Biomedical Engineering Reference
In-Depth Information
Z
(direction of the
laser beam axis)
Δ
S
Ablated
Material
q(s)
s(t)
ς
Ε
FIGURE 17.15
Ablation interface energy balance which is depicted as the amount of energy required to ablate
a portion
D
s
of the tissue.
and is to be vaporized in the next interval of time
. Using Fourier's law for heat flux,
Eq. (17.71), and after mathematical manipulations, the following equation for energy bal-
ance at the ablation interface can be derived
D
t
k
@
T
ð
s
,
t
Þ
f
L
L
ds
dt
¼
r
ð
17
:
76
Þ
@
z
where
is the water fraction parameter. Nonlinearity inherent in the problem can be rea-
lized from this equation in that it couples the temperature gradient at the ablation interface
to the rate of change of the front position, which is not known a priori. The solution requires
an iteration procedure that requires the solution of the heat conduction equation simulta-
neously with the ablation front equation, with application of proper boundary and initial
conditions.
Equation (17.76) is essential in providing information on the dynamics and thermody-
namics of ablation. When solved simultaneously with the heat conduction equation and
with the application of proper boundary and initial conditions, this equation provides the
information on the position and velocity of the front of ablation. Furthermore, an important
observation can be readily made about the temperature profile within the tissue, as dis-
cussed following.
Note that on the right-hand side of Eq. (17.76),
f
L
must be positive for the ablation
process to proceed. This means that on the left-hand side, the temperature,
ds
/
dt
must
be positive. Consequently, the subsurface temperature must be higher than the surface tem-
perature. That is, subsurface tissue must be superheated to temperatures higher than the
@
T
=@
z
