/cm
2
or 106 photons/(s cm
2
). The significant trans-
mission of light is due to the low absorption coefficient despite the high scattering coefficient.
Imaging resolution of pure laser imaging degrades with increased tissue thickness. The
temporal profiles of the scattered light may be detected using a streak camera. The early
portion of the profiles was integrated to construct the images of buried objects in a turbid
medium. This time-domain technique requires expensive short-pulse lasers and fast light
detectors.
Optical-coherence tomography (OCT) has emerged as a useful clinical tool. This tech-
nique is based on the Michelson interferometer (see Figure 17.9) with a short-coherence
length light source. One arm of the interferometer leads to the sample of interest, and the
other leads to a reference mirror. The reflected optical beams are detected at the photo-
detector. The two beams interfere only when the sample and the reference path lengths
are equal to within the source coherence length. Heterodyne detection is performed by
taking advantage of the direct Doppler frequency shift that results from the uniform
high-speed scan of the reference path length. Recording the interference signal magnitude
as a function of the reference mirror position profiles the reflectance of the sample, which
produces an image similar to an ultrasonic A scan. OCT has achieved less than 10
m
m
resolution with a penetration depth of approximately 1 mm.
OCT was extended to image blood flow in superficial vessels based on Doppler shift. The
blood flow causes a Doppler shift on the frequency of the light. Frequency analysis with
Fourier transformation of the optical interference signal yields the Doppler shift, which is
used to calculate the velocity of the blood flow.
