OFFICIAL ORGAN OF THE RADIATION RESEARCH SOCIETY

RADIATION R E S E A R C H

EDITOR-IN-CHIEF: ODDVAR F. NYGAARD

Volume 6 5 , 1976

Academic Press • New York and London

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RADIATION R E S E A R C H

OFFICIAL ORGAN OF THE RADIATION RESEARCH SOCIETY

Editor-in-Chief: O D D V A R F . N Y G A A R D , Department of Radiology, Case Western Reserve University, Cleveland, Ohio 44106

ASSOCIATE EDITORS

S . I . A U E R B A C H , Oak Ridge National L a b - G . J . K O L L M A N N , Albert Einstein Medical oratory Center

M . A B E N D E R , Brookhaven National L a b - J - B . L I T T L E , Harvard University o r a t o r y R . L O E V I N G E R , National Bureau of

J . A . B E L L I , Harvard University Standards W. A. B E R N H A R D , University of Rochester L - S. M Y E R S , University of California, L o s

Angeles X D L t ? , A p i r ^ i ^ , ; M ^ n ? t o b a n e r g y ° f ^ * N E T A , Carnegie Mellon University G . V . D A L R Y M P L E , University of Arkansas K U n i v e n d * ° f C * l U o v ™ >

P. W. D U R B I N , University of California, G > S I L I N I , Centro di Studi Nucleari della Berkeley Cassaccia, Roma, I ta ly

R . A . H O L R O Y D , Brookhaven National L . D . S K A R S G A R D , British Columbia Laboratory Cancer Institute, Vancouver, Canada

A. M . K E L L E R E R , Universität Wurzburg, H . R . W I T H E R S , M . D . Anderson Hospital Germany j M Y U H A S , Oak Ridge National L a b -

D . J . K I M E L D O R F , Oregon State University oratory

OFFICERS OF THE SOCIETY

President: R O B E R T H . SCHÜLER, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

Vice President (and President Elect): R O B E R T F . K A L L M A N , Department of Radiology, Stanford University, Palo Alto, California 94305

Secretary-Treasurer: W I L L I A M C . D E W E Y , Dept. R a d . and R a d . Biol . Colorado State University, Fort Collins, Colorado 80521

Editor-in-Chief: O D D V A R F . N Y G A A R D , Case Western Reserve University, Cleveland, Ohio 44106

Executive Director: R I C H A R D J . B U R K , J R . , 4720 Montgomery L a n e , Suite 506, Bethesda, Maryland 20014

ANNUAL MEETINGS

1976: June 27-July 2, San Francisco, California 1977: San Juan, Puerto Rico

VOLUME 65, 1976

Councilors Radiation Research Society 1975-1976

P H Y S I C S E . R . E p p , H a r v a r d U n i v e r s i t y A . M . Kel lerer , Universität W u r z b u r g , G e r m a n y

B I O L O G Y E . J . A i n s w o r t h , Argonne N a t i o n a l L a b o r a t o r y R . J . M . F r y , Argonne N a t i o n a l L a b o r a t o r y

M E D I C I N E J . I . F a b r i k a n t , U n i v e r s i t y of Connect i cut S. J . Ade ls te in , H a r v a r d U n i v e r s i t y

C H E M I S T R Y

J . G. B u r r , U n i v e r s i t y of O k l a h o m a M . S. Matheson , Argonne N a t i o n a l L a b o r a t o r y

A T - L A R G E

H . I . Ad le r , Oak Ridge N a t i o n a l L a b o r a t o r y A . P . Casarett , Corne l l U n i v e r s i t y

R A D I A T I O N R E S E A R C H 65, V-VU* (1976)

CONTENTS OF VOLUME 65 N U M B E R 1, J A N U A R Y 1976

C A T H A R I N E L . W I N G A T E A N D J O H N W . B A U M . Measured Radial Distributions of Dose and L E I 1 for Alpha and Proton Beams in Hydrogen and Tissue-Equivalent Gas. 1

A . 0 . F R E G E N E . A Comparison of L i F and FeSO^ Dosimetry with Cavity Theory for High-Energy Electrons. 20

M . D . S E V I L L A , C . C L A R K , A N D P . F A I L O R . E S R Study of the Anion Radicals of 5-Nitro-pyrimidines: Conversion to Iminoxy Radicals. 29

K . R . L Y N N A N D A . P . D . R A O U L T . y - I rradialion of Lima Bean Protease Inhibitor in Dilute Aqueous Solutions. 41

Z . S Z W E D A - L E W A N D O W S K A , M . P U C H A L A , A N D W . L E Y K O . Effects of Gamma Irradiation on the Structure and Function of Human Hemoglobin. 50

M A R I L Y N P . L A W , S H I R L E Y H O R N S E Y , A N D S T A N L E Y B . F I E L D . Collagen Content of Lungs of

Mice after X-Ray Irradiation. 60 R O Y C E L . G R A G G , R O N A L D M . H U M P H R E Y , A N D R A Y M O N D E . M E Y N . The Response of Chinese

Hamster Ovary Cells to Fast Neutron Radiotherapy Beams. I . Relative Biological Effective­ness and Oxygen Enlianccment Ratio. 71

J . K . G O N G , C . A . G L O M S K I , N . L . F R E D E R I K S E N , A . J . L A W S O N , A N D J . P . D A L E Y . Effects of

Low-Level (1.0 R) X - I rradialion on the Erythro id Response of the Rat Bone Marrow. 83 T . B R U S T A D , E . B O Y E , A N D E . W O L D . Toxic Effects upon Bacteria of Phosphate-Buffered

Saline Exposed in a High-Frequency Argon Discharge. 98 D O N A L D E . C A R L S O N A N D R O N A L D A . L U B E T . Effects of Sublethal Gamma Radiation on

T and B Cell Activity in the Antibody Response of Mice. I l l N O R M A N D . G L E N N A N D H O W A R D S. D U C O F F . Acute Lethality after Fast-Neutron and X-Irra-

diation of Tribolium confusum. 120 S H I G E T O S H I A N T O K U . Chemical Protection against Radiation-Induced DNA Single-Strand

Breaks in Cultured Mammalian Cells. 130 R A T N A D A T T A , A R T H U R C O L E , A N D S A N D R A R O B I N S O N . Use of Track-End Alpha Particles

from 241 Am to Study Radiosensitive Sites in CHO Cells. 139 B A R B A R A C . C O O K E , E . M A R T I N F I E L D E N , M A R G A R E T J O H N S O N , A N D C . E . S M I T H E N . Poly-

functional Radiosensitizers. I . Effects of a Nitroxyl Biradical on the Survival of Mamma­lian Cells in Vitro. 152

E X A C U S T O O I A N P Ä U S E C U , R O D I C A C H I R V A S I E , T R A I A N T E O D O S I U , A N D C O N S T A N T I N P Ä U N . Effects of 6 0 Co y-Radiaiion on the Hepatic and Cerebral Levels of Some Prostaglandins. 163

A . M . K E L L E R E R , E . J . H A L L , I L H . R O S S I , A N D P . T E E D L A . RBE as a Function of Neutron

Energy. I I . Statistical Analysis. 172

Correspondence.

J A N E V . W E B B , M . J . H O L L I N G S W O R T H , A . J . M I L L , A N D R . W . D A V I E S . Temperature-

Dependence of Repair of Sublethal Radiation Damage in Drosophila. 187 M . R . R A J U A N D E . B L A K E L Y , J . H O W A R D , J . T . L Y M A N , D . P . K A L O F O N O S , B . M A R T I N S ,

A N D C . H . Y A N G . Human Cell Survival as a Function of Depth for a High-Energy Neon Ion Beam. 191

E R R A T U M 195

N U M B E R 2, F E B R U A R Y 1976

J . A . S I M M O N S A N D D . K . B E W L E Y . The Relative Effectiveness of Fast Neutrons in Creating Stable Free Radicals. 197

v

vi C O N T E N T S O F V O L U M E 65

S I L V A N O G K E G O L I , M A R T I A L G L A S T , A N D A L B E R T B E R T I N C H A M P S . Free-Radical Formation in Deoxythymidine-o'-Monophosphate y-Ir radiated, in Frozen Solution. A Computer-Assisted Analysis of Temperature-Dependent E S R Spectra. 2 0 2

J A C K S C H M I D T A N D D O N A L D C . B O R G . Free Radicals from Purine Nucleosides after Hydroxy I Radical Attack. 2 2 0

M . F A R A G G I A N D J . G . L E O P O L D . Pulse Radiolysis Studies of Electron-Transfer Reaction in Molecules of Biological Interest. I I . The Reduction of Cu (Il)-Peptide Complexes. 2 3 8

H O W A R D B . M I C H A E L S , E R I C J . R A S B U R N , A N D J O H N W . H U N T . Interaction of the Radio-sensitizer Paranitroacelophenone with Radiation-Induced Radicals on Nucleic Acid Components. 2 5 0

S A R A H M . H E R B E R T A N D B E R T M . T O L B K R T . Chemical and Conformational Studies of Gamma-Irradiated Solid Lysozyme. 2 0 8

L A T I K A P . C H A N D E R K A R , S H A N T O O G U R N A N I , A N D G . B . N A D K A R N I . The Involvement of Aromatic Amino Acids in Biological Activity of Bovine, Fibrinogen as Assessed by Gamma-Irradiation. 283

D . K . M Y E R S . Effects of X-Radiation and Urethane on Survival and Tumor Induction in Three Strains of Rats. 292

I A N J . C O N S T A B L E , M I C H A E L G O I T E I N , A N D R E A S M . K O E H L E R , A N D R O B E R T A . S C H M I D T . Small-Field Irradiation of Monkey Eyes with Protons and Photons. 304

A . H . SPARROW, S U S A N S. S C H W E M M E R , A N D K . H . T H O M P S O N . Radiosensitivity Studies with Woody Plants. I I I . Predictions of Limits of Probable Acute and Chronic L D 5 o Values from Lognormal Distributions of Interphase Chromosome Volumes in Gymnosperms. 315

M O S T A P A N . A B D E L - H A L I M A N D M I L T O N B . Y A T V J N . Effects of X-Irradiation on Liver RNA

Metabolism in Specifically Shielded Rats. 3:27 A N T U N H A N , W A R R E N K . S I N C L A I R , A N D B R U C E F . K I M L E R . The Effect of N-Ethylmaleimide

on the Response to X Rays of Synchronized He La Cells. 3-37 S. P . S T E A R N E R , R . L . D E V I N E , A N D E . J . B . C H R I S T I A N . Late Changes in the Irradiated Micro-

vasculature: An Electron Microscope Study of the Effects of Fission Neutrons. 3.51 S. A . B I R K E L A N D , J . M O E S N E R , O . K A L N J B S , A N D T . S K O V J E N S E N . Endolymphatic Irra­

diation with 198Au and nP as Immunosuppression in Renal Transplantation. The Effect on Hematologic and Immunobiologic Parameters. 371

B O O K R E V I E W . 3:86

A N N O U N C E M E NTS. 3187

N U M B E R 3, M A R C H 1976

W A L T E R S C H I M M E R L I N G , K I R B Y G . V O S B U R G H , P A U L W . T O D D , A N D A L A N A P P L E B Y . Appa­ratus and Dosimetry for High-Energy Heavy-Ion-Beam Irradiations. 3)89

J . A . R A L E I G H , W . K R E M E R S , A N D R . W H I T E I I O U S E . Radiation Chemistry of Nucleotides: Sfi'-Cyclonuclcotide Formation and Phosphate Release Initialed by Hydroxyl Radical Attack on Adenosine Monophosphates. 4,14

J . A . K N I G H T . Radiolysis of Benzonitrile. 4123 C U R T I S P . S I G D E S T A D , A N D R E W M . C O N N O R , A N D R A L P H M . SCOTT. The Effect of S-2-(3-

Aminopropylamino)ethylphosphorothioic Acid (WR-2721) on Intestinal Crypt Survival. I I . Fission Neutrons. 4i30

J O H N T . L E I T H , K A Y H . W O O D R U F F , A N D J O H N T . L Y M A N . Early Effects of Single Doses of 875 MeVt Nucleon 20ATeon Ions on the Skin of Mice and Hamsters. 4^40

M O R T O N W . M I L L E R , S U S A N M . V O O R H E E S , E D W I N L . C A R S T E N S E N , A N D G A R Y E . K A U F M A N . The Effect of 2 MHz Ultrasound Irradiation on Pisum sativum Roots. 4451

K Y M B . A R C U R I , R O B E R T J . P I Z Z U T I E L L O , M O R T O N W . M I L L E R , G A R Y E . K A U F M A N , A N D E D W I N L . C A R S T E N S E N . Reduction in Mitotic Index in Pisum sativum Root Meristems by Pulsed Ultrasound Irradiation. 4t58

R A Y D . L L O Y D , C H A R L E S W . M A Y S , S U S A N S. M C F A R L A N D , D A V I D R . A T H E R T O N , A N D J E R R Y L . W I L L I A M S . Californium Studies in Beagles. 4462

M A R I L Y N W . P O R T E R , R O S A N N A N . C H U T E , A N D S H I E L D S W A R R E N . Incidence of Radiation-Induced Cataract in Single and Parabiotic Rats. 4174

C O N T E N T S O F V O L U M E 65 vii

N . D U B R A V S K Y , N . H U N T E R , A N D H . R . W I T H E R S . The Effect of Precooling on the Radialion Sensitivity of the Proliferating Hair Follicle. 481

M A S A H I R O S A I T O . Hybridizabilily of Gamma-Irradiated Lactic Dehydrogenase. 490 W A T U R U N A K A M U R A , F U M I A K I S A T O , Y O S H I O N I S H I M O T O , A N D N A O Y U K I K A W A S I I I M A .

Prediction of Radioscnsitivity of a Mouse from Its Physiological Characteristics before X-Irradiation. 500

W . C. D E W E Y A N D D . P . H I G H F J E L D . Gt Block in Chinese Hamster Cells Induced by X-Irra-diation, Hyperthermia, Cyclohcximidc, or Actinomycin-D. 511

J O H N E . B I A G L O W A N D R A L P H E. D U R A N D . The Effects of Nitrobenzene Derivatives on Oxygen Utilization and Radiation Response of an in Vitro Tumor Model. 529

A L M A H O W A R D A N D F . G . C O W I E . Induced Resistance in a Desmid Closterium moniliferum. 540 J O E A T S U T A A N D S H U N Z O O K A J I M A . Necessity of Glycolysis for Recovery from Ultraviolet

Killing of Saccharomyces cerevisiae. 550 J O E A T S U T A A N D S H U N Z O O K A J I M A . Relationship between Sensitivity to Ultraviolet Light and

Budding in Yeast Cells of Different Culture Ages. 558

Co RRESPO N DE N CE.

S T A N L E Y B . C U R T I S . The OER of Mixed High- and Low-LET Radiation. 566

A C K N O W L E D G M E N T S . 573

A U T H O R I N D E X FOR V O L U M E 65. 576

R A D I A T I O N RESEARCH 65, 172-186 (1976)

RBE as a Function of Neutron Energy1

II. Statistical Analysis

A . M . K E L L E R E R 2 , E . J . H A L L ; H . H . R O S S I , A N D P. T E E D L A

Radiological Research Laboratory, Department of Radiology, College of Physicians and Sargeons of Columbia University, 630 West 168th Street, New York,

New York, 10032

K E L L E R E R , A . M . , H A L L , E . J . , R O S S I , H . I L , A N D T E E D L A , P. R B E as a Func t i on of

Neutron Energy. I I . Statistical Analysis. Radial. Res. 6 5 , 172-186 (1976).

A n experimental study of the relative biological effectiveness of neutrons of various energies for the inact ivat ion of hamster celts has been reported previously ; the present article contains a detailed statistical analysis of the data.

Repeated determination of X - r a y survival curves made i t possible to assess the statistical f luctuations of survival rates. W i t h i n ind iv idual experiments the stat ist ical variations are close to those expected on theoretical grounds. However, between experi­ments substantial variations in the reaction to X rays occur; these fluctuations can be approximately described by dose-modifying factors. A n idealized surv iva l curve for X - i r r a d i a t i o n has been derived.

T h e survival curves for neutrons have been compared to the l inear -quadrat ic dose-effect relation and the two coefficients in this equation have been derived together w i t h their joined confidence regions. The linear coefficient for neutrons reaches a m a x i m u m for neutron energies of several hundred thousand electron vo l t s ; the coefficient of the quadratic component is increased at neutron energies below 1 M e V . The dependence of R B E on neutron energy and on neutron dose is derived f rom the estimated dose-effect relations. I n addit ion, the more rigorous nonparametric method is used to derive con­fidence intervals for the R B E of neutrons.

I N T R O D U C T I O N

A n extensive exper imenta l s t u d y of the co lony - f o rming a b i l i t y of V-79 hamster cells after n e u t r o n and X - i r r a d i a t i o n has been reported earlier (1). S u r v i v a l curves have been presented for var ious n e u t r o n energies and for X rays, and the re lat ive biological effectiveness ( R B E ) of neutrons as a f u n c t i o n of the i r energy has been g iven. The results were obta ined w i t h o u t the need of deta i led s ta t i s t i ca l analysis.

However , t h e experiments have been conducted i n such a w a y as t o p e r m i t an expl ic i t analysis of the s tat i s t i ca l errors i n the s u r v i v a l curves. T h e essential po in t

2 This investigation was supported b y Contract A T ( l l - l ) - 3 2 4 3 for the U . S. Energy Research and Development Admin i s t ra t i on and Public Hea l th Service Grant N o . C A 12536 from the Nat iona l Cancer I n s t i t u t e .

2 Present address: I n s t i t u t für M e d . Strahlenkunde der Universität, 8700 Würzburg, Versbacher Landstr . 5, German}-.

1 7 2

C o p y r i g h t © 1976 b y A c a d e m i c Press , I n c . All . r ights of reproduct ion i n a n y form r e s e r v e d .

ÜBE O F N E U T R O N S 173

is t h a t a separate X - r a y s u r v i v a l curve has been established s imultaneously w i t h each n e u t r o n exper iment . T h i s makes i t possible t o analyze the f luctuat ions i n cellular s e n s i t i v i t y over an extended per iod , w h i c h , i n the present case, spanned about 12 months . F u r t h e r m o r e , t h e d e t e r m i n a t i o n of s imultaneous n e u t r o n and X - r a y curves has made i t possible t o a p p l y the nonparamctr i c s ta t i s t i ca l analysis {2) to t h e d e t e r m i n a t i o n of the R B E of neutrons as f u n c t i o n of n e u t r o n dose.

T h e s ta t i s t i ca l fluctuations w i t h i n i n d i v i d u a l experiments and between separate experiments are dealt w i t h i n t h e first p a r t of th i s art i c le . T h e assessment of s ta t i s t i ca l errors is o ften c r i t i ca l for the i n t e r p r e t a t i o n of data obta ined f r o m i r r a d i a t e d cell cu l tures ; the s ta t i s t i ca l analysis is therefore presented i n consider­able d e t a i l . T h e analysis of R B E as a f u n c t i o n of n e u t r o n dose is dealt w i t h i n the last p a r t of the art i c le .

A N A L Y S I S O F T H E X - R A Y D A T A

Fluctuations of Survival Rates within Individual Experiments

Each p o i n t of the 11 s u r v i v a l curves for n e u t r o n i r r a d i a t i o n and of the s i m u l ­taneously established X - r a y curves t h a t have been presented i n the preceding p u b l i c a t i o n (Jf) has been obta ined b y exposing four vials f i l led w i t h cell suspension to a specified n e u t r o n or X - r a y dose. I f the on ly s tat i s t i ca l f luctuat ions are those due to the f ini te n u m b e r of s u r v i v i n g colonies, t h e n the s tandard error should on the average, i n accordance w i t h the properties of the Poisson d i s t r i b u t i o n , be equal t o the square root of the n u m b e r of s u r v i v i n g colonics. I f , on the other h a n d , there are systematic var ia t i ons between the i n d i v i d u a l v ials the s tandard dev ia t i on of the s u r v i v a l rates i n each group of four v ia ls w i l l on the average exceed the s t a n d a r d d e v i a t i o n of the s u r v i v a l rates t h a t is predicted according t o Poissonian stat is t i cs . W h e t h e r th i s is the case has been tested on the basis of the x 2 -d i s t r ibu -t i o n . The test has been per formed for a l l i n d i v i d u a l X - r a y doses, b u t i n a d d i t i o n also for a l l n e u t r o n doses, i n each experiment . A m o n g the 159 values of x

2

t h a t were obta ined for the 159 groups of four vials there were 15 values t h a t exceeded the theoret ica l va lue of x

2

on the 9 5 % level . T h i s is a s igni f i cant ly larger number t h a n the eight cases expected on s tat i s t i ca l grounds. Accord ing ly , one concludes t h a t the actual s tandard deviat ions exceed the theoret i ca l deviat ions . I t has no t been f o u n d t h a t the cases of increased s tandard dev ia t i on occur m a i n l y at h i g h doses. T h i s indicates t h a t the increase i n the s tat i s t i ca l f luctuat ions is no t due t o the fact t h a t di f ferent vials t h a t were assigned the same absorbed dose were i n fact exposed to s l i gh t ly di f ferent absorbed doses. I n other words, i t does n o t appear t h a t the increase of the s ta t i s t i ca l f luctuat ions is due t o inaccuracies i n dos imetry .

As an a d d i t i o n a l test the s u m of the x2

values for a l l po ints of each i n d i v i d u a l s u r v i v a l curve, i.e., t h e x 2-values pooled for a l l doses i n each i n d i v i d u a l exper i ­m e n t , have been compared to the theoret i ca l values. I t is f o u n d t h a t for 5 out of the 22 s u r v i v a l curves the resu l t ing x

2

exceeds the theoret ica l values on the 9 5 % significance level . T h i s test, based on the pooled x 2-values, therefore con­firms the conclusions f r o m the analysis of the i n d i v i d u a l po ints .

174 K E L L E R E R ET AL.

T o o b t a i n an estimate of t h e r a t i o b y w h i c h t h e a c tua l fluctuations exceed the theoret i ca l fluctuations, the t o t a l sums of x

2

pooled f r o m a l l doses a n d a l l s u r v i v a l curves have been computed .

For the X - r a y experiments the t o t a l observed value is x2

= 401, whi le t h e 95%

level of x2

is X95 2 = 346. A t the large number of 296 degrees of f reedom t h i s difference is h i g h l y s igni f icant . T h e h i g h s ta t i s t i ca l significance is due t o t h e large a m o u n t of d a t a ; i t does n o t i n itself i m p l y t h a t the ac tua l s tat is t i ca l fluctua­t ions exceed the theoret ica l values great ly . Indeed i t can be seen t h a t the excess is smal l . T o o b t a i n the ra t i o of the ac tua l s tandard deviat ions to the theore t i ca l s tandard deviat ions one m a y consider the theoret i ca l med ian value , X o o 2 . T h i s med ian value is equal to the number of degrees of freedom, and the r a t i o of t h e ac tua l s tandard deviat ions t o the theoret ica l s t a n d a r d d e v i a t i o n for the X - r a y experiments is therefore

Px = (xVxso2

)* = (401/296)* = 1.164. (1)

T h u s the s tat i s t i ca l fluctuations are increased b y a factor of on ly 1.16 r e la t i ve t o the fluctuations t h a t are expected on theoret ica l grounds. For m a n y p r a c t i c a l purposes th is factor is negligible. W i t h the exper imenta l technique employed i n the present s t u d y i t is therefore a good first a p p r o x i m a t i o n to give the theore t i ca l values of the s tandar d deviat ions, or of the confidence in terva l s . N a t u r a l l y one cannot generalize th i s conclusion, and i t m a y be necessary t o p e r f o r m s i m i l a r anafyses i f one deals w i t h di f ferent exper imenta l condit ions .

T h e finding for the X - r a y da ta is supported b y those for n e u t r o n i r r a d i a t i o n s . I f a l l n e u t r o n experiments are pooled one obtains the va lue x

2

= 427.9 a n d t h e theoret ical 95% va lue X 9 5 2 = 356 a t 314 degrees of freedom. T h i s again is a h i g h l y signif icant difference. B u t , as i n the case of X rays, the r a t i o of the ac tua l t o t h e theoret ica l fluctuations is n o t far f r o m 1. T h e n u m e r i c a l va lue is

P» = (x2

/x5o2

)* = (427.9/314)* = 1.167. (2)

I t has been ment ioned earlier t h a t no corre lat ion has been observed between the increased fluctuations and the dose, and t h a t th i s indicates t h a t dos imetr ic i n ­accuracies are n o t the cause of the increased s ta t i s t i ca l errors. T h e fact t h a t the t w o values p x and p n are near ly equal confirms th i s conclusion. I f dos imetr ic inaccuracies were responsible for t h e increased fluctuations one w o u l d expect t h i s influence t o be di f ferent for the t w o di f ferent r a d i a t i o n types . I t appears l i k e l y , therefore, t h a t the smal l increase of the observed s ta t i s t i ca l fluctuations over the theoret ica l values is due to other systematic factors t h a t influence the s u r v i v a l p r o b a b i l i t y i n the i n d i v i d u a l v ia ls . W e cannot a t present i d e n t i f y these factors , b u t t h e y are of m i n o r influence, and i n t h e next section i t w i l l be seen t h a t the fluctuations f r o m experiment to exper iment are considerably more i m p o r t a n t .

Fluctuations of Sensitivity between Experiments

T h e findings described above p e r m i t no conclusions on t h e extent of systematic fluctuations between di f ferent experiments. However , one can assess such syste-

R B E O F N E U T R O N S 175

T A B L E I

Comparison of the Observed Total x 2 for the Pooled Data from All X - R a y Experiments with the 9 5 % Value, X952

Absorbed dose (rad) Degrees of freedom

0 275.5 37.1

139.5 356.9 240.3 349.9 821.4

6.94

120.7 40.1 53.1 50.7 54.3 53.1 67.2 12.6

97 27 38 36 39 38 50

6

200 400 600 800

1,000 1,200 1,500

m a t i c fluctuations b y d e t e r m i n i n g the x2

values for the pooled da ta f r o m a l l successive experiments a t each i n d i v i d u a l X - r a y dose. Accord ing ly , a l l data a t each i n d i v i d u a l va lue of the absorbed dose of X rays were p u t i n t o the same g r o u p , so t h a t the obta ined x 2-value represents the deviat ions f r o m the common mean v a l u e . T h i s is i n contrast t o the analysis i n the preceding section where t h e X 2 - va lues were re lated t o the i n d i v i d u a l averages of the s u r v i v a l rates for each q u a d r u p l e t of v ia ls t h a t results i n one data p o i n t . Tab le I contains the results t h a t are obta ined i f a l l s u r v i v a l rates f r o m the di f ferent experiments a t each i n d i v i d u a l va lue of absorbed dose are combined. One finds t h a t i n the m a j o r i t y of t h e cases, and especially a t larger absorbed doses, the s ta t i s t i ca l fluctuations between di f ferent experiments are considerably larger t h a n theoret i ca l ly expected. F i g u r e 1 i l lustrates th i s fact . I t is a superposit ion of a l l i n d i v i d u a l data po ints

HAMSTER CELLS 250kV X-RAYS

.1 -o <

.001 0 500 1000 1500

ABSORBED DOSE (rod)

F I G . 1. Superposition of survival rates of Chinese hamster cells obtained in 10 different X - r a y experiments over a period of several months. T h e data correspond to X - r a y survival curves pre­sented in the earlier article ( ! ) . E a c h curve is normalized relative to its own controls.

176 K E L L E R E R E T AL.

T A B L E I I

Spearman Rank Order Correlation Coefficient for Surv iva l Rates i n E i g h t Separate Surv iva l Curves*

Absorbed dose (rad)

0 400 600 800 1,000

400 0.66 600 0.38 0.83 800 0.50 0.73 0.90

1,000 0.39 0.86 0.86 0.80 1,200 0.50 0.92 0.83 0.73 0.97

a Each coefficient measures the correlation of the two survival rates at two doses for a l l X - r a y experiments. Except i n the comparisons invo lv ing controls al l values exceed the 9 5 % confidence level of 0.643. This implies t h a t w i t h i n one experiment surv ival rates at a l l doses tend to deviate i n the same direction. Only those X - r a y experiments have been used that in addit ion to the contro l data have data at 400, 600, 800, and 1000 rad.

obta ined i n the var ious X - r a y experiments. I n v i e w of the large n u m b e r of p o i n t s no a t t e m p t is made to i d e n t i f y po ints belonging to the same curves ; the separate curves have been presented i n the earlier p u b l i c a t i o n (1). T h e theoret i ca l s t a n d a r d dev ia t i on for the i n d i v i d u a l po ints is t y p i c a l l y ±4%; the ac tua l dev iat ions arc obviously m u c h larger. E v e n i n th i s s impl i f i ed f o r m the p l o t therefore d e m o n ­strates t h a t t h e fluctuations between experiments exceed great ly the r a n d o m f luctuat ions due t o the finite number of colonies. T h e results c on f i rm the necessity t o derive the X - r a y s u r v i v a l curve r e p e a t e d ^ i n successive experiments . O n l y i n t h i s w a y can rel iable comparisons between n e u t r o n s u r v i v a l curves a n d X - r a y s u r v i v a l curves be achieved. T h e findings also make i t clear t h a t parameters of a s u r v i v a l curve cannot always be considered as absolute, constant characterist ics of a cell l ine .

T o ob ta in an unders tanding of the n a t u r e of the observed f luc tuat ions , one m a y ask whether the differences of s u r v i v a l rates i n t w o experiments a t d i f ferent doses are correlated. T h i s question has been analyzed on the basis of the Spear­m a n r a n k corre lat ion coefficient [see, for example, ( # ) ] for the d a t a f r o m a l l experiments at each pa ir of absorbed doses. T h e result is t h a t there is a h i g h l y s ignif icant corre lat ion for a l l pairs of absorbed doses. However , no s igni f i cant correlation is f o u n d between the differences a t a g iven absorbed dose a n d the differences between the contro l groups. I t appears therefore t h a t the s ta t i s t i ca l f luctuat ions are n o t l i n k e d to fluctuation of the p l a t i n g efficiency. N u m e r i c a l results are g iven i n Tab le I I .

These findings i m p l y t h a t systematic f luc tuat ions of t h e r a d i a t i o n s e n s i t i v i t y of the cells occur between i n d i v i d u a l experiments. I t is n o t clear whether these differences are due t o the fact t h a t the cells for d i f ferent experiments are taken f r o m different stock solutions, or whether they are due t o other factors , such as t r y p s i n a t i o n , t h a t m a y n o t be complete ly contro l led . Est imates of the magn i tude of sens i t iv i ty f luctuat ions are der ived i n the next section.

R B E O F N E U T R O N S 177

Idealized Survival Carve for X rays

I n v i ew of the fluctuations of s u r v i v a l rates between experiments i t is appro ­pr ia te t o relate each n e u t r o n s u r v i v a l curve t o the s imultaneously established X - r a y curve . T h i s approach is fo l lowed i n the next section However , i t is also of interest t o determine an idealized X - r a y s u r v i v a l curve. Var ious ways t o arr ive at such an idealized curve could be considered. One, and perhaps the simplest, way w o u l d be to average a l l s u r v i v a l rates a t each dose. However , th i s procedure is questionable because i t is n o t clear w h a t t y p e of average w o u l d have t o be employed. One m i g h t use an a r i t h m e t i c or a geometric m e a n ; since the fluctuations are subs tant ia l these averages do n o t coincide.

There are various a l ternat ives t o the unsat is factory averaging of s u r v i v a l rates. However , any m e t h o d m u s t be a r b i t r a r y insofar as i t requires assumptions on the nature of the systematic fluctuations. As long as these fluctuations are i n c o m ­plete ly understood one can on ly achieve an approx imate t r e a t m e n t . I n t h e fo l l owing such a t r e a t m e n t is a t t e m p t e d . I t is based on the s i m p l i f y i n g assumption t h a t the var ia t i ons between separate experiments are due t o a change i n sensi­t i v i t y of the cells t h a t corresponds t o a s imple dose-modi fy ing factor . One m u s t then search for those correct ion factors t h a t , appl ied t o the i n d i v i d u a l exper i ­ments, lead t o a set of X - r a y s u r v i v a l curves t h a t are i n closest agreement. A f t e r establishing these factors one m a y a p p l y t h e m t o the n e u t r o n s u r v i v a l curves t h a t have been established s imultaneous ly w i t h t h e i n d i v i d u a l X - r a y s u r v i v a l curves. T h i s , too, is t e n t a t i v e insofar as i t is n o t cer ta in t h a t the same dose-m o d i f y i n g factor should app ly to di f ferent r a d i a t i o n qual i t ies . However , i n the absence of be t ter i n f o r m a t i o n the t r e a t m e n t is at least a useful a p p r o x i m a t i o n .

The dose-modi fy ing factors can be obta ined b y a least-squares m e t h o d appl ied to the i n d i v i d u a l s u r v i v a l curves. However , such a s tat i s t i ca l procedure is re la ­t i v e l y compl icated and therefore i n the f o l l ow ing we present a s impler m e t h o d for the analysis of the results. T h i s m e t h o d is based on the de te rminat i on of the mean i n a c t i v a t i o n dose, D, for each of the s u r v i v a l curves and on the comparison of the resu l t ing values w i t h the i r average for a l l X - r a y s u r v i v a l curves.

The mean i n a c t i v a t i o n dose is a useful parameter of the s u r v i v a l curve because, unl ike the i n i t i a l slope or the parameter Do, i t measures the overal l reaction of the cell popu la t i on over the whole dose range. I t is the s ta t i s t i ca l mean t h a t belongs to the s u r v i v a l curve i f the l a t t e r is considered as the d i s t r i b u t i o n of s u r v i v a l probabi l i t ies as a f u n c t i o n of absorbed dose. T h e de f in i t ion of D is [ f o r a more detai led discussion see (4) J

(3)

B y p a r t i a l i n t e g r a t i o n one finds t h a t th is is equal to

(4)

178 K I v L L E J t E U E T AL.

T A B L E I I I

The Mean Inac t i va t i on Dose, D, for the I n d i v i d u a l X - R a y Surv iva l Curves 5

Neutron energy used simultaneously

(MeV)

Mean Inactivation dose, D, for the X-ray survival curve

{rad)

Dose-modifying factor f

50 35 15

6 2

44.2 447 466 416 424 437 396 394 391 400

0.95 0.94 0.90 1.01 0.99 0.96 1.06 1.065 1.075 1.05

1, 0.66 0.43 0.34 0.22 0.11

J5 A = 4 2 2 ± 2 3

a The f a c t o r / i s the rat io of the average value /3A of the mean inact ivat ion dose and the mean i n ­act ivat ion dose D obtained i n an experiment; this factor can be considered as a dose-modifying factor t h a t expresses fluctuations i n sensit ivity.

Accord ing t o th is f o r m u l a the mean i n a c t i v a t i o n dose, D, is equal to the area under the s u r v i v a l curve i n l inear representat ion. T h i s area has been de termined for a l l X - r a y s u r v i v a l curves. T h e resu l t ing values are l i s ted i n Tab le I I I . T h e average of the values for t h e 10 separate s u r v i v a l curves is 422 r a d , and t h e s tandard dev ia t i on is 23 r a d , i.e., 5 % .

Other parameters of these curves, such as the ex t rapo la t i on n u m b e r or t h e pseudothreshold number , have been quoted i n an earlier ar t i c le (5); t h e y e x h i b i t subs tant ia l ly larger fluctuations t h a n D. T h e parameter D is therefore m o r e meaning fu l . However , i t m u s t be noted t h a t the values D are subject t o i n t e r ­po la t i on errors i n t h e d e t e r m i n a t i o n of the area under the s u r v i v a l curve.

One can use the values D and t h e i r average, DA, t o rescale the i n d i v i d u a l sur ­v i v a l curves b y a dose-modi fy ing factor . T h e dose-modi fy ing factor for a par ­t i c u l a r experiment is / = T)AlT)) where D is the mean i n a c t i v a t i o n dose for t h i s experiment . T h e result is g iven i n F i g . 2 ; here each p o i n t is p l o t t e d a t the dose f-D. where D is the absorbed dose a t w h i c h i t has been obta ined , and / is t h e dose-modifying factor l i s ted i n Tab le I I I .

Some fluctuations of the s u r v i v a l rates between experiments r e m a i n . T h i s is t o be expected, since t h e correct ion procedure is o n l y an a p p r o x i m a t i o n . B u t the graph defines the idealized f o r m of the X - r a y s u r v i v a l curve m u c h more closely t h a n the unad justed superposit ion of the da ta i n F i g . 1.

I t is of interest t o compare the idealized s u r v i v a l curve for X rays w i t h the l i n e a r - q u a d r a t i c equat ion

for the co lony - forming a b i l i t y , S(D), as a f u n c t i o n of absorbed dose, Z>. T h e equat ion has earlier been appl ied b y Sinclair (6) a n d microdos imetr i c analysis

S(D) = e x p ( - « Z > - ßD2) (5)

J I B E O F N E U T R O N S 179

.00! 1 : : : : I : : : : I ; : : : : 0 500 1000 1500

ABSORBED DOSE (rod)

F I G . 2. The data f r o m F ig . 1 rescaled w i t h the factors / i n Table I I I that account for fluctuations of the sensit ivity of the cells between ind iv idua l experiments. The solid curve corresponds to E q . (5) w i t h a = 0.99 X 10~3 r a d " 1 , ß = 2.07 X 10~ 6 r a d " 2 .

has l e d to the conclusion (7) t h a t i t corresponds to a p r o p o r t i o n a l i t y of cellular damage to the square of specific energy i n sensitive sites of the cell w i t h d i m e n ­sions of fract ions of a micrometer or more. I n th is i n t e r p r e t a t i o n the l inear t e r m results f r o m the i n t e r a c t i o n of sublcsions formed i n the same part i c le t r a c k whi le the quadrat i c t e r m results f r o m i n t e r a c t i o n of sublcsions formed b y separate charged partic les .

I f E q . (5) is v a l i d for synchronous cell populat ions , then i t cannot be s t r i c t l y v a l i d for a m i x e d cell p o p u l a t i o n . As Gillespie et at. (9) p o i n t out , the deviat ions f r o m E q . (5) are r e l a t i v e l y smal l for an exponent ia l ly g r o w i n g popu la t i on . Nevertheless they can be read i ly detected i n the v e r y extensive X - r a y data represented i n F i g . 2. I n fact , a s tat i s t i ca l test of the overal l f i t of the data to the l i n e a r - q u a d r a t i c equat ion results i n re ject ion of the f i t . However , one can achieve a close f i t of the d a t a i f one disregards the range of lowest s u r v i v a l where the influence of the less sensitive mo ie ty of t h e cells causes the greatest d i s t o r t i o n . The sol id l ine i n F i g . 2 is the result of such a p a r t i a l f i t ; i t corresponds t o the parameters a = 0.99 X 10" 3 r a d " 1 and ß = 2.07 X 1 0 " 6 r a d " 2 . Since these est i ­mates are the result of on ly a p a r t i a l f i t , and since i t is d i f f i cu l t to assess the v a l i d i t y of the rescaling t h a t has been appl ied to the data , no confidence l i m i t s are g iven for a and ß.

R E L A T I V E B I O L O G I C A L E F F E C T I V E N E S S O F N E U T R O N S

Analysis of the Survival Curves

S u r v i v a l curves have been established for nine di f ferent n e u t r o n energies and for t h e broad energy d i s t r ibut i ons at the Texas A & M Var iab le Energy Cyc l o t ron

ISO K E L L E R E R E T AL.

T A H L 10 I V

Least-Squares .Estimates of the Parameters a and ß in E q . (5) for the Neutron Survival Curves and the Modi f ied Parameters a and ß' Obtained on the

Basis of the M o d i f y i n g Factors / Given in Table I I I

Neutron energy (MeV) (10-* rad~l)

a ß (10-' rar / - 2 ) (10~* rad-1)

a ß' (10-" rad'2)

50 35 15

6

2.65 3.8 3.45 4.55 8.1 9.45

10.0 J 2.8 12.8 12.2

8.6

2.91 2.9 0.8 0.7 1.7 1.7 6.8 6.0

12.1 9.6 8.7

2.79 4.04 3.83 4.51 8.18 9.84

10.42 12.08 12.02 11.35 8.19

3.22 3.28 0.99 0.69 1.73 1.84 7.37 5.34

10.67 8.31 7.89

2 1 0.66 0.43 0.34 0.22 0.11

( T A M V E C ) and at the N a v a l Research L a b o r a t o r y ( N R L ) C y c l o t r o n . T h e da ta have been presented i n the preceding p u b l i c a t i o n (1) and a comparison w i t h earlier invest igat ions of the R B E of neutrons (10-16) has been made. I n the f o l l owing , a more rigorous q u a n t i t a t i v e analysis of the n e u t r o n da ta is per ­formed . I n the present section the n e u t r o n s u r v i v a l curves arc re lated to the l i n e a r - q u a d r a t i c equat ion . I n the f o l l ow ing section t h e results are compared to the X - r a y data .

For a l l n e u t r o n s u r v i v a l curves a least-squares f i t to E q . (5) has been per formed. As stated i n the preceding section the l i n e a r - q u a d r a t i c equat ion cannot be s t r i c t l y v a l i d for nonsynchronized populat ions . The x 2-test indicates signif icant deviat ions f r o m the equat ion for the da ta obta ined w i t h 15 and w i t h 6 M e V neutrons, b u t n o t for the da ta obta ined a t other n e u t r o n energies. As an a l t e r n a t i v e to the l i n e a r - q u a d r a t i c equat ion one could use an a n a l y t i c a l expression w i t h three free parameters. However , such parameters w o u l d have l i t t l e b iophysica l meaning, and i t was therefore fe l t t h a t the simple t r e a t m e n t is to be preferred even i f i t is on ly an a p p r o x i m a t i o n . The least-squares estimates of t h e coefficients a and ß are l isted i n Tab le I V . The f i t has been per formed w i t h proper w e i g h t i n g factors of the i n d i v i d u a l observed points according to the i r observed variance . T h e estimates of a and ß together w i t h the i r j o i n t e l l ip t i ca l regions of v a r i a t i o n are depicted i n F i g . 3. T o o b t a i n greater c l a r i t y of th is g raph the ellipses have been d r a w n w i t h axes hal f the size of those for the 9 5 % significance level . T h e ellipses can therefore be considered as areas of s tandard dev ia t i on . Deta i l s of the s tat is t i ca l analysis have been described earlier (#) .

The est imated values of a and ß for X rays are inserted i n F i g . 3 for comparison. As po inted out i n the preceding section no confidence region has been derived for these values ; however, the data for X rays are m u c h more extensive t h a n the values for neutrons and i t can therefore be assumed t h a t t h e f rac t i ona l u n -

R B E O F N E U T R O N S 181

O 5.

COEFFICIENTS c*. AND ß FOR NEUTRON IRRADIATION OF HAMSTER CELLS

.34

50

X RAYS A

15

35 .66

(I0"3 rad-)

F I G . 3. Least-squares estimates of the linear and the quadratic coefficient in E q . (5) for the survival curves obtained w i t h neutrons. T h e shaded ellipses are the j o i n t regions of standard deviations of the two coefficients. The ellipses for the 9 5 % confidence l i m i t are double the size of the ellipses shown i n the graph. The isolated dot marks the estimated values of the parameters a and ß for X rays. The numbers refer to the neutron energy i n M e V .

c e r t a i n t y of the coefficients a and ß for X rays is considerably smaller t h a n t h a t for neutrons .

T h e d iagram of the regions of s tandard dev ia t i on of the l inear a n d quadrat i c coefficients at the di f ferent n e u t r o n energies m a y be misleading insofar as the ellipses t h a t belong to larger values of the coefficients, i.e., t o the more effective n e u t r o n energies, arc considerably larger. However , th is is a consequence of t h e l i n e a r i t y of the d iagram. T h e re lat ive error is p r o p o r t i o n a l not to the absolute size of an ellipse b u t t o the ra t i o of i ts axes and the coordinates of i ts center. I t is n o t convenient to choose a l ogar i thmic representat ion because the ellipses w o u l d then be d i s tor ted to a compl icated shape.

A second p o i n t should be noted i n connection w i t h the p l o t of the confidence regions of the coefficients. T h i s is the fact t h a t the s tat i s t i ca l analysis does n o t account for the systematic f luctuat ions between experiments t h a t have been discussed i n the earlier sections of th is paper. For X rays the fluctuations between experiments were described b y dose-modi fy ing factors w i t h a s tandard dev ia t i on of 5% f r o m u n i t y . For an a p p r o x i m a t i v e t r e a t m e n t one m a y assume t h a t the systematic fluctuations arc the same i n the case of the n e u t r o n i rrad iat ions . One can t h e n app ly the correct ion factors obta ined for X mys (see Tab le I I I ) to the n e u t r o n data . I n t h i s w a y the modi f ied coefficients i n t h e last t w o columns of T a b l e I V are obta ined . T h e adjusted value of the l inear coefficient is a / / ; the ad justed value of the quadrat i c coefficient is ß/p. T h e corrected coefficients are used i n F ig . 4, i n w h i c h theoret i ca l curves for the di f ferent n e u t r o n energies are compi led . The X - r a y s u r v i v a l curve f r o m F i g . 2 is added as a broken l ine for comparison. The o r ig ina l d a t a po ints are n o t inserted i n th i s f i gure ; they have been presented i n separate plots i n the preceding p u b l i c a t i o n ( i ) .

182 K E L L E R E I ! E T AL.

ABSORBED DOSE (rod)

F I G . 4. Theoretical approximation of the survival curves obtained w i t h different neutron energies according to the values a and ß' i n Table I V . The theoretical survival curve for X rays from F i g . 2 is inserted for comparison.

F r o m F i g . 4 one obtains the dependence of the R B E of neutrons on n e u t r o n energy a t dif ferent effect levels. T h e results, depicted i n F i g . 5, can be compared t o t h e analogous p l o t (1) t h a t has been obta ined d i re c t l y f r o m t h e data w i t h o u t s ta t i s t i ca l analysis. Confidence l i m i t s for the values of R B E are n o t inserted b u t t h e m a g n i t u d e of the s tat i s t i ca l errors can be est imated f r o m F i g . 3. Confidence i n t e r v a l s for the R B E are obta ined f r o m the nonparametr i c anah-sis of R B E t h a t is presented below.

T h e s tat is t i ca l uncertaint ies i n the coefficients a and ß are, as seen i n F i g . 3,

subs tant ia l . However , i t is apparent t h a t the va lue of a reaches a m a x i m u m at n e u t r o n energies between 200 and 400 k e V and t h a t i t decreases a t higher a n d a t l ower energies. A second observat ion is t h a t the quadrat i c component increases a t n e u t r o n energies below 1 M e V . I n v i ew of the s ta t i s t i ca l uncerta int ies i t is

I { B E O F N E U T R O N S 183

O* , , • , • • . • i • • ' < • — .1 I 10 100

NEUTRON ENERGY (MeV)

F I G . 5. Dependence of the R B E of neutrons on neutron energy according to the theoretical curves i n F ig . 4. The ind iv idua l curves belong, i n the order of decreasing R B E values, to the surv iva l levels 0.8, 0.37, 0.1, 0.01, and 0.001. D a t a are plotted at 35 and 50 M e V ; however, these are the m a x i m u m energies for broad energy spectra.

di f f i cu l t to q u a n t i f y th i s increase; accordingly the est imated values i n T a b l e I V m u s t be considered as t e n t a t i v e . However , even the q u a l i t a t i v e f ind ing is of con ­siderable i m p o r t a n c e ; i t corresponds to earlier observations [see (17)2 t h a t t h e R B E of neutrons remains larger t h a n 1 at h i g h doses.

As p o i n t e d ou t i n the earlier art ic le (1) the absorbed-dose rates were smallest and t h e i r r a d i a t i o n t imes were largest for the lowest n e u t r o n energies. T h i s m a y have l ed to some recovery of sublethal damage and m a y therefore have caused a decrease of the values of ß. One m u s t therefore assume t h a t the ac tua l values of ß at the lowest n e u t r o n energies m a y be even higher t h a n the observed values.

Nonparametric Determination of the RBE of Neutrons

T h e confidence l i m i t s of the values of R B E of neutrons as a f u n c t i o n of n e u t r o n dose can be obta ined b y the nonparametr i c m e t h o d t h a t has been described earlier (ß). T h i s m e t h o d is based on the d irect comparison of pairs of da ta p o i n t s for X rays and neutrons obta ined i n the same experiment . F igure 6 represents the results. T h e v e r t i c a l bars i n these graphs cover those ranges of R B E t h a t , according to the results of the nonparametr i c comparison of an X - r a y dose w i t h a n e u t r o n dose, can be excluded w i t h s tat i s t i ca l c e r t a i n t y exceeding 9 5 % . T h e wedges indicate t h a t , on the basis of the comparison, the R B E should be h igher or lower, b u t t h a t th i s conclusion is n o t s ignif icant a t the 9 5 % level .

I t can be concluded f r o m these results t h a t the dependence of the R B E on t h e n e u t r o n dose is i n a l l cases consistent w i t h the assumption (see (?')) t h a t the R B E of neutrons is inversely p r o p o r t i o n a l to the square roo t of the n e u t r o n dose i n a n i n t e r m e d i a t e dose range, whi le i t reaches an asympto t i c value at h igher doses t h a t ma} ' a t least i n some cases be larger t h a n 1. I t is also apparent t h a t t h e s t a t i s t i c a l accuracy is n o t sufficient to determine the m a x i m u m value of R B E t h a t can be reached a t l ow n e u t r o n doses. T h i s d i f f i cu l ty is inherent i n the exper i ­m e n t a l technique, since t h e s tat i s t i ca l accuracy of cel lular s u r v i v a l curves a t v e r y l o w doses is l i m i t e d b y the unavoidable fluctuations of p l a t i n g efficiency.

T h e nonparametr i c analysis is r igorous i n the sense t h a t i t is free f r o m assump­t i ons concerning models for the s u r v i v a l curves. I t s l i m i t a t i o n i n t h e present contex t is t h a t i t does n o t take i n t o account the i n f o r m a t i o n gained f r o m t h e r e -

184 K E L L E R E R E T AL.

10 20 50 200 100010 20 50 200 1000 NEUTRON DOSE (rad)

F I G . G. The R B E of neutrons as a function of neutron energy. The vert ical bars cover those ranges of R B E that according to the result of the nonparametric statist ical analysis can be excluded w i t h statistical certainty exceeding 9 5 % . The wedges indicate results that are not significant on the 9 5 % level. The solid curves are the theoretical relations according to the values a and ß' in Table I V and the value a = 0.99 X 10~3 r a d - 1 and ß = 2.07 X 10~ 6 r a d " 2 for X rays. N o diagram is given for the 50 M e V neutron beam because the X - r a y data for this experiment are incomplete.

peated assessment of the s u r v i v a l curves for X rays. For th i s reason curves have been inserted i n t o the g raph t h a t correspond to the theoret ica l s u r v i v a l curves i n F i g . 5.

C O N C L U S I O N S

T h e s tat i s t i ca l f luctuat ions w i t h i n a scries of X - r a y s u r v i v a l curves for n o n -synchronized Chinese hamster cells have been examined, and an idealized s u r v i v a l curve for X rays has been derived. A n approx imate a n a l y t i c a l f o r m of th is sur­v i v a l curve is

r D / D \ 2-| S(D) = exp — ) , (6)

L 1001 \697 / J where the absorbed dose, £), is expressed i n rads. T h i s ideal ized s u r v i v a l curve for X rays is compared w i t h s u r v i v a l curves obta ined for a scries of di f ferent n e u t r o n energies.

I t has been f o u n d t h a t the s tat i s t i ca l fluctuations of s u r v i v a l rates w i t h i n a g iven experiment are on ly s l i g h t l y larger t h a n the theoret i ca l fluctuations t h a t have to be expected due t o the finite number of s u r v i v i n g colonies. However , the

R B E O F N E U T R O N S 185

f luctuat ions of s u r v i v a l rates between separate experiments exceed the theoret ica l fluctuations subs tant ia l l y . I n a first a p p r o x i m a t i o n one can consider the fluctua­tions as the resul t of s e n s i t i v i t y fluctuations t h a t express themselves i n a constant dose-modifying factor for each exper iment . The s tandard dev ia t i on of th i s m o d i f y ­ing factor f r o m u n i t y is 5 % . Such dose-modi fy ing factors m a } ' appear to be re la ­t i v e l y ins ign i f i cant ; however, as seen f r o m the comparison of Figs. 1 and 2, t h e y can correspond t o substant ia l differences i n s u r v i v a l a t higher doses.

A least-squares f i t t o the l i n e a r - q u a d r a t i c equat ion has been per formed for the s u r v i v a l curves obta ined a t the var ious n e u t r o n energies. I n a d d i t i o n the regions of the j o i n t s tandard errors of the t w o parameters have been obta ined for the i n d i v i d u a l curves ; these regions are ellipses i n the plane of the t w o coefficients a and ß. T h e results con f i rm the observation t h a t neutrons are most effective a t energies between 200 and 400 keV . T h e values of R B E have been derived as a f u n c t i o n of n e u t r o n energy and of the absorbed dose of neutrons .

I t has been f o u n d t h a t the coefficient ß of the quadrat i c t e r m i n the absorbed dose is increased a t n e u t r o n energies below 1 M e V . T h i s finding is i m p o r t a n t for the i n t e r p r e t a t i o n of cel lular s u r v i v a l curves i n terms of microdos imetr ic data . A n earlier analysis of var ious effects of i on iz ing radiat ions on eukaryot i c cells (?) h a d led to the conclusion t h a t the p r i m a r y cellular damage, e, depends on the absorbed dose according t o t h e l i n e a r - q u a d r a t i c equat ion

e(D) = i ( f D + Z>2). (7)

I t has been shown t h a t th i s equat ion holds i f the cellular effect is p r o p o r t i o n a l to t h e square of the specific energy, z, produced i n a sensitive site of the cell. T h e quadrat i c dependence on energy deposit ion i n the cell results i f pairs of sublesions combine t o produce l e t h a l damage. I t has f u r t h e r m o r e been shown t h a t the q u a n ­t i t y f can be understood as the mean specific energy produced i n the sensitive site b}'- a single charged part i c le . T h e value of f is considerably larger for the more densely i on iz ing neutrons t h a n for X r a y s ; i n t h e or ig ina l analysis i t has therefore been assumed t h a t the increased I I B E of neutrons is solely due t o the larger l inear component i n the l inear- quadrat i c equat ion . F r o m th is assumption i t w o u l d fo l low t h a t a t h igh doses, where the quadrat i c component dominates b o t h for X rays and neutrons , the R B I ] of neutrons should approach the value 1. There have been several observations, however, t h a t indicate t h a t the asymptot i c va lue of R B E of neutrons at h i g h doses is larger t h a n 1. As po inted out b y Rossi (17) t h i s w o u l d i m p l y t h a t the coefficient, fc, i n E q . (6), w h i c h depends on the efficiency of the p roduc t i on of sublesions, is larger for neutrons t h a n for X rays . T h e present results conf i rm th is conclusion for neutrons below 1 M e V , i.e., for those neutrons t h a t produce the most densely i on iz ing p r o t o n recoils.

T h e l i n e a r - q u a d r a t i c equat ion for the s u r v i v a l curves m u s t be considered as an a p p r o x i m a t i o n , p a r t i c u l a r l y since the experiments have been per formed w i t h nonsynchronized cultures . For th i s purpose a more d irec t nonparametr i c d e t e r m i ­n a t i o n of the dependence of n e u t r o n R B E on absorbed dose has been performed. T h e results are consistent w i t h the conclusions based on t h e a n a l y t i c a l m o d e l ;

1 8 6 K E L L E R E I I ET AL.

however, t h e y demonstrate t h a t the present experiments give no de f in i t ive exper i ­m e n t a l evidence concerning the m a x i m u m value of R B E at l ow doses.

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