Page 59 - Veterinary Laser Therapy in Small Animal Practice

Light’s path to all these places in the body 45

Table 6.1 Values for the mean free path between scattering and absorption events (calculated as the inverse of μ ʹ the reduced
s
scattering coefficient and μ the absorption coefficient, respectively) for 800 nm infrared light in some common tissues. [193] The
a
last column shows how dominant scattering is over absorption.
Mean free path between scatter Mean free path between Average # scattering events
Tissue
events (cm) absorption events (cm) before absorption
Skin 0.04 40.00 944
Brain 0.09 32.73 378
Breast 0.10 47.62 487
Bone 0.06 42.21 654
Soft tissues 0.10 33.48 344
Fibrous tissues 0.08 35.32 420
Fatty tissue 0.07 50.43 671

if a photon moved in a straight line through the tissue, perpendicular to the surface), scatter is very much for-
it would go a long way before disappearing into tissue. ward-pointing, meaning the deflections to the angle of
But … it doesn’t. incidence are very small and most of the light contin-
So while the values in Table 6.1 start to answer ues in the same general direction – inside the patient.
the “how much” question, the bigger part of the story As the incident angle changes, the amount and angle
describes the “where.” of the scatter increases dramatically. This is called
But first we need to understand a little about the anisotropy, and again, we don’t deal with individual
importance of angles when it comes to light. An example photon paths, so we use a characteristic called the
from everyday life is very useful here. Why is it hotter anisotropy factor to describe things. Technically, this
in the summer than it is in the winter? I used to ask is defined as the average cosine of the deflected angle.
this question on the first day of my physics lectures to Or in English, if this value is 1, the average deflection is
the pre-meds and engineering majors and sadly 80% of straight ahead; if the value is 0, the average deflection
these brilliant minds that hold the future of our health is at a right angle to the original beam (lateral deflec-
and technology in their hands got it wrong – well, half tion); and if the value is −1, then the average deflection
wrong. Most people understood that it had to do with is reflection (straight back at you). Figure 6.2 helps to
the angle of the earth’s rotational axis relative to the illustrate this idea.
plane of the orbit around the sun, so that the northern/ Anisotropy is an important concept since as we saw
southern hemisphere is pointed toward/away from the earlier, scattering events happen very often (multiple
sun and therefore experiences summer/winter. During times per millimeter in some instances), making it
spring and fall the axis is pointed perpendicular to the virtually impossible to keep track of individual trajec-
sun and so they are about the same. tories. Instead, we deal with averages, and so the scat-
But the earth gets warmer NOT because the distance tering coefficient gets weighted by the anisotropy factor
from the sun to a hemisphere is shorter. In fact, because to give us a reduced scattering coefficient μ ʹ, calculated
s
of the earth’s elliptical orbit around the sun (that’s right, as μ ʹ = μ (1−g). The mean free paths in Table 6.1 used
s
s
it’s not a perfect circle), the earth is about 3,000,000 this reduced scattering coefficient in their evaluation
miles FARTHER from the sun on July 5th than it is (mfp = 1/μ ʹ).
s
s
on January 4th. But that’s only about a 3% difference, You can see from Figure 6.3 that most anisotropy
which is why it has virtually no impact. factors are in the range 0.75–0.90, meaning the average
Instead, the reason for our seasons is the incident deflection (again assuming you started the beam per-
angle of the sun’s light on each hemisphere during pendicular to the surface of the patient) is inside the
the summer/winter. Earth’s axis is tilted 23.5° and this patient, but at a 25–45° angle.
angle makes all the difference. Scatter is very VERY So now you’re supposed to say, “Final answer: how
angle-dependent. At right angles (when the beam is far does light get inside the patient?” Then I say, “A few

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