Biomedical Engineering Reference
In-Depth Information
where
is the absolute temperature (K), and A
(1/sec) and E (cal/mole) are constants to be determined experimentally. Total damage
accumulated over a period
R
is the universal gas constant (cal/mole),
T
can be found by rearranging and integrating Eq. (17.74):
t
dt
ð
t
E
RT
O
¼
A
exp
ð
17
:
75
Þ
0
The experimental constants A and E for pigskin were determined such that O
¼
1.0 cor-
responded to complete transepidermal necrosis and O
0.53 indicated the minimum
condition to obtain irreversible epidermal injury. The reported values are A
¼
10
98
¼
3.1
(1/sec), E
150,000 (cal/mole). These values result in a threshold temperature of about
45
C. Different values for other tissues have been reported. For instance, for human arterial
vessel walls, the values are A
¼
10
44
(1/sec), E
¼
4.1
¼
74,000(cal/mole). For these values
O
1.0 was defined as the threshold for histologically observed coagulation damage. It
should be noted that the coagulation process—that is, collagen denaturation—is a different
damage process than that seen in skin burns.
Once the heat conduction Eq. (17.72) is solved for the temperature field, the temperature
history at every point in the tissue can be used in (17.75) to predict the accumulated damage
at that point.
¼
17.5.3 Photothermal Ablation
The temperature rise in a biological tissue under laser irradiation cannot continue indefi-
nitely. A threshold temperature can be reached beyond which, if the rate of heat deposition
by the light/laser continues to be higher than the rate heat can be transported by heat trans-
fer mechanisms, intense vaporization of the water content of the tissue occurs. This results
in creation of vacuoles—vacuolization—followed by pyrolysis at higher temperatures. The
combined processes of intense vaporization—vacuolization—and pyrolysis of tissue macro-
molecule constituents is the “light/laser ablation process.” This is the primary underlying
mechanism for removal of tissue by laser surgery.
The large water content of most biological tissues suggests that the dominant part of the
ablation process is the intense vaporization process. Apart from a short discussion of pyrol-
ysis, intense vaporization is the main process of concern.
Following, a derivation is given for the ablation interface energy balance equation, which
introduces the mathematical nonlinearity of the problem of ablation as a moving boundary
problem. The section is concluded with a note on pyrolysis.
Ablation Interface Energy Balance Equation
The heat conduction equation alone cannot provide a mathematical model for determina-
tion of the dynamic behavior of the ablation front as a function of time. In fact, the motion
of the ablation front influences the heat transfer process. An energy balance at the ablation
front is needed in order to determine the motion of the front of ablation and its influence on
the temperature field.
Consider a portion of a material under light irradiation with unit cross-sectional area and
of thickness
D
s
, as shown in Figure 17.15, which is at the ablation threshold temperature
