ICTP 2019

Fundamental Radiobiology

Colin G. Orton, Ph.D.

Professor Emeritus,
Wayne State University,
Detroit, Michigan, USA
 Topics to be discussed
The 4 Rs of radiotherapy
• Repair
• Repopulation
• Reoxygenation
• Redistribution
The effect of the LET of the radiation
Which is the most important?

Repair!
 Repair: Single strand and
double strand damage
Single strand breaks (upper figure) are
usually considered “repairable”
Double strand breaks (lower figure) are
not usually “repairable” if the breaks
are close together, since an intact 2nd
strand of the DNA molecule is needed
for the repair enzymes to be able to
copy the genetic information
 The effect of dose
 At low doses, the two DNA strands are
unlikely to be both hit
• so single strand breaks will dominate i.e. repair
is common
 At high doses, double strand breaks will be
common i.e. little repair
• consequently survival curves get steeper as
dose increases
 As dose increases survival
curves become steeper
For types of cells
that have a high
capacity for repair,
the cell-survival
curve will be less
steep at low doses
and hence the
survival curve will
be “curvier”
 Survival curves:
normal vs cancer cells
Cancer cells do not “repair” damage at low
doses as well as do normal tissue cells
• survival curves will be straighter
There is a “Window of Opportunity” at low
doses where the survival of late-reacting
normal tissue cells exceeds that of cancer
cells
 Cell survival curve comparison:
the “Window of Opportunity”
At low doses, the
survival of normal
tissue cells (green
curve) exceeds that of
cancer cells

At high doses, the

survival of cancer cells
(red curve) exceeds that
of normal tissues
 Question!
Does this mean that, since you
cannot give more than about 4 Gy or
you will kill more normal cells than
cancer cells, and 4 Gy is not nearly
enough dose to kill all the cancer
cells in typical tumor, you can never
cure cancers with radiation alone?
 The solutuion is:
Fractionate!
 This is why we typically fractionate
radiotherapy at low doses/fraction
 We need to fractionate at doses/fraction
within this “Window of Opportunity” e.g.
typically about 2 Gy/fraction
 Normal vs cancer cells for
fractionation at 2 Gy/fraction
 Cell survival curve comparison: the
“Window of Opportunity”
Note that we have assumed that the
dose to normal tissues is the same
as the dose to the cancer cells
Is this a reasonable assumption if
we are using conformal teletherapy?
 No!
 Because the major advantage of conformal
radiotherapy is that the dose to normal tissues is
kept less than the tumor dose
 Hence the effective dose* to normal tissues will
usually be less than the effective dose to tumor
*the effective dose is the dose which, if delivered uniformly to the
organ or tumor, will give the same complication or cure rate as the
actual inhomogeneous dose distribution. Sometimes called the
Equivalent Uniform Dose (EUD)
 Geometrical sparing factor
We can define a “geometrical
sparing factor”, f, such that:
effective dose to normal tissues
f 
effective dose to tumor
For conformal radiotherapy f < 1
 The “Window of Opportunity” widens
with geometrical sparing
Even with a modest
geometrical sparing
of only 20%, the
“Window of
Opportunity” extends
to over 10 Gy
 This means that:
With highly conformal therapy we
can safely use much higher doses
per fraction
• for teletherapy i.e. hypofractionation
• for brachytherapy i.e. High Dose Rate
(HDR)
Let’s look now at hypofractionation

Hypofractionation is the use of

fewer fractions at higher
dose/fraction
• dose/fraction: about 3 – 20 Gy
• number of fractions: 1 - 20
 Hypofractionation:
potential problems
Historically, because of the risk of late
complications, the total dose was kept
considerably less than that needed to
cure cancers, and hypofractionation was
used for palliation only
• however, it is now being used for cure with
stereotactic body radiation therapy (SBRT)
 What we know
 Clinical trials around the world are beginning
to show that, with highly conformal therapy,
hypofractionation can be just as effective as
conventional fractionation (both for cure and
avoidance of normal tissue complications)
• we already knew this from stereotactic
radiosurgery in the brain, but now know it for
SBRT applied to other sites
 My prediction
 With even more conformation of dose
distributions using more sophisticated imaging,
image guidance, motion tracking, protons, etc.,
we’ll be using as few as five fractions for most
cancers in the near future
• treatments will cost less and be more convenient
• accelerated regimes will be more prevalent thus
reducing cancer cell proliferation during treatment
• cure rates will increase
What about dose rate and
time between fractions?
Repair takes time (half-time for
repair typically 0.5 – 1.5 hours),
hence repair decreases as
• time between fractions decreases
• dose rate increases
Importance of time between fractions

Because repair is more important

for normal tissues than for tumors,
enough time must be left between
fractions for full repair
• based on clinical results, this is
assumed to be six hours
 Importance of dose rate
Normal tissue cells repair better than
cancer cells and low dose rate
enhances repair
This is the basis of low dose rate (LDR)
brachytherapy and, especially,
permanent implants at very low dose
rate
 Questions!
Does this mean that LDR brachytherapy will
always be radiobiologically superior to HDR?
or
Might the advantage of geometrical sparing
outweigh the disadvantage of high dose rate?
and
Can the best modality be determined by some
type of modeling?
 Radiobiological modeling

We need a mathematical model

that describes the effects of
radiotherapy on cancer and
normal tissue cells
• this is the linear-quadratic model
The linear-quadratic model of cell
survival: two components
Linear component:
• a double-strand break caused by the
passage of a single charged particle e.g.
electron, proton, heavy ion
Quadratic component:
• two separate single-strand breaks caused
by different charged particles
So what is the equation for cell survival?

 This is based on Poisson statistics (the statistics

of rare events), since the probability that any
specific DNA molecule will be damaged is low
 According to Poisson statistics, the probability,
P0, that no event (DNA strand break) will occur is
given by:
P0 = e-m
where m is the mean number of hits per target
molecule
Single-particle events
 For single-particle events, m is a linear
function of dose, D
• so the mean number of lethal events per
DNA molecule can be expressed as aD
and P0 represents the probability that there
are no single-particle lethal events, i.e. it is
the surviving fraction of cells, S
 Then
S = e-aD
What causes these single-particle events

 For a single particle to damage both arms of the

DNA at the same time it has to be highly ionizing
 Hence single-particle events are caused primarily
by the high-LET component of the radiation
 For photon and electron beams, it is the very low-
energy secondary ionizing radiations (i.e. slow
electrons) that are high LET and hence give rise to
these single-particle events
 Two-particle events
 With two-particle events, the probability that one arm of a
DNA molecule will be damaged is a linear function of
dose, D, and the probability of damage in an adjacent
arm is also a linear function of dose, D
 Hence the probability that both arms are damaged by two
different single-particle events is a function of D2
 So the surviving fraction of cells due to these two-particle
events is given by:
-b D 2
S= e
 The linear-quadratic model

Single-particle
event

Two different
single-particle
events
The L-Q Model Equation
2 2)
Hence S = e-aD. e - b
= D e -( aD + b D

or lnS = -(aD + bD2)

where a represents the probability of lethal
single-particle (a-type) damage
and b represents the probability that
independent two-particle (b-type) events
have combined to produce lethal damage
What about Repopulation
 Cancer cells and cells of acutely-reacting normal
tissues proliferate during the course of therapy
(called “repopulation”)
 Cells of late-reacting normal tissues proliferate
little
 Hence the shorter the overall treatment time the
better
• but should not be too short otherwise acute reactions
will prevent completion of treatment
 Repopulation and the L-Q equation
 The basic L-Q model does not include the effect of
repopulation during the course of therapy
 Hence, it does not take into account the effect of overall
treatment time, T, or repopulation rate (represented by the
potential doubling time, Tpot)
 The L-Q model with repopulation correction assumes that
increase in surviving fraction due to repopulation is an
exponential function of time i.e. lnS increases linearly with
time
The L-Q equation with repopulation
Hence:

lnS = -(aD + bD2) + 0.693T/Tpot

Where:
T = overall treatment time (days)
Tpot = potential doubling time (days)
 What about Reoxygenation?
 Reoxygenation relates to the oxygen effect
 Oxygen is a powerful radiation sensitizer, so
tumors that are poorly oxygenated (i.e. are
hypoxic) tend to be resistant
 Hypoxic tumors can reoxygenate during a
course of treatment and become more
sensitive
The Oxygen Enhancement Ratio (OER)

 The degree of sensitization is expressed in

terms of the Oxygen Enhancement Ratio,
where:

to produce the same biological effect

 How the oxygen effect works
Oxygen reacts with the
broken ends of the DNA
molecule to make the damage
permanent i.e. to “fix” the
damage by preventing
recombination of the broken
ends

This is called the “oxygen

fixation process”
 OER is a function of
dose and dose rate
OER at high
doses (and dose
rates) tends to be
larger than the
OER at low
doses (and dose
rates)
 Why does OER decrease as
dose decreases?
O2 sensitization relates to “fixing” of
single-strand DNA breaks i.e. O2
enhances b-type damage
At low doses, a-type damage
dominates, so the effect of O2
sensitization is reduced
Reduced effect of O2 means lower OER
Might this be important in
radiotherapy?
 Yes, because the protective effect of
hypoxia in hypoxic cancers should be
reduced by treating at low dose/fraction or
low dose rate
• for teletherapy, this should be a benefit of
hyperfractionation
• for brachytherapy, this should be a benefit of
permanent implants
 Two types of hypoxia in
tumors: Chronic and acute
 Chronic hypoxia
• due to the limited diffusion distance of
oxygen through tissue
• cells may remain hypoxic for extended
periods
 Acute hypoxia
• due to temporary closing of a blood vessel
• transient
 Chronic and acute hypoxia

Acute
Chronic hypoxia
hypoxia

Blood vessel
Timing of reoxygenation
 Rapid component: reoxygenation of acutely
hypoxic cells due to blood vessels reopening
 Slow components:
• as the tumor shrinks, cells previously beyond the range
of oxygen diffusion (chronic hypoxia) find themselves
closer to blood vessels and reoxygenate
• revascularization of the tumor and killing of well-
oxygenated cells might increase oxygen availability
Reoxygenation in clinical
practice
 Spreading irradiation over long periods of
time by fractionation or very low dose rate
brachytherapy (e.g. permanent implants)
ought to be beneficial
 Modifications of the L-Q model to account
for the oxygen effect and reoxygenation
have been published but are not typically
used in clinical practice
 Finally, Redistribution
 Redistribution relates to the cell-cycle effect:
• Cells are most sensitive at or close to mitosis
• Survival curves for cells in the M phase are linear,
indicating the absence of any repair
• Cells in late G2 are usually sensitive, perhaps as
sensitive as cells in M
• Resistance is usually greatest in the latter part of the
S phase
What is Redistribution?
 Because of the cell cycle effect, immediately
after a radiation exposure the majority of cells
surviving will be those that were in a resistant
phase of the cell cycle at the time of irradiation,
such as late-S
 After exposure, cells are thus partially
synchronized. This is known as redistribution (or
reassortment)
 Redistribution with
fractionated radiotherapy
 The timing of the subsequent fraction will,
therefore, make a difference in the
response
 For example, if the next fraction is
delivered at a time when the synchronized
bolus of specific cells has reached a
sensitive phase of the cell cycle, then
these cells will be extra sensitive
 Redistribution with daily
fractionation
 Clearly, the effect of redistribution depends on
both the length of the various phases of the cell
cycle and the time between fractions
 Since 24 hours is much longer than the length
of the G2 phase of the cell cycle for most cells, it
is unlikely that such sensitization will play a
significant role for treatments delivered with
daily fractionation
 Redistribution in
clinical practice
 With twice or three-times-a-day fractionation,
sensitization by the redistribution effect is
conceivable and could be significant
 However, we have not yet found a way of utilizing
redistribution to our advantage
 Modifications of the L-Q model to account for the
redistribution have been published but are not
typically used in clinical practice
 Effect of LET of the radiation
 Repair decreases as LET increases, so the
biological effectiveness (RBE) increases, where:
𝑑𝑜𝑠𝑒 𝑜𝑓 𝑙𝑜𝑤 𝐿𝐸𝑇 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛
RBE =
𝑑𝑜𝑠𝑒 𝑜𝑓 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡
to produce the same biological effect
 The OER decreases as LET increases
 The cell-cycle effect decreases as LET increases
So when might high-LET radiotherapy
be most beneficial radiobiologically?
For the treatment of cancers that have
a high capacity for repair
For the treatment of hypoxic cancers
For the treatment of cancers that have
cells trapped in a resistant phase of the
cell cycle
 Summary
 Radiotherapy is governed by the 4 Rs
• Repair, Repopulation, Reoxygenation, and Redistribution
 Since normal tissue cells are better able to repair than
are cancer cells, there is a “Window of Opportunity” at
low dose/fraction or low dose rate
 With geometrical sparing of normal tissues, the
“Window of Opportunity” widens making
hypofractionation and HDR brachytherapy possible
 Summary (cont’d.)
The L-Q model can be used to calculate
effects of dose/fraction, overall
treatment time, and dose rate
High-LET has potential biological
advantages over conventional
radiotherapy to supplement the physical
advantage of the Bragg Peak