SIXTH SYMPOSIUM ON MICRODOSIMETRY

Brussels, Belgium, May 22-26, 1978

Edited by J . Booz and H. G. Ebert

Commission of the European Communities Directorate-General for Research, Science and Education

Biology, Radiation Protection and Medical Research

Volume I

Harwood Academic Publishers Ltd. for the Commission of the European Communities

OPENING SESSION VII

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 i n c o r p o r a t e d i n t o DNA o f c e l l s ; i m p l i c a t i o n s f o r r a d i a t i o n b i o l o g y 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 t h o u g h t s on t h e n a t u r e o f 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 f o r 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) 39

RBE-LET r e l a t i o n s f o r i n d u c t i o n o f r e p r o d u c t i v e death and chromosome a b e r r a t i o n s i n mammalian c e l l s 55

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 o f Η beta rays and o t h e r 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)

M i c r o d o s i m e t r y o f r a d i o a c t i v e n u c l e i i n c o r p o r a t e d i n t o t h e DNA o f mammalian c e l l s

125 DNA s t r a n d breaks induced by I i n c u l t u r e d human ki d n e y c e l l s and t h e i r r e p a i r

69

91

111

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 Ε.P. MALAISE

R a d i a t i o n s t u d i e s a t t h e p h y s i c a l , m o l e c u l a r , c e l l u l a r and macrocolony l e v e l

S u r v i v a l curves o f n e o p l a s t i c and non t r a n s f o r m e d 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 u s i n g d i f f e r e n t models

121

1A5

SESSION A Chairman WAGNER

J.L. MAGEE A. CHATTERJEE

M. TERRISSOL J.P. PATAU T. EUDALDO

Theory o f e l e c t r o n t r a c k s w i t h e x p l i c i t c o n s i d e r a t i o n o f t r a c k - e n d e f f e c t s 157

A p p l i c a t i o n ä l a m i c r o d o s i m e t r i e et ä l a r a d i o b i o l o g i e de la s i m u l a t i o n du t r a n s p o r t des e l e c t r o n s de basse e n e r g i e dans l'eau ä l ' e t a t l i q u i d e 169

SESSION 4 ( c o n t . ) VIII

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 o f energy d e p o s i t i o n events i n 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 p r e s s u r e c l o u d chamber s t u d i e s -I - Methods o f a n a l y s i s o f i o n i s a t i o n d i s t r i b u t i o n s

Low p r e s s u r e c l o u d chamber s t u d i e s -I I - The d e t e r m i n a t i o n o f a high r e s o l u t i o n t i s s u e -e q u i v a l e n t gas f o r t h e s t u d y o f α - p a r t i c l e t r a c k s

R e l a t i o n s o f secondary e l e c t r o n e m i s s i o n t o m i c r o d o s i m e t r y and a p p l i c a t i o n s t o t w o - t a r g e t t h e o r y

P h y s i c a l i n t e r a c t i o n s o f low-energy e l e c t r o n s i n s i n g l e and t w i n t a r g e t s

SESSION 6 Chairman : T.E. BURLIN

M.N. VARMA J.W. BAUM P. KLIAUGA

M i c r o d o s i m e t r i c r e s u l t s o b t a i n e d 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

W.E. WILSON L.H. TOBUREN H.G. PARETZKE

L-A. BRABY W.C. ROESCH

C a l c u l a t i o n o f energy d e p o s i t i o n s p e c t r a i n s m a l l gaseous s i t e s and i t s a p p l i c a b i l i t y t o condensed phase

D i r e c t measurements of f ( z ) f o r f a s t e l e c t r o n s

B. FORSBERG Μ. JENSEN L. LINDBORG G. SAMUELSON

D e t e r m i n a t i o n s o f t h e dose mean o f s p e c i f i c energy f o r c o n v e n t i o n a l X-rays by variance-measurements

SESSION 7 Chairman : M. TERRISSOL

POSTER SESSION I : P a r t i c l e t r a c k s t r u c t u r e and slo w i n g 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 d e t e c t e u r s p o l y meriques et p a r c o u r s " e f f i c a c e " des rayons 6'

A. CHATTERJEE J.L. MAGEE

R e l a t i o n s h i p of t h e t r a c k s t r u c t u r e o f heavy p a r t i c l e t o t h e 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 s p e c t r a o f degraded e l e c t r o n s i n water vapour and i n carbon

B. GROSSWENDT E. WAIBEL

D e t e r m i n a t i o n o f 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 f o r low energy e l e c t r o n s i n d i f f e r e n t gases

IX SESSION 7 ( c o n t . )

G.S. HURST S.D. KRAMER C.E. BEMIS, J r . J.P. YOUNG

D e t e c t i o n o f s i n g l e atoms i n p a r t i c l e t r a c k s 321

A. JANSSENS G. EGGERMONT R. JACOBS

Ex p e r i m e n t a l s t u d y o f t h e c a v i t y t h e o r y , u s i n g a high p r e s s u r e i o n i z a t i o n chamber 331

R.H. RITCHIE R.N. HAMM J.Ε. TURNER H.A. WRIGHT

The i n t e r a c t i o n o f s w i f t e l e c t r o n s w i t h l i q u i d water 345

M. SCHNEIDER J. BÖHM Κ. HOHLFELD Η. REICH

Β. SENGER Ε. WITTENDORP R.V. RECHENMANN

Eine A p p a r a t u r zur Messung des V e r l a u f s der Io n e n d o s i s an Gre n z s c h i c h t e n

<S-ray p r o d u c t i o n 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

355

361

J.E. TURNER R.N. HAMM H.A. WRIGHT R.H. RITCHIE R. KATZ

C a l c u l a t e d e l e c t r o n slowing-down s p e c t r a f o r 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 f o r photon RBE 375

E. WITTENDORP Β. SENGER J.B. SANDERS R.V. RECHENMANN

R. KATZ

Heavy se c o n d a r i e s e j e c t e d by p r i m a r y 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

Report on p o s t e r Session I

383

401

SESSION 8

A.M. KELLERER

R. KATZ

Chairman : Ε. HALL

R a d i a t i o n c a r c i n o g e n e s i s a t 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

405

423

SESSION 9 Chairman : R. GRILLMAIER

POSTER SESSION I I : A p p l i c a t i o n o f m i c r o d o s i m e t r y t o r a d i a t i o n t h e r a p y

H . I . AMOLS J.F. DICELLO M. ZAIDER

The RBE a t v a r i o u s p o s i t i o n s i n and near a l a r g e n e g a t i v e ρ i o n beam 433

L.S. AUGUST R.B. THEUS P. SHAPIRO

Gamma measurements w i t h a non-hydrogenous Rossi c o u n t e r i n a mixed f i e l d 441

G. BURGER Ε. MA I ER A. MORHART

R a d i a t i o n q u a l i t y and i t s r e l e v a n c y i n n e u t r o n r a d i o t h e r a p y 451

χ

SESSION 10 ( c o n t . ) XI

Μ. INOKUTI J.E. TURNER

Mean e x c i t a t i o n e n e r g i e s f o r stopping-power as d e r i v e d 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. GROB G. 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

D e t e r m i n a t i o n 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 l i q u i d e

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 r e c e n t n u c l e a r data and W measurements

Une approche p o s s i b l e de l' e t u d e du r a l e n t i s s e m e n t des p a r t i c u l e s chargees l o u r d e s

The s t o p p i n g power and s t r a g g l i n g f o r a l p h a p a r t i c l e s i n l i q u i d s

Range-energy r e l a t i o n s and s t o p p i n g power o f wate r , water vapour and t i s s u e e q u i v a l e n t l i q u i d f o r α p a r t i c l e s over t h e energy range 0.5 t o 8 MeV

Stopping power and energy d e g r a d a t i o n f o r e l e c t r o n s i n water vapor

E x p e r i m e n t a l r e s u l t s on W-values and t r a n s m i s s i o n o f low energy e l e c t r o n s i n gases

Phase e f f e c t s i n s t o p p i n g power f o r 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 t o measurements of st o p p i n g power f o r slow i o n s

Report on p o s t e r 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 t h e b i o l o g i c a l e f f e c t s o f u l t r a s o f t X-rays and m i c r o d o s i m e t r i c measurements and a p p l i c a t i o n

M i c r o - d o s i m e t r y and nano-dosimetry

Concepts and q u a n t i t i e s r e l e v a n t t o t h e 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

SESSION 13 XII

Chairman : H.H. ROSSI

R.P. VIRSIK D. HARDER

Chromosome a b e r r a t i o n s i n 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 t h * s u b l e s i o n i n t e r a c t i o n model

CR. GEARD

A. WAMBERSIE J. VAN DAM G. LAUBLIN

M i c r o d o s i m e t r y and chromosomal a b e r r a t i o n s f o r monoenergetic n e u t r o n s

RBE as a f u n c t i o n of depth i n a 650 MeV H e + +

beam dete r m i n e d f o r growth d e l a y i n v i c i a faba and f o r i n d u c t i o n o f chromosome a b e r r a t i o n s i n a l l i u m cepa

SESSION 14 Chairman : G.E. ADAMS

E.M. FIELDEN 0. SAPORA P.S. LOVEROCK

S. APELGOT J.P. ADLOFF

The r e l a t i o n between s u r v i v a l and t h e i n i t i a l y i e l d o f DNA s t r a n d breaks f o r Ε c o l i B/r

Tr a n s m u t a t i o n e f f e c t s o f ̂ P and "^P i n c o r p o r a t e d i n 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 o f c l a s s i c a l m i c r o d o s i m e t r y and advantages o f t r a c k s t r u c t u r e a n a l y s i s f o r r a d i a t i o n b i o l o g y

The m o l e c u l a r i o n experiment

SESSION 15

POSTER SESSION IV:

H.M.A. AL-SHAIBANI D.E. WATT

Chairman : D. HARDER

I n t e r p r e t a t i o n o f b i o l o g i c a l data

P h y s i c a l processes i n t h e i n a c t i v a t i o n o f enzymes by slow heavy i o n s

M. COPPOLA M. MARTINELLI L. TOMMASINO

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

R a d i a l dependence o f b i o l o g i c a l response o f 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 i o n s

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 m i c r o d o s i m e t r y w i t h r a d i a t i o n s of v a r y i n g q u a l i t y

R. KATZ E.C. PENNINGTON

R a d i o b i o l o g i c a l aspects o f s u p r a l i n e a r p h o t o g r a p h i c emulsions

H.P. LEENHOUTS K.H. CHADWICK M.J. SIJSMA

The i n f l u e n c e o f 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 t h e shape o f d o s e - e f f e c t curves

SESSION 15 ( c o n t . ) XIII

J.W. PURDIE E. R. INHABER N.V. KLASSEN

R.A. ROTH R. KATZ

M. SCHAFER H. BÜCKER R. FACIUS G. HORNECK G. REITZ G. KRAFT

F. SCHÖPFER 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 o f anoxic mammalian c e l l s i r r a d i a t e d w i t h s i n g l e p u l s e s at very h i g h dose r a t e s

Heavy i o n beam model f o r r a d i o b i o l o g y

High L E T - i r r a d i a t i o n o f 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 o f c e l l s by a c c e l e r a t e d heavy i o n s of very h i g h LET

The i n t e r r e l a t i o n s h i p between p u l s e l e n g t h and d o s e - r a t e w i t h i n t h e p u l s e i n t h e enhancement o f anoxic damage i n wet B a c i l l u s megaterium spores i r r a d i a t e d w i t h p u l s e s o f e l e c t r o n s

I n t r a c e l l u l a r measurement o f t h e i n a c t i v a t i o n o f ri b o s o m a l RNA genes i n d i p l o i d yeast c e l l s a f t e r exposure t o ̂ uCo-Ύ'-rays, 85 kV X-rays and 241-Americium-ct - p a r t i c l e s

Report on p o s t e r Session IV

SESSION 16

H.H. ROSSI

J.A. DENNIS

Chairman : A.M. KELLERER

R a 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 : t h e 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 t h e 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 f o r r a d i o l o g i c a l p r o t e c t i o n o f t h e 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 o t h e r DNA damaging agents

SESSION 18 Chairman : K.H. CHADWICK

J. KIEFER Η. KOCH Κ. KOESTER G. MOCK Ε. SCHNEIDER Κ. WEBER

The m o l e c u l a r and c e l l u l a r b a s i s o f t h e oxygen e f f e c t

SESSION 18 ( c o n t . ) XIV

Κ.F. BAVERSTOCK W.G. 8URNS R. MAY

The oxygen i n t h e t r a c k h y p o t h e s i s : M i c r o d o s i m e t r i c 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 s p e c t r a f o r n e u t r o n s based on rec e n t cross s e c t i o n e v a l u a t i o n s

M i c r o d o s i m e t r y o f 400 MeV/AMU 1 2C and 450 MeV/AMU AO, 'Ar beams

M i c r o d o s i m e t r i c study w i t h c y l i n d r i c a l w a l l e d and w a l l - l e s s p r o p o r t i o n a l c o u n t e r s

SESSION 20 Chairman : J. Β00Ζ

C. HERSKIND Κ.Α. JESSEN

W.C ROESCH

J. Β00Ζ

APPENDIX 1

Measurements i n i n t e r n a l m i c r o d o s i m e t r y w i t h 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 m i c r o d o s i m e t r y

C l o s i n g o f t h e Symposium

*Personal i m p r e s s i o n s and review s o f 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 t h e mechanisms o f s e n s i t i z e r s

Summary o f t h e d i s c u s s i o n s c o n c e r n i n g r a d i a t i o n mechanisms o f e x t e r n a l r a d i a t i o n s

I m p r e s s i o n s o f t h e 6th M i c r o d o s i m e t r y Symposium and i t s r e l e v a n c e t o r a d i o l o g i c a l p r o t e c t i o n

Summary o f d i s c u s s i o n s on e v a l u a t i o n o f m i c r o d o ­s i m e t r y data

Summary o f t h e d i s c u s s i o n s c o n c e r n i n g e l e c t r o n t r a c k s t r u c t u r e and m i c r o d o s i m e t r y

Summary o f t h e d i s c u s s i o n s c o n c e r n i n g i n c o r p o r a t e d r a d i o i s o t o p e s

APPENDIX 2 L i s t o f p a r t i c i p a n t s

405

RADIATION CARCINOGENESIS AT LOW DOSES

A.M.Kellerer

I n s t i t u t für Med.Strahlenkunde der Universität Würzburg, Versbacher S t r . 5

D -8700 Würzburg

ABSTRACT: Radiation carcinogenesis i s the major contributor to the r i s k

of small doses of ionizing radiations. Risk estimates are usually based

on the assumption of a linear dose-effect relation at small and even at

intermediate doses up to about TOO rod. The postulate that such linearity

should generally apply i s 3 however3 i n c o n f l i c t with microdosimetric ar­

guments, and experimental findings are here considered that exemplify non­

linear dose dependence even at small doses.

It is pointed out that dose-effect relations are always based on a some­

what arbitrary choice of the biological endpoint3 and that a well-designed

experiment must therefore be aimed at more complete information. The re­

levant quantities i n radiation carcinogenesis are the tumour rate r ( t ) 3 the integral tumour rate R ( t ) Λ or the cumulative prevalence lit).

The mathematical analysis can often be simplified if RBE is d i r e c t l y de­

termined as a function of absorbed dose. This requires the comparison of

the tumour incidence or prevalence i n pairs of experimental groups. The

largely unsolved problem of the construction of suitable s t a t i s t i c a l t e s t s

for t h i s purpose i s discussed.

Work supported by Euratom C o n t r a c t 208-76-7B10 D.

406

Introduction

The development o f nucl e a r technology and the widening medical a p p l i c a t i o n s

o f i o n i z i n g r a d i a t i o n s have brought q u e s t i o n s o f the r i s k o f small doses t o

la r g e p o p u l a t i o n s i n t o the c e n t e r o f p u b l i c i n t e r e s t . I t i s c u r r e n t l y be­

l i e v e d t h a t l a t e somatic e f f e c t s , i . e . , e s s e n t i a l l y r a d i a t i o n induced t u ­

mours, c o n t r i b u t e a t l e a s t as much t o the r i s k o f small doses as h e r e d i t a r y

e f f e c t s . ICRP i n i t s recent recommendations (1) bases r i s k e s t i m a t e s on the

assumption o f p r o p o r t i o n a l i t y t o dose e q u i v a l e n t . The t o t a l r i s k o f r a d i a -- 4

t i o n c a r c i n o g e n e s i s i s assumed t o be 10 per rem as the average f o r both

sexes and a l l ages. The t o t a l p r o b a b i l i t y t o d i e from cancer i s i n the U n i ­

ted States r o u g h l y 0.17 (see ( 2 ) ) ; a c c o r d i n g t o the ICRP number t h i s p r o ­

b a b i l i t y i s increased by 0.3 % i f an i n d i v i d u a l r e c e i v e s a dose e q u i v a l e n t

o f 5 rem. Small as t h i s increment may seem, i t i s s u b s t a n t i a l enough t h a t

the p e r m i s s i b l e l i m i t s may have t o be rec o n s i d e r e d i f t he ICRP val u e s should

t u r n out t o be r e a l i s t i c .

For comparison i t may be noted t h a t ICRP e s t i m a t e s the r i s k f o r h e r e d i t a r y

e f f e c t s , expressed i n the f i r s t two g e n e r a t i o n s , as 4 · 1 0 per rem. How­

ever, i f a l l subsequent g e n e r a t i o n s are i n c l u d e d , the r i s k i s b e l i e v e d t o

be a p p r o x i m a t e l y equal t o t h a t f o r r a d i a t i o n induced cancer. ICRP s t a t e s ,

t h a t the r i s k e s t i m a t e s a re proba b l y c o n s e r v a t i v e . Other s c i e n t i f i c bodies

have made s i m i l a r statements concerning t h e i r r i s k e s t i m a t e s ( 3 , 4 ) · How­

ever, t h i s i s o f t e n d i s r e g a r d e d .

There a re a l s o o c c a s i o n a l c l a i m s t h a t a c t u a l r i s k s are much h i g h e r than any

of the c u r r e n t e s t i m a t e s . A few years ago i t was s t a t e d ( 5 ) t h a t hot spots

o f PUO2 p a r t i c l e s have a v a s t l y h i g h e r e f f e c t i v e n e s s i n producing lung can­

c e r , compared t o the same a c t i v i t y o f α-particles evenly d i s p e r s e d i n the

lung. I t was in f a c t s t a t e d t h a t the l i m i t s f o r in h a l e d a c t i v i t y were more

than 100 000 times too low. These statements were based on a m i s i n t e r p r e ­

t a t i o n o f c e r t a i n e x p e r i m e n t a l data f o r the s k i n (6) t h a t were then s i m p l y

a p p l i e d t o the lung. A heated c o n t r o v e r s y was n e v e r t h e l e s s c r e a t e d , and

v a r i o u s assessments (see f o r example ( 7 - 9 ) ) o f the problem o f hot spots i n

the lung have been att e m p t e d . The general c o n c l u s i o n has been t h a t a c t i v i t y

i n p a r t i c u l a t e form i s u s u a l l y l e s s e f f e c t i v e than a c t i v i t y i n d i s p e r s e d

form. The reason i s , t h a t a gi v e n a c t i v i t y i r r a d i a t e s a much s m a l l e r number

of c e l l s , i f i t i s c o n c e n t r a t e d i n hot spots ( 1 0 ) . Experiments i n v a r i o u s

l a b o r a t o r i e s , and e s p e c i a l l y those o f Lafuma e t a 1 . ( 1 1 , 1 2 ) , have supported

407

t h e c o n c l u s i o n t h a t hot spots have a reduced e f f e c t i v e n e s s i n the produc­

t i o n o f lung cancer. The experiments are s t i l l i n p r o g r e s s . T h e i r a n a l y s i s

poses i n t r i g u i n g s t a t i s t i c a l problems t h a t w i l l be consid e r e d i n the l a s t

p a r t o f t h i s a r t i c l e .

A more recent s e n s a t i o n a l c l a i m o f unexpectedly l a r g e r i s k f a c t o r s i s made

i n r e p o r t s o f Mancuso, Stewa r t , and Kneale (13,14). These r e p o r t s deal w i t h

r a d i a t i o n workers i n Hanford. I t i s s t a t e d t h a t workers dead o f cancer i n

Hanford had received doses t h a t are s u b s t a n t i a l l y above the average f o r a l l

w o r k e r s . The authors e s t i m a t e from t h e i r a n a l y s i s t h a t a s i n g l e dose o f

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 o f 0.8 rad doubles the i n c i d e n c e o f bone marrow

cancer, and t h a t 7 and 6 rad double the chance t o d i e o f pancreas or o f

lung cancer.

In j u d g i n g these a s s e r t i o n s one must note t h a t the statements r e f e r o n l y t o

c e r t a i n cancer types and t o very few cases, and t h a t i t i s d i f f i c u l t t o as­

c e r t a i n t h a t these were not random f l u c t u a t i o n s . However, even i f a l l proper

c o r r e c t i o n s , i n c l u d i n g age c o r r e c t i o n s , are a p p l i e d , and i f a c o r r e l a t i o n

between cancer i n c i d e n c e and r a d i a t i o n exposure could a c t u a l l y be e s t a b l i ­

shed among the Hanford workers, t h i s need not be pr o o f f o r a causal r e l a t i o n .

For example, lung cancer r a t e s have been i n c r e a s i n g i n recent years i n the

United S t a t e s . At the same time the t o t a l doses accumulated by workers i n

Hanford must have been i n c r e a s i n g and must now be hig h e r than those o f peo­

p l e d y i n g e a r l i e r a f t e r a s h o r t e r employment i n Hanford. Lunq cancer r a t e

and average doses have a c c o r d i n g l y both been h i g h e r i n workers d y i n g r e ­

c e n t l y . This i s an example of a s p u r i o u s c o r r e l a t i o n w i t h o u t causal connec­

t i o n . Various o t h e r s p u r i o u s c o r r e l a t i o n s may w e l l p l a y a r o l e , and the Han­

f o r d study must t h e r e f o r e be examined v e r y c r i t i c a l l y . D o u b t l e s s l y i t con­

t a i n s a l l the d i f f i c u l t i e s o f an assessment o f the e f f e c t s o f low doses on

human p o p u l a t i o n s . Nevertheless s t u d i e s o f human data are o f g r e a t e s t im­

por t a n c e . They have t o be performed, even i f i t i s o f t e n e x c e e d i n g l y d i f f i ­

c u l t t o e s t i m a t e doses. Perhaps the most imp o r t a n t s et o f o b s e r v a t i o n s i s

t h a t made on the Japanese atomic bomb s u r v i v o r s . H.H.Rossi has, as o t h e r s

have done, analysed these data and i n p a r t i c u l a r the leukemia d a t a . U n l i k e

o t h e r s he has s t r e s s e d the f a c t t h a t the o b s e r v a t i o n s , i n agreement w i t h

general b i o p h y s i c a l c o n s i d e r a t i o n s , c o n t r a d i c t the p r o p o r t i o n a l i t y t o dose

f o r both s p a r s e l y and d e n s i l y i o n i z i n g r a d i a t i o n s ( 1 5 ) . He has a l s o made the

imp o r t a n t p o i n t t h a t the RBE-dose r e l a t i o n i s more fundamental than dose-

e f f e c t r e l a t i o n s . These m a t t e r s are being discussed i n t h i s symposium by

4 0 8

Rossi (16) and p a r t i c u l a r emphasis i s g i v e n t o t h e human da t a . These a r e ,

t h e r e f o r e , not considered i n the pre s e n t a r t i c l e . Animal experiments a r e

less r e l e v a n t t o r i s k e s t i m a t e s . However, they w i l l remain the b a s i s o f any

att e m p t t o understand t he b i o p h y s i c a l basis o f r a d i a t i o n c a r c i n o g e n e s i s ,

and they w i l l here be considered under t h i s aspect.

Arguments for the Linear Hypothesis

Because r a d i a t i o n energy i s t r a n s f e r r e d i n d i s c r e t e e v e n t s , a l l r a d i a t i o n

e f f e c t s must u l t i m a t e l y be l i n e a r a t small doses. At small doses most c e l l s

w i l l r e c e i v e no energy; the number o f c e l l s s u b j e c t t o an event w i l l be p r o ­

p o r t i o n a l t o dose. I f r a d i a t i o n c a r c i n o g e n e s i s were due s o l e l y t o t h e t r a n s ­

f o r m a t i o n o f i n d i v i d u a l c e l l s one would t h e r e f o r e have t o f i n d a l i n e a r do­

s e - e f f e c t r e l a t i o n a t doses o f f r a c t i o n s o f a rad 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 and a t c o n s i d e r a b l y l a r g e r doses f o r neutrons and o t h e r d e n s e l y

i o n i z i n g r a d i a t i o n s .

In vitro experiments i n d i c a t e , i n f a c t , t h a t a l i n e a r component e x i s t s . I t

e x i s t s f o r c e l l i n a c t i v a t i o n and i t e x i s t s f o r chromosome a b e r r a t i o n s , and

i t i s o f t e n s u r p r i s i n g l y l a r g e . Brown (17) has r e c e n t l y made a s t r o n g p o i n t

f o r t h e general e x i s t e n c e o f a l i n e a r component up t o about 100 r a d . He

argues w e l l f o r the p o s t u l a t e o f the l i n e a r - q u a d r a t i c d o s e - e f f e c t r e l a t i o n

t h a t i s based on b i o p h y s i c a l c o n s i d e r a t i o n s and on m i c r o d o s i m e t r i c d a t a ,

and he concludes t h a t e x t r a p o l a t i o n s from h i g h doses and h i g h dose r a t e s

are c o n s e r v a t i v e . However, he a l s o s t a t e s t h a t the s a f e t y f a c t o r i s p r o ­

bably not l a r g e r than r o u g h l y 2. He concludes t h i s p r i n c i p a l l y from a s u r ­

vey o f chromosome a b e r r a t i o n data t h a t i n d i c a t e a v a l u e o f OL\/OL2 i n t h e

l i n e a r - q u a d r a t i c dose r e l a t i o n o f about 100 rad.

Brown's arguments are w e l l taken, b u t , they r e s t , as he s t a t e s , on the

assumption t h a t c a r c i n o g e n e s i s r e f l e c t s the a c t i o n o f r a d i a t i o n on i n d i v i ­

dual c e l l s . I t i s d i f f i c u l t t o e s t a b l i s h t h a t t h i s should be so.

I t i s obvious t h a t the y i e l d o f tumours i s not equal t o the y i e l d o f t r a n s ­

formed c e l l s . In experiments o f Borek and H a l l (18) on the in vitro t r a n s ­

f o r m a t i o n o f mammalian c e l l s the t r a n s f o r m a t i o n r a t e i s l a r g e r than 10

per rad f o r x - r a y s . Even i f one were t o assume t h a t o n l y a minor f r a c t i o n

o f the t i s s u e s i n the human body i s s e n s i t i v e , one would s t i l l o b t a i n sev­

e r a l transformed c e l l s every minute due t o background r a d i a t i o n a lone i f

the same or s i m i l a r t r a n s f o r m a t i o n r a t e s were t o apply in vivo. O b v i o u s l y a

409

tran s f o r m e d c e l l must have a r a t h e r i n f i n i t e s i m a l chance t o produce a can­

c e r .

One can n e v e r t h e l e s s argue t h a t each transformed c e l l may have a small but

f i n i t e p r o b a b i l i t y t o produce a tumour. The number o f r a d i a t i o n induced t u ­

mours would then be p r o p o r t i o n a l t o the number o f transformed c e l l s . But

even i n those cases where a mono-clonal o r i g i n o f a tumour i s e s t a b l i s h e d

t h i s w i l l not n e c e s s a r i l y imply a l i n e a r dose r e l a t i o n . The p r o b a b i l i t y o f

a transformed c e l l t o grow i n t o a macroscopic tumour may w e l l depend on

immunological f a c t o r s or on the mutual i n f l u e n c e between damaged c e l l s ( 1 9 ) .

A l t h o u g h t h e i r n a t u r e i s n o t , a t p r e s e n t , d e t ermined, i t i s known t h a t i n t e r ­

c e l l u l a r f a c t o r s e x i s t which can lead t o n o n - l i n e a r dose r e l a t i o n s a t small

doses. T h i s has been demonstrated f o r the i n d u c t i o n o f mammary tumours i n

the Sprague-Dawley r a t .

Induction of Mammary Tumours in the Rat; An Example for Infra-Linearity

at Small Doses of Densily Ionizing Radiations

There are cases o f r a d i a t i o n induced tumours t h a t are n o n - l i n e a r i n dose

even a t low doses o f d e n s i l y i o n i z i n g r a d i a t i o n s . Marshall and Groer (20)

have found a q u a d r a t i c dose dependence f o r the i n d u c t i o n o f osteosarcomas

by α-rays. Mammary tumours produced i n the Sprague-Dawley r a t are an oppo­

s i t e example. In t h i s case t he dose-dependence i s n e i t h e r l i n e a r nor supra-

l i n e a r (dose exponent >1) but in s t e a d i t i s i n f r a - l i n e a r (dose exponent < 1 ) ;

The tumours are m o s t l y adeno-fibromas and fibro-adenomas and they occur i n

the o l d e r animal w i t h l a r g e spontaneous frequency. I t i s t h e r e f o r e o f t e n

s t a t e d t h a t t h i s i s a somewhat abnormal e x p e r i m e n t a l system; on the o t h e r

hand, an i n c i d e n c e s t e e p l y r i s i n g w i t h age i s t y p i c a l f o r v a r i o u s tumours.

Vogel and Z a l d i v a r (21) and S h e l l a b a r g e r e t a l . (22) have e a r l i e r r e p o r t e d

a dose dependence o f mammary tumours i n the Sprague-Dawley r a t t h a t i s i n f r a -

l i n e a r f o r n e u t r o n s . In the meantime a d d i t i o n a l work has been performed and

is s t i l l i n progress. Broerse e t a l . (23) have presented an i n t e r i m a n a l y s i s

of a l a r g e experiment t h a t i n c l u d e s d i f f e r e n t s t r a i n s o f r a t s and t h a t i s

a l s o concerned w i t h hormonal i n f l u e n c e s on the r a d i a t i o n response. The com­

p l e t e r e s u l t s o f a l a r g e experiment by S h e l l a b a r g e r e t a l . w i l l soon be pub­

l i s h e d . This experiment has been s p e c i f i c a l l y designed towards the d e t e r m i n a ­

t i o n o f the e f f e c t s o f very small neutron doses. Some o f the e s s e n t i a l r e ­

s u l t s w i l l here be summarized, and they w i l l then be used t o i n d i c a t e funda­

mental aspects o f the mathematical assessment o f tumour i n d u c t i o n by i o n i ­

z i n g r a d i a t i o n s .

4 1 0

In the experiment r a t s were exposed t o s i n g l e doses e i t h e r o f 430 keV

neutrons or o f x-rays a t age 60 days. Mammary tumours were then observed

and s u r g i c a l l y removed as they o c c u r r e d . In t h i s way s e v e r a l tumours could

be observed i n i n d i v i d u a l animals. In the c o n v e n t i o n a l a c t u a r i a n way a mor­

t a l i t y c o r r e c t e d c u m u l a t i v e tumour i n c i d e n c e i s o b t a i n e d as a f u n c t i o n o f

time f o r each i r r a d i a t e d group. F i g . l g i v e s an example, namely the curve

f o r 0.4 rad o f neutrons compared t o the c o n t r o l group. These curves r e p ­

resent fibro-adenomas p l u s adeno-fibromas. The curves f o r the i r r a d i a t e d

and the c o n t r o l group are n e a r l y p a r a l l e l and the same seems t o a p p l y a t

o t h e r doses. One can o c c o r d i n g l y s t a t e t h a t the e f f e c t o f the i r r a d i a t i o n

i s a s h i f t f orward i n time o f the tumour i n c i d e n c e .

F i g . l

The i n t e g r a l tumour r a t e , R ( t ) f o r adeno-fibromas and fibro-adenomas as a f u n c t i o n o f time a f t e r i r r a ­d i a t i o n i n the experiment o f S h e l l a b a r g e r e t a l . on Sprague-Dawley r a t s . The upper curve a p p l i e s t o a dose o f 0.4 rad o f 430 keV neutrons (89 animals) the lower curve t o the c o n t r o l group (167 a n i m a l s ) . The shaded areas g i v e the standard d e v i a t i o n s .

There a r e , i n f a c t , many ways t o c o n s t r u c t d o s e - e f f e c t r e l a t i o n s from the

t o t a l i t y o f the data o b t a i n e d i n the experiment. The d e t e r m i n a t i o n o f a

time s h i f t i s one p o s s i b i l i t y ( F i g . 2 a ) . Another p o s s i b i l i t y i s the s p e c i f i ­

c a t i o n o f the excess i n c i d e n c e a t a s e l e c t e d time ( F i g . 2 b ) . S t i l l a n other

p o s s i b i l i t y i s the d e t e r m i n a t i o n o f a q u a n t i t y t h a t i s perhaps more meaning­

f u l as a measure o f d e t r i m e n t ; t h i s i s the loss of tumour-free l i f e span,

i . e . the expected tu m o u r - f r e e l i f e span o f the animals i n the c o n t r o l group

minus the tumour-free l i f e span i n the i r r a d i a t e d group ( F i g . 2 c ) . One can

not a priori expect t h a t the v a r i o u s d o s e - e f f e c t r e l a t i o n s are o f equal or

even o f s i m i l a r shape, and i t f o l l o w s t h a t statements on the l i n e a r i t y or

n o n - l i n e a r i t y o f d o s e - e f f e c t r e l a t i o n s have l i t t l e a b s o l u t e meaning.

4 1 1

O^/GRAY

ο 1 es .1

a) Forward s h i f t i n time o f the occurrence o f mammary tumours f o r d i f f e r e n t neutron and x - r a y doses.

b) Excess mammary tumours per animal i n the experiment o f S h e l l a b a r g e r e t a l . a t 800 days a f t e r i r r a d i a t i o n .

D x / G R A Y

c) Reduction o f tumour-free l i f e span i n the experiment o f S h e l l a b a r g e r e t a l .

O v /GRAY

Fig. 2

V a r i o u s d o s e - e f f e c t r e l a t i o n s f o r the i n d u c t i o n o f mammary tumours i n the Sprague-Dawley r a t .

The dose scales f o r neutrons and x-rays d i f f e r by a f a c t o r o f 10.

However, i n the present case i t appears t h a t t h e v a r i o u s d o s e - e f f e c t r e l a ­

t i o n s d e p i c t e d i n Fig. 2 are g e n e r a l l y o f the same shape. In agreement w i t h

e a r l i e r r e s u l t s one f i n d s a n e a r l y p a r a b o l i c dependence on neutron dose a t

doses t h a t are so small t h a t most c e l l s have no energy d e p o s i t i o n i n t h e i r

n u cleus. The p o s s i b i l i t y o f such dose r e l a t i o n s i s o f obvious r e l e v a n c e t o

the problems of r a d i a t i o n p r o t e c t i o n . I t i s a l s o i m p o r t a n t t h a t v e r y h i g h

RBE values o f 100 or more are reached a t low doses. However, these m a t t e r s

w i l l not be f u r t h e r considered i n t h i s a r t i c l e . Instead t h e experiment w i l l

be used t o e x e m p l i f y basic q u a n t i t i e s r e l e v a n t t o the assessment o f r a d i a t i o n

care i nogenes i s.

4 1 2

Basic Quantities Relevant to the Assessment of Radiation Carcinogenesis

A d o s e - e f f e c t r e l a t i o n c o n t a i n s , as seen i n the example o f the mammary t u ­

mours, o n l y l i m i t e d i n f o r m a t i o n . The a c t u a l q u a n t i t y o f i n t e r e s t i s the

tumour rate as a f u n c t i o n o f age or o f time a f t e r i r r a d i a t i o n . The tumour

r a t e , r ( t ) , i s the p r o b a b i l i t y per i n d i v i d u a l per u n i t time t o develop a

tumour. The e s t i m a t e o f the tumour r a t e f o r t h e c o n t r o l s i n the experiment

o f S h e l l a b a r g e r e t a l . i s gi v e n i n F i g . 3 . I t i s a f u n c t i o n t h a t increases

s t e e p l y w i t h age f o r these p a r t i c u l a r tumours.

F ig .3

The t h r e e b a s i c q u a n t i t i e s r ( t ) , R ( t ) , and I ( t ) f o r the spontaneous i n c i d e n c e o f mammary tumours i n the Sprague-Dawley r a t s i n the experiment o f S h e l l a b a r g e r e t a l .

R A T M A M M A R Y T U M O R S C O N T R O L S

( S h e l l a b a r g e r et oi. )

I N T E G R A L T U M O R R A T E

R(t) = /r lOdt* / -

R(t)/ C U M . I N C I D E N C E

- / JUL—

I t i s o f t e n d i f f i c u l t t o e s t i m a t e tumour r a t e s , s i n c e i n most experiments

an i n s u f f i c i e n t number o f tumours i s observed per time i n t e r v a l . I t i s then

more p r a c t i c a l t o determine the integral tumour rate, R ( t ) . T h i s q u a n t i t y

i s equal t o the time i n t e g r a l o f the tumour r a t e up t o time t , and i t i s

a l s o equal t o the mean number o f tumours per s u r v i v i n g a n i m a l , i f m u l t i p l e

tumours can be scored and if m o r t a l i t y i s u n r e l a t e d t o tumour i n c i d e n c e .

The e s t i m a t e o f the i n t e g r a l tumour r a t e and o f i t s standard d e v i a t i o n i s

gi v e n by the r e l a t i o n :

R(t) = I 1 t . < t N ( t . ) -A

1

<t N ( t . ) 2

4 1 3

t . a r e the times o f inc i d e n c e o f the i n d i v i d u a l tumours up t o time t , a,nd

N ( t . ) are the numbers of animals s t i l l a t r i s k a t these times, ( f m u l t i p l e

tumours can not be observed, t he i n t e g r a l tumour r a t e i s o b t a i n e d by the

same f o r m u l a . The o n l y change i s t h a t animals a re considered a t r i s k o n l y

u n t i l they i n c u r t h e i r f i r s t tumour.

R ( t ) has been termed 'mean number o f tumours' i n F i g , 1 . However, i n g e n e r a l ,

t h e term i n t e g r a l tumour r a t e i s more s u i t a b l e , R ( t ) has no d i r e c t meaning

i f m u l t i p l e tumours can not be observed, but i t i s c l o s e l y r e l a t e d t o the

p r o b a b i l i t y of an animal t o have a t l e a s t one tumour. The l a t t e r q u a n t i t y ,

l ( t ) , d e f i n e d by the e q u a t i o n i n Fig.3 has been c a l l e d cumulative prevalence

by Broerse e t a l . ( 2 3 ) ; t h i s appears t o be a s u i t a b l e term t h a t c o u l d be

genera 11y adopted.

D e t e r m i n a t i o n o f r ( t ) , R ( t ) , or l ( t ) should i d e a l l y be the aim of a w e l l

designed experiment. However, one may f r e q u e n t l y be unable t o use s u f f i ­

c i e n t l y l a r g e e xperimental groups. Then s i m p l e r q u a n t i t i e s and approxima^

t i v e concepts are d e s i r a b l e . I t i s s t i l l v e r y common t h a t q u a n t i t i e s such as

fraction of animals with at least one tumour or mean number of tumours per

animal are quoted w i t h r e f e r e n c e e i t h e r t o t o t a l l i f e time or t o a s p e c i f i e d

o b s e r v a t i o n p e r i o d but w i t h o u t any m o r t a l i t y c o r r e c t i o n . In f a c t , these may

s t i l l be the most commonly quoted q u a n t i t i e s . The m o r t a l i t y c o r r e c t i o n i s

o f no importance a t low doses. However, low dose s t u d i e s w i l l always be per~

formed i n the c o n t e x t o f experiments t h a t i n c l u d e a l s o h i g h e r doses where

m o r t a l i t y c o r r e c t i o n s are e s s e n t i a l . The u n c o r r e c t e d q u a n t i t i e s a r e t h e r e ­

f o r e o f l i m i t e d u s e f u l n e s s , and may, i n f a c t , be m i s l e a d i n g .

Another s i m p l i f i e d concept t h a t i s commonly a p p l i e d , a l t h o u g h i t i s not a l ~

ways m e a n i n g f u l , i s the so c a l l e d latent period. I t would be d i f f i c u l t t o

d e f i n e t h i s concept r i g o r o u s l y , but i n p r a c t i c e i t i s most o f t e n equated

w i t h t h e time t o the appearance o f the f i r s t tumour i n an ex p e r i m e n t a l group.

Obviously t h i s i s u n s a t i s f a c t o r y s i n c e the r e s u l t w i l l depend on the s i z e o f

the e x p erimental group. For example, the i n c i d e n c e o f the mammary tumours

increases s t e e p l y w i t h age, and t h i s suggests t h a t the concept o f a l a t e n t

p e r i o d may indeed a p p l y . The t r u e ' l a t e n t p e r i o d ' a c c o r d i n g t o the e s t i m a t e

f o r the c o n t r o l s i n Fig. 3 i s about 100 days a f t e r the be g i n n i n g o f the ob­

s e r v a t i o n , However, the time t o the f i r s t tumour w i l l g e n e r a l l y be c o n s i d e r ­

a b l y l a r g e r than the t h e o r e t i c a l v a l u e ; t h i s i s the case even f o r e x t r e m e l y

l a r g e experimental groups. In Fig. 4 the median o f the time t o the f i r s t t u -

4 1 4

mour i s p l o t t e d as a f u n c t i o n o f the s i z e o f the e x p e r i m e n t a l group and i t

i s apparent t h a t no r e a l i s t i c e s t i m a t e o f the t r u e v a l u e i s p o s s i b l e . The

l a t e n t p e r i o d i s t h e r e f o r e a somewhat m i s l e a d i n g concept; i t should be used

w i t h g r e a t c a u t i o n , and whenever p o s s i b l e i t should be s u b s t i t u t e d by o t h e r ,

m o d i f i e d parameters.

Fig.4

The median (and the 50 % range) f o r the time from the b e ginning o f the ob­s e r v a t i o n (age 60 days) t o the occurrence o f the f i r s t tumour i n groups c o n t a i n i n g d i f f e r e n t num­bers o f animals. The dot re p r e s e n t s the a c t u a l occurrence o f the f i r s t tumour i n the c o n t r o l £ groups o f the experiment by S h e l l a b a r g e r e t a l . 100' ' ' 1 1 1

y 10 100 GROUP SIZE

i t has been s t a t e d e a r l i e r t h a t the d e t e r m i n a t i o n o f RBE i s o f t e n more f u n ­

damental than the d e t e r m i n a t i o n o f the dose dependence o f v a r i o u s b i o l o g i c a l

e n d p o i n t s . I t i s then not necessary t o e s t a b l i s h d o s e - e f f e c t r e l a t i o n s , and

i t i s s u f f i c i e n t t o perform simple comparisons between i r r a d i a t e d groups.

A c c o r d i n g l y one needs a s u i t a b l e s t a t i s t i c a l t e s t t h a t p e r m i t s the compari­

son o f the tumour in c i d e n c e i n two groups, such as a group o f animal exposed

t o an x-ray dose and a group o f animals exposed t o a neu t r o n dose. I f such a

t e s t i s a v a i l a b l e one can determine the RBE dose dependence i n the d i r e c t

non-parametric way which has been d e s c r i b e d e a r l i e r ( 2 4 ) .

Purpose o f the s t a t i s t i c a l t e s t i s the examination o f the nu11-hypothesis,

i . e . the assumption t h a t the tumour r a t e s a re equal i n the two groups t h a t

a r e t o be compared. In orde r t o o b t a i n a t e s t w i t h s u f f i c i e n t power one w i l l

a v o i d an approximate t r e a t m e n t where the o b s e r v a t i o n p e r i o d i s s u b d i v i d e d 2

i n t o several f i n i t e i n t e r v a l s , and where then t h e χ - t e s t o r the F i s h e r

exact p r o b a b i l i t y t e s t i s a p p l i e d . Instead a t e s t i s d e s i r a b l e t h a t i s based

on t he f u l l e x p e r i mental o b s e r v a t i o n s . The Mann-Whitney rank o r d e r t e s t

c o u ld be used i f a l l , or n e a r l y a l l , animals s u r v i v e d u n t i l they developed a

tumour. Animals could then be ranked a c c o r d i n g t o t h e i r tumour f r e e l i f e

t ime and a p p l i c a t i o n o f the Mann-Whitney t e s t would be s t r a i g h t f o r w a r d .

4 1 5

However, in a l l experimental groups t h e r e i s a s u b s t a n t i a l number o f a n i ­

mals t h a t d i e w i t h o u t d e v e l o p i n g a mammary tumour. The Mann-Whitney t e s t i s

t h e r e f o r e not a p p l i c a b l e .

However, a non-parametric t e s t has been developed t h a t has n e a r l y the same

powe r - f u n c t i o n as the Mann-Whitney t e s t (25) w h i l e i t i s a p p l i c a b l e even i f

loss o f elements from the two observed groups occurs . The t e s t has e a r l i e r

been a p p l i e d i n o r d e r t o o b t a i n the RBE dose dependence f o r the neutrons i n

the experiment o f S h e l l a b a r g e r e t a l . ( 2 2 ) . I t s d e t a i l s need not be d i s ­

cussed i n the present c o n t e x t ; however, i t i s f e l t t h a t r e f e r e n c e t o i t s

e x i s t e n c e i s u s e f u l , s i n c e the t e s t may be s u i t a b l e i n v a r i o u s e x p e r i m e n t a l

s i t u a t i o n s where r a d i a t i o n c a r c i n o g e n e s i s i n two groups i s t o be compared.

Ovary Tumours in the Mouse; An Example of a Quadratic Dose

Dependence for Sparsely Ionizing Radiation

Yuias has r e p o r t e d (26) a l a r g e experiment on the r a d i a t i o n i n d u c t i o n o f

ovary tumours in the mouse. The tumours are i n most cases l e t h a l and are

t h e r e f o r e r e a d i l y d i s c o v e r e d . Groups o f 200 mice each were exposed t o v a r i ­

ous doses o f γ-rays a t v a r i o u s d u r a t i o n s Τ o f the exposure. The data are r e ­

presented in Fig.5. The spontanous i n c i d e n c e which i s q u i t e small i s sub-

a: raw data b: t h e o r e t i c a l f i t

F i j . 5

Cunulative prevalence o f mouse ovary tumours ( - c o n t r o l v a l u e ) versus absor­bed dose a t v a r i o u s d u r a t i o n s o f exposure t o γ-rays.

4 1 6

t r a c t e d . Yuhas has concluded from these data t h a t the dose dependence i s

n e a r l y q u a d r a t i c . Lam and Rossi (27) have, more r e c e n t l y , reanalysed the

r e s u l t s . They have a p p l i e d an i n t r i g u i n g a n a l y s i s , t h a t assumes t h a t the

c u m u l a t i v e prevalence f o l l o w s an e q u a t i o n :

I ( t ) = f(α-D + q ( T ) . D 2 )

where the form o f the f u n c t i o n f ( . . ) i s l e f t open and where a r e c o v e r y o f

the q u a d r a t i c component i s assumed and accounted f o r by the r e d u c t i o n f a c ­

t o r q ( T ) . On the basis o f recovery f a c t o r s t h a t correspond t o an exponen­

t i a l decay o f s u b l e s i o n s a decay time o f 15 hours has been o b t a i n e d f o r an

o p t i m a l f i t t o the d a t a . Furthermore the v a l u e a=5 rad has been deduced.

T h i s i s a much s m a l l e r l i n e a r component than the v a l u e o f r o u g h l y 100 rad

t h a t has been p o s t u l a t e d f o r human data i n g e n e r a l , and t h a t i s i m p l i c i t l y

u t i l i z e d i n the d e d u c t i o n o f v a r i o u s r i s k f a c t o r s . The r e s u l t i s t h e r e f o r e

o f importance and deserves f u r t h e r c o n s i d e r a t i o n .

I t i s o f p a r t i c u l a r i n t e r e s t whether the somewhat a r b i t r a r y assumption of

an e x p o n e n t i a l decay o f s u b l e s i o n s i s c r i t i c a l f o r the magnitude o f the

l i n e a r component t h a t i s o b t a i n e d i n the a n a l y s i s . To answer t h i s q u e s t i o n

one must ask s i m u l t a n e o u s l y f o r the o p t i m a l f u n c t i o n f ( . . ) , the o p t i m a l

value a, and the o p t i m a l r e p a i r f u n c t i o n q ( T ) . There are numerical proce-

MOUSE OVARY TUMORS w l i u . e

D O S E . r e d u c t i o n f a c t o r / gray

Fig.6

a) Cumulative prevalence o f mouse ovary tumours ( - c o n t r o l v a l u e ) vs. absorbed dose times dose r e d u c t i o n f a c t o r

EXPOSURE TIME / DAYS

b) f unc-Dose r e d u c t i o n f a c t o r as a t i o n o f exposure t i m e . The r e d u c t i o n due t o l o s s o f sen­s i t i v i t y a t i n c r e a s i n g age (26) p l a y s o n l y a minor r o l e ^ a s i n ­d i c a t e d by the upper c u r v e .

417

dures t h a t can p r o v i d e the r e s u l t s w i t h s u i t a b l e c o n s t r a i n t s t h a t ensure

smooth f u n c t i o n s f ( . . ) and q ( T ) . No a n a l y t i c a l e x p r e s s i o n a re invoked, i . e .

the f u n c t i o n s are represented by a r r a y s o f numerical v a l u e s . The mathemati­

c a l technique i s the n o n - l i n e a r o p t i m i z a t i o n by the method o f the g e n e r a l ­

ized reduced g r a d i e n t ( 2 8 ) .

Fig.5 b r e p r e s e n t s the r e s u l t . The o p t i m a l v a l u e o f α i s z e r o , w i t h a de­

pendence o f the sum o f l e a s t squares on α t h a t appears t o exclude values o f

α l a r g e r than roughly 4 rad. The curves i n Fig.5 b are s h i f t e d p a r a l l e l t o

the a x i s i n accordance w i t h the dose r e d u c t i o n f a c t o r s . For a c l e a r e r com­

p a r i s o n o f the data and the t h e o r e t i c a l curves a p l o t o f the c u m u l a t i v e i n ­

cidence versus the ' e f f e c t i v e dose' q(T)°'5-D i s g i v e n i n Fig.6 a . T h i s

b r i n g s a l l t h e o r e t i c a l curves i n t o c o i n c i d e n c e and bunches t he observed

in c i d e n c e s around the t h e o r e t i c a l c u r v e . In view o f the expected f l u c t u a ­

t i o n s o f observed tumours i n the low dose range the agreement between ob­

s e r v a t i o n s and t h e o r e t i c a l curve i s e x c e l l e n t . The e s s e n t i a l r e s u l t i s ,

t h a t no l i n e a r component i s found and t h a t s i m p l e p r o p o r t i o n a l i t y between

i n c i d e n c e and the q u a d r a t i c component r e s u l t s over a wide dose-range. In

Fig.6 b the time f a c t o r s , i . e . the dose m o d i f y i n g f a c t o r s are g i v e n as a

f u n c t i o n o f d u r a t i o n o f exposure T. I t i s o f i n t e r e s t t o note how p r e c i s e ­

l y recovery can be determined i n a w e l l designed experiment.

The two examples o f the ovary and the mammary tumours make i t q u i t e obvious

t h a t no u n i v e r s a l l y v a l i d dose dependence can be expected f o r r a d i a t i o n i n ­

duced tumours. I t i s t h e r e f o r e r e q u i r e d t h a t d e t a i l e d and r i g o r o u s l y a n a l y ­

sed s t u d i e s be performed on as many ex p e r i m e n t a l systems as p o s s i b l e , both

w i t h s p a r s e l y and w i t h d e n s i l y i o n i z i n g r a d i a t i o n s . Such s t u d i e s a r e r e l a ­

t i v e l y simple i n those cases where tumours are r e a d i l y d i s c o v e r e d , and a

d i r e c t e s t i m a t e o f tumour i n c i d e n c e i s t h e r e f o r e p o s s i b l e . In o t h e r e x p e r i ­

mental systems where tumours are not r e a d i l y d i s c o v e r e d the s t a t i s t i c a l

problems are much more s e r i o u s . One i s then f o r c e d t o e s t i m a t e p r e v a l e n c e

i n s t e a d o f i n c i d e n c e . T h i s w i l l be considered by r e f e r e n c e t o r e c e n t s t u ­

d i e s o f Lafuma e t a l .

S t a t i s t i c a l Problems in the Determination of Tumour Prevalence

I n h a l a t i o n s t u d i e s w i t h d i f f e r e n t a- and 3 - e m i t t e r s i n v a r i o u s chemical

forms and a p p l i e d i n v a r i o u s temporal p a t t e r n s have i n recent years been

performed i n a number o f l a b o r a t o r i e s . These s t u d i e s pose v a r i o u s d i f -

4 1 8

f i c u l t s t a t i s t i c a l problems, as the r a d i a t i o n induced lung tumours are

even i n t h e i r m a l i g n forms u s u a l l y not l e t h a l . The tumours can t h e r e f o r e

o n l y be observed when the animals d i e f o r o t h e r causes or a r e s a c r i f i c e d .

An example from s t u d i e s by Lafuma e t a l . may serve t o i l l u s t r a t e the s i t u a ­

t i o n .

F ig.7 r e f e r s t o s t u d i e s w i t h i n h a l e d radon. These s t u d i e s do not i n v o l v e

low doses; however, they are aimed a t a c l a r i f i c a t i o n o f t h e e f f e c t s o f

low doses t h a t can not be d i r e c t l y analysed. S t u d i e s w i t h h i g h doses are

r e l e v a n t because the m i c r o s c o p i c p a t t e r n o f energy d e p o s i t i o n by α-partic­

le s or by α-emitting hot spots i s the same f o r h i g h and f o r low doses. How­

ever, d i f f i c u l t i e s a r i s e due t o r a d i a t i o n induced m o r t a l i t y . I t i s o b v i o u s ­

l y meaningless t o compare d i f f e r e n t modes o f i r r a d i a t i o n on the b a s i s o f

tumour prevalence a t the death o f the animals because a h i g h e r dose o r a

more e f f e c t i v e temporal p a t t e r n o f the a p p l i c a t i o n o f the a c t i v i t y may shor­

ten t h e l i f e span o f the animals c o n s i d e r a b l y . Tumour pr e v a l e n c e i n t h e dead

animals may be reduced s i g n i f i c a n t l y because animals d i e t o o e a r l y . Methods

a r e t h e r e f o r e r e q u i r e d t o compare tumour prevalences i n a way t h a t i s i n d e ­

pendent o f r a d i a t i o n induced m o r t a l i t y .

Fig.7 r e f e r s t o two groups o f mice t h a t have been exposed t o radon a t the

l e v e l o f 7000 WLM (Working Level Months) and 1470 WLM. While lung tumours

are c l a s s i f i e d i n t o v a r i o u s stages, o n l y animals w i t h m a l i g n a n c i e s a r e , f o r

the purpose o f t h i s a n a l y s i s , d i s c r i m i n a t e d from the o t h e r a n i m a l s , The ob­

served data a r e i n d i c a t e d by the two panels. The upper d o t s i n these panels

symbolize animals d y i n g w i t h m a l i g n a n c i e s ; the lower d o t s symbolize animals

d y i n g w i t h o u t m a l i g n a n c i e s . The animals i n group 1 a r e d y i n g c o n s i d e r a b l e

e a r l i e r than the animals i n group 2. I t i s t h e r e f o r e d i f f i c u l t t o j u d g e how

s t r o n g l y prevalence i s increased i n group 1 i n comparison t o group 2,

No general s o l u t i o n o f the problem has a p p a r e n t l y been developed; however,

a r e l a t i v e l y simple method w i l l be d e s c r i b e d t o e s t i m a t e a time s h i f t i n

tumour prevalence between the two groups.

The method i s based on the n o t i o n o f inversions. The term i n v e r s i o n a p p l i e s

t o a p a i r o f animals not i n the same group. The p a i r forms an i n v e r s i o n i f

the animal t h a t d i e s e a r l i e r has a malignancy, w h i l e the animal t h a t d i e s

l a t e r has none. By c o n s i d e r i n g a l l p a i r s o f animals one can d e t e r m i n e t h e

t o t a l number o f i n v e r s i o n s , i f the number o f i n v e r s i o n s i s h i g h t h i s may

4 1 9

GROUP I r ­i n L

animals

CROUP 2r-

animals , •

FORWARD S H I F T / D A Y S

7000 WIM {43 DAYS)

1470 W L i ( 2· DAYS]

200 400

T I M E / DAYS

F i g . 7

Comparison o f two groups o f radon exposed r a t s from experiments by Lafuma e t a l .

The d o t s i n the two panels r e p r e s e n t deaths o f animals a t the i n d i c a t e d t i m e s . Upper d o t s : animals w i t h m a l i g n a n c i e s ; lower d o t s : animal w i t h o u t m a l i g n a n c i e s ; small d o t s : 1 a n i m a l ; i n t e r m e d i a t e d o t s : 5 a n i m a l s ; l a r g e d o t s : 15 animals. The e s t i m a t e o f the r e l a t i v e t i me s h i f t o f prevalence i s o b t a i n e d from the l o c a t i o n o f the minimum o f the number o f i n v e r s i o n s (see t e x t ) .

be an i n d i c a t i o n t h a t tumours occur e a r l i e r i n one o f t h e two groups. The

number o f i n v e r s i o n s f o r the two groups represented i n F i g . 6 i s 3 6 5 ·

One may now c o n s i d e r the p o s s i b i l i t y t h a t the preva l e n c e i s s h i f t e d f o r w a r d

by a t i m e At i n group 1 compared t o group 2. I t w i l l be r e a d i l y seen t h a t

a r e v e r s e s h i f t by At o f the observed p a t t e r n s leads t o a c o n f i g u r a t i o n

w i t h a decreased number o f i n v e r s i o n s . Fig.7 r e p r e s e n t s t he number o f i n ­

v e r s i o n s f o r d i f f e r e n t time s h i f t s . The minimum number o f i n v e r s i o n s i s ob­

t a i n e d when group 1 i s s h i f t e d w i t h respect t o group 2 by r o u g h l y 230 days.

One can prove t h a t t h i s p r o v i d e s a s u i t a b l e e s t i m a t e o f the time s h i f t o f

p r e v a l e n c e . The methods i s r e a d i l y a p p l i e d , and can be u t i l i z e d even w i t h

small groups. However, i t poses a number o f i n t r i c a t e s t a t i s t i c a l problems

which w i l l r e q u i r e f u r t h e r s t u d y .

Whenever an experiment i n v o l v e s l a r g e number o f animals and a c o n s i d e r a b l e

number o f ex p e r i m e n t a l groups, one can o b t a i n an a c t u a l e s t i m a t e o f the age

4 2 0

dependence of prev a l e n c e . To t h i s purpose t he maximum l i k e l i h o o d method i s

combined w i t h the n o n - l i n e a r o p t i m i z a t i o n method, t h a t has been mentioned

e a r l i e r i n the c o n t e x t o f the ovary tumours. F i g . 8 r e p r e s e n t s the r e s u l t

f o r t h e radon experiment. One common prevalence curve i s here o b t a i n e d f o r

a l l groups. But the curve i s s h i f t e d i n time i n the v a r i o u s groups which

have been s u b j e c t e d t o d i f f e r e n t l e v e l s o f radon i n h a l a t i o n . I t i s o f i n ­

t e r e s t t o note t h a t f o r the two groups considered i n Fig. 7 the s h i f t ob­

t a i n e d by the two methods i s the same.

AAA T I M E / D A Y S i n n o

F i g . 8

Maximum 1i k e l i hood e s t i m a t e o f lung cancer prevalence i n mice a f t e r radon i n h a l a t i o n (Exper­iments by Lafuma e t a l . ) .

The same curve t h a t i s merely s h i f t e d i n time i s assumed f o r a l 1 groups. The shape o f the curve r e s u l t s from non­l i n e a r o p t i m i z a t i o n .

The d o t s r e p r e s e n t deaths o f animals and a re t o be un­derstood i n the same way as i n Fig.7. The v e r t i c a l broken 1ines a re markers t o i n d i c a t e the time s h i f t .

4S00 W L M

« 5 D A Y S

7100 141

•250 174

• n ° T I M E / D A Y S

C e r t a i n s o l u t i o n s o f the problem o f e s t i m a t i o n o f i n c i d e n c e or pr e v a l e n c e

of r a d i a t i o n induced tumours have been i n d i c a t e d i n t h i s a r t i c l e . However,

421

t h e r e i s an obvious need f o r f u r t h e r development o f s u i t a b l e s t a t i s t i c a l

c o ncepts and methods. A coherent conceptual framework and improved s t a t i s ­

t i c a l methods w i l l be r e q u i r e d i n any comprehensive e f f o r t t o a r r i v e a t

b e t t e r r i s k e s t i m a t e s and u l t i m a t e l y a t a deeper u n d e r s t a n d i n g o f r a d i a ­

t i o n c a r c i n o g e n e s i s .

References

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