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 .

References

1) ICRU Report 19 Radiation Quantities and Units. Internat.Commission

on Radiation Units and Measurements, Washington, D.C. (1971)

2) Carlsson 6.A. D e f i n i t i o n of energy imparted. A new formulation

adapted to exact solutions of the absorbed dose equation under non-

equilibrium conditions. Radiat.Res. in p r i n t

3) K e l l e r e r , A.M. and Chmelevsky, D. Concepts of Microdosimetry.

I I.Probabi 1ity D i s t r i b u t i o n s of the Microdosimetric V a r i a b l e s .

Rad.and Environm.Biophys. J_2, 205-216 (1975)

h) Paretzke, H.G., Leuthold, G., Burger, G. and Jacobi, W.

Approaches to physical track s t r u c t u r e c a l c u l a t i o n s . In: Proc.^th

Symposium on Microdosimetry (Ebert,H.G.,Ed.) Euratom, 5122 d-e-f,

123-138, Luxembourg (197*0

868

T e r r i s s o l , Μ., and Patau, J.P. Simulation du transport d'electrons

d'energie i n f e r i e u r e ä un keV par une methode de Monte-Carlo.

In: Proc.4th Symposium on Microdosimetry (Ebert, H.G. »Ed.) Euratom,

5122 d-e-f, 717-730, Luxembourg (197*0

Hodges, D.C., D e l a f i e l d , H.J. and Dennis, J.A. Preliminary measure­

ments using a low pressure cloud chamber of the ranges of low energy

e l e c t r o n s . In: Proc.3rd Symposium on Microdosimetry (Ebert, H.G.,Ed.)

Euratom, 4810 d-f-e, 455-^67, Luxembourg (1972)

K e l l e r e r , A.M. and Chmelevsky, D. Concepts on microdosimetry.

I I I . Mean values of the microdosimetric d i s t r i b u t i o n s . Rad and E n v i -

ronm.Biophys., U, 321-335 (1975)

K e l l e r e r , A.M. and R o s s i , H.H. A Generalized Formulation of Dual

Radiation Action. Radiat.Res. in p r i n t

Chmelevsky, D. D i s t r i b u t i o n s et moyennes des grandeurs microdosi-

metriques ä P e c h e l l e du nanometre. Rapport CEA-R-4785, S e r v i c e de

Documentation, C.E.N.Saclay (1976). B.P.2 - F-91190 Gif s.Yvette

K e l l e r e r , A.M. and R o s s i , H.H. The Theory of Dual Radiation Action

In: "Current Topics in Radiation Research Quarterly', 8, 85-158 (1972)

(M.and A.Ebert, Eds.) North-Holland

Rossi, H.H. et a l . The Molecular Ion Experiment. 6th Symposium on

Microdosimetry (1978)

Matheron, G. Random Sets and Integral Geometry. John Wiley δ Sons,

New York-London-Sydney-Toronto, 1974

Serra, J . Introduction ä l a Morphologie Mathematique. Les Cahiers du

Centre de Morphologie. Mathematique de Fontainebleau, Fase.3 (1969)

Lam, Y.-M.P. et a l . Biophysical Studies with s p a t i a l l y c o r r e l a t e d ions

IV. A n a l y s i s of c e l l s u r v i v a l data for diatomic deuterium; in prep.

Goodhead, D.T. I n a c t i v a t i o n and mutation of cultured mammalian c e l l s

by aluminium c h a r a c t e r i s t i c u l t r a s o f t X-rays. I I I . Implications for

theory of dual r a d i a t i o n a c t i o n . I nt. J .Radiat . B i o l . 3j2, 43-70 (1977)

V i r s i k , R.P., Harder, D. and Hansmann, I . The RBE of 30 kV X-Rays

for the Induction of D i c e n t r i c Chromosomes in Human Lymphocytes.

Rad. and Envi ronm.Biophys. |_4, 109-121 (1977)