Fundamentals of Radiotherapy
Dr Simon Thomas
Medical Physics
Addenbrookes Hospital.
Fundamentals of radiotherapy
Radiotherapy is the use of ionising radiation
to treat disease (nearly always cancer)
Aim of radiotherapy is to destroy cancer
cells, whilst not causing unacceptable
damage to healthy tissue.
Need to ensure that radiation is targeted to
the disease, giving as little dose as possible
to healthy tissue
Target volume (prostate) surrounded
by organs at risk (bladder, rectum,
femoral heads)
Choice of energy
How to produce MV x-rays
120
Need to accelerate an electron and fire it
into a target
Efficiency of x-ray production increases
with electron energy
Efficiency of x-ray production increases
with Z of target
250kV
100
percentage depth dose
4M V
16M V
80
60
40
20
0
0
10
15
20
25
30
d e p t h in c m
How to accelerate electrons
linear accelerators
Direct potential (20kV to 2MV)
Indirect methods needed at higher energies
Linear accelerators
Betatrons
Microtrons
etc.
Linear accelerators are the standard
equipment used in radiotherapy
Accelerating waveguides
Microwaves of 3GHz (10cm) in tuned
resonant cavities
Accelerating waveguide made form a series
of cavities
Travelling wave or standing wave can be
used
Can accelerate electrons by approx 15 MeV
per metre
Linear
accelerator
Electron gun
Magnetron
Accelerating waveguide
Target+ Flattening filter
Ion chamber
Collimators
Back to the patient what arrangement
of beams should we use?
Simplify square tumour in square patient
Outline
Target
Treatment planning aims:
Normalise 100% of dose to centre of target
Dose in target 95%-107%
Dose outside target as low as possible
Single 6MV Beam
Calculate isodose distribution
Colour wash and Isodose lines
Build up region 1 to 3cm
target coverage
75% to 130%!
Isodose lines
Add an opposed field
Hot spot = 178%
Field edge =
50% isodose
Hot spot = 116%
Widen beams by
12mm each side
to get 95% to
cover ROI
Field edge =
50% isodose
target coverage
now 95% to
104%!
Isodoses
neck
inwards
Add two lateral beams
Four Field Brick
Max dose outside
target = 61%
Hot spot =101%
12mm margin;
95% isodose is now too large
Reduce field widths
to 7mm margin
3 Field Brick
Remove posterior beam and add lateral wedges
40 wedges,
70% weighting
~30% dose in
posterior region
Max dose outside
Target Volume =
87%
Superior / Inferior coverage
Field lengths ~15mm
margin round volume
due to necking
Coronal View cubic volume
7mm field margins
Sup/Inf
95%
Isodose
Field widths
~7mm margin
Coronal View cubic volume
15mm field margins
Sup/Inf
Conformal Volumes
95%
Isodose
Conformal MLCs
Clinical applications Prostate with MLCs
Different margins!
95% isodose
surrounds target
volume
Coronal View spherical volume
Different margins &
asymmetric fields
MLCs and wedges
Intensity Modulated
Radiotherapy (IMRT)
modification of the
intensity of radiation
across the beam
profile to match the
tumour. And avoid
critical structures.
Can get more complex
dose distributions in
3D than with simple
shaped fields.
60 wedged field. Collimator 90
Open field. Collimator 0
Types of IMRT
Multiple static fields (step and
shoot)
Dynamic MLC (Sliding
window) similar, but radiation
stays on whilst MLCs move.
Faster, but more to go wrong.
Rotational IMRT gantry rotates
continuously whilst beam on and
MLC varies. Known as Rapid
Arc or VMAT (volumetric
modulated arc therapy)
Tomotherapy Rotational IMRT
on non-standard linac, with CTlike gantry and helical delivery.
Helical Tomotherapy
Purpose-built, integrated
device for IMRT & IGRT
(of which more later)
Helical delivery
Fast
Potential for high level of
modulation
Types of IMRT
Multiple static fields (step and
shoot)
Dynamic MLC (Sliding
window) similar, but radiation
stays on whilst MLCs move.
Faster, but more to go wrong.
Rotational IMRT gantry rotates
continuously whilst beam on and
MLC varies. Known as Rapid
Arc or VMAT (volumetric
modulated arc therapy)
Tomotherapy Rotational IMRT
on non-standard linac, with CTlike gantry and helical delivery.
Tomotherapy IMRT delivery
Based on same idea as spiral CT
50-300 rotations, treated as 51
projections per rotation.
At each projection, choose how
long each of the 64 binary MLCs
is open for
Delivery Sinogram for Helical Tomotherapy
Designed for IMRT
Low leakage/scatter
No flattening filter => simple
beam modelling
Spiral CT
Giving high dose to prostate, medium
dose to nodes, and sparing the rectum.
Dose calculation algorithms
How do we calculate the dose distributions
in radiotherapy treatment plans?
Lots of algorithms in clinical use, with a
trade-off between speed and accuracy.
One that is widely used is the
convolution/superposition algorithm.
Dose deposition kernel (probability distribution from a single photon
interaction) can be derived from Monte Carlo (Stochastic) models.
The dominant interaction is Compton; also PP and PE).
Can store pre-calculated kernels, or can fit to mathematical
models: e.g.
a r
b r
2
hw (r , ) = ( A e
+ B e
)/r
Where A,a,B and b are functions of angle, tabulated for a number
of energies by Ahnesjo 1989.
The first term relates mainly to primary dose (short range), the
second mainly to scattered photons (long range).
50cm
5 cm
TERMA
Total Energy Released per unit Mass
It measures the energy removed from the
primary beam. Similar to KERMA, but
TERMA includes the energy lost to scattered
photons. KERMA does not.
Convolve the TERMA with the energy
deposition kernel, to get the dose.
Convolution
FFT ( f g ) = FFT ( f ) FFT ( g )
f g = FFT 1 ( FFT ( f ) FFT ( g ))
3D convolution is inherently an N6 problem
Using FFT reduces it to an N3log(N) problem (about a million
times faster for N=256)
Primary radiation attenuation depends on electron density
TERMA changes
Attenuation of electrons and scattered photons depends on
electron density kernel scaling
The shape of the kernel now depends on the densities between the
interaction point and the dose calculation point. Therefore no
longer a true convolution, so cannot be done in Fourier space.
So no longer an N3 log(N) problem, but back to a N6 problem
This would be impossible, without an algorithm to speed it up.
The one most people use in called the collapsed cone algorithm
Calculating TERMA
Need to know the attenuation coefficient for
each point in the patient.
This will depend on
The energy of the radiation (so you need to know the
spectrum)
The electron density at each point (which can be
calculated from the CT values)
Strictly also need the physical density (since
TERMA proportional to /) but generally can
assume that tissue is scaled water.
Allow for geometrical penumbra by convolving
with one or more gaussians
The collapsed cone algorithm
Divide space around a point
into a series of cones
Approximate that all energy
released in the cone is
transported and deposited
along the axis
Calculation time is of the
order of M N3 where M is
the number of cones
considered for each point.
Collapsed cones
Not like this
Geometric uncertainty
Or this
Gross Tumor Volume
More like this
Clinical Target Vol.
Planning Target Vol.
Perhaps furled umbrella
would be a better name
than collapsed cone
Clinical Target Volume
The CTV is a tissue volume that contains a
demonstrable Gross Tumour Volume (GTV)
and/or subclinical malignant disease, which
has to be eliminated. This volume thus has
to be treated adequately in order to achieve
the aim of radical therapy. (ICRU62)
Why do
we need a
CTV to
PTV
margin?
Planning Target Volume
The PTV is a geometrical concept used for
treatment planning, and it is defined to
select appropriate beam sizes and beam
arrangements, to ensure that the prescribed
dose is actually delivered to the CTV.
You might
actually be doing
this
To ensure that
the dose
distribution
covers the
CTV after
organ motion
and errors.
Types of errors
Gross errors
include incorrect anatomical site or patient orientation, incorrect field
size, shape or orientation or incorrect isocentre position of 3 standard
deviations or more of the random error.
Or this
Systematic errors
occur in the same direction and are of a similar magnitude for each
fraction throughout the treatment course. They may arise due to target
delineation error, a change in the target position, shape and size,
phantom transfer errors or set up errors.
Random errors
vary in direction and magnitude for each delivered treatment fraction.
They arise from varying, unpredictable changes in the patients position,
internal anatomy or equipment between each delivered fraction.
Systematic errors
Also known as preparation errors
Errors that apply to all fractions in the
same direction - these cause a shift in the
cumulative dose distribution relative to
the CTV
Unknown and different for each patient
(if known can be corrected for and
removed)
Combining errors
Systematic errors can be combined in quadrature
with other systematic errors
(sum the squares of all the errors, then take the
square root)
STV = CTV + margin for systematic errors
examples of systematic errors
CT scan used for planning is a snapshot - it
may be at one end or the other of the
random errors - setup and motion
difference between simulator isocentre and
linac isocentre, laser accuracy, CT-MR
registration etc. transfer (made of linac laser
CT CT-MR film etc.)
Doctors delineation errors doctor
Margin for systematic errors
The probability distribution follows a
Gaussian in three dimensions
if you are on the 10% level on the 3D Gaussian
means you miss the CTV for all fractions on 10% of
patients. It can be shown (for a perfectly conformal
95% isodose round a sphere) that.
Mar gin = 2.5
Gives 95% isodose surrounding 90% of the patients.
This is the CTV to STV margin.
Random errors
Examples of random errors
Also known as execution errors
Set-up errors
Set-up of skin marks relative to linac
moves
Bony landmarks vary relative to skin
marks
Motion errors
Organ moves from day to day relative to
bony landmarks
Error can be translation or rotation
Recipe for margin - random errors
Margin for random errors
2
2
2 = setup
+ motion
((
mar gin = 2 + 2p
0.4
0.35
0 .5
0.3
mar gin 0.7
0.25
Series1
0.2
0.15
0.1
1.2
0.05
-2
-1
full formula
0
-3
0.7 * sigma
=1.64 for single beam,
slightly smaller for
multiple beams.
margin/cm
Assume that they follow a Gaussian with
parameter
Calculate dose distribution over course of
radiotherapy allowing for error distribution
Observe how much smaller the 95% isodose
is
Thats your margin
0.45
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
sigma/cm
Overall recipe
((
mar gin = 2.5 + 2 + p2
0 .5
mar gin 2.5 + 0.7
Systematic errors are worse than random
errors
Practical process of radiotherapy
treatment planning.
CT scan (and possibly MRI and/or PET)
Outline on the images to delineate the target
volumes and organs at risk.
Add appropriate margins for geometrical
uncertainty.
Decide on appropriate doses
Choose appropriate arrangement of beams
either: Forward Planning (choose arrangement of
beams until you get what you want).
or: Inverse Planning (specify what you want, and get
the computer choose the beams to achieve it).
10
Forward planning
Inverse planning
IMRT is too complex to just choose arrangement
of beams manually until the plan looks OK
Instead have software that optimises the plan to
produce the best treatment plan
For this to work, you need to have some measure
of what makes a good plan; you need some
mathematical objective function that you can
minimise.
These can be based on Dose (minimum, maximum
etc. to volume), or on Dose Volume Histograms
Dose Volume Histograms
The Ideal DVH
250.0
standard
200.0
IMRT
150.0
120
100.0
50.0
100
0.0
80
85
90
95
100
105
110
115
% volume
cc
300.0
Either:
What volume receives
a particular dose
(differential DVH)
What volume receives
at least a particular
dose (cumulative
DVH)
percentage dose
80
OAR
60
40
PTV
20
0
0
20
40
60
80
100
120
% dose
Use of DVH as prescription
Examples for PTV
At least 99% of the
volume >95% of
prescribed dose
Less than 1% of the
volume to exceed
105%
Median to be
between 99% and
101%
Use of DVH for organs at risk
Organ
Rectum
Dose
(%)
68
81
88
95
100
Bladder 68
81
100
Fem.Heads
68
Max
Vol (%)
60
50
30
15
5
50
25
5
50
11
Dose-based penalty
Prescriptions for IMRT
400
Dose based:
350
Penalty
I want the PTV to get 60Gy
I want the OAR to get less than 50Gy
300
Penalty increases with square
of difference.
250
200
150
100
50
Dose volume based:
0
40
I want no more than 5% of the PTV to be below 60Gy
I want no more than 50% of the rectum to exceed 50Gy
50
55
60
65
70
75
80
Dose to point in target
OAR has no penalty for under
dosing.
400
350
penalty
Planning system will use these objectives to form an
Objective Function (otherwise known as a cost
function)
45
300
Penalty is small if you only
250
200
just fail. Thats why people
150
100
tend to cheat by telling
50
0
30
40
50
60
Dose to point in OAR
DVH objectives and constraints
Target
At least X% of the target should
receive at least dose Y
Target
OAR (and some targets)
No more than X% of the volume
should receive more than dose Y
Hard Constraint
If it does not achieve the
constraint, then do not allow the
solution.
Objective or soft constraint
Apply a penalty for failure,
increasing the more you fail
- penalty
= w 2
70
planning system a lower
limit than the one they really
want.
Optimise to reduce objective function
Gradient based (need to be able to take derivative
of objective function with relative to weight of all
the sub-beams). Relatively fast, but can potentially
get trapped in local minima
Stochastic (e.g. simulated annealing) much
slower, but less risk of local minima.
In practice you need to keep modifying your
objective function to produce a clinically acceptable
plan mathematically optimal is not always
clinically optimal.
Where PTV extend into build-up region, the use of
the PTV for optimisation can introduce problems.
The larger w the harder the
constraint
Linear Quadratic theory
Fractionation in radiotherapy
If radiation given as a course of small
fractions of radiation, recovery occurs
between fractions
If normal tissue can recover more quickly
than tumour, this improves the therapeutic
ratio
Most fractionation schemes are empirical,
based on clinical experience
ln(target cell survival) = (d + d 2 )
If dose Dx is given in fractions of dx , this is gives
equivalent cell killing to a dose of D2 in 2 Gy fractions,
where
D2 = Dx
( + d x )
( + 2Gy)
can also define a Biologically Equivalent Dose equal to
dose in notional tiny fractions
BED = D1 +
/ is typically 10-20Gy for tumours, typically 2 Gy for
later-responding side effects
12
Fractionation in radiotherapy
Image-guided Radiotherapy
1
0
/ 2
0.1
/ 10
0.01
Delivering dose as a series of small fractions will reduce the difference
between the two curves, and cause less harm to normal tissues for the
same tumour kill
Normal tissues have greater power to recover between fractions of
radiotherapy than tumour has
A course of radiotherapy is typically 50 to 74 Gy, given in 2Gy daily
fractions (5 per week)
IGRT
MV helical CT on
Tomotherapy unit
If you can image the patient every day in the
treatment position, you can reduce the systematic
and random errors. This should enable a smaller
margin to be used, and hence reduce normal tissue
damage.
Image patient from exit beam.
Can reconstruct CT-image
Cone-beam using detector on conventional linac
Dedicated tomotherapy unit based on CT gantry
IGRT
kV cone-beam CT on Elekta
Synergy.
IGRT
Brachytherapy
13
What is Brachytherapy?
The placement of radiation sources in or near
the patient. Three categories :1) Intra-cavity - sources placed inside natural
body cavity. e.g. Ca cervix treated with
uterine / vaginal sources.
2) Interstitial - sources surgically implanted in
and around tumour. e.g. iridium in breasts.
iodine seeds in prostate
3) Mould - the use of surface applicators to hold
sources next to patients skin. e.g. skin
tumours
Interstitial (seeds implant to
prostate)
Ideal Source for Brachytherapy
1) -ray emitter. High enough energy to minimise
scatter and avoid increased energy deposition in
bone by PE. Low enough energy to minimise
protection requirements. This gives the range 200
- 400 keV.
2) Half life. Long enough to minimise decay
corrections during treatment. Too avoid frequently
buying new sources, a very long half-life is
desirable. For permanent implants, shorter halflives are needed.
3) Charged particle emissions absent or easily
screened.
Intracavitary Treatment (Cervix)
Interstitial (Iridium to the tongue)
4) No gaseous disintegration products.
5) High specific activity
6) Insoluble and non-toxic chemical form.
7) Does not powder/ disperse if casing
damaged.
8) Can be made into different sizes and shapes
(tubes, needles, spheres, flexible wires). If in
wire form must be able to be cut without
causing contamination.
9) Not damaged during sterilisation.
10) Cheap/ easily available (especially for
"disposable" sources).
14
Sources - what is available:
Isotopes : naturally occurring.
reactor produced :- fission products.
neutron activation (n,) products.
Radium and Radon no longer used.
Most commonly used isotopes are Ir-192 and
I-125
Cs-137, Co-60 and Pd-103 used in some
applications
Isodose Plot
Commonly used gamma-emitting
Nuclides
Nuclide
Co-60
Cs-137
Ir-192
Pd-103
I-125
Transmission
through 2cm
Pb (%)
19
12
1.9
(<0.1%)
(<0.1%)
Gammaray
energy
(MeV)
Half life
1.17
and
1.33
0.66
5.3
years
30 years 74 days
HVL=1.3cm
tissue
0.3-0.6 0.02
(mean=
0.36)
17 days
0.03
59 days
Isodose plots and dose-volume
histograms
If one evaluates dose over a grid of points and then
joins the points of equal dose, we get an isodose
plot (cf external beam treatment planning)
Radiotherapy Physics. Summary
Most radiotherapy given with external beam xrays, mostly with linear accelerators.
Multiple beams used to give good target coverage.
Intensity modulated radiotherapy (IMRT) enables
shaping of high dose regions in three dimensions.
Fractionated doses given to improve therapeutic
ratio.
Geometrical uncertainties mean we need to add
margins. Image Guided Radiotherapy has
potential to reduce these margins.
Brachytherapy puts sources inside the patient, to
irradiate from within.
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