172
]. KIEFER
initial damage to be distributed according to Poisson's law, the surviving
fraction of the whole population will be
00
s.f. = ~>-VD(1_q)N(vD)NjN!
N=O
= e- qvD
with v as parameter.
In agreement with the experimental results an exponential survival
curve is obtained.
Let us now consider another limiting case: The dose-rate of the irradiation may be low enough to allow recovery or fixation before another "hit"
is received by the cell. If A is the fixation probability, the surviving fraction
will be
00
s.f. = I(1-q)Ne-?VD(AVD)NjN!
N=O
= e-?'qvD
Here again, an exponential survival curve is obtained but its slope is
less steep. This result is also in agreement with experimental finding (see
e.g. [7]). These remarks are obviously rather qualitative; the model certainly
requires a more refined statistical treatment, particularly on the basis of the
theory of stochastic processes, but the mathematics involved is rather
complicated. Work on this problem is in progress and will be published
elsewhere.
Let us now turn back to the two recovery mechanisms discussed in
this paper: as the combination of LHR and split-dose experiments shows,
fixation of lesions is completed if full recovery from sublethal damage has
occurred [4] and, on the other hand, sublethal damage can not be repaired
by the PR-procedure. It might be argued that sublethal and potentially
lethal damage are qualitatively different, but this assumption is not necessary. The reasoning we should prefer is along the lines of the model suggested: under normal growth conditions recovery and fixation proceed in
competition. The split-dose technique allows us to measure merely the
unfixed lesions remaining at the time of the second exposure. In terms of
the model, sublethal lesions are unfixed lesions. Thus, if a certain experimental treatment favours recovery as against fixation, while the rate of
disappearance of unfixed damage is unchanged, the split-dose curves will
remain approximately unaltered. This hypothesis may be able to explain
the relative stability of the recovery pattern as studied by fractionated
irradiation. Nevertheless, the experiments using metabolic inhibitors ought
to be checked very carefully because of the following reasoning: If the
survival level is altered by a post-irradiation treatment, the starting point
]. KIEFER
initial damage to be distributed according to Poisson's law, the surviving
fraction of the whole population will be
00
s.f. = ~>-VD(1_q)N(vD)NjN!
N=O
= e- qvD
with v as parameter.
In agreement with the experimental results an exponential survival
curve is obtained.
Let us now consider another limiting case: The dose-rate of the irradiation may be low enough to allow recovery or fixation before another "hit"
is received by the cell. If A is the fixation probability, the surviving fraction
will be
00
s.f. = I(1-q)Ne-?VD(AVD)NjN!
N=O
= e-?'qvD
Here again, an exponential survival curve is obtained but its slope is
less steep. This result is also in agreement with experimental finding (see
e.g. [7]). These remarks are obviously rather qualitative; the model certainly
requires a more refined statistical treatment, particularly on the basis of the
theory of stochastic processes, but the mathematics involved is rather
complicated. Work on this problem is in progress and will be published
elsewhere.
Let us now turn back to the two recovery mechanisms discussed in
this paper: as the combination of LHR and split-dose experiments shows,
fixation of lesions is completed if full recovery from sublethal damage has
occurred [4] and, on the other hand, sublethal damage can not be repaired
by the PR-procedure. It might be argued that sublethal and potentially
lethal damage are qualitatively different, but this assumption is not necessary. The reasoning we should prefer is along the lines of the model suggested: under normal growth conditions recovery and fixation proceed in
competition. The split-dose technique allows us to measure merely the
unfixed lesions remaining at the time of the second exposure. In terms of
the model, sublethal lesions are unfixed lesions. Thus, if a certain experimental treatment favours recovery as against fixation, while the rate of
disappearance of unfixed damage is unchanged, the split-dose curves will
remain approximately unaltered. This hypothesis may be able to explain
the relative stability of the recovery pattern as studied by fractionated
irradiation. Nevertheless, the experiments using metabolic inhibitors ought
to be checked very carefully because of the following reasoning: If the
survival level is altered by a post-irradiation treatment, the starting point