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SIXTHJSYMPOSIUM ON MICRODOSIMETRY
Brussels, Belgium, May 22-26, 1978
Commission of the European Communities Directorate-General for Research, Science and Education
Biology, Radiation Protection and Medical Research
Edited by J . Booz and H. G. Ebert
Volume II
AG B I B L I O T H E K . I
Phys. re^ n . \
Harwood Academic Publishers Ltd. for the Commission of the European Communities
OPENING SESSION
V I I
Chairman : W.K. SINCLAIR
G. SCHUSTER
L.E.FEINENDEGEN
Address of Welcome
B i o l o g i c a l damage from r a d i o a c t i v e n u c l e i incorporated into DNA of c e l l s ; i m p l i c a t i o n s for r a d i a t i o n biology and r a d i a t i o n p r o t e c t i o n ( i n v i t e d paper)
SESSION 1 Chai rman A. WAMBERSIE
J.R.K. SAVAGE
G.W. BARENDSEN
Some thoughts on the nature of chromosomal a b e r r a t i o n s and t h e i r use as a q u a n t i t a t i v e end-point for r a d i o b i o l o g i c a l s t u d i e s ( i n v i t e d paper)
RBE-LET r e l a t i o n s for induction of reproductive death and chromosome a b e r r a t i o n s in mammalian c e l l s
SESSION 2 Chairman J.A. DENNIS
V.P. BOND
D.E. CHARLTON J. BOOZ J. FIDORRA Th. SMIT L.E. FEINENDEGEN
G. TISLJAR-LENTULIS P. HENNEBERG Th. MIELKE L.E. FEINENDEGEN
RBE of Η beta rays and other low-LET r a d i a t i o n s at low doses and/or dose r a t e s ( i n v i t e d paper)
Microdosimetry of r a d i o a c t i v e n u c l e i incorporated into the DNA of mammalian c e l l s
125 DNA strand breaks induced by I in cultured human kidney c e l l s and t h e i r r e p a i r
SESSION 3 Chairman : N. PARMENTIER
D. FRANKENBERG Μ. FRANKENBERG-SCHWAGER W. GRUNDLER E. H. KRÜGER H.G. PARETZKE W. POHLIT G. RIMPL
B. FERTIL P. DESCHAVANNE B. LACHET E.P. MALAISE
Radiation s t u d i e s at the p h y s i c a l , molecular, c e l l u l a r and macrocolony l e v e l
S u r v i v a l curves of n e o p l a s t i c and non transformed human c e l l l i n e s : s t a t i s t i c a l a n a l y s i s using d i f f e r e n t models
SESSION 4 Chairman : S. WAGNER
J.L. MAGEE A. CHATTERJEE
M. TERRISSOL J.P. PATAU T. EUDALDO
Theory of e l e c t r o n t r a c k s with e x p l i c i t c o n s i d e r a t i o n of track-end e f f e c t s
A p p l i c a t i o n ä la microdosimetrie et ä la ra d i o b i o l o g i e de la simulation du transport des o l e c t r o n s de basse energie dans l'eau ä l ' e t a t l i q u i d e
SESSION 4 ( c o n t . )
V I I I
R.N. HAMM H.A. WRIGHT J.E. TURNER R.H. RITCHIE
S p a t i a l c o r r e l a t i o n of energy dep o s i t i o n events in i r r a d i a t e d l i q u i d water
SESSION 5 Chairman : R.V. RECHENMANN
T. BUDD M. MARSHALL
C S . KWOK M. MARSHALL
B.J. FORSBERG Τ.Ε. BURLIN
R. BLOHM D. HARDER
Low pressure cloud chamber s t u d i e s -I - Methods of a n a l y s i s of i o n i s a t i o n d i s t r i b u t i o n s
Low pressure cloud chamber s t u d i e s -I I - The determination of a high r e s o l u t i o n t i s s u e -equivalent gas for the study of α - p a r t i c l e t r a c k s
R e l a t i o n s of secondary e l e c t r o n emission to microdosimetry and a p p l i c a t i o n s to two-target theory
P h y s i c a l i n t e r a c t i o n s of low-energy e l e c t r o n s i n s i n g l e and twin t a r g e t s
SESSION 6 Chairman : T.E. BURLIN
M.N. VARMA J.W. BAUM P. KLIAUGA
W.E. WILSON L.H. TOBUREN H.G. PARETZKE
L.A. BRABY W.C. ROESCH
Microdosimetric r e s u l t s obtained by p r o p o r t i o n a l counter and i o n i z a t i o n chamber methods : a comparison
C a l c u l a t i o n of energy deposition spectra in small gaseous s i t e s and i t s a p p l i c a b i l i t y to condensed phase
Direct measurements of f ( z ) for f a s t e l e c t r o n s
B. FORSBERG Μ. JENSEN L. LINDBORG G. SAMUELSON
Determinations of the dose mean of s p e c i f i c energy for conventional X-rays by variance-measurements
SESSION 7 Chairman : M. TERRISSOL
POSTER SESSION I : P a r t i c l e track s t r u c t u r e and slowing down
A. CHAMBAUDET Ph. ROMARY H. ROULET A. BERNAS
Diametre des t r a c e s r e v e l e e s dans quelques detecteurs polym£riques et parcours " e f f i c a c e " des rayons 6'
A. CHATTERJEE J.L. MAGEE
Rel a t i o n s h i p of the tr a c k s t r u c t u r e of heavy p a r t i c l e to the p h y s i c a l d i s t r i b u t i o n and chemical e f f e c t s of r a d i c a l s
D. COMBECHER J . KOLLERBAUR G. LEUTHOLD H. G. PARETZKE G. BURGER
Energy spectra of degraded e l e c t r o n s in water vapour and in carbon
B. GROSSWENDT E. WAIBEL
Determination of b a c k s c a t t e r i n g c o e f f i c i e n t s for low energy e l e c t r o n s in d i f f e r e n t gases
SESSION 7 (cont.)
IX
G.S. HURST S.D. KRAMER C.E. BEMIS, J r . J.P. YOUNG
Detection of s i n g l e atoms in p a r t i c l e t r a c k s
A. JANSSENS G. EGGERMONT R. JACOBS
Experimental study of the c a v i t y theory, using a high pressure i o n i z a t i o n chamber
R.H. RITCHIE R.N. HAMM J.Ε. TURNER H.A. WRIGHT
The i n t e r a c t i o n of swift e l e c t r o n s with l i q u i d water
M. SCHNEIDER J. BÖHM Κ. HOHLFELD Η. REICH
Β. SENGER Ε. WITTENDORP R.V. RECHENMANN
Eine Apparatur zur Messung des V e r l a u f s der Ionendosis an Grenzschichten
<5-ray production along medium energy α p a r t i c l e s c r o s s i n g t i s s u e - l i k e media
J.E. TURNER R.N. HAMM H.A. WRIGHT R.H. RITCHIE R. KATZ
Ca l c u l a t e d e l e c t r o n slowing-down spectra for l i q u i d water i r r a d i a t e d by X and gamma rays - I m p l i c a t i o n s for photon RBE
Ε. WITTENDORP Β. SENGER J.B. SANDERS R.V. RECHENMANN
Heavy secondaries e j e c t e d by primary medium energy α p a r t i c l e s c r o s s i n g dense t i s s u e - l i k e media
R. KATZ Report on poster Session I
SESSION 8 Chairman : E. HALL
A.M. KELLERER
R. KATZ
Radiation c a r c i n o g e n e s i s at low doses ( i n v i t e d paper)
High LET c o n s t r a i n t s on low LET s u r v i v a l
SESSION 9 Chairman : R. GRILLMAIER
POSTER SESSION I I : A p p l i c a t i o n of microdosimetry to r a d i a t i o n therapy
H.I. AMOLS J.F. DICELLO M. ZAIDER
The RBE at various p o s i t i o n s in and near a large negative pion beam
L.S. AUGUST R.B. THEUS P. SHAPIRO
Gamma measurements with a non-hydrogenous Rossi counter in a mixed f i e l d
G. BURGER Ε. MAI ER A. MORHART
Radiation q u a l i t y and i t s relevancy in neutron radiotherapy
SESSION 9 (cont.)
J.F. DICELLO M. ZAIDER
I n v e s t i g a t i o n of the microdosimetric c h a r a c t e r i s t i c s of broad, t h e r a p e u t i c beams of negative pions at LAMPF
J. FIDORRA J. BOOZ
The Local d i s t r i b u t i o n of r a d i a t i o n q u a l i t y of a collimated f a s t neutron beam from 15 MeV deuterons on B e r y l l i u m
R.M. HENKELMAN G.K.Y. LAM
Pr e d i c t i o n of b i o l o g i c a l e f f e c t of pion i r r a d i a t i o n using the s t a r d i s t r i b u t i o n to determine the high LET dose
B. HOGEWEG J. ZOETELIEF J . J . BROERSE
R.b.e. for c e l l s u r v i v a l at d i f f e r e n t p o s i t i o n s in co l l i m a t e d neutron beams in r e l a t i o n to d i f f e r e n c e s in l i n e a l energy sp e c t r a
M.A. KENAWY A.M. SAYEO
Neutron absorbed dose measurements in phantom from 252 .
cf source
J.B. LEROUX Y. HERBAUT J. ROUILLON J* GIROUX
Spectres de depots d'energie pour l e s rayonnements de f a i b l e TLE - d i s c r i m i n a t i o n neutron gamma dans un champ mixte η - γ
Μ. MAKAREWICZ S. PSZONA
The c a l c u l a t e d mean energy de p o s i t i o n pattern in an ion chamber for neutrons
H.G. MENZEL Η. SCHUHMACHER Η. BLATTMANN
Experimental microdosimetry at high-LET r a d i a t i o n therapy beams
J.P. PATAU C.E. VERNES Μ. TERRISSOL Μ. MALBERT
C a l c u l des c a r a c t e r i s t i q u e s q u a l i t a t i v e s (TEL, F.Q. equivalent de dose) d'un f a i s c e a u de photons de fre i n a g e ä usage m e d i c a l , par simulation de sa c r e a t i o n et de son tr a n s p o r t
A.G. PERRIS O.R. PERRY *F.A. SMITH
LET i n dose d i s t r i b u t i o n s , from s p e c t r a l measurements of charged p a r t i c l e s emitted at the capture of negative pions in b i o l o g i c a l l y s i g n i f i c a n t m a t e r i a l s
G. PFISTER P. STILLER G. HEHN
R e c o i l spectra in neutron i r r a d i a t e d t i s s u e s and TE-materiaIs
J. ZOETELIEF B. HOGEWEG J . J . BROERSE
Radiation q u a l i t y and absorbed dose at d i f f e r e n t p o s i t i o n s in the primary beam and around the s h i e l d i n g of a neutron generator
J . J . BROERSE Report on poster Session I I
SESSION 10 Chairman : A. ALLISY ( j o i n t l y organized by ICRU and EURATOM)
M.J. BERGER Planned compilation of stopping power and range data
H.H. ANDERSEN Higher-order Z^ c o r r e c t i o n s to the Bethe stopping-power formula
J.A. DENNIS The dependence of stopping-power on p h y s i c a l and D. POWERS chemical s t a t e s
SESSION 10 (cont.) X I
Μ. INOKUTI J.Ε. TURNER
Mean e x c i t a t i o n energies for stopping-power as derived from o s c i L L a t o r - s t r e n g t h d i s t r i b u t i o n s
SESSION 11
POSTER SESSION I I I :
J . CASANOVAS R. 6R0B 6. BRUNET R. SABATTIER J.P. GUELFUCCI D. BLANC
Chairman : M.J. BERGER
Stopping power and r e l a t e d s u b j e c t s
Determination du p o t e n t i e l d ' i o n i s a t i o n de c e r t a i n s hydrocarbures en phase Liquide
J . J . COYNE L.J. GOODMAN
P. GOUARD M. CHEMTOB V.D. NGUYEN N. PARMENTIER
A.K.M.M. HAQUE M.J. GEARY
R.B.J. PALMER A. AKHAVAN-REZAYAT
H.G. PARETZKE M.J. BERGER
B.G.R. SMITH J. BOOZ
D.I. THWAITES D.E. WATT
T.K. YEUNG D.E. WATT
D.E. WATT
W , computed from recent nucLear data and W measurements
Une approche p o s s i b l e de l'etude du ralentissement des p a r t i c u l e s chargees lourdes
The stopping power and s t r a g g l i n g for alpha p a r t i c l e s in l i q u i d s
Range-energy r e l a t i o n s and stopping power of water, water vapour and t i s s u e equivalent l i q u i d for α p a r t i c l e s over the energy range 0.5 to 8 MeV
Stopping power and energy degradation for e l e c t r o n s in water vapor
Experimental r e s u l t s on W-values and t r a n s m i s s i o n of low energy e l e c t r o n s in gases
Phase e f f e c t s in stopping power for low-energy heavy charged p a r t i c l e s
M u l t i p l e s c a t t e r i n g c o r r e c t i o n s to measurements of stopping power for slow ions
Report on poster Session I I I
SESSION 12 Chairman : W. POHLIT
D.T. G00DHEAD J. THACKER R. COX
P.D. HOLT
D. CHMELEVSKY A.M. KELLERER H.H. ROSSI
The c o n f l i c t between the b i o l o g i c a l e f f e c t s of u l t r a s o f t X-rays and microdosimetric measurements and a p p l i c a t i o n
Micro-dosimetry and nano-dosimetry
Concepts and q u a n t i t i e s r e l e v a n t to the e v a l u a t i o n of charged p a r t i c l e t r a c k s
SESSION 13
X I I Chairman : H.H. ROSSI
R.P. VIRSIK D. HARDER
Chromosome a b e r r a t i o n s in human lymphocytes induced by photon and e l e c t r o n r a d i a t i o n s , and the su b l e s i o n i n t e r a c t i o n model
C R . GEARD
A. WAMBERSIE J. VAN DAM G. LAUBLIN
Microdosimetry and chromosomal a b e r r a t i o n s f o r monoenergetic neutrons
RBE as a function of depth in a 650 MeV H e + +
beam determined for growth delay i n v i c i a faba and for induction of chromosome a b e r r a t i o n s in a l l i u m cepa
SESSION 14 Chairman : G.E. ADAMS
E.M. FI EL DEN 0. SAPORA P.S. L0VER0CK
S. APELGOT J.P. ADLOFF
The r e l a t i o n between s u r v i v a l and the i n i t i a l y i e l d of DNA strand breaks for Ε c o l i B/r
Transmutation e f f e c t s of 3 2 P and 3^P i n c o r p o r a t e d in DNA
H.G. PARETZKE
H.H. ROSSI R. BIRD R.D. COLVETT A.M. KELLERER N. ROHRIG Y-M.P. LAM
On l i m i t a t i o n s of c l a s s i c a l microdosimetry and advantages of t r a c k s t r u c t u r e a n a l y s i s for r a d i a t i o n biology
The molecular ion experiment
SESSION 15
POSTER SESSION IV:
H.M.A. AL-SHAI8ANI D.E. WATT
M. COPPOLA M. MARTINELLI L. T0MMASIN0
Chairman : D. HARDER
I n t e r p r e t a t i o n of b i o l o g i c a l data
P h y s i c a l processes in the i n a c t i v a t i o n of enzymes by slow heavy ions
C e l l s u r v i v a l and r a d i a t i o n q u a l i t y
R. FACIUS H. BÜCKER G. REITZ M. SCHÄFER
Radial dependence of b i o l o g i c a l response of spores of B a c i l l u s s u b t i l i s around t r a c k s of heavy ions
R.E. GRILLMAIER L. BIHY H.G. MENZEL Η. SCHUHMACHER
Chromosome a b e r r a t i o n s t u d i e s and microdosimetry with r a d i a t i o n s of varying q u a l i t y
R. KATZ E.C PENNINGTON
Ra d i o b i o l o g i c a l aspects of s u p r a l i n e a r photographic emulsions
H.P. LEENHOUTS K.H. CHADWICK M.J. SIJSMA
The i n f l u e n c e of r a d i a t i o n s t i m u l a t e d r e p a i r processes on the shape of d o s e - e f f e c t curves
X I I I
SESSION 15 ( c o n t . )
J.W. PURDIE E.R. INHABER N.V. KLASSEN
R.A. ROTH R. KATZ
Μ. SCHÄFER Η. BÜCKER R. FACIUS G. HORNECK G. REITZ G. KRAFT
F. SCHOPFER J. KIEFER E. SCHNEIDER G. KRAFT
A. TALLENTIRE D.J.W. BARBER
K.J. WEBER J. KIEFER
J . KIEFER
I n c r e a s e d s e n s i t i v i t y of anoxic mammalian c e l l s i r r a d i a t e d with s i n g l e pulses at very high dose r a t e s
Heavy ion beam model for radiobiology
High L E T - i r r a d i a t i o n of B a c i l l u s s u b t i l i s spores
The i n a c t i v a t i o n of c e l l s by a c c e l e r a t e d heavy ions of very high LET
The i n t e r r e l a t i o n s h i p between pulse length and dose- r a t e w i t h i n the pulse in the enhancement of anoxic damage in wet B a c i l l u s megaterium spores i r r a d i a t e d with pu l s e s of e l e c t r o n s
I n t r a c e l l u l a r measurement of the i n a c t i v a t i o n of ribosomal RNA genes in d i p l o i d yeast c e l l s a f t e r exposure to 6 0 c o - Y ^ r a y s , 85 kV X-rays and 241-Arnericiurn-ct - p a r t i c les
Report on poster Session IV
SESSION 16 Chairman : A.M. KELLERER
H.H. ROSSI
J.A. DENNIS
Ra d i a t i o n q u a l i t y and q u a l i t y f a c t o r ( i n v i t e d paper)
Dose l i m i t s and q u a l i t y f a c t o r s : the D e v i l ' s view
SESSION 17 Chairman : J . J . BROERSE
C L . GREENSTOCK R.H. WIEBE
K.H. CHADWICK Η.P. LEENHOUTS
Chemical mechanisms of the i n t e r a c t i o n between r a d i a t i o n and chemical carcinogens
The i m p l i c a t i o n s for r a d i o l o g i c a l p r o t e c t i o n of the s y n e r g i s t i c i n t e r a c t i o n between r a d i a t i o n and other DNA damaging agents
SESSION 18 Chairman : K.H. CHADWICK
J. KIEFER Η. KOCH Κ. KOESTER G. MOCK Ε. SCHNEIDER Κ. WEBER
The molecular and c e l l u l a r b a s i s of the oxygen e f f e c t
SESSION 18 (cont.) X I V
Κ.F. BAVERSTOCK W.G. BURNS R. MAY
The oxygen in the track hypothesis: Microdosimetric i m p l i c a t i o n s
SESSION 19 Chai rman H. DE CHOUDENS
R.S. CASWELL J . J . COYNE
P. KLIAUGA R.D. COLVETT L.J. GOODMAN Y.M. LAM
A.K.M.M. HAQUE S.A. SAQ'AN
Energy d e p o s i t i o n spectra for neutrons based on recent cross s e c t i o n e v a l u a t i o n s
Microdosimetry of 400 MeV/AMU 1 2 C and 450 MeV/AMU ^ A r beams
Microdosimetric study with c y l i n d r i c a l walled and w a l l - l e s s p r o p o r t i o n a l counters
SESSION 20 Chairman : J . BOOZ
C. HERSKIND Κ.Α. JESSEN
W.C ROESCH
J. BOOZ
APPENDIX 1
Measurements i n i n t e r n a l microdosimetry with a w a l l - l e s s p r o p o r t i o n a l counter
I n t e r n a l microdosimetry
Closing of the Symposium
Personal impressions and reviews of d i s c u s s i o n s
G.E. ADAMS
J. BOOZ
J.A. DENNIS
L. LINDBORG
Μ. TERRISSOL
G. TISLJAR-LENTULIS
Some d i s c u s s i o n comments on the mechanisms of s e n s i t i z e r s
Summary of the d i s c u s s i o n s concerning r a d i a t i o n mechanisms of e x t e r n a l r a d i a t i o n s
Impressions of the 6th Microdosimetry Symposium and i t s relevance to r a d i o l o g i c a l p r o t e c t i o n
Summary of d i s c u s s i o n s on e v a l u a t i o n of microdosimetry data
Summary of the d i s c u s s i o n s concerning e l e c t r o n t r a c k s t r u c t u r e and microdosimetry
Summary of the d i s c u s s i o n s concerning incorporated r a d i o i s o t o p e s
APPENDIX 2 L i s t of p a r t i c i p a n t s
855
CONCEPTS AND QUANTITIES
RELEVANT TO THE EVALUATION OF CHARGED PARTICLE TRACKS
D.Chmelevsky, A.M.Kel 1erer, H.H.Rossi
I n s t i t u t für Med .Strahlenkunde der Universität Würzburg, Versbacher S t r . 5 ,
D -8700 Würzburg
R a d i o l o g i c a l Research L a b o r a t o r y , Dept.of Radiology, Columbia U n i v e r s i t y ,
630 West 168th S t . , New York, N.Y. 10032
ABSTRACT: The s t o c h a s t i c v a r i a b l e s ε, ζ and y have o r i g i n a t e d i n c l o s e
c o n n e c t i o n w i t h e x p e r i m e n t a l m i c r o d o s i m e t r i c t e c h n i q u e s , and t h e i r d e f i n i
t i o n s r e f l e c t these t e c h n i q u e s . Recently o t h e r q u a n t i t i e s have been de
f i n e d t h a t correspond more c l o s e l y t o the c o m p u t a t i o n a l approach i n m i c r o -
d o s i m e t r y . Of p a r t i c u l a r importance among the new concepts i s the n o t i o n
of energy transfers and t h a t o f the distance distribution t ( x ) . These
n o t i o n s are c o n s i d e r e d .
A general e q u a t i o n f o r dual r a d i a t i o n a c t i o n ( l e s i o n s produced by p a i r s o f
s u b l e s i o n s ) can be f o r m u l a t e d i n terms o f t ( x ) and an analogous f u n c t i o n
s ( x ) t h a t d e s c r i b e s the geometry o f the s e n s i t i v e s t r u c t u r e s i n the c e l l .
T his f o r m u l a i s a general e q u a t i o n f o r t h e random o v e r l a p o f two geo
m e t r i c a l o b j e c t s ( p a r t i c l e t r a c k and s e n s i t i v e s t r u c t u r e s o f the c e l l ) ; i t
determines the magnitude o f the l i n e a r component f o r the f o r m a t i o n o f
l e s i o n s . As a f u r t h e r i l l u s t r a t i o n o f the i m p l i c a t i o n s o f the d i s t a n c e
d i s t r i b u t i o n t ( x ) the concept o f intra-traek dose Δ(χ) i s i n t r o d u c e d .
Work supported by Euratom C o n t r a c t 208-76-7B10 D and by Grant Numbers CA 15307 and 12536, awarded by the N a t i o n a l Cancer I n s t i t u t e , DHEW, and by C o n t r a c t EP -78-S -02-A733 from the U.S. Department o f Energy.
856
Introduction
M i c r o d o s i m e t r y i s t h e p a r t of d o s i m e t r y t h a t deals w i t h the s t a t i s t i c a l
f l u c t u a t i o n s o f energy a b s o r p t i o n i n i r r a d i a t e d m a t t e r . S t o c h a s t i c q u a n t i t i e s
such as energy imparted ε specific energy ζ and lineal energy y d e s c r i b e
these f l u c t u a t i o n s . T h e i r p r o b a b i l i t y d i s t r i b u t i o n s ( u s u a l l y r e s t r i c t e d t o
s p h e r i c a l r e g i o n s ) have been the o b j e c t o f e x p e r i m e n t a l as w e l l as t h e o r e t i
c a l s t u d i e s . In f a c t m i c r o d o s i m e t r y i s sometimes, i n a somewhat too narrow
d e f i n i t i o n , i d e n t i f i e d w i t h the study o f the p r o b a b i l i t y d i s t r i b u t i o n s o f
ε, ζ or y.
The e s t a b l i s h e d s t o c h a s t i c q u a n t i t i e s ε, ζ, and y are i m p o r t a n t and u s e f u l ;
however o t h e r q u a n t i t i e s and concepts have been i n t r o d u c e d which may even
t u a l l y assume an e q u a l l y i m p o r t a n t r o l e . These n o t i o n s have o r i g i n a t e d from
the e v a l u a t i o n o f charged p a r t i c l e t r a c k s and they w i l l here be summarized.
The d e f i n i t i o n o f energy imparted can serve as a s t a r t i n g p o i n t f o r t h e i r
cons i d e r a t i o n .
The notion of energy transfers and the definition of energy imparted
Energy imparted i s the fundamental s t o c h a s t i c q u a n t i t y o f d o s i m e t r y . I t i s
d e f i n e d as t h e d i f f e r e n c e o f r a d i a t i o n energy ( k i n e t i c energy o f i o n i z i n g
p a r t i c l e s ^ ) f l o w i n g i n t o and f l o w i n g out o f the r e f e r e n c e volume ( l ) .
D e t a i l s o f the d e f i n i t i o n t h a t account f o r the change o f r e s t mass i n p a r
t i c l e t r a n s f o r m a t i o n s need, f o r the present purpose, not be c o n s i d e r e d .
The ICRU d e f i n i t i o n o f energy imparted i s s c h e m a t i c a l l y represented i n
F i g . l a . This d e f i n i t i o n r e f e r s t o f i n i t e domains and invokes merely the
o v e r a l l i n f l o w and o u t f l o w o f r a d i a t i o n energy. I t does not account f o r the
a c t u a l processes of energy t r a n s f e r w i t h i n the volume nor does i t account
f o r t h e i r s p a t i a l d i s t r i b u t i o n . The d e f i n i t i o n corresponds t h e r e f o r e t o t h e
e x p e r i m e n t a l d e t e r m i n a t i o n o f the q u a n t i t i e s ε, ζ, or y, where t o t a l energy
The term ionizing has not been e x p l i c i t e l y d e f i n e d i n ICRU r e p o r t 19. In the present c o n t e x t i t i s s u f f i c i e n t t o note t h a t c e r t a i n minimum k i n e t i c e n e r g i e s can a r b i t r a r i l y be s p e c i f i e d f o r v a r i o u s types o f part i c l e s so t h a t these p a r t i c l e s a r e not considered as i o n i z i n g i f t h e i r k i n e t i c energy ( i . e . energy minus r e s t energy) i s below the s p e c i f i e d v a l u e .
857
t r a n s f e r (approximated i n terms o f t o t a l number o f ions) i s determined
w i t h o u t regard t o the s p a t i a l d i s t r i b u t i o n w i t h i n the s e n s i t i v e r e g i o n o f
the d e t e c t o r .
Carlsson (2) has r e c e n t l y proposed a d e f i n i t i o n o f energy imparted t h a t i s
e q u i v a l e n t t o the ICRU d e f i n i t i o n but has a d i f f e r e n t form. In t h i s d e f i n i
t i o n the energy imparted i s the sum o f c o n t r i b u t i o n s Δε. from i n d i v i d u a l
processes, such as e l e c t r o n i c c o l l i s i o n s , o c c u r r i n g in the r e f e r e n c e volume.
T h i s form o f the d e f i n i t i o n corresponds t o those recent m i c r o d o s i m e t r i c
s t u d i e s which u t i l i z e t h e a c t u a l c o o r d i n a t e s o f charged p a r t i c l e t r a c k s .
In f a c t the d e f i n i t i o n o f the c o n t r i b u t i o n s Δε. i s i d e n t i c a l w i t h the d e f
i n i t i o n o f energy transfers^ i n the e v a l u a t i o n o f charged p a r t i c l e t r a c k s
( 3 ) .
Energy t r a n s f e r s Δε. are d e f i n e d f o r those p o i n t s T. where i o n i z i n g par
t i c l e s undergo an i n t e r a c t i o n . Each p o i n t Τ. i s termed a transfer point.
The v a l u e Δε. i s equal t o the k i n e t i c energy o f t h e i o n i z i n g p a r t i c l e i n
c i d e n t on the t r a n s f e r p o i n t minus t he k i n e t i c energy o f t h e i o n i z i n g par-
t i c l e ( s ) emerging from t he p o i n t .
I t must be noted, t h a t k i n e t i c energy i s not counted i f i t i s lower than
the l i m i t s p e c i f i e d f o r i o n i z i n g p a r t i c l e s . T h i s i m p l i e s t h a t energy d i s
s i p a t i o n by n o n - i o n i z i n g p a r t i c l e s i s d i s r e g a r d e d . There w i l l be numerous
t r a n s f e r p o i n t s where an i n c i d e n t i o n i z i n g p a r t i c l e loses s u f f i c i e n t ener
gy t o emerge as a n o n - i o n i z i n g p a r t i c l e . The number o f emerging i o n i z i n g
p a r t i c l e s may then be zero, and the energy t r a n s f e r i s s i m p l y equal t o the
k i n e t i c energy o f the incoming p a r t i c l e .
I t w i l l a l s o be noted t h a t i n t e r a c t i o n s between charged p a r t i c l e s do n o t ,
s t r i c t l y , take place a t a p o i n t . For the purpose o f the pre s e n t d i s c u s s i o n
t h i s can, however, be d i s r e g a r d e d .
For those d e t a i l s o f the d e f i n i t i o n t h a t deal w i t h changes i n r e s t mass i n
p a r t i c l e t r a n s f o r m a t i o n s one may r e f e r t o the a r t i c l e by Ca r l s s o n .
+^The energy t r a n s f e r s have e a r l i e r (3) been symbolized by ε., but Carlsson's n o t a t i o n Δε. i s now used.
858
The d e f i n i t i o n o f energy imparted i n terms o f i n d i v i d u a l energy t r a n s f e r s
i s s c h e m a t i c a l l y represented i n Fig. 1 b . In t h i s f i g u r e dots stand f o r the
energy t r a n s f e r s Δε..
1a l b
F i g . 1 Two e q u i v a l e n t d e f i n i t i o n s o f energy imparted.
The symbols T_^ and T ^ i n Fig.1a stand f o r the k i n e t i c e n e r g i e s o f i n c i d e n t and o u t - g o i n g p a r t i c l e s .
The dots i n F i g . l b r e p r e s e n t energy t r a n s f e r s Δε. t h a t may be i o n i z a t i o n s or e x c i t a t i o n s .
859
The spatial pattern of energy transfers as an explicit description
of particle tracks
The c o o r d i n a t e s o f a l l energy t r a n s f e r s t o g e t h e r w i t h the values Δε.
a f f o r d a n e a r l y e x h a u s t i v e d e s c r i p t i o n o f a charged p a r t i c l e t r a c k . The
term particle track i s here used t o d e s i g n a t e energy d e p o s i t i o n by a par
t i c l e and i t s i o n i z i n g secondaries.
The s p a t i a l d i s t r i b u t i o n s o f energy t r a n s f e r s are u s u a l l y o b t a i n e d by
Monte C a r l o methods ( ^ , 5 ) · S i m i l a r i n f o r m a t i o n i s sought i n experiments
t h a t aim a t the d e t e r m i n a t i o n o f the c o o r d i n a t e s o f i n d i v i d u a l i o n i z a t i o n s
i n a c l o u d chamber ( 6 ) . The unprocessed i n f o r m a t i o n , i . e . t he c o l l e c t i o n
o f t h e c o o r d i n a t e s o f energy t r a n s f e r s , c o uld i n p r i n c i p l e be u t i l i z e d
d i r e c t l y i n a Monte Carlo s u p e r p o s i t i o n o f s i m u l a t e d charged p a r t i c l e
t r a c k s and s i m u l a t e d c e l l u l a r s t r u c t u r e s . However t h i s w i l l o f t e n r e q u i r e
d e t a i l e d i n f o r m a t i o n on c r i t i c a l c e l l o r g a n e l l e s t h a t i s not a v a i l a b l e . I t
i s t h e r e f o r e d e s i r a b l e t o o b t a i n a c h a r a c t e r i z a t i o n o f the s p a t i a l p a t t e r n
o f energy t r a n s f e r s t h a t i s more compact and t h a t can be a p p l i e d i n a more
general way. The distance distribution, t ( x ) , of energy t r a n s f e r s i s such
a compact c h a r a c t e r i z a t i o n .
The distance distribution t ( x ) as an implicit description of
the charged particle tracks
The m i c r o s c o p i c d i s t r i b u t i o n s of energy produced by d i f f e r e n t types o f
i o n i z i n g r a d i a t i o n s vary by the degree o f s p a t i a l c o r r e l a t i o n o f energy
t r a n s f e r s . With e n t i r e l y u n c o r r e l a t e d energy t r a n s f e r s (random d i s t r i b u
t i o n o f t r a n s f e r s ) t h e r e would be no increased p r o b a b i l i t y f o r o t h e r energy
t r a n s f e r s i n the v i c i n i t y o f a t r a n s f e r p o i n t . However u n c o r r e l a t e d energy
t r a n s f e r s are produced o n l y by UV i r r a d i a t i o n ; w i t h i o n i z i n g r a d i a t i o n s
energy t r a n s f e r s occur i n c l u s t e r s (designated v a r i o u s l y as b l o b s , spurs,
δ-rays , t r a c k s e t c ) .
L i n e a r energy t r a n s f e r i s one concept t o c h a r a c t e r i z e t h e a g g r e g a t i o n o f
energy t r a n s f e r s , but i t i s i n many ways a poor concept. The y - d i s t r i b u -
t i o n s a f f o r d a more r e a l i s t i c c h a r a c t e r i z a t i o n o f the s p a t i a l c o n c e n t r a
t i o n o f energy t r a n s f e r s . Another p o s s i b i l i t y c o n s i s t s i n q u o t i n g an a c t u a l
860
parameter o f c o r r e l a t i o n . The d i s t a n c e d i s t r i b u t i o n i s such a parameter o f
c o r r e l a t i o n . I t has been g i v e n t h e f o l l o w i n g d e f i n i t i o n ( 7 ) :
t n ( x ) dx i s the expected energy imparted w i t h i n a d i s t a n c e χ t o x+dx
from an energy t r a n s f e r randomly s e l e c t e d .
W ith no c o r r e l a t i o n t h i s would be:
t D ( x ) = W 2 p D (1)
where D i s the absorbed dose, and ρ i s the d e n s i t y .
For a c t u a l p a r t i c l e s one o b t a i n s an a d d i t i o n a l term t ( x ) which r e p r e s e n t s
c o r r e l a t e d energy t r a n s f e r s , i . e . energy t r a n s f e r s from t h e same t r a c k :
t D ( x ) = t ( x ) + W 2 p D ( 2 )
The dose-dependent term i s t r i v i a l . I t i s t h e r e f o r e s u f f i c i e n t t o c o n s i d e r
the f u n c t i o n t ( x ) which can be used t o c h a r a c t e r i z e r a d i a t i o n q u a l i t y . This
f u n c t i o n i s c a l l e d t h e distance distribution o f energy t r a n s f e r s ; one can
show t h a t i t i s i n f a c t t h e (non-normalized) d i s t r i b u t i o n o f d i s t a n c e s o f
randomly s e l e c t e d p a i r s o f t r a n s f e r s i n t h e same p a r t i c l e t r a c k . However
the term proximity function has a l s o been used ( 8 ) .
One can a l s o use the i n t e g r a l :
χ T ( x ) = J t ( x ' ) dx' (3)
0
which i s equal t o the expected energy imparted i n a sphere o f r a d i u s χ
centered a t a randomly s e l e c t e d t r a n s f e r p o i n t .
Computation of t ( x ) and T ( x ) from the coordinates of
charged particle tracks
For a g i v e n s p a t i a l p a t t e r n o f energy t r a n s f e r s one can compute t h e c o r r e
sponding f u n c t i o n s t ( x ) and T ( x ) . Since an a c t u a l p a t t e r n comprises a l a r g e
but f i n i t e number o f energy t r a n s f e r s , t ( x ) w i l l be a sum o f Di r a c δ-dis-
t r i b u t i o n s , and T ( x ) w i l l c o n s i s t o f d i s c r e t e s t e p s .
Let Δε. ( i = l , 2 , ... i ) be the energy t r a n s f e r s and l e t x.^ be t h e d i s t a n c e
between t he t r a n s f e r p o i n t s T. and T^. Then the formulae f o r t ( x ) and T ( x )
ar e :
861
I I ι
t ( x ) = l l ό(χ. -χ) Δε Δε / I Δε m
1 = 1 k=1 , Κ 1 Κ ί = 1 ' w
and J j .
Τ(χ) = £ Ζ Δε. Δε. / \ Δε. (5) i=1 k ' Κ i=1 '
where the summation extends over a l l k w i t h χ., < χ ι k
The terms w i t h i=k are inc l u d e d so t h a t T(o) has the f i n i t e v a l u e
Δ ε . 2 / Δε.,that i s the energy average o f the i n d i v i d u a l energy t r a n s f e r s .
Fig.2 g i v e s a schematic two-dimensional example f o r the c a l c u l a t i o n o f the
d i s t a n c e d i s t r i b u t i o n . As w i l l u s u a l l y be the case i n numerical e v a l u a
t i o n s , the 6 - d i s t r i b u t i o n s are approximated by d i s t r i b u t i o n s o f f i n i t e
w i d t h . For s i m p l i c i t y t h e energy t r a n s f e r s are a l l taken t o be o f t h e same
va l u e ; t h i s corresponds t o the case where one observes o n l y i o n i z a t i o n s ,
Fig.2 A schematic, two-dimens i o n a l example f o r an inchoate distribution (3) o f energy t r a n s f e r s and the corresponding d i f f e r e n t i a l and i n t e g r a l d i s tance d i s t r i b u t i o n .
A c t u a l d i s t r i b u t i o n s t ( x ) and T ( x ) belong not t o one sample o f p a r t i c l e t r a c k but are the average o b t a i n e d f o r many samples.
862
w h i l e e x c i t a t i o n s a r e d i s r e g a r d e d . In a c t u a l m i c r o d o s i m e t r i c computa
t i o n s one o b t a i n s smooth curves which a re the r e s u l t o f the s u p e r p o s i t i o n
o f d i s t r i b u t i o n s b e l o n g i n g t o many p a r t i c l e t r a c k s .
A l i m i t e d number o f d i s t a n c e d i s t r i b u t i o n s has been computed by sev e r a l
a u thors from s i m u l a t e d p a r t i c l e t r a c k s ( 4 , 5 , 9 ) . A s y s t e m a t i c e f f o r t t o
o b t a i n such d i s t r i b u t i o n s f o r e l e c t r o n s and f o r heavy charged p a r t i c l e s
o f v a r i o u s e n e r g i e s i s d e s i r a b l e .
Applicability of the distance distributions
An e a r l i e r t h e o r e t i c a l t r e a t m e n t which has been termed t h e t h e o r y o f dual
r a d i a t i o n a c t i o n (10) has u t i l i z e d t h e m i c r o d o s i m e t r i c q u a n t i t y s p e c i f i c
energy z. The main r e s u l t o f the t h e o r y i s a l i n e a r - q u a d r a t i c dose de
pendence f o r c e l l u l a r l e s i o n s t h a t r e s u l t from t he combinations o f p a i r s
o f s u b l e s i o n s . The use o f the q u a n t i t y ζ had made i t necessary i n the
e a r l i e r t r e a t m e n t t o assume c e r t a i n s i t e s i n the nucleus o f t h e c e l l where
s u b l e s i o n s would be produced and where they would i n t e r a c t w i t h c o n s t a n t
p r o b a b i l i t y r e g a r d l e s s o f t h e i r s e p a r a t i o n . There i s no e x p e r i m e n t a l e v i
dence t o support such an assumption. I t must i n s t e a d be assumed t h a t sub
l e s i o n s can be produced throughout t he nucleus and t h a t they combine w i t h
a p r o b a b i l i t y t h a t depends on t h e i r s e p a r a t i o n .
In s p i t e o f i t s approximate n a t u r e the e a r l i e r t r e a t m e n t was judged t o be
s a t i s f a c t o r y f o r charged p a r t i c l e s w i t h ranges l a r g e r than o r comparable
t o t h e dimensions o f the nucleus. Such p a r t i c l e s w i l l always spread
energy t r a n s f e r s over a l a r g e p a r t o f a s p e c i f i e d m i c r o s c o p i c r e g i o n .
A c c o r d i n g l y the b i o l o g i c a l e f f e c t s w i l l be s i m i l a r a t equal v a l u e s o f z;
the i n t e r n a l d i s t r i b u t i o n o f energy t r a n s f e r s w i t h i n the r e g i o n w i l l be
of minor importance.
The d e f i n i t i o n o f t ( x ) i s g i v e n i n a form t h a t i n c l u d e s a l l energy t r a n s f e r s . I t i s obvious t h a t t h i s c o uld be m o d i f i e d . I f b i o l o g i c a l evidence should i n d i c a t e t h a t e x c i t a t i o n s have l i t t l e o r no e f f e c t i v e ness, one may r e d e f i n e t ( x ) as w e l l as ε, ζ, or y t o r e f e r o n l y t o i o n i z i n g i n t e r a c t i o n s
863
3a 3b
Fig.3 An event where the same s p e c i f i c energy ζ i s produced by a p a r t i c l e o f long range (a) and a p a r t i c l e of s h o r t range (b)
The s i t u a t i o n i s d i f f e r e n t f o r p a r t i c l e s o f ve r y s h o r t range such as the
e l e c t r o n s from s o f t x - r a y s . As i n d i c a t e d i n F i g . 3 , a narrow c l u s t e r o f
energy t r a n s f e r s may r e s u l t which i s s u b s t a n t i a l l y more e f f e c t i v e than the
same increment o f ζ produced by long range p a r t i c l e s . T h i s must be so i f
c l o s e l y n e i g h b o u r i n g s u b l e s i o n s have an enhanced p r o b a b i l i t y of i n t e r a c t i o n .
A r e c e n t g e n e r a l i z a t i o n o f the t h e o r y i s based not on the q u a n t i t y ζ but on
the d i s t a n c e d i s t r i b u t i o n s . T h i s g e n e r a l i z e d t r e a t m e n t i s v a l i d a l s o f o r
short-ranged p a r t i c l e s , and i t i s e q u a l l y a p p l i c a b l e t o s t u d i e s such as the
molec u l a r ion beam experiment d e s c r i b e d by Rossi e t a l . ( l l ) . An e x p l i c i t
t r e a t m e n t has been gi v e n elsewhere ( 8 ) , but a b r i e f statement o f the essen
t i a l r e s u l t w i l l f o l l o w .
General formula for dual action
I t i s assumed t h a t s u b l e s i o n s a re produced by i n d i v i d u a l energy t r a n s f e r s
w i t h i n an extended c e l l u l a r s t r u c t u r e which may be the nucleus o f the c e l l
or a p a r t o f the nucleus. This s t r u c t u r e i s termed the sensitive matrix.
According t o t h i s assumption the su b l e s i o n s w i l l be a subset o f the energy
t r a n s f e r s w i t h i n the m a t r i x .
I t i s f u r t h e r assumed t h a t s u b l e s i o n s can combine t o form l e s i o n s . The aver
age combination p r o b a b i l i t y o f two s u b l e s i o n s separated by the d i s t a n c e χ
is denoted by g ( x ) .
864
An a d d i t i o n a l p o s t u l a t e i s t h a t the t o t a l number o f s u b l e s i o n s exceeds
c o n s i d e r a b l y the t o t a l number o f l e s i o n s , i . e . i t i s assumed t h a t the
magnitude o f g ( x ) i s s m a l l . I f t h i s assumption i s i n v a l i d , as i t may be
f o r v e r y densely i o n i z i n g r a d i a t i o n s , one w i l l have t o account f o r compe
t i t i o n between s u b l e s i o n s . The i n t e r a c t i o n p r o b a b i l i t y o f two s u b l e s i o n s
w i l l then depend on the presence o f o t h e r , n e i g h b o u r i n g s u b l e s i o n s . T h i s
more complicated case w i l l not be c o n s i d e r e d . I t w i l l a l s o be assumed t h a t
e i t h e r the i r r a d i a t e d c e l l s are randomly o r i e n t e d , or t h a t the r a d i a t i o n
f i e l d i s i s o t r o p i c .
Under these assumptions one o b t a i n s the l i n e a r - q u a d r a t i c dependence o f t h e
mean number o f s u b l e s i o n s per c e l l ( 8 ) :
C(D) = k U D + D 2 ) (6)
where the c o e f f i c i e n t ξ i s determined by the f o l l o w i n g e q u a t i o n :
ξ = J t ( x ) g(x) s ( x ) d x / J
g ( x ) s ( x ) ,
χ ( 7 )
ο 4πχ2ρ ο
The f u n c t i o n s ( x ) i s e n t i r e l y analogous t o the f u n c t i o n t ( x ) . However i t
r e f e r s t o the m a t r i x , i . e . , the s e n s i t i v e s t r u c t u r e o f the c e l l , and not t o
the charged p a r t i c l e t r a c k . s ( x ) d x i s the expected volume o f the m a t r i x a t
d i s t a n c e χ t o x+dx from a p o i n t randomly s e l e c t e d in the m a t r i x . In mathe
m a t i c a l morphology the f u n c t i o n s ( x ) i s c a l l e d the covariance o f a geo
m e t r i c a l o b j e c t ( 1 2 , 1 3 ) . I t depends o n l y on the geometry o f the m a t r i x . For
a sphere i t i s o f s i m p l e a n a l y t i c a l form ( 7 ) ; f o r o t h e r geometries i t can
be o b t a i n e d n u m e r i c a l l y .
The general formula f o r ξ appears s u r p r i s i n g l y s i m p l e i n view o f the f a c t
t h a t i t accounts both f o r the c o m p l i c a t e d t r a c k s t r u c t u r e and f o r the geo
metry o f the m a t r i x .
A p r e l i m i n a r y a n a l y s i s o f the m o l e c u l a r ion experiment (14) and o f e x p e r i
ments w i t h low energy e l e c t r o n s (15,16) has led t o the c o n c l u s i o n t h a t sub
l e s i o n s can i n t e r a c t over d i s t a n c e s o f the o r d e r o f micrometers but t h a t
t h e r e i s a g r e a t l y enhanced p r o b a b i l i t y f o r the i n t e r a c t i o n o f s u b l e s i o n s
over much c l o s e r d i s t a n c e s o f the o r d e r o f 0.1 pm. T h i s may be due t o the
f a c t t h a t the i n t e r a c t i o n p r o b a b i l i t y g ( x ) r i s e s s h a r p l y a t small separa-
865
t i o n s χ. I t could a l s o r e s u l t from the f a c t t h a t the m a t r i x c o n s i s t s o f
small c l u s t e r s o f DNA randomly spread over l a r g e r r e g i o n s o f the nucleus.
The notion of intra-track dose Δ(χ)
Absorbed dose i s d e f i n e d as expected energy imparted t o a r e g i o n d i v i d e d
by the mass i n t h i s r e g i o n . t(x)/kvpx^ i s the expected energy imparted t o
a s p h e r i c a l s h e l l centered a t a t r a n s f e r p o i n t , d i v i d e d by the mass o f
the s h e l l . A c c o r d i n g l y one can c o n s i d e r t h i s q u a n t i y as a conditional ab
sorbed dose i n the v i c i n i t y o f an energy t r a n s f e r :
Δ(χ) = t ( x ) / 4πχ 2ρ (8)
This c o n d i t i o n a l dose i s due t o energy imparted by the same p a r . t i c l e t r a c k ;
i t w i l l t h e r e f o r e be termed intra-track dose. One may note the s i m i l a r i t y
o f t h i s concept t o the f r e q u e n t l y invoked n o t i o n o f a r a d i a l dose d i s t r i
b u t i o n around the t r a c k o f heavy charged p a r t i c l e s . C o n t r a r y t o oc c a s i o n a l
c r i t i c i s m i t i s j u s t i f i e d t o apply t h e term dose i n t h i s c o n t e x t .
Fig.h g i v e s t h e f u n c t i o n s t ( x ) and T ( x ) f o r d i f f e r e n t p a r t i c l e s and Fig. 5
r e p r e s e n t s the cor r e s p o n d i n g i n t r a - t r a c k doses Δ(χ). In Fi g . 6 the r e s u l t s
Fig.h D i f f e r e n t i a l and i n t e g r a l d i s t a n c e d i s t r i b u t i o n s t ( x ) and T ( x ) f o r 1 keV e l e c t r o n s ( t o t a l t r a c k ) , f o r f a s t e l e c t r o n s , and f o r 20 MeV p r o t o n s . Data from ( 9 ) .
866
>104 >103 >10? >10 GRAY
1—100nm 1
m • • 1 keV ELECTRON FAST ELECTRON 20 MeV PROTON
Fig.6 Schematic r e p r e s e n t a t i o n o f the s p a t i a l d i s t r i b u t i o n o f i n t r a - t r a c k dose, i . e . , the data from Fig.5 i n t h e form o f an i s o - A ( x ) diagram.
are g i v e n i n a more i 1 l u s t r a t i v e , s c h e m a t i c form. The b i o p h y s i c a l i m p l i c a
t i o n s are r e a d i l y apparent. The i n t r a - t r a c k dose i n the c l o s e v i c i n i t y o f
an energy t r a n s f e r i s l a r g e even f o r s p a r s e l y i o n i z i n g r a d i a t i o n s . At ab
sorbed doses o f a few hundred rad i t i s t h e r e f o r e v e r y l i k e l y t h a t the
neighbours o f an energy t r a n s f e r , ( o r of a s u b l e s i o n ) belong t o the same
p a r t i c l e t r a c k ; i t i s very u n l i k e l y t h a t they belong t o independant p a r
t i c l e t r a c k s . This must be so because the frequency y o f n e i g h b o u r i n g energy
t r a n s f e r s from the same t r a c k i s p r o p o r t i o n a l t o the i n t r a - t r a c k dose Δ(χ),
w h i l e the frequency o f energy t r a n s f e r s from o t h e r t r a c k s i s p r o p o r t i o n a l
t o absorbed dose D. The l i n e a r term i n the dose r e l a t i o n must t h e r e f o r e
exceed the q u a d r a t i c term whenever Δ(χ) exceeds D.
867
A comparison of the data given in Figs.4 to 6 for the three d i f f e r e n t
r a d i a t i o n s brings out c h a r a c t e r i s t i c d i f f e r e n c e s . In particu1ar, one r e a l
izes that for small separations the i n t r a - t r a c k dose is l a r g e s t for the
1 keV e l e c t r o n (track ends), while for larger separations (x>50nm) i t is
smaller and even approaches zero.
One may consider the hypothetical case where two sublesions are always
produced at a separation a. The dose dependence of l e s i o n s i s then:
£ ( D ) = k(A(a) D + D 2) (9)
T h i s is r e a d i l y derived from Eq(7) with s ( x ) ^ 6 ( a - x ) .
Furthermore one concludes from Eq(7) that ξ w i l l always exceed A(a) i f the
l i n e a r dimensions of the matrix are smaller than a or i f the maximum in t e r
action distance of sublesions i s smaller than a. The i n t r a - t r a c k dose A(a)
provides therefore a lower l i m i t for the quantity ξ. This applies regard
l e s s of the complexities of track s t r u c t u r e and the geometry of the sen
s i t i v e c e l l o r g a n e l l e s .
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