Quantitative Mathematical Models in Radiation Biology: Proceedings of the Symposium at Schloss Rauisch-Holzhausen, FRG, July 1987

201 Pages·1988·3.911 MB·English

by  J. Kiefer (auth.), Prof. Dr. Jürgen Kiefer (eds.)

Jurgen Kiefer (Ed.)
Quantitative
Mathematical Models
in Radiation Biology
Proceedings of the Symposium
at Schloss Rauisch-Holzhausen, FRG, July 1987
With 57 Figures and 6 Tables
Springer-Verlag
Berlin Heidelberg New York London Paris Tokyo
Prof. Dr. Jiirgen Kiefer
Strahlenzentrum der lustus-Liebig-Universitat
Leihgesterner Weg 217,0-6300 GieBen
ISBN-13: 978-3-540-50453-5 e-ISBN-13: 978-3-642-46656-4
DOl: 10.1007/978-3-642-46656-4
Library of Congress Cataloging-in-Publication Data
Quantitative mathematical models in radiation biology: proceedings of
the symposium at Schlol3 Rauisch-Holzhausen, FRG, July 19881 Jiirgen Kiefer (ed.). p. cm.
ISBN-13: 978-3-540-50453-5
1. Radiobiology-Mathematical models-Congresses. I. Kiefer, J. (Jiirgen), 1936- .
QH652.Q36 1988
574.19'15'0724-dc19 88-3922
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PRE F ACE
This volume contains a collection of papers which were given at a
symposium on
"Quantitative mathematical models in radiation biology"
held in July 1987 at Schloss Rauisch-Holzhausen near Giessen, Germany.
Some of the authors were not able to attend the meeting but kindly
supplied the manuscript. Two introductory papers were added.
I like to thank all people and institutions who helped at several
stages with the symposium and the preparation of these proceedings.
These include the Justus-Liebig-Universitat Giessen and the
Gesellschaft fUr Schwerionenforschung, Darmstadt but above all my
coworkers. Without their support both would not have been possible. In
particular I should like to mention Dr. K. Weber, Dr. E. Schneider and
Dipl. Phys. M. Kost.
We have tried to give a fairly comprehensive overview on current ideas
in this field. It is impossible to cover all aspects, we apologize for
omissions.
Giessen, September 1988 Jiirgen Kiefer
CON TEN T S
Prelude:
Why and to what end mathematical models in radiation biology
J. Kiefer 1
Models of cellular radiation action - an overview
K.J.Weber 3
Finestructures of energy deposition - introductory remarks
J.Kiefer, M.Kost 29
Analytics required by the multiple nature of radiation effects
in cells
E.L.Powers 41
Problems in theoretical track structure research for heavy
charged particles
H.G.Pare~zke 49
Radiobiological modeling based on track structure
R.Katz 57
The role of energy distributions of charged particles in the
mutagenic radiation action
S.Kozubek, E.A.Krasavin, K.G.Amirtayev, B.Tokarova,
L.P.Chernenko, M.Bonev 85
Relative biological effectiveness: review of a model
K.Gunther, W.Schulz 97
Saturation in dual radiation action
H.H.Rossi, M.Zaider 111
VIII
Hit-size effectiveness approach in biophysical modeling
M.N.Varma, V.P.Bond 119
Interpreting survival observations using phenomenological models
J.M.Nelson, L.A.Braby, N.F.Metting, W.C.Roesch 125
Cluster theory of the effects of ionizing radiations
C.A.Tobias, E.Goodwin, E.A.Blakely 135
The LETHAL AND POTENTIALLY LETHAL model - a review and recent
development
S.B.Curtis 137
DNA double-strand breaks and their relation to cytoxicity
K.H.Chadwick, H.P.Leenhouts, E.Wijngaard, M.J.Sijsma 147
The pairwise lesion interaction model
D.Harder 159
A repair fixation model based on classical enzyme kinetics
J.Kiefer 171
Formal, empirical and mechanistic equations in cellular
radiation biology
R.H.Haynes 181
PRELUDE:
WHY AND TO WHAT END
MATHEMATICAL MODELS IN RADIATION BIOLOGY.
J. Kiefer
There can be Ii ttle doubt that radiation biology is that branch of
biological sciences which can boast with the largest number of
mathematical models: During the early parts - but to a large part
still today - radiation biology was dominated by physicists, or at
least by scientists whose basic training was physics. There is a
strong and widely held belief among this group, namely that real
science has not only to be quantitative but has to be formulated in
mathematical terms. Differential equations are the hallmarks of real
achievement! But this is only part of the story and may be not the
most important one. Radiation is the agent among all environmental
factors which may damage biological systems that is not only easily
quantifiable but can also be measured with unsurpassed resolution. Its
primary effects on atoms and molecules is well understood, the
secondary processes can be followed by sophisticated experimental
techniques again a domain of physicists. The quantum nature of
interactions and the importance of stochastic variations call for an
exact - and this means, of course, mathematical description. The task
is by no means simple, quite on the contrary, it presents a challenge,
both to the experimentalist and to the theoretician. The problems of
track structure which are discussed in several contributions to this
volume exemplify this statement. This, however, hgw interesting it may
be, is not merely an exercise in basic physics. The intimate
relationship between the spatial pattern of energy deposition and the
biological effect constitutes a link between physics and life.
Unravelling it means to contribute to the problem of Erwin
Schr8dinger's - a physicist - famous essay: What is life? Thus, model
building in radiation biology is part of the philosophy of life
sciences. Even a minor success conveys the feeling to understand "was
die Welt im Innersten zusammenha,lt" as Goethe phrased it. (And please
remember, no scientific address in Germany without reference to
Goethe!).
But there are more earthbound goals. Radiation is of great practical
relevance, be it in energy production or the treatment of tumours. A
J. Kiefer (Ed.)
Quantitative Mathematical Models
in Radiation Biology
© Springer-Verlag Berlin Heidelberg 1988
2
quantitative understanding of its effect on biological systems which
is open to test and hopefully to extrapolation would be of great
predictive value. It is the hope that a generally acceptable formalism
would help to quantify radiation responses, both in radiation
protection and radiation therapy, and make it possible to move from a
purely empirical approach with all its fallacies to a real
understanding.
Obviously there is still a long way to go. The contributions in this
volume give an idea of the multitude of approaches, and it is not
tried to convey a unified picture. It does not yet exist but certain
common principles are obvious. The importance of the spatial pattern
of energy deposition, irrespective whether it is termed "track
structure" or "microdosimetry" - is one of these, the relevance of
repair processes another.
Theoretical radiation biology had its share to pave the way to present
day's molecular biology. This demonstrates that it is not just a
playground for theoreticians but may have great impact on the
development of science.
MODELS OF CELLULAR RADIATION ACTION -
AN OVERVIEW.
K.J. Weber
Strahlenzentrum der
Justus-Liebig-Universitat
Giessen, W.-Germany
1. Introduction
The fundamental concept underlying our understanding of the effects of
ionizing radiation is directly related to the quantum nature of
primary physical energy transfer processes. Discreteness and random
distribution of energy absorption events were readily realized as
determinant of two basic features in radiation action: the remarkable
energetic effectiveness of X-rays in producing biological effects and
the apparent lack of threshold dose levels, well known for common
pOi~/ons, both for cell killing and mutagenesis (Blau and Altenburger,
1923; Dessauer, 1922; Timofeeff-Ressovsky, Zimmer and Delbrlick, 1935).
The early mathematical/statistical interpretation of dose
relationships for the number of eventually expressed phenotypes, dead
or mutant among a population of viable cells, had to consider, among
others, two major experimental observations: firstly, many cellular
systems exhibit an increased effectiveness per unit dose increment
with increasing dose levels; this led to the assumption of an ability
to "accumulate" damage before lethality is expressed. Secondly, the
effectiveness of a given unit dose depends on the spatial correlation
of the discrete energy transfer events in single charged particle
tracks, characteristic for different types of radiation
(LET-dependence) . Any theoretical approach, therefore, has to
postulate the production of (some) expressible damage due to more than
one tranfer process to account for single-track effects.
The observations that the temporal pattern (protraction or
fractionation) by which dose is delivered to cells greatly influences
the response led to the introduction of the idea of reversable damage
commonly referred to as recovery phenomena. The finding of enzymatic
repair mechanisms capable of correcting structural alterations in the
J. Kiefer (Ed.)
Quantitative Mathematical Models
in Radiation Biology
© Springer-Verlag Berlin Heidelberg 1988
4
genetic material gave a molecular interpretation of the recovery
phenomena.
Although many of these crucial experimental results were not available
at the middle of this century, D.E. Lea in his unique contributions to
radiobiology (Lea, 1946) emphasized important conceptual aspects that
were introduced into numerous models on radiation effects developed
thereafter. Namely:
accumulation should occur via a binary reaction between (pairs of)
lesions.
- cells are capable to recover from damage production by a mechanisn
that reverses initial lesions. Considering the binary reaction to
occur on the biochemical time-scale interaction between lesions from
separate tracks (dose-square dependent damage production) may be
modified by their production rate, e.g. protraction or fractionation
of total dose.
- the amount of intra-track interaction (proportional to dose) depends
on the balance between interaction distance and track-structure,
thus predicting LET-effects.
Two different basic concepts in theories on cellular radiation action
may be identified.
The "interaction type models" assume induction of sublesions
pliroportional to dose with the accumulation phenomenon being envisaged
as physical interaction between pairs of sublesions from separate
tracks. This binary fixation competes with lesion removal by a repair
process having first order kinetics.
In contrast, the saturable repair models postulate the linear
induction of effective lesions some of them will be acted on by dose
dependent repair - a process whose efficiency declines with increasing
dose. In this approach direct lesion interaction may be restricted to
small distances (single tracks) whereas the multi-track effects can be
envisaged as long-range interaction mediated by cellular repair
factors.
Principal reflections on the concepts of radiation action models are
given in these proceedings by Haynes.
Following this introduction various models will be discussed in some
more detail. Emphasis is given to their basic formalism without an
attempt to specify the mathematical elaborations extensively. Those