Biomedical Engineering Reference
In-Depth Information
TABLE 2.3
R
CEM
for Collected Representative Arrhenius Kinetic Coefficients
Process Parameters
Process
A
(s
−1
)
E
a
(J mole
−1
)
Notes
R
CEM
44°C
Cell Death
Sapareto
2.84 × 10
99
6.18 × 10
5
0.479
CHO Cells
Beckham
6.9 × 10
116
7.3 × 10
5
0.419
without Hsp70
3.7 × 10
157
9.8 × 10
5
0.311
with Hsp70
Bhowmick
7.78 × 10
22
1.61 × 10
5
0.825
H. Prostate Apoptosis
Bhowmick
1.66 × 10
91
5.68 × 10
5
0.508
AT-1 Cells < 50°C
173.5
1.97 × 10
4
0.977
AT-1 Cells > 50°C
Borrelli
2.984 × 10
80
5.064 × 10
5
0.547
BhK Cells
He
4.362 × 10
43
2.875 × 10
5
0.710
SN12 cells, suspended
3.153 × 10
47
3.149 × 10
5
0.687
SN12 cells, attached
Erythrocytes
Lepock
7.6 × 10
66
4.55 × 10
5
0.581
Hemoglobin denaturation
Przybylska
a
1.08 × 10
44
2.908 × 10
5
0.707
Hemolysis Normal
a
3.7 × 10
43
2.88 × 10
5
0.709
Hemol. Down's Syndrome
Skin Burns
Henriques
Not
Recommended
3.1 × 10
98
6.28 × 10
5
Diller
0.487
8.82 × 10
94
6.03 × 10
5
T
≤ 53°C (same data)
1.297 × 10
31
2.04 × 10
5
T
> 53°C
Weaver
0.394
2.19 × 10
124
7.82 × 10
5
T
≤ 50°C
T
> 50°C
1.82 × 10
51
3.27 × 10
5
Brown
1.98 × 10
106
6.67 × 10
5
0.452
Microvessels
Retinal Damage
We l c h
3.1 × 10
99
6.28 × 10
5
0.473
Whitening
a
Value of
A
estimated from Wright's line (Equation 2.11b).
consequently, it is sensible to limit Ω and
d
Ω/
dt
calculations
to that neighborhood in numerical model work. CEM calcu-
lations do not have this limitation. Both Arrhenius and CEM
estimates may be easily included in commercial numerical
modeling software that permits superposition of additional
model modes on the model space. All that is necessary is the
superposition of one or more additional model modes (i.e.,
one mode for each active damage process calculation) that
can accomplish integration by time:
temperature, shorter exposures since it will be overwhelmed by
faster processes that develop at the higher temperatures.
To illustrate this behavior, Figure 2.7 compares the apopto-
sis/necrosis coefficients to a high energy process, the murine
fibroblasts (with Hsp 70 production intact,
E
a
= 9.8 × 10
5
),
at 2 hours (Figure 2.7a) and 2 minutes (Figure 2.7b) of exposure.
The long exposure shows more damage at lower temperatures
for the apoptosis coefficients, and the short exposure is plainly
dominated by the murine fibroblast damage process at the lower
temperatures.
∂
∂
y
t
(2.23)
=
f
2.5.2 alterations in Structural proteins: Muscle
and Collagen thermal Damage Examples
where
y
is either Ω or CEM and
f
, the forcing function, is either
from Equation 2.6 or 2.20.
Muscle and collagen are birefringent in their native state—that
is, able to rotate the polarization angle of a polarized light beam.
Their birefringence properties arise from ordered arrays that act
as a sort of “quarter-wave transformer” because of the specific
dimensions of the proteins. In muscle cells it is the organized
structure of the actin-myosin array in the sarcomere. In collagen
it is the regimented ordering of the rope-like macromolecular
twists. In both cases thermal alterations disrupt the arrays and
2.5.1 apoptosis/Necrosis Example prediction
The low value of
E
a
in the apoptosis/necrosis coefficients,
1.61 × 10
5
(J mole
−1
),
(57)
indicates that it is a slow process; it devel-
ops over long times at lower temperatures (in combination with
the low value for
A
), and is likely not to be observed in higher
