Biomedical Engineering Reference
In-Depth Information
For example, if the LET is 0.9 keV/nm, as in the vicinity of the Bragg peak
for C ions, 0.2% of this energy goes to biodamage, and the average energy loss
per lesion is 3 eV, then the lesion density is of the order of 2
10
3
nm
3
and
then the average number of lesions per nucleosome is 2. Then we can calculate the
probabilities of -fold cluster damage in this nucleosome as p.; 2/.Therearetwo
parameters in this estimate, the average energy per lesion and the percent of energy
going to biodamage. The average energy per lesion can be found from quantum
chemistry as the weighted average between the thresholds of all included processes.
The energetics of these processes is known even if the cross sections are not. The
second number includes the probability or cross sections of these processes. These
values are available and for now, they can be taken from available experiments, e.g.,
on interactions of electrons with DNA [
13
].
Which of the two ways is preferable for the calculation of the distribution of
cluster damage? If the number densities of agents at any distance to from the
track are known, i.e., if it is possible to compare their calculations with nano-
dosimetric experiments, along with the probabilities of inducing certain lesions, the
first route leads to the radial distribution of clustered damage. This radial distribution
potentially can be compared to the distribution of damaged cells. Then the first way
is definitely preferable. If only the survival rate dependence on the distance of the
track and the radial dose distribution are known, then the second route is the only
resort and one can calculate the unknown parameter assuming the relation between
a certain degree of clustering and cell death.
17.2.3
Integral damage complexity, distribution along the track
Still another path can be taken if we decide to ignore the radial distribution of dose
or number density and just consider the longitudinal distribution of clusters. This
may be relevant for the current experimental state of the art. When experimentalists
study foci, which reveal the efforts of the proteins to fix the damaged DNA, they
observe that the foci are very large, compared to the scale of radial distribution of
the dose. The experimentalists can measure the linear density of clusters along the
track and they hypothesize about the number of certain lesions, such as DSB, per
unit length [
14
].
In order to obtain the longitudinal distributions, we can integrate the radial
distribution of the complex damage starting from (
17.2
) substituted to (
17.1
) with
a chosen over the radius and thus present the longitudinal distribution of the
complex damage.
Z
1
N.r//
N.r/
Š
P
./
D
exp .
2 rdr;
(17.4)
0
