BIOLOGICAL EFFECTIVENESS O F ALPHA PARTICLES A S A
FUNCTION OF ION CONCENTRATION PRODUCED
I N THEIR PATHS
R. E. ZIRKLE1
(Eldridge Reeves Johnson Foundation for Afedical Physics, Universitg of Pennsylvania)
It is an old and very generally accepted view (e.g., Aschkinass and
Caspari, 1901; Redfield and Bright, 19'2'4; Packard, 1931) that the biological effects of x-rays, cathode rays, and radiations from radio-active
substances are associated in some way with the ionization they produce
in the living material. However, there is as yet no general agreement
concerning the exact nature of the part played by the ions.2 I n particular, there is still wide divergence of opinion concerning the existence
of any effect due to distribution. of the ions in the irradiated tissue.
This question is especially controversial among workers with x-rays and
gamma rays, for the much discussed factor of wavelength, if existent,
must operate through differences in distribution of ions.s
In any discussion concerning distribution of ions it must be borne
in mind that the formation of ions is far from uniform throughout the
irradiated volume of tissue. The ions are produced in the paths of the
ionizing particles (electrons, alpha particles, o r other bodies) and can
exist as such for only a fraction of a second. At any given instant, the
total volume of the ionization paths is only a small fraction of the total
irradiated volume. Hence, it is essential to distinguish sharply between
average ion concentration and ion concentration in the paths. This is
especially true when the ionizing particles are of relatively low velocity
and produce relatively high ion concentrations in their paths. The
question of an ion distribution factor may then be put as follows:
Has a given intensity of irradiation, expressed as the number of ions
produced per unit time per unit irradiated volume, the same effectiveness when the ions are produced in relatively few units of path with
relatively high production of ions per unit path as when the ions are
produced in relatively many units of path with relatively low production of ions per unit path?
It is evident that, in order to compare the effectiveness of any two
types of ion distribution, one must be able (a,) t o make comparable
National Research Fellow in the Biological Sciences.
Various speculations concerning this point have been summarized by Packard (1931).
8 It is apsumed here that careful control is kept 011 factors such as absorption and scattcriiig, which in 8ome cases might result in the productiou of different numbers of ions in the
tissue when a given number of r-units is produced by different wavelengths. The literature
concerning the wavelength factor has been reviewed by Packard (1931, 1932) and by Failla
(1933).
558
1
2
BIOLOGICAL E F F E C T I V E N E S S O F A L P H A PARTICLES
559
measurements of the ionization per unit volume produced under the
two conditions. Moreover, if any quantitative relationships are to be
derived, one must know ( b ) the distribution of the ions under the two
conditions, and such knowledge must include (1) the relative total
lengths of ionization paths in unit volume, (2) the relative numbers of
ions per unit path, and preferably (3) the variation in number of ions
per unit path under each condition. When beta, gamma, x, o r cathode
rays are used, the paths of the ionizing particles are so non-uniform in
length and direction, and secondary phenomena are so complicated, that
the determination of any of the quantities mentioned under b i s prac-
Pos/hom o f mc/eus
FIG. 1. FULL-LINE
WRVE:RELATIONBETWEEN IONIZATION
PER UNIT PATHOF A BEAMOF
ALPHA RAYS PROM POLONIUM
AND DISTANCEFROM THE ENDOF THE PATH. DASH-LINE
CURVE: SAME
EXCEPT
THAT IONIZATION
IS RAISEDTO THE FIVEHALVES
POWER
Circles 1 to 7 are drawn below the various portions of the path from which the nuclei
(spheres 10 p i n diameter) absorbed energy. (Ionization curve adapted from Curie and
Behounek, J. phys. radium, 7 : 125, 1926.)
tically impossible. The attainment of a is not impossible but presents
serious technical difficulties. It is hence plain that the effect of ion
distribution cannot, f o r the present a t least, be satisfactorily investigated with these radiations.
On the other hand, every requirement of cc and b can be met by the
use of alpha particles from a source consisting of a single radio-active
substance, such as polonium. The number of alpha particles emitted
in unit time by such a source can be counted directly and independently
of ionization measurements and varies with time according to a simple
exponential law. Moreover, the paths of the particles are straight and
560
R. E. ZIRKLE
nearly uniform in length. Hence, it is easy a t any time to calculate
the number of alpha particle paths which traverse any given small
volume a t a given distance from the source. Thus it is possible to
satisfy condition b 1 above. The number of ions produced per linear
unit of path is not the same all along the path, but varies in a characteristic and well known way with the distance from the end of the path
(Fig. 1, full line curve). This makes it possible to meet conditions a,
b 2, and b 3. At the same time this variation in ion production along
the path makes feasible the ‘study of effects of ion distribution. If one
uses a biological object which is considerably less in diameter than the
total length of path, this object can be given any certain dose of ions
either by a relatively small number of alpha particles which traverse
it when they are near the ends of their paths, where the number of ions
produced per unit path is relatively high, o r by a relatively large number of particles which pass through it near the beginning of their paths,
where the ionization per unit path is relatively low. If, under these
two conditions, the degree of biological effect obtained is the same, it is
evident that distribution of ions is not a factor and that the total number of ions produced in the biological object is the decisive factor. I n
other words, the biological effectiveness per alpha particle under the
two conditions is simply proportional to the number of ions produced
per unit path. On the other hand, if the degree of biological effect
produced by a given total number of ions is not the same under the
two conditions, then obviously distribution must be a factor, and its
effect must be due to the difference in ionization per unit path. Likewise the biological effectiveness per alpha particle must be other than
a linear function of the ionization per unit path.
Throughout this paper quantitative relationships will be expressed
in terms of ionization per unit length of path, since accurate physical
measurements of this variable are available. It is not possible to state
that the radius of the ionized path is exactly uniform throughout the
length of the path, but cloud track photographs indicate that it is approximately so. Hence, any relationship which is derived for ionization
per unit length of path will hold approximately f o r the ion concentration
produced in the path.
PROCEDURE
The general method, as indicated above, “as to determine the relative numbers of alpha particles required to produce a given degree of
effect when a small biological object is traversed by particles ( a ) near
the ends of their paths, where the ionization is high (Fig. l ) ,( b ) near
the beginnings of their paths, where the ionization is low, and (c) at
various intermediate parts of the paths. The biological object used
was the nucleus of the spore of the fern Pteris Zongifolia. This body is
a sphere 10 p in diameter, whereas the total length of the alpha particle
path is 32 p in tissue. Seven positions of the nucleus along the path
BIOLOGICAL EFFECTIVENESS OF A L P H A PARTICLES
561.
were investigated. These positions are indicated in Fig. 1by the seven
circles drawn to the same scale as the abscissae for the ionization curve.
F o r each of these nuclear positions, data for a complete survival-dosage
curve were obtained. The numbers of alpha particles required at the
various nuclear positions to reduce survival to any given degree were
then inversely proportional to the biological effectiveness per alpha
particle. The relative effectiveness per alpha particle a t the seven
nuclear positions could then be compared with the ionization per alpha
particle produced in the nucleus at the respective positions.
I n a recent paper (Zirkle, 1932) I have included descriptions of the
preparation and standardization of the polonium sources of alpha rays,
the morphology and normal germination of the fern spore, and the
three processes-eell division, chlorophyll development, and cracking
of the spore wall-whose degrees of inhibition are used as measures
of biological effect. Also in this paper it was shown that these germination activities of the fern spore a r e much more easily inhibited by
irradiation of a fraction of the cell containing the nucleus than by
irradiation of an equal volume lacking this structure. Although a
highly accurate calculation is impracticable, it seems certain that, when
the nucleus is in the irradiated volume, at least 95 per cent and probably more of the inhibiting action is due t o ionization of nuclear material even though the total irradiated volume is at least Seven times the
volume of the nucleus. It is, therefore, justifiable in the present paper
to disregard extranuclear ionization and deal only with nuclear ionization.
The nucleus of the fern spore is eccentric and directly adjacent t o a
Y-shaped set of wall sutures which can readily be identified. This
eccentricity made it necessary, in experiments involving penetration, to
use only spores whose nuclei were oriented toward the source of radiation. Lots of ten rows, each of ten spores, were arranged on filter
paper by means of a needle mounted in one unit of a microdissection
apparatus. An attempt was made to orient each individual spore with
the nucleus upwards. This was successful in about 65 per cent of the
spores. The locations of those spores (about 35 per cent) whose nuclei
deviated more than 15 degrees from the upward position were recorded
after irradiation, and these were disregarded in compiling the experimental results.
The arrangement f o r irradiation is shown diagrammatically in Fig.
2. Several small rectangles ( A ) of filter paper, each bearing a lot of
100 spores, were arranged in a circle so that each was inclined 45 degrees from the horizontal. The circular source BB (diameter 4 mm.)
was supported at such a height that it was intersected a t its center by
the normals from the centers of all lots of spores. The distance from
Source t o spores was 21.2 mm. So great a distance was necessary to
reduce t o less than 0 . 2 ~the variation in penetration due t o the solid
angle subtended by the source about the spore. I n air considerable
non-uniformity of penetration would result from the emission of alpha
particles from parts of the source variously distant from the spores.
562
R. E. ZIRKLE
This was eliminated by putting the entire apparatus of Fig. 2 in an
air-tight vessel and reducing the stopping power of the air to a negligible amount by evacuation to a pressure less than 1mm. of Hg. Extensive control experiments proved that the air-dry spores suffered no
harm from exposure to this low pressure.
The adjustment of penetration into the spores was accomplished
entirely by the interposition of aluminum screens (S, Fig. 2) of suitable
thicknesses, these being held directly above and parallel to the various
lots of spores. The penetration of the rays which passed through each
screen was determined as follows. The residual range in air was
determined directly by the scintillation method (Rutherf ord, Chadwick,
and Ellis, 1930). The residual range in tissue was calculated by multiplication of the residual range in air by the ratio of the total range
in tissue (32 p ) to the total range in air (38.7 mm.). The penetration
into the protoplast was then obtained by subtracting 4 p (the thickness
/
/
/
/
/
A
FIff. 2.
ARRANGEMENT FOR IRRADIATION (SEE
TEXT)
of the spore wall) from the residual range in tissue. These data are
summarized in Table I, in which the screens are numbered 1 to 7 to
correspond to nuclear positions 1t o 7 in Fig. 1.
TABLE
I: Data Concerning Penetration of Alpha Rays after Traversing Aluminum Screens of Various
Thickness
Screen
Residual range
in air
Residual range
in tissue
Penetration into
protoplast
16.2 mm.
19.0 mm.
23.0 mm.
26.0 mm.
30.3 mm.
33.7 mm.
38.7 mm.
13.4 p
15.7 p
19.0 p
21.5 p
25.0 p
27.8 p
32.0 p
9.4 /.l
11.7 p
15.0 p
17.5 p
21.0 p
23.8 p
28.0 p
I have previously described (Zirkle, 1932) the general method of
calculating doses in terms of the number of alpha particles which strike
a protoplast of average size. The only essential modification due to
the present experimental arrangement is involved in the calculation of
the fraction of the total alpha particles emitted by the source per unit
BIOLOGICAL EFFECTIVENESS O F ALPHA PARTICLES
563
time which strikes unit area at the distance of the spore from the source.
The details of this calculation, for which I am indebted to Dr. A. L.
Patterson, will not be reproduced here. The result can be obtained
within one per cent of the precisely calculated value by the assumption
that the source is a point source.
The entire experimental procedure may be summarized as follows :
Lots of 100 spores each were prepared. Seven lots were placed in the
apparatus of Fig. 2 and covered with the seven screens of various thickness. The source was set in position, and the entire apparatus was
quickly placed in an air-tight vessel. The latter was evacuated rapidly,
and the irradiation was allowed to continue for the length of time
calculated to deliver the desired number of alpha particles per protoplast. Air was rapidly admitted into the vessel, and the source was
removed. Each spore was examined under the compound microscope,
and a record was kept of all whose nuclei were inclined more than fifteen
Jhou.5ands o f &pwhc/es p e r
5pore
FIQ.3. CURVESSHOWING
RELATIONBETWEEN SURVIVAL
(WITH CELL DIVISION AS CRITERION)
AND DOSAGE
IN ALPHAPARTICLES
PER SPORE
The curves numbered 1 to 7 correspond t o nuclear positions 1 to 7 respectively in Fig. 1.
To avoid crowding, the experimental points are omitted f o r curves 3, 5, and 6. Dosage in alpha
particles per iiucleus is 0.069 times alpha particles per spore.
degrees from the upward position. All spores were set to germinate
in their same positions. After ten days each spore was examined and
a record made as t o whether or not it had cracked, become green, or
accomplished cell division. (The entire procedure of irradiation was,
of course, repeated f o r other desired doses of alpha particles per
protoplast. )
RESULTS
I n Fig. 3 are shown the curves obtained by plotting, for each of the
nuclear positions, 1 to 7, the percentages of the spores which survive
i r r a d i a t i o n n e l l division being the criterion of survival-against dosage expressed in number of alpha particles striking an average protoplast. With the exception of positions 1 and 2, for which the data fit
the same curve, it is obvious that the effectiveness per alpha particle
in producing inhibition of division varies with the part of the alpha ray
564
R. E. ZIRKLE
path from which the ionizing energy is absorbed. Numerical comparisons of the effectiveness a t positions 1 to 7 may be made as follows:
Big. 3 shows that at position 1 (or 2) the number of alpha particles per
protoplast which reduces division to 50 per cent is 2400, while at
position 7 the number required t o produce the same degree of effect is
10,600. If the effectiveness per alpha particle at position 1 be taken
as unity, then the effectiveness per alpha particle at position 7 is
2400/10,600 or 0.23. The same result is obtained if one compares the
numbers of alpha particles per protoplast necessary at the two positions
to reduce division t o 70 per cent or any other fraction.* I n a similar
way the relative degrees of effectiveness per alpha particle at positions
3 to 6 inclusive are obtained. These are tabulated in the second column
of Table 11.
TABLE
11: Comparison of Observed Biological Effectiveness of Alpha Particles with Their Ionizing
Ability and with the Five Halves Power of Their Ionizing Ability
Observed relative biological effectiveness
Nuclear
position
1
Theoretical biological
effectiveness predicted
by assumption of:
I___
Division
2
1 .oo
1 .oo
.60
.46
.37
.3o
.23
Chlorophyll
development
Cracking
S
4
Average
6
1.oo
1 .oo
.58
.46
.38
.26
1 .oo
1 .oo
.62
.47
.34
.27
.23
1 .oo
1.oo
.60
.46
.36
-28
.23
.22
Linear
relationship
6
Five halves
power
relationship
7
1.00
1.00
1 .oo
.97
235
.61
.47
.35
.29
.23
.77
.68
.62
.58
_
Curves similar to those of Fig. 3 are also obtained when inhibition
of chlorophyll development, or of cracking of the spore wall, is taken
as the criterion of biological effect. It is not necessary to reproduce
these curves here, but they have been used, as just described for the
curves of Fig. 3, to obtain measures of biological effectiveness per alpha
particle at positions 1 to 7 . These figures are listed in the third and
fourth columns of Table 11. There is close mutual agreement between
these two columns and the second column. That is, no matter which
of the three criteria-division, chlorophyll development, or crackingis used, the observed biological effectiveness for each of positions 1to 7
is essentially the same. F o r any given position, the best experimental
value f o r general biological effectiveness should be the mean of the
three values obtained with the three different criteria. These averages
for positions 1 to 7 are listed in column 5.
4111 other words, the seven survival curves have the same shape but different slopes. The
seven slopes are inversely proportional t o the biological effectiveness per alpha particle a t the
seven respective nuclear positions.
BIOLOGICAL EFFECTIVENESS O F ALPHA PARTICLES
565
COMPARISON
OF BIOLOGICAL
EFFECTIVENESS
WITH IONIZATION
It is now desirable to attempt a correlation between the experimental
results and the ionization produced in the nucleus. An arbitrary value
for the ionization produced at position 5, f o r example, may be obtained
as follows: Since alpha particles which are retarded by screen 5 penetrate the protoplast 21.011. (Table 11),and since the nucleus is adjacent
to the spore wall and has a diameter of 10 11. (Zirkle, 1932), it is clear
that the general portion of the path effective in ionizing the nuclear
volume is represented by the portion of the area under the ionization
curve (Fig. 1) which is bounded by ordinates erected at 2 1 . 0 ~and
11.0 P. A sufficiently accurate integration of the total nuclear ionization may now be obtained in arbitrary units by dividing the nucleus
into slabs 1p thick by planes perpendicular to the direction of the rays
and summing the products of the volume of each slab by the ordinate
of the ionization curve at the position corresponding to the middle of
the slab. These arbitrary values for nuclear positions 1t o 7 are listed
in column 6 of Table 11. (Position 1 is arbitrarily taken as unity.)
If a given degree of biological effect were determined simply by total
number of ions produced in the nucleus, the biological effectiveness per
alpha particle should have these same values at positions 1to 7 . However, with the exception of position 2, the figures in columns 5 and 6
display no agreement, the discrepancy increasing as one proceeds down
the columns. It is therefore evident that the biological effectiveness
per alpha particle cannot be a linear function of the total number of
ions produced in the nucleus. It must be in some way dependent upon
the distribution of the ions in the path.
At this point arises the question: I s it possible t o find any simple
relationship between ionization and biological effectiveness 1 One such
relationship is represented by the equation B = kI", where B is biological effectiveness per alpha particle, k a proportionality constant, I
the ionization per unit path and n a number greater than unity. This
relationship has been tested f o r n = 2, n = 2.5, and n = 3, as follows.
A curve is derived from the ionization curve of Fig. 1 by raising the
ordinates t o the power of 9% being tested. (The resulting curve for
n =2.5 is the dash-line curve of Fig. 1.) The biological effectiveness
predicted by this relationship for each nuclear position may then be
integrated by the method just described f o r testing a possible linear
relationship between ionization and biological effect (in other words
f o r n= 1). The values calculated for B = kI"." are tabulated in the
last column of Table 11. The agreement between these figures and the
corresponding ones of column 5 is obvious. On the other hand, a
similar set of values calculated f o r n = 2 diverges, as one proceeds from
position 1 to position 7 , to figures which are too high; an opposite divergence occurs if n = 3. It is hence plain that a simple power law
( B = k P ) describes fairly accurately the observed variation of biological effectiveness with ionization per unit path in the nucleus. Moreover, since the ionization per unit path varies at least approximately as
566
R. E. ZIRKLE
the colzcelztration in the path, it is reasonable to substitute the concentration C f o r I in the equation B = kl". The exponent may not prove
to be exactly 2.5 but should lie between 2 and 3, so that one should be
able to state confidently that the biological effectiveness varies along
the alpha particle path as the square or cube of the concentration of
ions produced.
DISCUSSJON
The empirical equation B = k P 5 is a convenient summary of the
experimental results just described. The most significant feature of
this relationship is, of course, that the exponent of I is not unity, indicating that B is not only a function of the nuclear ionization per alpha
particle and hence of the total number of ions formed in the nucleus,
but is also in some way dependent on the variable concentration of ions
formed in different portions of the path of the alpha partic1e.O It is
important to inquire whether or not this result has any bearing upon
the question (see first paragraph of this paper) of the relative effectiveness of various wavelengths of x-rays. Since ion concentration in the
path of the alpha particle certainly is a factor influencing the effects of
this agent upon the fern spore, one may be tempted to predict that, at
least on the same organism, an r-unit of soft x-rays should be more
effective than one of hard, since the average concentration of ions is
higher in the paths of the relatively slow electrons ejected by the former.
However, this reasoning involves a considerable extrapolation. The
concentration of ions in the path of an alpha particle is much higher
than that produced in the path of an electron ejected by even a soft
x-ray quantum. It may be that the concentration effect observed with
alpha particles becomes detectable only at the high concentrations
produced in the paths of this type of radiation.
The fact that biological effectiveness may be expressed as a simple
power function of the ionization per unit path (or the concentration in
the path) suggests that the biological effect is due t o only one reaction,
but it is certainly not to be taken as proof that this is true. The exact
value 2.5 for the exponent of I , is, at the present stage of the work,
probably not of great significance. The experimental data are not
accurate enough t o justify any claim for great precision in its determination.
The experimental method described in this paper should be used
upon other biological material. It would be interesting to determine
5 As f a r as I am aware, the only other investigation of the effectiveness of alpha rays a t
various portions of their path is that of RedfieId and Bright (1924). These authors foulld
that the thickness of the perivitelliiie space in the fertilized Nereis egg is increased by ionizing
radiations, and studied the effect of placing this space a t various positions in a heterogeneous
beam of alpha particles. Their data clearly demonstrate that maxima and minima of biological
effectiveness are spaced along the path in the same way as known maxima and minima of
ionization. However, it would be difficult to conclude froin their data whether or n o t the
effectiveness varied with the first or some other power of the ionization-that is, whether the
degree of effect was determined simply by the total number of ions produced in the perivitellille
space or whether it was influenced also by the concentration of ions in the paths of the alpha
particles.
BIOLOGICAL EFFECTIVENESS O F A L P H A PARTICLES
567
whether the ion distribution factor operates in all biological reactions
to alpha radiation or only in certain special cases.
SUMMARY
When the spore of the fern Pteris ZomgifoZia is irradiated with alpha
particles, the resulting inhibition of cell division, of chlorophyll development, and of cracking of the spore wall, is due primarily to irradia.
tion of the nucleus.
The ionization per unit path (and hence the ion concentration in
the path) of an alpha particle varies in a characteristic manner along
the path. Various lots of spores have been arranged so that their
nuclei were traversed by alpha particles at different parts of their
paths. Seven portions of the path were thus investigated.
The biological effectiveness of these seven portions deviated widely
from direct proportionality t o the ionization produced in the respective
portions. This shows that biological effectiveness is not simply a
function of the number of ions produced in the nucleus, but is also a
function of the variable ion concentration produced in the paths of the
alpha particles.
The biological effectiveness has been found empirically to vary about
as the 2.5 power of the ion concentration in the path.
It is a pleasure to express my appreciation of the cooperation and interest of Professor
Detlev W. Bronk, Director of the Johnson Foundation. I am also indebted to Dr. J. L.
Weathemax, Philadelphia General Hospital, for the greater part of the polonium used.
The remainder was obtained from the Memorial Hospital, New York, and the United States
Radium Corporation, through the kindness of Professor Herman Schlundt, Dr. Gc. Failla,
and Mr. H. H. Barker.
LITERATLJRE
CITED
ASCHKINASS,
E., AND CASPARI,W.: Uber die Wirkung dissoziierenden Strahlen auf organisierte Substanzen, insbesondere iiber die bakterienschadigende Wirkung der
Becquerel-Strahlen, Arch. ges. Physiol. 86 : 603-618, 1901.
FAILLA,
G.: Relative effects produced by 200 kv. roentgen rays, 700 kv. roentgen rays,
and gamma rays. VII. Correlation of experimental results, Am. J. Roentgenol. 29 :
352-362, 1933.
PACKARD,
C. : The biological effects of short radiations, Quart. Rev. Biol. 6 : 253-280, 1931.
PACKARD,
C. : The biological effectiveness of high-voltage and low-voltage x-rays, Am. J.
Cancer 16 : 1257-1274, 1932.
REDFIELD,
A. C., AND BRIGHT,E. M. : The physiological action of ionizing radiations. 11.
I n the path of the a-particle, Am. J. Physiol. 68: 62-69, 1924.
RUTHERFORD,
E., CHADWICK,
J., AND ELLIS, C. D. : Radiations from radioactive substances,
New York, Ed. 1, 1930.
ZIRKLE,R. E. : Some effects of alpha radiation upon plant cells, J. Cell. & Comp. Physiol.
2 : 251-274, 1932.