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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5255_Библиотеки_им_академика_М_И_Перельмана
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262
Medical Cyclotron: Basic Principles and Operation
From equation-3 it seems that the time required for the ion to traverse a circular path in
a dee is independent of its velocity and the radius. If the frequency of the RF oscillator is
tuned to the mass and charge of the particle and also to the applied magnetic field then the
ion will constantly stay in phase with change in polarity between the dees. The velocity and
hence the energy of the particles keep on increasing as it passes through the gap between the
dees with increase in radius of the orbit. As the ion spirals outward and reaches the periphery
of the dees, with energy in the million electron volts (MeV) range, it is extracted by means
of an extractor assembly for the production of radioisotopes. The radius at which the ion is
removed from acceleration is called the extraction radius.
Once it acquires the desired energy, an electrostatic deflector operating at opposite
potential takes out the beam from its orbit for bombarding the target in case of positive ions.
For negative ions a thin carbon foil strips off the electrons and the proton or deuteron beam
is allowed to bombard the target material placed in the path of the beam but outside the
cyclotron vacuum tank.
Negative ion cyclotrons
Almost all the medical cyclotrons available today prefer to accelerate negative ions (3). The
hydrogen atom for example has a capacity to accommodate two electrons in its K shell and
if hydrogen gas is passed through an electric arc where electrons are amply available it may
accept one electron and become negative ion (H–). Negative ion cyclotrons have several
advantages and the most important is the extraction of electrons from the beam with the
help of a thin carbon foil (5 m thick). The carbon foil strips the electrons easily. Carbon
foils are positioned at different angles of the carbon
carousel in beam extraction assembly. In a dual beam
facility there are two beam extraction assemblies so
that the proton/deuteron beam can easily be directed
towards the target (Figure 3).
The extraction efficiency is extremely high (nearly
100%) as compared to positive ion acceleration.
Another big advantage with negative ion cyclotron is
the reduction in size. Negative ion cyclotrons are quite
compact. Further electron stripping does not induce
radioactivity thus the interior portion of the cyclotron
remains almost free of radioactivity. Once the
electrons are stripped, the positive ions (protons)
move outward due to change in polarity thus making
the extraction much simpler. However, the vacuum
requirement is more stringent with negative ion
machines to prevent their neutralization during
acceleration. Beam extraction in a positive ion
GSPant\Newbook\Final-2008\17-chp\262
Figure 3: Carbon foils fixed in two
different beam extraction systems in
a cyclotron. Normally 2-3 carbon foils
are placed in one carousel. Any one
foil can be selected for beam
extraction.
Medical Cyclotron: Basic Principles and Operation
2
2
c
263
cyclotron is complex and utilizes a curved and narrow electrostatic channel of some length
through which the high energy, accelerated beam is carefully steered. The extractor assembly
makes system more complex with low extraction efficiency as compared to negative ion
beam systems. Further, the unextracted high energy beam has chance of undergoing nuclear
reactions with the internal parts of the cyclotron making them radioactive.
Axial focusing of charged particles
In a cyclotron, the charged particles orbit inside hollow dees in a plane between the magnetic
poles known as median plane. Particles that deviate from the median plane are restrained by
the magnetic field to remain in this plane (axial focusing). For this force to prevail the
magnetic field should decrease with radius. This gradient of magnetic field acts as a focusing
lens and directs the particles back to median plane from moving above or below the median
plane.
Secondly the mass of the particle increases with increasing velocity in accordance with
Einstein’s special theory of relativity.
m
m =
o
1
(4)
Where m0 is the rest mass, m is the mass of the particle moving with velocity v and c is
the velocity of light in vacuum. Increase in mass due to increase in velocity will disturb the
phase synchronization and particle may reach the gap behind scheduled time. To compensate
for the relativistic increase in mass, the magnetic field should increase (more bending of the
beam) with radius so that particle reaches the gap in time to maintain phase. Thus the
relativistic increase in mass and axial focusing impose contradictory requirements on the
magnetic field.
Azimuthally varying field (AVF) cyclotron
To meet these two contradictory and important requirements azimuthally varying field (AVF)
magnet is used. For this purpose both the pole pieces of the magnet are typically made using
hill and valley design as shown in figure 4. The elevated portion is called hill and the
depressed portion is called valley. The poles come closer during cyclotron operation with
too little gap between the opposing hills and large gap between the valleys. The magnetic
field is intense between the hills and much less between the valleys. As the radius keeps on
increasing the there is increase in path between the hills that creates more bending of the
particles and reduce the path length so that they reach the gap in time. At the same time
after passing the hill the particles pass through valley where there is decrease in magnetic
field that is needed for axial focusing. Thus in an AVF cyclotron, the magnetic field increases
and decreases in a sinusoidal manner with increase in radius of the acceleration orbit satisfying
GSPant\Newbook\Final-2008\17-chp\263
264
Medical Cyclotron: Basic Principles and Operation
both requirements.
Most of the modern medical cyclotrons have this hill and valley design usually termed
as deep valley design. This produces a magnetic field strength in the hills that is much
stronger than the field strength in the valleys. The hill to valley ratio in a cyclotron depends
upon its make/manufacturer. In RDS-111 (CTI, Inc/Siemens) 11 MeV cyclotron the ratio is
27:1 for hill and valley gap. This makes much stronger magnetic field in hill region as
compared to the valley. As the accelerating ion passes through the hill region, its trajectory
is sharply bent due to the strong magnetic field. On the other hand, the ion experiences only
a weak magnetic field in the valley, and its path is nearly a straight line but the beam
experiences focusing in this region. After passing the valley it passes through the next hill
and so on. One hill and one valley forms a sector (Figure 4). Since the medical cyclotrons
used to produce PET tracers are compact in design, there are usually four sectors either in
pie or spiral shape.
Figure 4: Hill and valley design of magnetic poles in a cyclotron. There are two poles like
this very close to each other. There is intense magnetic field between the hills of two poles.
The magnetic field between two corresponding valleys is much less in comparison to that between
the hills.
The AVF cyclotron has major modification and improvement over the uniform-field
cyclotron. The four dees of the cyclotron are placed in the valley. Focusing of particles
using this method is known as Thomas focusing (4). With proper choice of focusing elements,
the magnetic field variation balances the relativistic mass increase, resulting in a constantrevolution frequency. The effective limit to the velocities attainable will be fixed by the
possibility of adjusting the magnetic field exactly for resonance. An AVF cyclotron with this
property is known as isochronous cyclotron. All these cyclotrons are designed to accelerate
GSPant\Newbook\Final-2008\17-chp\264
Medical Cyclotron: Basic Principles and Operation
265
the beam to a fixed energy. Commercially available cyclotrons provide beam energy from
around 10 MeV to 18 MeV.
Radioisotopes Production
In this chapter we confine our discussion to medical cyclotrons primarily designed to produce
the positron emitters. Under a given set of irradiation conditions, the yield of the radioisotope
production depends upon various parameters that govern the nuclear reaction. Some of the
cardinal parameters that are relevant in this regard are discussed here.
(a) Energy of the beam
(b) Beam intensity (beam current): Sufficient beam current is required to get practical
yields
(c) Target volume (size): Larger volume makes more number of target atoms available
for nuclear reaction resulting in higher yield.
(d) Time of irradiation: Increase in irradiation time increases the yield of nuclear
reaction but not linearly beyond certain time. The saturation yield depends upon the
physical half-life of the positron emitter being produced.
There are few more factors, which may influence the yield and will be described later in
this chapter.
Energy of the beam
The production of radionuclides in a cyclotron demands that particle beams must have
sufficient energy to bring about the required nuclear reactions. Now the question arises what
energy is enough to give a desired yield. Cyclotrons for the production of PET tracers are
available in fixed energies from various manufactures with energy from 10-18 MeV. The
cyclotrons, which use deuterons as projectile, are of higher energies. For example cyclotron
from GE healthcare system (PET trace) accelerates proton beam to 16.5 MeV and deuterons
to only 8 MeV and 18 MeV cyclotron from IBA (Cyclone) accelerates proton beam to 18
MeV and deuterons to 9 MeV. The proton beam is more commonly used for radioisotope
production. If we confine ourselves to proton beam we ought to know the threshold energy
that is required to bring about a given nuclear reaction. This energy is called the threshold
energy. Before going to threshold energy let us understand the Q value of a nuclear reaction.
The nuclear reaction energy, commonly known as Q value represents the release or
absorption of energy during a nuclear reaction. When it is positive the reaction is called
exoergic and energy is released during nuclear reaction but when it is negative (endoergic),
energy needs to be supplied for the reaction to take place.
In endoergic reaction the threshold energy will be the sum of coulomb barrier and the Q
value. It may be difficult to estimate the coulomb barrier there are methods to estimate the
threshold energy for a reaction. As an example the Q value of 18O(p,n)
explained below.
18
F reaction is
GSPant\Newbook\Final-2008\17-chp\265
266
O p F n Q
A A
18 1
18
MeV
18 18
Medical Cyclotron: Basic Principles and Operation
Where Q = rest mass of (18O + P) – rest mass of (18F + n)
From nuclear tables it can be shown that Q = –2.438 MeV (3)
Threshold energy (Et)
Once Q value is estimated, the threshold energy can be calculated by the following
equation:
Et=
where, A1 = mass number of target nucleus and A2 = mass number of the bombarding
particle. Using the above equation the threshold energy for any nuclear reaction can be
calculated. For 18O(p, n)18F reaction the threshold energy :
1 2
Q
A
1
(5)
Et=
( 2.438)
Et= 2.57 MeV
It is now clear that 18O(p, n)18F reaction can not start below a beam energy of 2.57 MeV.
For exoergic reactions, Q values are positive and the threshold energy should be able to
cross the coulomb barrier (5). The starting energy (Es) has to be slightly more than coulomb
barrier and is given by the following equation.
The starting energy, Es required to overcome the coulomb barrier and to transmit
momentum to the reaction system during collision could be calculated by the following
equation-3.
Es=
0.96
Z Z A A
1 1
3 3
A A
1 2
1 2 1 2
A
1
(6)
Where Z1 and Z2 are the atomic numbers of the target and the particle respectively and
A1 and A2 are their respective mass numbers. The first term on the right hand side of
equation-6 provides the value for the Coulomb barrier alone while the second term represents
the fraction of the energy of the particle needed for the conservation of momentum.
For example the starting energy for proton in 18O(p, n)18F reaction can be calculated as
follows:
GSPant\Newbook\Final-2008\17-chp\266
Medical Cyclotron: Basic Principles and Operation
MeV
(1 )
t
0.96 8 1 18 1
Es=
1 1
3 3
18 1
18
267
Es= 2.24 MeV
For an endoergic reaction to take place, the minimum energy that the particle should
have is given by the larger of the threshold energy (Et) or the starting energy (Es). Hence, for
18
O(p, n)18F reaction, the minimum proton energy required is given by (Et), which is 2.57
MeV.
Saturation condition and irradiation time
The rate of production of a radionuclide is affected by its radioactive decay. Initially the rate
of formation is more and there is a linear growth. After a long time there will be competition
between the growth and decay. For short-lived nuclides, the rate of formation and decay will
come to equilibrium after sufficiently long time of bombardment. After saturation the
production rate is equal to the rate of decay and no more product can be expected with
increase in bombardment time (7).
The rate of formation in this case is given by:
R =
e
(7)
Where;
R is the rate of formation of nuclei (dN/dt)
N is the number target nuclei present at the end
is the decay constant
t is the time of bombardment
The term in the denominator of equation-7 is referred to as the saturation factor. There is
another term called saturation yield which refers to the theoretical maximum rate of production
of radioisotope for given beam energy conditions
Increase in beam energy increases the yield. As mentioned earlier (proton) beam energies
from 10-18 MeV are available from various manufacturers. Duration of bombardment is
N
another parameter that influences the yield. The yield after long bombardment times (>
2h
for 18F production) does not increase linearly therefore bombardment beyond certain time
duration is not practically beneficial. The irradiation time in day-to-day practice depends on
many factors besides the beam energy and beam current such as target status, requirement of
activity, enrichment of 18O water, status of delivery lines etc. If all the parameters are at
GSPant\Newbook\Final-2008\17-chp\267
268
Medical Cyclotron: Basic Principles and Operation
their optimum performance then irradiation time is usually kept less than 2 h. More appropriate
to say that the time of production run depends on the requirement on a particular day.
Beam current
The second important factor that influences the yield is the beam current. More the beam
current (more protons/deuterons) more is the chance for nuclear reaction to take place and
resultant yield is more. This optimum/maximum value of this parameter is usually fixed for
a given machine. However, the machine can be operated at lesser beam current if required.
Operational aspects of a medical cyclotron
Medical cyclotrons used for producing positron emitters for PET studies are growing in
number enthusiastically all over the world. It should be noted that this is not a push button
type of machine. It has various components and all of which must function optimally. The
main components of a cyclotron include the ion source system, radiofrequency (RF) oscillator
system, vacuum system, magnet system and targetry. The most important condition for all
of them is the maintenance of ambient temperature and humidity. Since cyclotron is operated
at high voltage (RF system) and current (magnet) humidity beyond tolerance limit is extremely
dangerous for the machine. It is essential that the humidity at 55% and temperature around
20C should be maintained in the cyclotron room. Chilling plant circulates cold water in
components that are heated up during cyclotron operation; helium gas circulates to cool the
target window. The status of the chilling plant and helium pump need to be checked before
initialization the machine for operation. Malfunctioning of any of the components will
simply make the cyclotron inoperable.
Ion source system
The ion source system produces negative ions (hydrogen/deuteron) in an internal, axially
mounted ion source optimized for this purpose. The ion source is controlled by software
during normal automated operation and therefore no user intervention is required under
normal operating conditions. The ion source contains two tantalum cathodes located
equidistant from an anode. A potential gradient between the cathodes and anode ionizes the
hydrogen/deuteron gas supplied to this region of the ion source. The ionized gas forms the
plasma from which negative ions are extracted (pulled with a bias voltage) for acceleration.
During normal operation, the control system regulates the ion source arc current to maintain
the desired target current. The anode and cathodes get eroded and need replacement after
some time of operation. The process of cleaning the ion source system and changing few
vital components is called it’s rebuild which is normally done semiannually by the service
engineer.
GSPant\Newbook\Final-2008\17-chp\268
Medical Cyclotron: Basic Principles and Operation
269
Radio frequency (RF) System
The RF system is the most important and sensitive components of the cyclotron, which
supplies an alternating high voltage potential to the dee structure, which in turn imparts
energy to the H–/D– ions. The structure is composed of four pie-shaped electrodes, which are
mounted in the magnet valleys and supported by dee-stems extending down from mounting
plates at the top of the magnet yoke. For this part of cyclotron to work smoothly, RF
conditioning is advisable. In RF conditioning the RF voltage is brought down from supra to
sub optimal voltage in steps. In the beginning it should be brought in steps of 0.25 kV and at
each step the magnet current is kept ON and OFF for one minute each. Thus the system
remains at one voltage for 2 minutes. In RDS-111 system the voltage is brought down from
40 to 15 kV in steps of 0.25 kV. Once it reaches 15 kV then the voltage is raised in steps in
the same manner up to 40 kV. Once the process is complete the system is set at the operating
voltage say 34 kV of RDS systems. Since this type of RF conditioning takes very long time
and therefore should be done on any off days. On routine basis short form of RF conditioning
is used which does not take more than 30 minutes. With our experience it is advisable to
tune RF system (conditioning) before starting the production run for smooth functioning of
RF system during a production run.
Vacuum system
The vacuum system consists of a vacuum chamber contained within the magnet yokes.
There are mechanical and diffusion pumps, which help both in creating and maintaining,
desired vacuum in the tank by constantly removing gas from the ion source and other
particles from surfaces inside the vacuum chamber. The vacuum is necessary in the main
acceleration region of the cyclotron to maintain the desired acceleration to the ion beam
without any loss of ions and their energy. Vacuum is maintained all the time whether
cyclotron is in operation or not. Therefore the desired pumps are working all the time.
Malfunctioning of any one of them will show sub optimal conditions of vacuum in the
cyclotron. It is therefore advisable to check the functioning of these pumps once in the
morning before operating the machine and also in the evening so that immediate corrective
measure can be taken immediately by the service engineer.
Magnet system
The magnet system provides the bending force that confines the beam to the circular orbit
centered between the upper and lower magnet poles. The magnet system includes the upper
and lower magnet yokes with integral pole pieces, the magnet coil, and the magnet power
supply. Applying current to the coil mounted between the upper and lower magnet yokes
energizes the magnet. The field generated by the magnet coil is concentrated in the small
gap between the upper and lower poles where the beam is accelerated. Each magnet pole
consists of four pie shaped wedges extending from the yoke toward the opposing pole.
These pie-shaped wedges are called hills. Each of the recessed regions between adjacent
GSPant\Newbook\Final-2008\17-chp\269
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Medical Cyclotron: Basic Principles and Operation
hills is termed a valley region. Very high current is applied to make the yokes as strong
magnet. Large amount of heat is generated in the coils for which chilling plant circulates
cold water to bring down the temperature.
Target system
The target system consists of target body, target changer, collimator assembly and target
material. The target body holds the target material during irradiation and is usually made of
silver for 18F production. Better targets with titanium and niobium are now available. For
other positron emitters the target body may be of other material like aluminum etc. During
target irradiation the beam passes through a vacuum isolation window, helium cooling space,
the target window and finally the target material. As the beam passes through the windows it
loses energy. This energy loss is converted into heat, which is removed from the windows
through helium jet cooling. In most of the cyclotron the four clinically useful positron
emitting radionuclides such as 18F, 15O, 13N and 11C are produced. The target changer assembly
controls the movement of the selected target into bombardment position and accommodates
as many as 8 or 4 targets in RDS system. Any ports not occupied by an isotope production
target are usually filled with dummy targets. Water and helium gas are circulated through
the target changer to remove heat from the target body. The collimator, and a carbon disk of
less than 1 cm central hole, is mounted at the exit before the vacuum window inside the
cyclotron (RDS systems). This ensures a relatively uniform beam profile across the target
volume.
Extraction system
The extraction system consists of one, or two (depending upon the available beam lines),
beam extractors that intercept the accelerated (H-/D-) beam with a carbon foil, which strips
the loosely bound electrons from the hydrogen nuclei. This polarity change from negative to
positive ions reverses the bending force exerted on the beam by the magnetic field. Once
stripped of electrons, the positively charged beam arcs outward toward the exit port and
target. Extractor carousels are located in positions so as to allow beam extraction to the
alternate targets in systems with the dual extraction option. The dual beam option allows
two extractor foils to be moved into the beam path, thus splitting the beam between two
targets.
Most of the modern medical cyclotrons are operated by computer controls. Before
initializing the system various parameters such as temperature, humidity, vacuum status, gas
pressures and chiller status have to be at their optimum conditions. The desired radionuclide
is selected through computer controls, which loads the target material in the target assembly
automatically. The required proton beam current is selected and the bombardment process is
started for a desired duration depending upon the amount of activity required and saturation
yield of the targetry. Once the radionuclide is produced it is unloaded from the targetry and
transferred to radiochemistry laboratory for further synthesis of positron emitting
GSPant\Newbook\Final-2008\17-chp\270
Medical Cyclotron: Basic Principles and Operation
271
radiopharmaceuticals. For example when 18O water is bombarded to produce 18F, 18F-FDG is
synthesized in the radiochemistry synthesis box.
Factors affecting the yield of radionuclide production
Various factors affect the end of bombardment (EOB) yield. The most influential factors
as describe above are the energy of the beam, beam current, target volume and duration of
bombardment. In addition, cleanliness of the target is extremely important to get better
yield. This may be achieved by rinsing the target immediately after the production run is
over. Whenever the yield of the radioisotope production is less than the expected activity,
target rebuild is required. Target rebuild is the process in which the target body is cleaned
with chloroform, methanol, acetone and water. Before beginning the target rebuild process,
the target window should be removed and stored at a safe place for physical decay, as it is a
solid radioactive waste. The first bombardment on a newly rebuild target should be carefully
observed for target pressure as there are chances that either the target window or vacuum
window may be blown off due to incorrect positioning of target window in the target body.
There are few important parameters, which should be monitored during the bombardment
period. The applied potential to the RF system, target current and target pressure should be
stable throughout the bombardment for better yield.
Table 1: Physical characteristics of radionuclides produced from 11 MeV cyclotron for PET
Nuclide Target material Nuclear Chemical Half-life Decay Maximum Maximum
reaction form (min) mode energy range in
(MeV) air
11
C Unenriched
14
N(p,)11C Carbon dioxide 20.4 + (100%) 0.96 4.1
Nitrogen gas gas (CO2) in
with 2.5% O
2
Nitrogen gas
(N2)
13
N 5 mMol Ethanol16O(p, )13N Ammonium ion 9.98 + (100%) 1.19 5.4
in HPLC water (NH4) in water
15
O
15
N enriched
15
N(p,n)15O Oxygen gas (O2) 2.03 + (100%) 1.7 8.0
Nitrogen gas in Nitrogen gas
with 2.5% O
18
F
18
O enriched
2
18
O(p,n)18F Fluoride ion (F–) 109.8 + (97%), 0.69 2.4
(N2)
water EC (3%)
18
F2 gas18O enriched gas18O(p,n)18F Fluorine gas (F2) 109.8 + (97%), 0.69 2.4
EC (3%)
References:
1. Livingston MS. Particle Accelerators: A Brief History. Harvard, UP. 1969.
2. Livingston MS and Blewett JP. Particle Accelerators. McGraw – Hill Book company, 1962.
GSPant\Newbook\Final-2008\17-chp\271
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