int. j. radiat. biol 1997 , vol. 71 , no. 6 , 649 ± 655
Param eters of linear-quadratic radiation dose-eå ect relationships:
dependence on LET and m echanism s of reproductive cell death
G . W . BA REN DSE N
A b stract. A n analysis of m am m alian cell radiation± dose survival curves, based on the linear± quadratic form alism , is shown
to yield insights in the various com ponents of dam age that
contribute to cell reproductive death . R B E ± LET relation ships of
single-track letha l dam age, sublethal dam age, potentiall y letha l
dam age and DNA double-strand breaks are com pared. Singletrack letha l dam age is derived to be com posed of two com ponents: (1) dam age that rem ains unrepaired in an interval betw een
irradiation and assay for proliferative capac ity, w ith a very strong
dependence on LET, and (2) potentiall y letha l dam age that is
only w eakly dependent on LET, sim ilar to sublethal dam age and
DNA double-strand breaks. The results of this analysis lead to
new interpretation s of published experim enta l results and to
suggestion s for applications in radiotherap y.
1. Intro d u ctio n
Ever since the ® rst results obtained by the cloning
technique of Puck and M arcu s (1956) w ere pu blished,
diå erences in shapes of m am m alian cell survival
curves have been discussed by m any investigators,
am ong them Tikvah A lper qu ite prom inently (A lp er
et al. 1960). Interest in this subject derived not only
from its relevance to the understanding of m echanism s of biological radiation dam age, bu t also from
the im plications for dose± eå ect relations in radiotherapy of m alignant diseases. Norm al tissue dam age
as w ell as tum our control dep ends on radiation
responses of constituent cells, in particular im pairm ent of their capacity for unlim ited proliferation. Of
special im portance is the induction of rep rod uctive
death by m echanism s that yield lethal lesions as a
linearly increasing function of the dose and independ ent of the dose-rate. These m echanism s determ ine
to a large extent the eå ectiveness at sm all doses of
0± 2 G y, w hile the contribution of dam age du e to
accum ulation and interaction of sublethal lesions
starts to dom inate at larger doses (Barendsen 1962,
1979, 1982). Insights w ith respect to m echanism s of
induction and rep air of variou s typ es of dam age
involved in responses of m am m alian cells and tissues
contribute to a rational basis for the selection of
optim al doses and treatm en t schedu les to achieve
tum our control w ithout unacceptab le norm al tissue
dam age (Fowler 1989).
Laborator y for Radiobiology, U niversity of A m sterdam ,
Lindelaan 35, 2267 BJ Leidschendam , The Netherlands.
In studies concerning m echanism s that determ ine
radiosensitivities of m am m alian cells, three diå erent
approaches can be distingu ished w hich com plem ent
each other and together ev entually should result in
a com plete description of the processes of induction
and expression of cellular dam age (Barendsen 1990).
In the biophysical approach dose± eå ect relations
are studied w ith respect to their dep endence on tw o
m ajor physical factors: (1) the distribution of dose in
tim e and (2) the spatial distribution of energy dep osition along the tracks of ionizing particles in cells.
Stud ies of the in¯ uence of dose fractionation and
dose-rate have shown the im portance of the contribution of sublethal dam age (SLD) to cell lethality and
of the tim e interval in w hich rep air of this dam age
can be com pleted (Elkind and Su tton 1960, Elkind
and W hitm ore 1967, Fowler 1989). A ccum ulation
and interaction of sublethal dam age yield s the
increase in slope of survival curves w ith increasing
doses of radiation of low linear energy transfer (LET)
(Elkind and W hitm ore 1967). In addition to lethal
and sublethal lesions, the induction and expression
of potentially lethal dam age (PLD ) has been established and rep air of PLD has been assessed as a
function of the tim e interval after irradiation (Phillips
and Tolm ach 1966, Iliakis 1988).
Stud ies of the in¯ uence of energy dep osition den sity along tracks of ionizing particles and in volum es
of subcellular dim ensions, using diå erent ionizing
particles, have shown that local clustering of dam age
is a m ajor factor in the induction of cell rep rod uctive
death and chrom osom al dam age in m am m alian cells
(Barendsen et al. 1960, 1963, B arend sen 1967, 1979).
In particular, lethal lesions that increase linearly w ith
dose are m ore eæ ciently prod uced as the LET
increases, reaching a m axim u m in the region of 100±
200 keV/ m m . Su blethal dam age is m uch less dep endent on LET (Barendsen 1993). M icrodosim etric
inform ation is of m ajor im portance for the interpretation of these diå erences in dep endence of the relative
biological eå ectiveness (R B E ) on LET (Barendsen
1962, 1964, 1979, K ellere r and Rossi 1972,
G ood head 1989). In the past tw o decades m ore
detailed inform ation has becom e available on the
track structures of ionizing particles. The in¯ uence
0955 ± 3002/97 $12.00 Ñ 1997 Taylor & Francis Ltd
650
G . W . B arendsen
of LET on cellular eå ects can now be related to the
eå ectiveness for the induction of DN A dam age, e.g.
single-strand breaks (ssb), doub le-strand breaks (dsb)
and base dam age, w ith the aim of evalu ating w hich
targets and m echanism s are critical in the initiation
of cellular dam age. C harlton et al. (1989) calculated
on the basis of this typ e of inform ation that the
induction of DN A dsb increases w ith the am ount of
energy betw een 100 and 300 eV dep osited locally in
DN A, bu t that the R B E does not attain valu es as
high as obtained for cell inactivation. This result is
in agreem ent w ith experim ental data on the LET
dep endence of DN A dsb.
In the biochem ical approach studies are directed
at assessm en t of the chem ical processes w hich cause
changes in variou s constituents of cells, in particular
in DN A. These studies involve evalu ation of the
contributions of w ater radicals, of the in¯ uence of
sensitizing and protecting com pound s, e.g. m olecu lar
oxygen, SH -com pounds, alkylating agents, and of
other cytotoxic agents. A lper is w ell known for her
contribution to this typ e of studies (A lp er and B ryant
1974). Ward (1990) has concluded from a review of
the yield s of dam aged m oieties in intracellular DN A
that OH radicals are responsib le for about 60 % of
the strand breaks. H e has suggested that lethal lesions
result from locally m ultiply dam aged sites (LM D S)
in DN A. If the dam ages in these LM DS are w ithin
a few base pairs of each other, loss of base sequen ce
inform ation can occur du ring rep air by variou s
pathways.
A n im portant ded uction from studies of radiationinduced eå ects in DN A is that in m am m alian cells
the nu m ber of DN A ssb is approxim ately 1000 tim es
larger and the nu m ber of DN A dsb is approxim ately
50 tim es larger than the nu m ber of lethal ev ents and
chrom osom e aberrations induced by a given dose.
This inform ation has led to the insight that in
particular m am m alian cells have a very large capacity
for rep air of radiation-induced dam age. It is w ell
known that, related to the am ount of DN A present
in cells, m am m alian cells are m ore resistant than
yeast, bacteria or viruses, suggesting that lethal events
in DN A are less eæ ciently induced in m am m alian
cells (Terzi 1961, K aplan and M oses 1964). This can
be interpreted to be du e to a stronger clustering of
dam age in DN A being req uired to cause rep rod uctive
death in m am m alian cells as com pared to other typ es
of cells. This hypothesis is consistent w ith the observation that for m am m alian cell rep rod uctive death the
strongest increase of R B E as a function of LET is
obtained, a consequence of the ineæ cient production
of strongly clustered dam age by low -LET radiations.
Stud ies on the m odi® cation of DN A structure, e.g.
by the up take of halogenated pyrim idines w hich
increases radiosensitivity, can provide further insight
in the typ e of changes causing cellular dam age
(Szybalski 1974, M iller et al. 1992, Jones et al. 1995).
The third approach, w hich in particular in the last
decen nium has contributed to dev elopm ents in radiobiology, is based on m olecu lar biology m ethods.
M any studies using these m ethods are now directed
at the elucidation of cytogenetic m echanism s of rep air
of DN A dam age, of control of cell cycle progression
and of carcinogenesis. A nu m ber of genes involved
in DN A rep air has been identi® ed and their function
characterized (Lohm an et al. 1995). It has been
suggested that tum our cells m ay diå er w ith respect
to their rep air pro® ciency and that this factor m ay
aå ect the response to therapy (Weischelbau m et al.
1984). H owev er, com parison of cell lines w ith diå erent radiosensitivities has not revealed consistent
diå erences in rep air rates. C hrom osom e aberrations
can now be detected and analysed in m ore detail
using the technique of chrom osom e painting. It has
been shown that ionizing radiations cause eå ects
m ainly by induction of deletions rather than by point
m utations (Rydberg 1996).
A ll three typ es of approaches m entioned contribute
to the dev elopm ent of m odels designed to describe
the com plete sequen ces of changes induced by ionizing radiations, starting w ith energy dep osition in
critical structures or m olecu les in cells, enhancem ent
by the clustering of dam age, m odi® cation by rep air
m echanism s and ® nally resulting in rep rod uctive
death, or carcinogenesis. To be useful in radiotherapy
and radiation protection, the results of these descriptions m ust be expressed in term s of param eters that
provide qu antitative data on probabilities for the
end points consid ered, in particular at low doses
relevant to these applications. In the follow ing sections som e insights concerning the in¯ uence of clustering of dam age, m ainly derived by the biophysical
approach, w ill be discussed and im plications for
radiotherapy w ill be brie¯ y indicated.
2. S urvival curve s a nd the ir d ep e nd en ce o n
L ET
The ® rst radiation dose± survival curve of m am m alian cells in culture, pu blished by Puck and M arcus
(1956), w as interpreted by assum ing that tw o targets
had to be inactivated to cause cell rep rod uctive
death. A m ultitarget m echanism results in a survival
curve characterized by an initial low -dose region
starting w ith a zero slope, follow ed beyond a shoulder
region by an exponential decrease of the surviving
fraction at larger doses in excess of about 5 ± 10 G y.
On a sem ilogarithm ic plot extrapolation of the exponen tial region to dose zero yield s the extrapolation
651
L inear- quadratic param eters and L E T dependence of cell inactivation
nu m ber (A lp er et al. 1960). This nu m ber w as soon
observed to vary greatly for diå erent cell typ es and
w ith variou s conditions of culture. The m ultitarget
m odel had to be adapted to accom m odate this
variation and as a consequence the biophysical signi® cance of the extrapolation nu m ber rem ained
am biguous (Elkind and W hitm ore 1967).
The initial suggestion that survival curves of m am m alian cells for low -LET radiations cannot be
adequately described by m ultitarget m odels, bu t that
a com ponent w ith linear dep endence on the dose is
req uired to ® t the low -dose region of the curves, w as
based on a com parison of survival curves m easured
for low - and high-LET radiations (Barendsen et al.
1960, 1963, B arend sen 1962). The ® rst survival curve
of m am m alian cells, irradiated in vitro w ith alphaparticles at a high LET of 140 keV/ m m showed an
exponential decrease of the surviving fraction w ith
the dose:
S (D )/S (0) = exp Õ
a 1D .
This result w as interpreted by the assum ption that
cell rep rod uctive death can be induced by the passage
of a single particle through a critical structure or
m olecu le of the cell (Barendsen 1962). This typ e of
lethal event is den oted single-track lethal dam age
(STLD ). Su bsequent studies w ith alpha particles and
deu terons covering a w ide range of LET betw een 10
and 200 keV/ m m showed a decreasing contribution
of the linear com ponent w ith decreasing LET
(Barendsen et al. 1963, B arend sen 1967). H owev er,
ev en at 10 ± 20 keV/ m m a signi® cant linear com ponent could be determ ined, causing an initial negative
slope of the survival curves at low doses. This result
suggested that also w ith other radiations of low LET,
e.g. electrons generated by photons, an im portant
contribution of a linear com ponent should be present.
This com ponent is du e to dam age induced by slow
electrons, w hich have an increased LET at the end
of their tracks. This w as later veri® ed by m any studies
w ith sm all doses per fraction and w ith doses delivered
at low dose-rate (Barendsen 1962, 1979, H all 1972).
To describe m am m alian cell survival curves that
show on a sem ilogarithm ic plot an increase in slope
w ith increasing dose, the m ost sim p le equ ation is
obtained by adding in the exponent a term qu adratic
in the dose:
S (D )/S (0) = exp Õ
(a 1D + a 2D 2 ) .
² This rep resentation provides a generally adequate
² The notatio n w ith the param eters a 1 and a 2 is preferre d in
this m athe m atical form ula instea d of a and b as used by othe r
authors bec ause the latter sym bols are associated w ith m any
othe r pheno m ena in physics, biology and statistics, e.g. alphaand beta-particles, alpha-PLD and beta-PL D, etc.
description of the shapes of survival curves up to
doses of about 10 G y. It describes a curve w hich
continues to increase in slope w ith increasing dose
(Barendsen 1962, 1979, K ellere r and Rossi 1972).
For survival curves w hich at large doses show an
exponential decrease in survival, another rep resentation, includ ing a term sim ilar to the m ultitarget
form ula, can provide a satisfactory ® t to the data.
This form ula req uires tw o param eters, D n and n, in
addition to the param eter describing the linear com ponen t:
S (D )/S (0) = ( exp Õ
a 1D )(1 Õ
(1 Õ
exp Õ
D /D n ) n ) .
The follow ing discussion w ill be con® ned to the
region of surviving fractions betw een 1 and 0.01 for
m ost cell typ es corresponding to doses or doses per
fraction in the range of 0 ± 5 G y for w hich the rep resentation by the linear± quad ratic form ula is adequate.
3. L ET d ep e nd en ce o f S T LD
The com ponent of lethal lesions that increases
linearly w ith the dose is generally observed to show
a strong increase of the R B E w ith LET betw een
10 and 100 keV/ m m , to m axim u m valu es in the
range 5± 10, w ith a subsequen t decrease at
LET > 200 keV/ m m (Barendsen 1979, 1990). A n
exam ple of this relationship is given in Figure 1. The
R B E rep resent the ratios a 1H /a 1L , in w hich these
linear param eters a 1H and a 1L rep resent the eå ectiveness of high- and low -LET radiations at low doses
respectively. The tw o diå erent R B E curves in
Figure 1 pertain to oxygenated and hypoxic conditions. The larger R B E in hypoxic conditions are du e
to the fact that the oxygen enhancem ent ratio (O E R )
is larger for low -LET radiation than for high-LET
radiations. This diå erence can be interpreted by
assum ing that in hypoxic conditions, because part of
the chem ical changes are rendered ineå ective, lethality is only induced by events w hich involve larger
clusters of energy dep osition than req uired in oxygenated conditions (Barendsen 1967). This stronger clustering is m uch less eæ ciently produced by low -LET
radiation than by high-LET radiations.
To ev alu ate the in¯ uence of hypoxia m ore qu antitatively, it is of interest to com pare the corresponding
eå ective cross-sections, w hich are also presented in
Figure 1, as a function of LET (Barendsen 1967). It
can be concluded that the cross-section for oxygenated cells increases m ost steeply betw een 50 and
80 keV/ m m , w hile for hypoxic cells the steepest
increase is observed betw een 80 and 120 keV/ m m .
The m axim u m valu e of about 35 m m 2 is the sam e for
both conditions of exposure. Thus the curve of the
cross-section for lethal eå ects in hypoxic cells is
652
G . W . B arendsen
4. L ET d ep e nd en ce o f sub le thal d am age
(S LD )
Figure 1. R B E (circles) and cross-sections (triangles) as a function of LET for inactivation of T-1 cells of hum an origin
in culture, irradiated in oxygenate d conditions (open
sym bols) or in hypoxic conditions (closed sym bols). Data
points pertain to a 1 calculated on the assum ption that
survival curves can be described by S (D )/S (0) =
exp Õ (a1D + a 2D 2 ). The eå ective cross-sections w ere calculated from a 1 as the inverse of the associated particle
¯ uences, corresponding to the dose required to yield an
averag e of one letha l event per cell. Data from B aren dsen
et al . (1963) and B aren dsen (1964, 1967).
shifted towards higher LET as com pared w ith oxygenated cells. A particle of 90 keV/ m m passing
through a cell in hypoxic condition is associated w ith
a cross-section about equ al to the cross-section
obtained w ith a particle of 60 keV/ m m for oxygenated cells. This shift can be interpreted as a red uction
in eå ective local dam age by 30 ± 40 % , caused by the
absence of oxygen in the cells. Thus a larger O E R of
2± 3, e.g. for low -LET radiations, can be explained
by a relatively m odest increase in the req uirem ent
for local clustering of dam age.
The cross-section curves can provide yet another
typ e of basic insight. From a com parison of the
m axim u m cross-section of 35 m m 2 w ith the crosssectional area of the cell nu cleus of about 70 m m 2 ,
and consid eration of the packing of DN A in the cell
nu cleus, the suggestion has been derived that,
although the prob ability for induction of cell rep rodu ctive death is only about 0.5 per particle, the
nu m ber of DN A dsb induced by an alpha particle
passing through a cell nu cleus m ay be as large as
20± 40 (Barendsen 1990, 1994a). This is in agreem ent
w ith evidence from other typ es of studies, suggesting
that m ost DN A dsb in m am m alian cells are rep aired
(Radford 1986).
The frequ ency of sublethal lesions, w hich can
interact to cause m am m alian cell rep rod uctive death,
is rep resented by the square root of a 2 in the linear±
qu adratic form ula. Su blethal lesions are produced
not only by low -LET radiations bu t also by radiations
of high LET, w hich yield survival curves that are
indistinguishable from exponential. This has been
qu anti® ed in experim ents in w hich high-LET radiations w ere sequen tially com bined w ith low -LET
radiations (Bird et al. 1983, M cNally et al. 1988,
B arend sen 1993). The R B E of SLD can be derived
from the square roots of a 2’ s calculated for survival
curves for ionizing particles w ith LET < 25 keV/ m m .
For larger LETs experim ents on the interaction of
dam age from high-LET particles w ith SLD from
low -LET X -rays have yield ed m ore accurate R B E s.
The R B E ± LET relationship for SLD derived from
both typ es of data has been shown to increase by a
factor of at m ost 2± 3 betw een 10 and 100 keV/ m m .
A s illu strated schem atically in Figure 2, this relationship is very sim ilar to the R B E for induction of
doub le-strand breaks in DN A (Barendsen 1993). It
has been hypothesized that a fraction of the DN A
dsb constitute the sublethal lesions, and that these
sublethal lesions are equ ivalent to the locally m ultiply
dam aged sites (LM D S), suggested by Ward (1990) to
be associated w ith DN A dsb (Barendsen 1994).
5. L ET d ep e nd en ce o f p ote ntially le thal
d am age (PL D )
Potentially lethal dam age has been detected experim entally as a typ e of lesion that is subject to rem oval
or expression, dep ending on conditions to w hich cells
are exposed after irradiation. In particular, by m aintaining cells in a resting phase or by tem porary
im pairm ent of cellular m etab olism after a given dose
of radiation, rep air of PLD results in enhancem ent
of clonogenic capacity. Iliakis (1988) has reviewed
ev idence suggesting that at least tw o typ es of conditions can aå ect the expression of PLD: (1) conditions
that red uce the eå ectiveness of a radiation dose by
preventing ® xation of PLD and thereb y allow ing
rep air to proceed, and (2) conditions that increase
the eå ectiveness of a dose by ® xation of PLD that
m ight have been rep aired in stand ard post-irradiation
conditions. PLD has been shown to contribute to the
induction of dam age rep resented by the linear term
as w ell as the qu adratic term in the LQ form alism
(Fertil et al. 1988). The dep endence of PLD on LET
has been studied experim entally by Yang et al. (1985)
for plateau -phase C 3H 10T1/2 cells irradiated w ith
L inear- quadratic param eters and L E T dependence of cell inactivation
Figure 2. Schem atic representatio n of R B E ± LET relation ships
for the diå eren t types of dam age in m am m alian cells
w hich contribute to cell reproductive death : STLD =
single track letha l dam age caused by individual ionizing
particles and their associated secondaries, STLD (unr) =
STLD that rem ains eå ective after the com ponen t of PLD
is repaired, PLD = potentially letha l dam age, that contributes to the linear as w ell as to the quadratic term in the
dose± response relation ship, SLD = sublethal dam age that
determ ines the quadratic term in the dose response
relation ship, DNA dsb = DNA double-strand breaks,
DNA ssb = DNA single-strand breaks.
heavy ions of a w ide range of LETs, and by B ertsche
and Iliakis (1987) for Ehrlich ascites tum our cells
irradiated w ith variou s light ions. These data have
been analysed and interpreted recently w ith respect
to the in¯ uence of LET on the tw o param eters of
the LQ form ula (Barendsen 1994a). The diå erences
of the corresponding a 1 valu es for im m ediate plating
and for delayed plating respectively, w ere calculated
to derive the linear param eters a 1 for PLD as a
function of LET. From this analysis the ded uction
w as m ade that the R B E for the com ponent of single
track lethal dam age (STLD ), w hich rem ains eå ective
after PLD had been elim inated by rep air du ring a
delay in plating, is signi® cantly stronger dep endent
on LET by a factor of about 2, attaining valu es in
the range of 10± 20 as com pared w ith the total ST LD
derived from data on im m ediate plating. This is
illu strated schem atically in Figure 2. B y contrast, the
valu es of a 1 for the PLD com ponent of ST LD, w hich
is subject to rep air, do not increase w ith LET by
m ore than a factor 2 ± 3. This PLD com ponent shows
653
a sim ilar dep endence on LET as SLD and DN A dsb.
In a sim ilar w ay as for ST LD, the SLD w as analysed
to distingu ish a com ponent of PLD rep resented in
the qu adratic term . It w as concluded that the R B E
valu es of the square root of the param eter a 2 did not
diå er for im m ediate and delayed plating respectively,
and that for both conditions a sim ilar dep endence
on LET w as obtained as for DN A dsb. This supp orts
the hypothesis that sublethal lesions are a subset of
the DN A dsb.
These ded uctions concerning diå erent contributions of variou s com ponents of biological dam age to
the expression of cell rep rod uctive death in m am m alian cells, are com patible w ith the suggestion of
G ood head (1989) that several classes of initial physical dam age can be distingu ished. These classes range
from sparse single ionizations w hich are relatively
ineå ective, to sm all and m oderate clusters produced
by track end s of electrons or delta-r ays from fast
nu clei, to large clusters caused by high-LET particles,
and ® nally to very large clusters unique to very
den sely ionizing particles. The results discussed here
indicate that a signi® cant part of radiation dam age,
ev en from low -LET electrons, can cause ST LD that
is not rep aired by delayed plating. In addition, highLET radiations are shown to produce, albeit w ith a
relatively low R B E , the sam e SLD and PLD as is
produced by low -LET radiation.
6. Im p lica tions o f insights d erived fro m
R B E ± L ET relatio nship s fo r rad io therap y
The identi® cation of tw o distinct com ponents of
dam age causing cell rep rod uctive death w hich can
be induced by single-particle tracks, provides the
possibility to interpret diå erences am ong cell typ es
w ith respect to their radiosensitivity and R B E . Stem
cells in variou s typ es of norm al tissues are known to
exhibit signi® cant diå erences in sensitivity to low LET radiations as w ell as in R B E of high-LET
radiations. For instance, bone m arrow stem cells are
m ore radiosensitive than stem cells of skin or intestine
in the sam e anim al, notw ithstanding the identical
DN A content. A ssociated w ith the higher sensitivity,
R B E of high-LET radiations for the induction of
lethal ev ents in bone m arrow stem cells are generally
low . A n extrem e exam ple is provided by cells from
patients w ith ataxia telangiectasia (AT). These cells
show little PLD rep air. R B E ± LET relationships for
AT cells show a m axim u m R B E of about 2 at
100 keV/ m m (Cox 1982). On the basis of the present
analysis yield ing tw o distinct com ponents of dam age
in the linear term , it can be suggested that for cells
w ith a high sensitivity, PLD or PLD-like dam age
provides a large contribution to the linear term of
654
G . W . B arendsen
cell rep rod uctive death, directly associated w ith the
low R B E for this typ e of dam age. From an analysis
of pu blished survival curves of cells of hu m an origin,
Fertil et al. (1988) suggested that an im portant part
of the radiation dam age contributing to the initial
slope of survival curves is rep airable, w ith rep air of
this PLD enhancing diå erences am ong cell strains.
Diå erences in R B E can in this context be ascribed
to diå erences in the contributions of the rep airable
and unrepairable com ponents of ST LD w hich diå er
in their dep endence on LET.
A further interpretation of experim ental data can
be derived w hich relates to the R B E of high-LET
radiation for dam age to late-re sponding tissues. It
can be hypothesized that the contribution of the
PLD-like com ponent of ST LD dep ends on the rate
of proliferation of critical cells in tissues. Late
responding tissues contain a large fraction of noncycling cells and are generally characterized by low
a 1 /a 2 ratios, possibly associated w ith a low a 1 , du e
to a m ore eæ cient rep air of the PLD com ponent of
the linear term . A sm aller contribution of PLD w ou ld
also be expected to yield a higher R B E . This hypothesis is consistent w ith the observation that R B E of
fast neu trons for dam age to late-re sponding tissues
are generally larger than for early responding tissues.
In late-re sponding tissues m any cells are non-cycling
or have a long life span, associated w ith am ple tim e
available for rep air of PLD.
A large contribution of PLD or PLD-like dam age
could also be responsib le for low R B E of fast neu trons
for responses of som e typ es of tum ours. For slowgrowing tum ours frequ ently high R B E w ere obtained
in clinical studies (Batterm ann et al. 1981). If the
hypothesis is correct that in slow growing tum ours
the high R B E of fast neu trons is du e to a large
com ponent of non-cycling cells w hich rep air PLD
eæ ciently, than an im portant suggestion can be
derived w ith respect to the application of fast neu trons. In several typ es of tum ours an increased rate
of rep op ulation of surviving cells has been suggested
to start after a nu m ber of dose fractions has induced
suæ cient cell death to ev oke a proliferative response
(Fowler 1989). In these rapid ly proliferating cells less
rep air of PLD m ight occur and as a consequence of
the large com ponent of PLD rem aining eå ective, the
R B E of high-LET radiations m ight be low er. Thus
the application of high-LET radiation m ight be m ore
ben e® cial in the ® rst few w eeks of a protracted
treatm en t, w hen m ore cells are in a resting state,
than in the later w eeks. A further suggestion w hich
can be derived from the identi® cation of tw o com ponents contributing to ST LD, is of interest w ith respect
to the application of predictive testing for radiosensitivity to stand ard treatm en ts w ith low -LET radiations,
using cells cultured from tum ours in patients. The
variability of the contribution of PLD suggests that
it is not suæ cient to assess the radiosensitivity of
exponentially growing cells in culture, bu t that assays
are also req uired to m easure the capacity of the
tum our cells for rep air of PLD, e.g. by analysis of
the radiosensitivity of cells in plateau phase, using
im m ediate and delayed plating proced ures, or in
future dev elopm ents by m ethods of m olecu lar biology. This inform ation w ould be im portant to predict
the responsiveness of slow-growing hu m an tum ours
to X -rays, as w ell as the R B E of high-LET radiations.
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