Biomedical Engineering Reference
In-Depth Information
an excellent description of skin burn physical and physiological
processes. In a related study Brown et al.
(39)
determined process
parameters for normal muscle microvasculature that agree very
well in model work with the published skin burn values. That
study also illuminated the thermal hypersensitivity of KHT
fibrosarcoma microvasculature.
In their original skin burn experiments, Henriques and Mortiz
calculated only Ω values, defining Ω = 0.53 as corresponding to
superficial irreversible erythema (first-degree), Ω = 1.0 to tran-
sepidermal necrosis (partial thickness, or second-degree), and
Ω = 10
4
to complete involvement of the dermis (full-thickness,
or third-degree). The reported Ω values refer to the thermal his-
tory at the skin surface in their work, as previously mentioned.
The value of Ω at the damage propagation front is much lower,
however. Numerical model studies
(40)
suggest that a threshold of
C
(τ) = 80 to 85% (i.e., 15% to 20% predicted damage) provides
a reasonable estimate of the depth of skin burn under both the
Diller-Pearce coefficients(40)
(40)
and the Weaver-Stoll coefficients.(41)
(41)
A word of caution: the Arrhenius coefficients originally
reported by Henriques and Moritz
(22)
have since been widely used
but actually do not fit their own data very well—Diller et al.
(27)
reanalyzed their original data and developed the values listed in
Table 2.1, and these are recommended in their stead. Weaver and
Stoll
(41)
studied thermal radiation skin burns with similar results.
In both sets of data there is a breakpoint, 53°C in the Henriques
and Moritz data and 50°C in Weaver and Stoll's measurements.
τ
∫
(2.17)
WC
() 1( )1exp
τ=−τ=− −β
Ttdt
( )
0
where the integration kernel is given by:
0,
Tt
()
<
T
C
β=
Tt
()
(2.18)
N
AT tT
[()
−
]
Tt
()
≥
T
C
C
with:
T
C
= the “critical temperature” (°C), and a particular value
for
W
,
W
crit
, indicates “cell death” and is held by the authors to
combine several cell-damage processes. Their original notation
has been slightly modified to coincide more closely with that
used in this chapter. The fit parameters
A
and
N
are determined
by experiment—and this
A
is not the frequency factor from
Equation 2.1. It remains to be seen whether this model gives
predictions significantly different from the classical Arrhenius
approach.
To approach this question, we take as a calculational frame-
work a constant temperature exposure of 2 minutes duration,
such as might be observed in an ablation procedure. For illus-
tration we select mid-range parameters from
(42)
:
A
= 0 . 0 0 6 7,
N
= 1.0672,
T
C
= 45.65°C with
W
crit
= 0.6782—i.e.,
C
(τ) = 0.3218.
Three of the comparison processes in Figure 2.6 agree remark-
ably well with the Equation 2.17 prediction—surprisingly, the
BhK cells and murine fibroblasts (with Hsp70 intact) are virtu-
ally identical for this exposure time and agree extremely closely
with the calculation of Equation 2.17.
Using the 32% remaining undamaged cell criterion (i.e.,
C
(τ) = 0.322) for comparison, this occurs just slightly above
47. 5°C for the two cell lines and just above 47°C in the Equation
2.17 calculation. The two thermal damage models are indistin-
guishable in this example for all practical purposes. It is interest-
ing to note that CHO cells appear to be much more thermally
sensitive, the muscle microvasculature is an acceptably close
2.3.3.4 recent Models for ablation
In two recent publications, Breen et al.
(42)
and Chen and Saidel
(43)
have suggested a different calculational approach that they claim
(without demonstration) has advantages over the more tradi-
tional Arrhenius models in predicting ablation results. Their
calculation preserves much of the form of Equation 2.6 but relies
on elaborate curve fitting independent of consideration of the
processes listed in Table 2.1. In brief, the damage is calculated
from:
(42)
1.00
CHO cells
Murine fibroblasts w/Hsp70
BhK cells
0.75
Breen model
Skin WS
C
(τ)
0.50
Muscle µVasculture
0.25
0.00
45
50
55
T(°C)
FIGURE 2.6
Comparison of the damage prediction from the formulation of Breen et al.
(42)
with representative processes from Table 2.1 for
2-minute exposures.
