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34 CHAPTER 2 Diagnostic imaging in cancer
The guided equation for photo-thermoacoustic computed tomography (CT) is
explained as follow:
1 ∂ 2 β ∂
∇ pr t(, ) − 2 2 pr t) =− Hr t ,) (2.4)
(
(,
2
2
2
∇ p(r→,t)−1vS2∂ ∂t p(r→,t)=−βCp∂∂ v S ∂t C p ∂x
2
xH(r→,t)
H(r→,t) where Hr t(, ) heating function, v is the speed of sound in the medium, C specific
S
p
heat capacity, and β is thermal expansion coefficient. To assure that heat diffusion
is negligible during pulse laser irradiation, the pulse laser frequency is chosen much
P(r→,t) shorter than the thermal relaxation time. Pr t(, ) in the above equation is obtained as
follow:
β dr ′ ∂Hr )
( ′′ t,
(,
pr t) = ∫ r − ′ r / v s (2.5)
p(r→,t)=β4πCp∫dr′→r→−r′→∂Hr′ 4 πC p r − ′ r ∂ ′ t t ′=− t
→,t′∂t′t′=t−r→−r′→/vs
when laser pulse frequency is much shorter than laser relaxation time, the stress is
confined and as a result, the above equation is rewritten as follow:
r
1 ∂ 1 r − ′
′
(,
pr t) = 2 ∫ dr ′pr () δ t − (2.6)
0
p(r→,t)=14πvS2∂∂t1vst∫dr′→p (r′→ 4 πv S ∂ t vt v S
s
0
)δt−r→−r′→vS
where p is the initial photoacoustic pressure.
0
2.4.1.2 Electrical impedance tomography
EIT is a kind of noninvasive medical imaging determines the electrical permittivity,
conductivity and impedance of the interior part of the body from surface electrode.
Conducting surface electrodes are attached to the skin and small alternating currents
at a single or multiple frequency are applied to the electrodes, then the electrical
potentials are measured and used to build a tomographic image of the target. EIT
imaging technic is based on the measuring the tissue impedance consisting of mem-
branes, cells, and fluids. Cells and membranes act as small imperfect capacitors with
high resistivity, while fluids are the resistive component that contribute a frequency
dependence for liquids in the outside of the cells. At high frequencies (in the range of
MHz), the only resistive component is related to the conduction through extracellular
and intracellular fluid, while at low frequencies (in the range of Hz to kHz), mem-
branes impede the current and can be used to obtain valuable information regarding
the size, morphology, and electrical properties of cells [32]. There are two types of
EIG systems including absolute EIT and difference EIT. Difference EIT focuses on
the study of the changes in conductivity during a period of time. Absolute EID is
more difficult since channel noise and electrode impedance need to be calculated.
One of the most clinical applications of EID for cancer diagnosis is related to the
detection of malignant breast tumors from benign lesions [33].
2.4.1.3 Near-infrared optical tomography
NIR optical tomography is a noninvasive imaging technic with high contrast features
for blood cells. This is mainly due to the fact that hemoglobin absorbs NIR light
