Biomedical Engineering Reference
In-Depth Information
17.5.5 Biochemical Damage Analysis
The Arrhenius model for prediction of damage was introduced previously. The damage
function was defined in Section 17.5.2. For numerical computation, it is more convenient
(due to large values of
A
and
E
) to rewrite the integrand of this function in an equivalent
form so Eq. (17.83) becomes
ð
t
E
RT
ð
z
O
ð
z
,
t
Þ¼
exp ln
A
dt
:
ð
17
:
82
Þ
,
t
Þ
0
, one for pigskin and another for human vessel
wall. The value of O(z,t) can be determined by replacing for T(z,t) from the analytical solu-
tion of the last section. The preablation solution should be used up to the onset of ablation,
and after that, the ablation stage solution should be used.
The extent of damage or the position of the “damage front” at a given time
Two sets of values were used for
A
and
E
t
can be found
by setting O
, Eq. (17.82)
can be integrated by a controlled variable time-step procedure up to the time when O
¼
1inEq. (17.82) and solving for
z
. Alternatively, for every point
z
1.
The latter method was used to determine the position of the damage front as a function of
time, and the difference in the value integrand at the upper and lower bounds of integration
was monitored and used to change the time step. An example of such a calculation was
done for a 5-watt laser pulse of 500 ms duration. The calculation was done using both
values for
¼
from both the pigskin and another for human vessel wall. The results,
along with the position of the ablation front as a function of time (details of that are beyond
the scope of this chapter), are shown in Figure 17.17.
The vertical line at about 0.0035 seconds indicates the onset of ablation, which helps to show
that there had been biochemical damage in the tissue before the onset of ablation. After the onset
of ablation, the difference between the damage front and ablation front is the actual extent of
damage in the tissue intact. The important observation from this graph is the difference in pre-
diction of the extent of damage using the two different sets of values for
A
and
E
. For the same
irradiation conditions, thermal damage would propagate faster in skin than it would in vessel
wall. This is expected, since the damage mechanisms for vessel wall and skin are different.
A
and
E
FIGURE 17.17
Damage front as a function of time.
