Biophotonics_Concepts_to_Applications

absorbed energy density whereμais the absorption coefficient and H is the local
opticalfluence.
Typical PAT laser pulses have durations of about 10 ns. In this case the stress
confinement condition holds so that the fractional volume expansion dV/V is
negligible. Thus from Eqs. (10.23) and (10.24) the local photoacoustic pressure rise
p 0 immediately after the laser pulse can be written as

p 0 ¼

bT

j

¼

bAe

jqCV

¼ClaH ð 10 : 25 Þ

Here the dimensionless factorΓis the Grueneisen parameter, which is defined as

C¼

b

jqCV

¼

bv^2 s

CP

ð 10 : 26 Þ

where the isothermal compressibility is expressed as

j¼

CP

qv^2 sCV

ð 10 : 27 Þ

with CPbeing the specific heat capacity at constant pressure.

Example 10.12Consider a PAT procedure that uses short laser pulses with a

fluence of 12 mJ/cm^2 to irradiate a soft tissue for which the absorption

coefficient isμa= 0.1 cm−^1. What are the temperature rise and pressure rise

for this setup?

Solution: Using Eq. (10.24) yields a temperature rise of

T¼

laH

qCV

¼

ð 0 :1cm^1 Þð12 mJ=cm^2 Þ

ð1gm=cm^3 Þ½4000 mJ=ðgmKފ

¼ 0 :30 mK

Using Eq. (10.25) withβ≈ 4 × 10 −^4 K−^1 andκ≈ 5 × 10 −^10 Pa−^1 yields

a pressure rise of (1 bar = 10^5 Pa)

p 0 ¼

bT

j

¼

ð 4  10 ^4 K^1 Þð 3  10 ^4 KÞ

5  10 ^10 Pa^1

¼ 2 : 4  102 Pa¼ 2 :4 mbar

After the photoacoustic pressure wave is generated, it travels through the tissue
sample and is detected by an ultrasonic probe or detector array. The shape of the
wave depends on the geometry of the object. For example, a spherical object
generates two spherical waves, one of which travels outward and the other travels
inward. This results in a bipolar-shaped photoacoustic signal wherein the distance
between the two peaks is proportional to the size of the object. Thus, a smaller
object produces a photoacoustic signal with higher frequency components.

10.5 Photoacoustic Tomography 315