4T3 Radiation Therapy

8/13/2019 4T3 Radiation Therapy

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Physics of Radiation Therapy

Biological basis Physical goal Brachytherapy Teletherapy Measurement of dose C lcul tion of dose

Download overheads atwww.science.mcmaster.ca/medphys/faculty/22-michael-patterson.html

You might also read:

M. Oldham, Radiation physics and applications in

therapeutic medicine, Physics Education 460-467 (2001).

There are also many texts on the subject - the classic isThe Physics of Radiology by H. E. Johns and J. R. Cunningham


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Biological basis of radiation therapy

1. Cells can be killed by ionizing radiation.

2. Most important target appears to be nuclear DNA.

3. Radiation damage to DNA results in non-viable offspring.

4. Rapidly dividing cell populations are the most sensitive toionizing radiation (e.g. tumors, epithelial cells, hemopoietic cells.

Assessing biological effects

Want to quantify the effect of a specific dose of ionizing radiation.In this context, dose has a well-defined physical meaning: theenergy absorbed per unit mass. The SI unit is Gy = J kg -1. Youmay still encounter the rad: 1 Gy = 100 rad or 1 rad = 1 cGy.

Biological damage can be measured at the level of the cell, theorgan, or the complete organism.

At the cellular level, the classic endpoint is cell survival.


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A classic cell survival experiment


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e.g. effect of oxygen on survival curves. It is believed that thiseffect is clinically important because many cells in a tumor can behypoxic.


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e.g. change in survival when dose is given in a series of fractions.Clinically, it has been found that allowing for repair betweenfractions gives better results - presumably because malignant cellsare repair deficient.

In vivo assays: Here we might measure animal survival, tumor

regression or growth delay, organ function. Using a range ofdoses we can construct a dose-response curve. Consider whatthis would look like for cure, assuming that we have to kill everytumor cell in order to achieve a cure..


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At a high enough dose we would have a high probability of curingevery tumor. Unfortunately, we must also irradiate some normal

tissue and its response usually limits the dose that can be used.


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The physical goal of radiation therapy

Bearing this in mind, from a physics perspective the goal ofradiation therapy could be simply stated as

Deliver a high dose to all parts of the tumor while minimizing thedose to surrounding normal tissue.

100%

0%

As we will see, this ideal dose distribution is not physicallyachievable, but we attempt to satisfy it through two generalstrategies: brachytherapy and teletherapy.

Brachytherapy

In brachytherapy radiation sources are placed adjacent to orwithin the target volume. The sources may be implantedpermanently or temporarily. Temporary implants may beperformed at high dose rate (HDR, treatment time of minutes) or

low dose rate (LDR, treatment time of days).


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Quick refresher on radiation - tissue interactions

Photons (gamma rays or x-rays) interact with matter through thephotoelectric effect, the Compton effect, or by pair production.The relative importance of these three is shown below:

All of these produce high energy electrons. Because electrons arecharged particles, they interact strongly with atoms in tissue anda single high energy electron can ionize many atoms along itstrack. To a good approximation, the electron loses energy at aconstant rate of about 2 MeV/cm. Therefore electrons have afinite range in tissue that is proportional to their initial energy. Onthe other hand, a photon beam is attenuated exponentially with

distance, so that there is a small but finite probability that a highenergy photon can penetrate a concrete wall two meters thick! Itis important to realize that even when photons are used inradiation therapy, it is actually the electrons that do most of thebiological damage.


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Back to brachytherapy

Source

P1

P2

r2r1

For a point gamma ray sourcethe dose will fall off with

distance due to the inverse-square law and tissue attenuation,so we expect the ratio of doses atPoints 1 and 2 to look somethinglike

exp (-r1)

exp (-r2) r12

r22

X

D1

D2

Note: is about 0.17 cm -1 for 100 keV photons

So, from a physics perspective, brachytherapy makes a lot ofsense. Note that if we used an electron (beta particle) source of

the correct energy, we would be even better off because of thefinite range in tissue. In either case, multiple sources are usuallynecessary to achieve a useful dose distribution. Although betaemitters are used to treat small malignant deposits, the range ofreadily available beta emitters is too short, so most brachytherapyis performed with gamma emitters. These are obtained either asfission products or as the result of neutron capture reactions.There are many possible isotopes that could be used but

consideration must be given to half-life, gamma energy, cost, andphysical form. The isotopes used most commonly in brachy-therapy are Cs137, Ir192, and I125.


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Cesium 137 30 yr half life 0.66 MeV gamma

Iridium 192 60 d half life 0.136 - 1.06 MeV gamma

Iodine 125 60 d half life 0.025 MeV gamma

So why not do brachytherapy all the time?

1. Access to the tumor may require surgery.

2. Patient may be a poor surgical risk.

3. It is not practical to implant large tumors.

4. May require hospitalization.

5. Radiation protection issues (see below).

6. Time consuming and technically more difficult.

Technical aspects

Brachytherapy was firstperformed using radioactive

sources (e.g. radium needles)which were implanted duringthe surgical procedure. Thisresulted in a significant radiationexposure to the physician and otheroperating room staff.


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The advent of afterloadingtechniques greatly reduced thedose received by OR staff.Instead of working directlywith the radioactivematerial, the physician firstimplants or inserts a catheteror applicator. Once the correctarrangement is achieved, theradioactive material (e.g. Iridiumwire) is inserted and secured.This does not remove the dose

received by those who care for the patient.

This idea can be extended further by using remote afterloading.The applicators or catheters are connected to a unit that moves

Catheter

Radioactive wire

the radioactive sources into position pneumatically or by a wire.The sources can be shuttled back into the shielded containerwhen it is necessary for staff to care for the patient.

To patient

Shielded container

Radioactive sources

Flexible hose


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An interesting recent development is the use of brachytherapyto prevent re-stenosis of coronary arteries after balloon angio-plasty. A radioactive source is inserted in the vessel underfluoroscopic guidance, or a radioactive stent can be permanentlyplaced in the vessel. The correct dose of radiation will preventproliferation of endothelial cells and re-stenosis.

Teletherapy

In teletherapy an external source at a distance of about onemeter from the patient is used to irradiate the tumor. A series ofdaily fractions, each about 2 Gy, is used. It takes about one

minute to deliver the actual treatment, but typically 15 minutes toposition the patient and deliver beams from different directions.

P1

P2

r2 r1

d1

d2

exp (-d1)

exp (-d2) r12

r22

XD1

D2

For normal tissue closer to thesource, both attenuation and

the inverse-square law workagainst achieving an acceptabledose distribution. However, theadvantages of using teletherapyare many...


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Advantages of teletherapy

1. Any anatomical site can be treated.

2. Large fields (even the whole body!) can be accommodated.

3. Treatment is quick and convenient.

4. Usually done as an outpatient procedure.

5. Noninvasive.

6. Can be performed on patients who are not well.

7. No significant radiation dose to staff, family members, etc.

8. The physical disadvantages can be largely overcome.

Dose distribution from a photon beam

To understand #8 above, we need to understand the dose

distribution from an external photon beam. We need to consider:

1. Dose is due mainly to electrons.

2. Electrons have finite range.

3. Attenuation of primary photons.

4. Inverse square law.

5. Compton scattered photons.


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Simple model for dose near the surface...

1 2 3 4 5 6 7 8 Electron range

Assume each high energy electron is launched in the forwarddirection and that each has the range shown. The dose in eachlayer of tissue will be proportional to the number of electrontracks per unit volume. If there is no substantial attenuation ofthe photon fluence over this distance we would expect:

D2 = 2D1, D3 = 3D1, D4 = 4D1, D5 = 5D1, D6 = 6D1, but afterthis layer (in which we reach an equilibrium in electron fluence),the dose would be approximately constant. But as depthcontinues to increase the photon fluence will decrease due tothe inverse square law and attenuation.


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From this simple model we expect the dose versus depth curve tolook something like...

Build-up region

Approx. exponential attenuation

Dose

Depth

Here are some examplesof real depth-dose curves.Our simple model doespredict the general

nature of these curves,but not the quantitativedetails.


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This detailed plot of the build-up region shows the shift of thepeak with photon energy. Note that the surface dose is not zerobecause of backscattering and electron contamination in thebeam. Overall, we see that a lot can be gained by selecting thephoton energy to match the clinical problem.

Photon sources for teletherapy

Gamma rays

Radioactive isotopes. The only one in wide use now is Cobalt 60.Each beta decay of Co60 results in the emission of two gammarays - the average energy is about 1.2 MeV. Cobalt 60 is producedin a nuclear reactor by (n, ) reactions. The half-life is about 5years which means that sources must be periodically replaced and

adjustments must be made to treatments to account for sourcedecay. A typical therapy source is about 10 kCi or 370,000 GBq. Asource like this could deliver a lethal whole body dose of gammarays in a minute, so special handling and shipping procedures arenecessary.


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X-rays

X-rays can be produced by decelerating electrons - this is knownas bremsstrahlung. The electrons are first accelerated by anelectric field. At energies below 250 keV this can be accomplished

in a relatively simple x-ray tube. For higher energies, anexpensive and complicated electron linear accelerator is used.The electrons are stopped in a metal target and a polyenergeticx-ray beam is produced. The highest photon energy in thespectrum is equal to the electron energy and the mean photonenergy is about one third of this.

Schematic diagram of an x-ray tube used to produce x-rays inthe 50 - 300 kV range. Note the symbol kV refers to the effectivevoltage used to accelerate the electrons. A 100 kV x-ray beamwould consist of a wide spectrum of energies with 100 keVbeing the highest.


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It is not practical to run x-ray tubes at voltageshigher than a few hundred kV, so how do weget high energy x-rays?

E vectort

t + 0.083 ns

Waveguide structureMicrowave source

t + 0.167 ns

t + 0.250 ns

t + 0.333 ns

Microwave frequency = 3 GHz (period = 0.333 ns)Wavelength = 10 cm


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An electron linear accelerator uses microwaves propagating ina special waveguide to accelerate the electrons. The largest linacaccelerates electrons to 2 GeV, but medical accelerators operatein the 4 - 25 MeV range. As shown below, the electron beam isfocused onto a metal target (usually tungsten). At high energies

the bremsstrahlung beam is forward peaked, so a metalflattening filter is used to produce a more uniform beam. A setof moveable collimators allow the user to define rectangularbeams of dimensions from 4 to 40 cm. An ionization chamber(more on these later) measures the radiation output in real timeand is the means by which the dose to the patient is controlled.


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Typical clinical linear accelerator

Axis of rotation

When the beam is not on, a light field is projected onto thepatient which is coincident with the radiation field. This aids in

patient setup. Other devices, such as wall-mounted lasers areused in conjunction with marks on the patient. Note thatrotation of the entire accelerator assembly allows a photonbeam to be directed at the patient at any angle without movingthe patient. This is called an isocentric setup.


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Cut-away view of modern linear accelerator


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Typical teletherapy installation...

Because even the scattered and leakage radiation dose ratesare quite high in the room, only the patient can be present during

the actual irradiation. A specially designed shielded room (orbunker) is needed to protect staff and often the general public.In a typical bunker for a high energy accelerator the primaryradiation barriers (see above) are about 2 m thick! These roomsare fairly expensive to build. Total cost of room and acceleratoris in the 2 - 4 million dollar range.

Primary barrier


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Recent Technology Innovations

Multi-leaf collimators:up to 120 independentleaves.

Image guidance:high energy or lowenergy x-ray imaging

systems


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We have seen how the correct selection of photon energy canmitigate the physical disadvantages of brachytherapy. Howevera single beam of photons still produces a dose distribution thatis far from ideal...

Consider what happens if you use two beams entering thepatient from opposite directions. The resulting dose distribution

will be the sum of the contributions from the two fields. Plottingthe dose along the central axis of this opposing pair of fields weget something that looks like...


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These examples show that even with this simple arrangementwe can get more dose in a deep-seated tumor than in the over-lying normal tissue. This idea can be extended to more complexarrangements ranging from standard 3, 4 or more field geometries

to quite complex individualized plans that incorporate beammodifiers.


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Split Absolute7500 cGy7200cGy6996 cGy

6500 cGy6000 cGy5940 cGy5500 cGy5000 cGy4500 cGy4000 cGy3500 cGy3200 cGy

3000 cGy2500 cGy

Dose distribution superimposed

on CT scan of patient anatomy


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PTV(tumor)

Intensity Modulated Radiation Therapy (IMRT)


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With a linear accelerator it may also be possible to extract theelectron beam before it hits the thick target. This beam is usuallyscattered by a thin metal foil to produce a large, reasonably flatfield. Recall that electrons have a finite range in tissue and thatdose is deposited in roughly equal amounts per unit pathlength.Therefor we might expect a broad electron beam to produce adepth-dose curve that is constant up to the range of the electronand then falls off rapidly. Real depth-dose curves show roughlythese features..


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Electron scattering is responsible for blurring of the sharp fall-offand also results in a relatively fuzzy edge to the beam.

These isodose plots show that the distribution tends to deteriorate

with depth. Nonetheless, electron beams are very useful intreating targets relatively close to the surface, especially whensensitive normal tissues (such as the spinal cord) lie directlybeneath the target volume.


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Other types of radiation, such as protons, can produce excellentdose distributions with a single field. However, these installationsare an order of magnitude more expensive than photon facilitiesand it is questionable whether they are justified when modern

conformal photon techniques can produce competitive results.

Depth-dose curve for a single beam of 187 MeV protons.The so-called Bragg peak near the end of the range occursbecause the proton energy loss per unit pathlength is a strongfunction of energy.


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The need for accurate dosimetry (or why cancer centres shouldemploy medical physicists.)

Pr

obabilityofcontrol

Recall the theoretical dose-response curve constructed fromcell-survival data. Complete dose-response curves do not existfor human tumors but there is some clinical trial data andanecdotal data that suggest the curve is very steep in the regionof typical clinical operation. A change of only 5% in the dosedelivered can result in a detectable difference in clinical response.Thus it is common to state that the absolute dose at any pointin the patient should be known to 5% or better. This dosemeasurement should be traceable to a national standard so thatthe results of clinical trials in one centre are comparable to thosein another centre in the same country or a different one. InCanada, national standards for dose are the responsibility ofthe National Research Council.


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So how hard can it be? Source

Beam modifier

Polyenergeticphoton beam

Electron contamination

Arbitrary distance

Irregular shape

Electrons

P

n omogeneous me um

Scattered photons

Considering all of the variables in the problem (some of whichare illustrated above for a typical teletherapy setup), statingthe dose at an arbitrary point P to within 5% is actually a very

challenging problem. In general there are two ways we couldtackle this problem...


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Strategy #1

If we knew the radiation beam properties (e.g. photon spectrumand fluence rate everywhere in the beam) and the characteristicsof the patient (e.g. spatial distribution of the electron density), wecould, in principle, calculate the dose at every point. In practice,not all the information is readily available and the calculation(e. g. a Monte Carlo simulation) is too slow. (This last constraintis on the verge of disappearing as computing power gets

cheaper and cheaper.)

Strategy #2

We could measure the dose directly using a suitable instrument. ,

it is not possible to do this in most cases. One could think aboutmanufacturing a simulated patient from tissue substitutes and

measuring the dose within it, but it is hard to imagine this asa practical solution when thousands of patients are treated peryear at a large centre. (Hamilton 4000 pts. per year)

A hybrid solution

Measure the dose delivered to a tissue-like material under afinite number of standard conditions. Use these data along with

a reasonable physical model to calculate the dose underthe sort of arbitrary conditions illustrated on the previous page.


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An example of standard conditions...

Flat surface

Source

100 cmSquare field10 cm X 10 cm

P ( 10 cm depth)

How do we measure the dose at P under

these standard conditions?


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A physicists view of the perfect patient


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Measurement of Dose

Possible Methods

Calorimetry: Temperature increase (1 Gy -> 0.24 mK in water)

Thermoluminescence: Absorbed radiation raises electrons tolong-lived traps. Heating removes electrons from traps and theirreturn to the valence band is accompanied by light emission. Thiscan be detected and related to dose. Cannot measure dose rate.

Fricke dosimetry: Radiation induced chemical changes in asolution can be detected by absorption spectroscopy.

Ionization chamber: Radiation ionizes gas molecules. These areco ec e y a g vo age resu ng n a sma curren

(typically nA).

In the clinical environment an ionization chamber is the bestchoice because:

1. Convenient.

2. Real time (rate or integrated dose).

3. Sufficiently sensitive.

4. Can be shipped to standards lab for calibration.

5. Detector is small enough to provide adequate spatial resolutionunder most circumstances.


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Calculating dose from ionization charge

Air

Plastic

If the air cavity is smallenough, it will not cause a

significant perturbation of theradiation field in the medium,in this case a plastic tissuephantom. This assumptionis the basis of Bragg-Graycavity theory.

The total energy deposited in the air cavity is equal to theproduct of the charge and the energy required to produce aunit charge. In air it takes an average of 33.7 eV to ionize onemolecule. The dose to the air, Dair , is equal to this total energy

.

If the cavity is a true Bragg-gray cavity, there is a simple

relationship between the Dair and Dplastic, the dose that would bedelivered to the volume of plastic that would replace the air. Tocalculate this we need to know the stopping powers for airand plastic. The stopping power is a measure of electron energyloss per unit pathlength. It is a weak function of electron energyso we need to know something about the energy spectrum ofelectrons in the medium. Putting this together, we have

Dplastic = Dair XStopping power for air

Stopping power for plastic


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In practice a real ionization chamber (see above, for example)is not an ideal Bragg-Gray cavity and corrections must be madefor:

1. Changes in density of the air.

2. Incomplete collection of charge produced.

3. Effects of the chamber wall.

4. Perturbation of the radiation field.

5. Differences in the electron energy spectrum compared tocalibration conditions.

When all these factor and their uncertainties (as well asuncertainties associated with calibration and charge measure-ment) are taken in to account, the overall uncertainty in ameasurement of absolute dose under standard conditions maybe as high as 2 - 3%. Given this, the goal of 5% for any point inany patient is tough to meet.


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Calculation of the dose under non-standard conditions

Approach #1

Source

dV

P

r

r'

Dose ( r ) = Dp ( r ) + V Ds ( r , r )

Easy Difficult

The functions Dp and Ds are derived from dose measurementsin phantoms. For example:

P

If we measure the dose at P for the

smaller field and then increase thefield size, the increment in dose toP is due to the annular region markedA in the diagram. We could thencalculate the contribution from thesegment marked S.

A

S


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This allows us to do the integral shown on the previous page...

Approach # 2

Measure or calculate thethree dimensional dosedistribution due to a pencilbeam in water.

Any other beam can be considered a summation orsuperposition of elemental pencil beams. Each of thesepencil beams is weighted to reflect their contribution to thetotal dose. For example, a wedge shaped beam modifierwould affect the weight of each pencil beam that passesthrough it.


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Weightedpencilbeams

We then add all of these appropriately weighted pencil beamstogether to get the final dose distribution. This process is

.

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