L1-INTRO 39.pdf

Università degli Studi di Padova Course Proton Therapy Physics part Lesson 1 – Introduction Prof. Alessandro Patelli [email protected] Dept Physics and Astronomy 049 827 7039 – Room 108, via Marzolo 8 Radiation therapy for cancer therapy A large portion of cancer patients, e.g., more than...

Università degli Studi di Padova Course Proton Therapy Physics part Lesson 1 – Introduction Prof. Alessandro Patelli [email protected] Dept Physics and Astronomy 049 827 7039 – Room 108, via Marzolo 8 Radiation therapy for cancer therapy A large portion of cancer patients, e.g., more than half of all cancer patients in the United States, receive radiation therapy during the course of treatment. Radiation therapy is used either as the sole treatment or, more typically, in combination with other therapies, including, for instance, surgery and chemotherapy. Radiation interacts with tissue via atomic and nuclear interactions. The energy transferred to and deposited in the tissue in such interactions is quantified as “absorbed dose” and expressed in energy (Joules) absorbed per unit mass (kg), which has the units of Gray (Gy). What radiation can do? DNA mutation functional disruption death biological mechanism Cells repair Organ immune response Issues Eradicating cancerous tissue while minimizing the irradiation of healthy tissue. not possible ! uncertainties in target volume uncertainties in delivering the therapeutic dose as planned radiation requires the beam to penetrate healthy tissue to reach the target Critical DOSE for tumor type Treatment Planning “therapeutic ratio”defines the maximally tolerated dose of a treatment to the minimally efficacious dose trade-off between administering the prescribed target dose and the dose to healthy tissue maximum dose not toxic for healthy tissue minimum efficace dose photons vs protons intensity modulated intensity modulated photon treatment (IMRT) proton treatment (IMPT) dose difference Dosimetric comparison between intensity-modulated photon radiotherapy (IMRT) and intensity-modulated proton therapy (IMPT), in a patient with low-grade glioma. Combined distribution fi fi Homogenous intensity-modulated proton therapy dose distribution in the target for a head and neck case resulting from the combination of heterogenous individual eld (F1, F2, F3, F4) dose distributions. (Adapted from a gure provided by A. Lomax, PSI, private communication) photons vs protons X-rays 16 MeV spread out Bragg peak 180 MeV After a short buildup region, photon beams show an exponentially decreasing energy deposition with increasing depth in tissue. few mm Protons The energy transferred to tissue by protons is inversely proportional to the proton velocity. As protons lose their energy mainly in electromagnetic interactions with orbital electrons of atoms. The more the protons slow down, the higher the energy they transfer to tissue per track length, causing the maximum dose deposition at a certain depth in tissue Physical selectivity - Active Raster Scanning Which is the “best” radia on for radiotherapy? physical selec vity (dose conformity) ti ti ti ti biological selec vity (LET/ RBE conformity, Targeted Enhancement with radiosensi zers, etc.) Linear Energy Transfer The RBE (Relative Biological Effectiveness) is a relative measure of the biological damage caused by different kinds of radiation compared with 200-keV x-rays (which are assigned RBE = 1) Radiation interaction with matter Radiation energy loss in matter Radiation interaction with matter Radiation energy loss in matter Relative Biological Effectiveness Different kinds of radiation cause different amounts of biological damage, even if the absorbed dose is the same. The health effects also depend on what kind of tissue is exposed. To account for these factors, a quantity called the relative biological effectiveness (RBE) is assigned to each type of radiation. The RBE is a relative measure of the biological damage caused by different kinds of 60 radiation compared with 200-keV X-rays or Co γ-rays (1.17/1.33 MeV), which are assigned RBE = 1. The RBE varies depending on the kind of radiation (alpha, beta, gamma), the energy of the radiation, the kind of tissue exposed, and the biological effect under consideration. Biologically Equivalent Dose To measure the biological damage caused by exposure to radiation, we calculate the biologically equivalent dose. BED = AbsDose × RBE (Sv):biologically effective dose (in sieverts) = absorbed dose (in grays) × RBE Another commonly used unit for biologically equivalent dose is the rem: 1 rem = 0.01 Sv = 10 mSv The average American receives an annual dose 360 millirem = 3.6 mSv per year, about 80% from natural sources. A roundtrip transcontinental flight gets you an extra 5 mrem Example A 60.0-kg patient about to have a brain scan is injected with 7.4E8 Bq (Activity = decays per second) of the radionuclide technetium-99m, 99mTc (The “m” stands for metastable). The metastable state 99mTc decays to the ground state with a half-life of 6.0 h. The 99mTc nucleus decays by emitting a 143-keV photon. Assuming that half of these photons escape the body without interacting, what biologically equivalent dose does the patient receive? The RBE for these photons is 0.97. Assume that all of the 99mTc decays while in the body. Università degli Studi di Padova Course Proton Therapy Physics part Lesson 2 – Basic Physics Prof. Alessandro Patelli [email protected] Dept Physics and Astronomy 049 827 7039 – Room 108, via Marzolo 8 Proton/Matter interaction Radiotherapy protons (kinetic energy between 3 and 300 MeV) interact with matter in three ways. 1. They lose energy and eventually stop by multiple electromagnetic (EM) collisions with atomic electrons (and to a much smaller degree, atomic nuclei). We call this process stopping. 2. They scatter a few degrees by multiple EM collisions with atomic nuclei (and to a smaller degree, electrons). This is called multiple Coulomb scattering (MCS). 3. Finally, they occasionally undergo single hard scatters either by the nucleus as a whole or by constituents of the nucleus (protons, neutrons, or clusters such as αparticles). Hard scatters are also called nuclear interactions, though they may involve either the nuclear (strong) force or the EM force. Only 1 % /cm of water, ∼ 20 % total protons. Start with definitions Energy (MeV) The MKS unit of energy is the joule (J). In particle physics, however, we normally use the electron volt (eV) or mega electron volt (MeV). The electron volt is defined as the kinetic energy gained by one electron in falling through a potential difference of 1 volt. Since energy = charge × potential difference ΔE = qΔV for the electron q = e = 1.602 × 10 −19 C −19 1 eV = 1.602 × 10 J Binding energies of atomic electrons are of order eV. Energy to remove a proton or neutron from the nucleus is of order MeV. Proton energies of concern in radiotherapy are 3-300 MeV. Areal Density (g/cm proton ) 2 The range of a 160 MeV proton is 17.6 cm in water. In air it is 16700 cm (167 m). Most of this very large difference comes from the fact that air under normal conditions is a gas with a density of only 0.0012 g/cm3. To reveal the underlying physics, that is, to eliminate the essentially trivial role of density, we normally think of a degrader not in terms of its thickness Δx (cm) but its areal density same areal density The two are the same for water, whose density ρ is 1 g/cm3 by definition. By this measure the range of our 160 MeV proton in air is 20.0 g/cm2 so we see that the stopping powers of air and water are not so different after all. There is no special symbol for areal density. In computation it is convenient to think of it as thickness × density, but if you have a degrader and wish to measure its areal density you should weigh it and divide by the area, usually a much more accurate method. Mass Stopping Power (MeV/ (g/cm )) 2 When a proton slows down its specific energy change dE/dx is negative: as x increases, E decreases. The positive quantity S ≡ – dE/dx (MeV/cm) is called the stopping power of the material. It depends on the material and on the proton’s speed (or energy). We rarely use stopping power by itself. Instead we use the mass stopping power S 1 dT =− ρ ρ dz single proton 160 MeV MeV 2 g/cm lost energy areal density The mass stopping power of 160 MeVprotons in 2 water is 5.2 MeV/ (g/cm ). We’ll generally use z as the beam direction and T as the kinetic energy, so to be strictly consistent we should have denoted the stopping power –dT/dz. However, everyone calls it dE/dx. Fluence (protons/cm 2 ) Fluence characterizes the number of protons in a beam. In beam line design the protons always travel in the same direction ± a few degrees We can use a plane element of area and define fluence by where dA is an infinitesimal element of area perpendicular to the beam and dN is the number of protons passing through it. The fluence rate is sometimes denoted by lowercase ϕ and earlier called ‘flux’. Fluence and fluence rate are scalar fields which vary with x, y, z and t. The Fundamental Formula for Dose area A N protons Δx The equation relating dose to fluence and stopping power is the starting point of most beam line design problems. From the figure : energy −dN (dT/dz) dz dN 1 dT S D= = = × − =Φ× ( dA ) ( ρ dz ) mass ρdAdt ρ dose = fluence × mass stopping power Gy D = ΦS/ρ in Practical Units J/Kg = Gy is a perfectly good unit of dose but (protons/m2) for fluence and J/(Kg/m2) for mass stopping power are not convenient. A better form is where Φ is in Gp/cm2 and S/ρ is in MeV/(g/cm2). The gigaproton = 1 Gp = 109 protons is a handy unit for proton therapy. If we use charge areal density instead of fluence that gets rid of the constant and we find where q/A is the total proton charge divided by the area through which it passes (nC/ cm2) (nC = nanoCoulomb). Finally, taking the time derivative where iP/A is the proton current density (nA/cm2). Therapy doses are of the order of 1 Gy, target areas are of the order of cm2, S ≈ 5 MeV/(g/cm2) (160 MeV protons in water) and currents of nanoAmps to the proton nozzle. · D= 1nA MeV Gy Gy × 5.167 = 0.0164 = 1 π102cm 2 g/cm 2 s min Relativistic Proton Kinematics Therapy protons are relativistic: the beam at HCL (160 MeV) traveled at just about half the speed of light. Fortunately, you can relate anything to anything else for a proton by juggling just three formulas. They are v pc β= = c E E = T + mc 2 E = (pc) + (mc ) 2 2 2 2 in which c = speed of light, v = proton speed, p = proton momentum, T = proton kinetic energy, E = proton total energy and mc2 = proton rest mass = 938.27 MeV. For instance, the quantity pv used in multiple scattering theory, is given by or that 160 MeV protons have β = 0.5 as claimed. Three Handy Formulas In proton radiotherapy we most frequently think in terms of the proton kinetic energy T (MeV) and we want to express other kinematic quantities in terms of T. The three equations below cover most 2 2 requirements. τ is the reduced kinetic energy τ = T/mpc where mpc is the proton rest energy, 938.27 MeV. β→0 β→ limits τ non-relativistic τ→0 relativistic τ≫1 pv → 2T pv → T 2 pc → 2mc T ( ) 2 (pc) → T 2 2 Stopping When protons pass through matter they slow down and stop by millions of collisions with atomic electrons. The ‘Bethe-Bloch’ theory for this process was worked out by 1933. The theory contains one parameter whose value cannot be computed from first principles with sufficient accuracy, the mean excitation energy I, a property of the material’s atomic or molecular structure. I increases with atomic number Z, ranging from approximately 20 to 1000 eV over the periodic table. I is chosen to fit experimental results when available, and by interpolation otherwise. Hans Bethe 1906-2005 Bethe-Bloch model Bethe’s formula for the electronic mass stopping power of a proton is atomic numbers L(β) Stopping number Wn S 1 dT Z 1 2 = = 0.3072 ln − β 2 ) ρ ρ dz cB constant A β ( I relativistic term In the 3 - 300 MeV regime for protons where Wm is the largest possible energy loss in a single collision with a free electron I is the mean excitation energy of the medium 2 2 2mec β Wm = 1 − β2 MeV 2 g/cm Mean Excitation Energy I Experimentally derived This graph shows the dependence of I on atomic number Z. Irregularities in I/Z vs. Z are caused by atomic shell structure. It’s obvious that interpolating I accurately between measured values (from range or stopping power measurements) is not easy. Mixtures, Compounds and Molecules Mixtures obey the Bragg additivity rule, which is easily derived by assuming the absorber to be composed of several discrete sheets: Compounds and molecules are more complicated because I is affected by chemical bonding. Water turns out to be a particularly difficult case, which is unfortunate. R (160, water) = 17.648 g/cm2 (Bragg Rule) = 17.806 (+0.9%) (Experimental) Range Proton range is the integral of inverse stopping power. The proton enters at T and stops when the kinetic energy is 0. 1 dT ρR (Tinitial) = ∫T ( ρ dx ) initial Tfinal −1 dT = Tfinal ∫T dT (T) S/ρ [ ] initial Strictly speaking, the integrals we have written down are the proton pathlength. However, protons scatter very little so for practical purposes the pathlength equals the projected range. Experimentally, the computed range is interpreted as the depth by which half the protons have stopped, is written r0, and is called the mean projected range or just range. Measuring Range range 50% r0 The simplest arrangement (left) consists of a beam monitor and a stack of known degraders placed in front of a Faraday cup. This measures (in accordance with the definition of range) the number of surviving protons (not the dose!) as a function of projected depth in CH2 or aluminum. Data show a gradual falloff as protons succumb to nuclear reactions: charged secondaries will mostly miss the FC because of the distance. r0 is the x value of the halfway point measured from the corner (y ≈ 0.37) not the entrance (y ≈ 0.53). The open circles were taken with a different FC with the CH2 much closer to the charge collector. Measuring Range Faraday Cup r0 where arrive half of the initial protons not taking into account hard scatters Multilayer Faraday Cup Dosimeter in water tank r0 where stronger variation in protons fluency r0 = d80 where the dose is at 80% respect maximum at distal end rule of thumb (not analytical) Range straggling Range straggling refers to the spread in proton ranges (even in a monoenergetic beam) because energy loss is a statistical process that occurs in discrete steps. The spread can be characterized by a Gaussian with an rms value σS , which is nearly proportional to r0. This nearly material-independent behavior has important consequences: it means we can assume the Bragg peak in H2O has a constant shape even if some stopping occurred in Pb. Power law interpolation In the 5 - 500 MeV range R = ae bT log R = log a + bT LOOK UP tables can be used ! Water Equivalence Since the human being is mainly made up of water, All properties of materials, as also RANGE rM, are described with quantities “water equivalent”, rW. The thickness of water tW that gives the same energy loss as a thickness tM of some other material, at incident energy Ei Attention: Energy loss depends on Energy !! NB: Polymers have same dependance of water Energy Spread ΔT ΔT T T roughly constant ′ ′ 1.2% Because EM stopping involves multiple discrete and random energy transfers, protons stop at slightly different depths. This range straggling yields a Gaussian distribution of stopping depths, characterized by σS. The fact that the coefficient is not very materialdependent is of practical importance. If materials other than water reduce the incident proton energy, the Bragg curve will not be very different from that observed in water alone. That greatly simplifies the design of passive range modulators or the computation of dose in a heterogeneous terrain. Energy Degraders Used With Cyclotrons Cyclotron-based therapy facilities use degraders to change the beam energy because variable-energy cyclotrons are very expensive and energy changes are very slow. The resulting increase in energy and angular spread is pared away by slits but a lot of beam is lost in the process. Multiple Coulomb Scattering (MCS) L x0 θ0 MP When protons pass through a slab of material they suffer millions of collisions (EM interactions) with atomic nuclei. The statistical outcome is a multiple scattering angle whose distribution is approximately Gaussian. For protons, this angle is always small so the projected displacement in any measuring plane MP is also Gaussian. The width parameter of the angular distribution is θ0. The corresponding displacement, x0, can easily be measured by scanning a dosimeter across the MP. The task of multiple scattering theory is to predict θ0 given the scattering material and thickness, and the incident proton energy. Molière Theory Many statistical processes obey the Central Limit Theorem: the random sum of many small displacements is a Gaussian distribution. However, the displacements must all be small , in a sense that can be made mathematically precise. Scattering from the screened Coulomb field of the atomic nucleus does not obey the 4 Central Limit Theorem because the single scattering cross section falls off only as 1/θ , too slowly. Therefore the angular distribution is approximately Gaussian for small angles 4 but eventually tends to a ‘single scattering tail’ ≃ 1/θ. Molière who in 1947 published the definitive theory, uniting the Gaussian region with the largeangle region in a precise and elegant way. He computed the distributions of both the space and projected angles for arbitrarily thick targets as well as compounds and mixtures, and produced numerical results long before the general availability of digital computers. His numerical evaluations were later improved somewhat by Bethe, who considered the overall Molière theory to be good to 1%. An early measurement with electrons Hanson et al., ‘Measurement of multiple scattering of 15.7 MeV electrons,’ Phys. Rev. 84 (1951) 634-637 studied electron scattering by thin and thick foils of Be and Au. They also gave a formula for computing the width of the best Gaussian fit to the exact theory. Their overall measurements agree well with Molière not only in the small angle (Gaussian) region but also in the single scattering tail. The theoretical transition between the two regions was improved by Bethe later on. Comprehensive Test of Molière Theory Gottschalk et al., ‘Multiple Coulomb scattering of 160 MeV protons,’ Nucl. Instr. Meth. B74 (1993) 467-490. Molière theory predicts the multiple scattering angle correctly over the periodic table, three decades of normalized target thickness and over two decades of angle. Compounds and mixtures (not shown) are also covered. The theory has no empirical parameters! Molière Theory Target thickness χc is a characteristic single scattering angle: B characterises target thickness (long computation): 2 χc beam energy = c3t/ (pv) 2 logarithmic normalised thickness B ∝ log (t/mean range) 1 θ′ = Moliere’s critical angle θM is analogous to θ0 : The 2D probability density is: 1 1 (0) f (θ′) f (θ′) (θ′ ) f(θ) = f + + 2 2 [ 2πθM B B2 ] (1) θ0 = θH =    Hanson’s expedient (1951):  , θ 2 θM θM = 2 χc B 1 1 2 χc B − 1.2 (2) Hanson’s critical angle Physica interpretation of B Molière’s reduced target thickness B is proportional to the logarithm of the normalized target thickness (t/range) as this graph (Gottschalk et al. 1992, Table 1) shows. The constant of proportionality depends on the target material. Molière’s b is identified by him as the natural logarithm of the effective number of collisions in the target. Gaussian approximation Molière angular distribution for various values of B , plotted so a Gaussian becomes a straight line. Shows the relative insensitivity to B , the slow approach to single scattering, and the large deviation from a Gaussian at larger angles. Inset: the dashed line is Molière’s Gaussian term. The distribution at small angles is well approximated by a Gaussian, but one with a somewhat smaller characteristic width. Gaussian approximation Projected angle distributions for 158.6 MeV protons on 1 cm of H2O (σ ≈ 6.7 mrad). On a linear plot the Molière/Fano distribution is indistinguishable from Gaussians using the Molière/Fano/ Hanson or Highland θ0. However, it peels away at 2.5σ , and at 5σ is more than 100× higher. We need the correct distribution only if we are looking for rare anomalous events, not if we are estimating the resolution of a spectrometer. Nuclear Reactions Some (about 23% for 160 MeV protons in water) have a head-on collision with an atomic nucleus. Though the proton survives this train wreck, it generally comes out with much less energy and at some large angle to the beam, accompanied by other charged and neutral secondaries and a residual nucleus. In addition to multiple soft EM interactions, protons stopping in matter undergo single hard scatters. These throw dose out to large radii, creating the nuclear halo. Neutral secondaries MCS Electronic slowdown Hard Scatters 1. The core is the compact central region due to primaries 2. The halo is the surrounding dose from charged secondaries 3. The aura is the very large region due to neutral secondaries. 4. The spray, additional low dose outside the core which enters with the beam (due to beam line design) The four regions overlap, but each has distinct characteristics. Classification The possible varieties of nuclear reaction for purposes of radiation therapy calculations are defined by ICRU Report 63, ‘Nuclear Data for Neutron and Proton Radiotherapy and for Radiation Protection’ (2000). Oxygen Elastic Inelastic Non elastic Hydrogen Elastic 16 16 p+ O→p+ O 16 16 p + O → p + O* 16 15 p+ O→p+p+ N 16 14 p+ O→d+ N 16 14 p+ O→p+n+ N 1 p+ H→p+p or or 16O (p, p) 16O or 16O (p, p) 16O* or or or 16O (p,2p) 15N 16O (p, d) 14N 16O (p, pn) 14N 1H (p, p) p Hard balls scatter angle 90° What Are the Secondaries? The relative importance of different secondaries can be measured by estimating what fraction of the energy each kind carries off. 150 MeV protons on O (Simulation estimates) Many people think that the nucleus ‘breaks up’ in an inelastic reaction. That almost never happens. Light nuclei don’t undergo fission! Protons are always the most common secondaries by far. Neutrons are next. Think of the incident proton as knocking out another proton, neutron or small cluster, with additional protons or neutrons sometimes resulting from a cascade of direct interactions. C (p, p) 12 Coulomb interference Diffraction minima by nuclear force Moliere tail Elastic scattering differential cross section 96-MeV protons on carbon 12C Local Energy Deposition Secondaries (mostly protons) have short ranges and large angles. Long ranges only for neutrons and photons. The reaction cross section is nearly independent of energy so the pattern of energy deposition only varies slowly with depth. flattened entrance dashed: NO Nuclear Reactions reduced Bragg Peak Because nuclear reactions are hard to model, we take them into account by using a measured (rather than predicted) Bragg peak to deduce an effective stopping power which includes nuclear reactions. Effect on RBE Some nuclear secondaries have very high dE/dx (energy loss per unit distance or LET) and are therefore expected to have a considerably higher RBE than protons. What is the average effect throughout the SOBP? short ranges - Secondary protons contribute about 10% of the dose proximal to the SOBP. - RBE there may be about 8% higher due to secondaries (protons and α’s). - Distal to the Bragg Peak, however, RBE enhancement is due to the low energies of the primary protons and the RBE mas be as high as 1.3. - The net RBE effect of residual nuclei (which certainly have very high LET and short range ≈3μm) and concluded it was negligible. In sum, charged secondaries from nonelastic reactions appear to increase RBE by a barely significant amount. Unwanted neutron dose since are long range is another issue. AURA HALO CORE The reactions shown are 16O(p,pn)15O 1H(p,p)p 16O(p,2p)15N Can you identify them? 16O(p,p)16O How much is the Halo radius? Longest range secondaries must be protons from reactions with fewest secondaries: 1H(p,p)p and 16O(p,2p)15N. Conservation of energy and momentum dictate how far sideways they will go. Note the bump around midrange at large radii. If we do the previous plot at various energies and note the maximum radius, we obtain this graph. Halo size ≈ 1/3 × beam range The experiment Gottschalk, Cascio, Daartz, Wagner, Phys. Med. Biol.6 (2015) BEAM MONITOR 96.8 × Exradin T1 CURRENT INTEGRATOR 10 pC/count PRESCALER ÷ 10,000 3.1415 6.45 × 109 p / MU 2.004 Keithley 6512 PRESET BEAM ON/OFF The experiment Gottschalk, Cascio, Daartz, Wagner, Phys. Med. Biol.6 (2015) Experiment results AURA HALO CORE Our data in semilog, absolute, 295 points, 5 decades. 1 MeV/g = 0.1602 nGy Virtual Transverse scan d = 12 cm (midrange) d = 21 cm (end of range) Beam shape Contours of modelindependent fit at.9.8.5.2.1.0316.01....00001 × maximum dose. Experimental check Pedroni et al. (Phys. Med. Biol. 50 (2005) 541-561) ‘frame’ technique. Measurement and fit at 177 MeV. Contribution outside B, 3 × 3 cm, is very small. 5.0 3.5 2.5 1.5 0 A B C D Effective Mass Stopping Power area A N protons Δx The equation relating dose to fluence and stopping power is the starting point of most beam line design problems. From the figure : dose = fluence × mass stopping power effective experimental stopping power Experimental check ‘Bragg peak chamber’ PTW R = 4 cm, IBA ‘Stingray’ R = 6 cm Experimental check Ionisation chambers IBA Stingray PTW 34070 Transverse equilibrium Suppose we apply a large number of Pencil Beams (PBs) close together and do a depth scan with a small IC Because of both multiple EM and hard scatters, not all the protons initially aimed at the IC actually reach it. However, those that scatter away from the IC are exactly compensated by those from neighboring PBs that scatter into it. Therefore, near the center of a sufficiently broad beam in a uniform medium, the exact transverse coordinate of the IC does not matter. This condition is called transverse equilibrium. The effective mass stopping power is equivalent if measured by using a small IC in a sufficiently broad beam, or by a sufficiently large “pancake” IC straddling a single PB. Transverse Equilibrium The fluence on the central axis of a pencil beam decreases with depth because of out-scattering of the protons. The dose on axis (fluence × stopping power) therefore goes down; the Bragg peak vanishes. A scan along the axis with a small ion chamber would show this; a scan with a large one would not. In a broad beam the axial fluence is restored by in-scattering from neighboring pencils (transverse equilibrium). A scan along the axis with a small ion chamber will therefore measure the ‘true’ Bragg peak. It is essential to use this ‘broad beam’ geometry if we wish to use the measured Bragg peak to design range modulators. Bragg Peak The Bragg peak is the on-axis depth-dose distribution, in water, of a quasi-monoenergetic proton beam. Listing the most important factor first, the shape of the Bragg peak depends on: the fundamental variation of stopping power with energy the transverse size of the beam, range straggling 3 2 i=1 beam energy spread nuclear interactions low energy contamination effective source distance (S/ρ)1 Φ22 N2 the dosimeter used in the measurement. Because of range straggling, the peak of the depth-dose distribution increases in absolute width as beam energy increases. range modulator by adding appropriately weighted Bragg peaks Anatomy of the Bragg Peak overall shape from increase of dE/dx as proton slows 1/r2 and transverse size set peak to entrance ratio the dosimeter matters width from range straggling and beam energy spread nuclear buildup or low energy contamination this part is a guess nuclear reactions take away from the peak and add to this region depth from beam energy Anatomy of the Bragg Peak in Words 1. The increase of dE/dx as the proton slows down causes the overall upwards sweep. 2. The depth of penetration (measured by d80 ) increases with beam energy. 3. The width of the peak is the quadratic sum of range straggling and beam energy spread. 4. The overall shape depends on the beam’s transverse size. Use a broad beam. 5. Non-elastic nuclear reactions move dose from the peak upstream. 6. A short effective source distance reduces the peak/entrance ratio. Be sure you know and record your source distance. 7. Low energy beam contamination (as from collimator scatter) may affect the entrance region. Use an open beam. 8. The exact shape depends somewhat on the dosimeter used. Use the same dosimeter you plan to use later in QA. Bragg Peak Shape vs. Beam Energy Bragg peaks from 69 to 231 MeV (courtesy IBA) normalized so the entrance value equals the tabulated dE/dx at that energy. Straggling width relative to range is almost independent of energy so absolute straggling width increases with energy. Therefore the Bragg peak gets wider. The change in shape makes active range modulation more complicated than passive, where we simply ‘pull back’ a constant shape. The Disappearing Bragg Peak collimator radius Behavior of the Bragg peak as the beam cross section is made smaller : W.M. Preston and A.M. Koehler, ‘The effects of scattering on small protons beams,’ unpublished manuscript (1968) Harvard Cyclotron Lab, available on BG Web site. As depth increases, energy decreases and stopping power increases. At the same time, fluence decreases because MCS spreads the beam out (the 2D Gaussian grows wider), and there is no compensating in-scatter from neighboring PBs. The decrease in fluence ultimately wins out, and the BP disappears. The Effective Mass Stopping Power The Bragg peak is a depth-dose distribution taken under specific conditions. Beam line design programs, generally speaking, compute proton fluence from multiple scattering theory and need to use dose = fluence × stopping power to compute the dose. Therefore we would like to derive from the measured Bragg peak an effective mass stopping power (a function of equivalent depth in water) for that particular cohort of protons. To do this we use the fundamental equation to define d is depth in water, D(d) is the BP measurement and Φ(d) is the fluence at BP measurement time. That can be approximated by 1/r2 if we know the source distance. To distinguish the effective stopping power from tabulated stopping powers we assign it the units Gy/(gp/cm2) (gp ≡ 109 protons). The effective stopping power includes nuclear reactions, energy straggling, beam energy spread and all other effects relevant to range modulator design. If you want, you can just think of it as the Bragg peak corrected for 1/r2 at measurement time to bring it into a standard form. Dosimeter response Ionisation Chamber vs Faraday Cup Bragg curves for ionization chambers of different shapes Conclusions EM stopping —> Range Multiple Coulomb Scattering—> core width Hard Scatters —> Halo Effective Mass Stopping Power from experimental data Straggling proportional to depth Halo radius 1/3 of the range Energy loss mainly in the Bragg Peak The deeper the Bragg Peak the wider Università degli Studi di Padova Course Proton Therapy Physics part Lesson 3 – Secondary particles and Montecarlo Prof. Alessandro Patelli [email protected] Dept Physics and Astronomy 049 827 7039 – Room 108, via Marzolo 8 Proton beam As outlined before the main RBE in the patient due to proton beam interaction is due to primary protons, however secondary particles are produced by protons interaction with matter (beam line elements, apertures or range modulators, patient, …) Proton therapy accelerators operate in the intermediate energy range. Proton energies are classified as follows (where Ep is the energy of the incident proton): Very Low Energy: Low Energy: Intermediate Energy: High Energy: Ep < 10 MeV 10 MeV ≤ Ep < 50 MeV 50 MeV ≤ Ep ≤1,000 MeV (1 GeV) 1 GeV < Ep The prompt radiation field produced by protons in the therapeutic energy range of interest, i.e., 67–330 MeV is comprised of a mixture of charged and neutral particles as well as photons, with neutrons being the dominant component. The neutrons have energies as high as the incident proton energy and dictate the shielding for proton accelerators. Secondary Radiation Production The interaction of protons with any material in their path results in the production of secondary radiation. Primary beam losses can occur in the synchrotron and cyclotron during injection during energy degradation in the cyclotron during beam transport to the treatment room in passive scattering systems range degraders and modulators in beam-shaping devices such as collimators, apertures, and range compensators placed near the patient Secondary radiation consists of both prompt and residual radiation. Prompt radiation is produced only while the machine is on. Residual radiation is produced by materials that have become radioactive during beam operation (referred to as “activated material”). Secondary Radiation Production In elastic interactions, kinetic energy is conserved in the interaction between the proton and the nucleus In inelastic interactions, kinetic energy is not conserved in the interaction between the proton and the nucleus but the final nucleus is the same as the target nucleus. In non-elastic interactions, kinetic energy is not conserved in the interaction between the proton and the nucleus and the final nucleus is not the same as the target nucleus. A schematic representation of various stages of an intranuclear cascade Evaporation and the intranuclear cascade are the two important nuclear processes in secondary radiation production for protons in the therapeutic range Low energy protons The interaction of low-energy protons (Ep < 10 MeV) with a nucleus can be described by the compound nucleus model. The incident particle is absorbed by the target nucleus, resulting in the formation of a compound nucleus. The compound nucleus is in an excited state with a number of allowed decay channels. The preferred decay channel is the entrance channel. A schematic representation of various stages of an intranuclear cascade As the energy of the incident particle increases, the number of levels available to the incident channel increases considerably. Instead of discrete levels in the quasistationary states of the compound nucleus, there is a complete overlapping of levels inside the nucleus. Intermediate energy protons The interaction of protons in the energy range of 50–1000 MeV with matter results in the production of an intranuclear cascade (spray of particles). The indecent proton has enough energy to interact with individual nucleons in a nucleus, producing a spray of particles, such as protons, neutrons, and π mesons (pions). At particle energies < 100 MeV, all interactions occur just between nucleons and the process is called nuclear cascade. As the incident particle > 100 MeV, the threshold energies for particle production in nucleon–nucleon collisions are exceeded. —> Nucleons and Fragments Evaporation A schematic representation of various stages of an intranuclear cascade Evaporation The scattered and recoiling nucleons resulting from the interaction proceed through the nucleus (precompound phase). Emission of particles with energy similar to incoming proton. Each nucleon interacts with other nucleons in the nucleus, leading to the development of a cascade (pre-equilibrium phase). The energy is distributed among the remaining nucleons in the nucleus, leaving it in an excited state. It then de-excites (“evaporates”) by emitting particles, mainly neutrons and protons, alpha particles and some fragments. The rest of the energy is equally distributed among nucleons in the nucleus (equilibrium phase). When particle emission is no longer energetically possible, the remaining excitation energy is emitted in the form of gamma rays. A schematic representation of various stages of an intranuclear cascade Evaporation The evaporated particles are emitted isotropically in the laboratory system. Energies range from 0.5 to 8 MeV. Charge particles are easily stopped by coulomb barriers. Neutrons can deposit energy on longer distances. Proton impact on heavy elements in the beam line can produce also spallation of the target which can remain activated and slowly decay with the emission of further particles. A schematic representation of various stages of an intranuclear cascade Neutrons Neutrons are the longer range particles within secondaries. Neutrons are classified according to their energy as follows: Thermal: Intermediate: Fast: Relativistic: High-Energy Neutrons: En ≤ 0.5 eV 0.5 eV 100 MeV Matter interaction Elastic reaction is one in which the total kinetic energy of the incoming particle is conserved. Inelastic scattering can occur only at energies above the lowest excited state (or inelastic scattering threshold) of the material. The neutron can also be captured or absorbed by a nucleus in reactions such as (n, 2n), (n, p), (n, α), or (n, γ). These reactions result in the change of the atomic mass number and/or the atomic number of the target nucleus. Thermal neutrons Thermal neutrons undergo radiative capture, i.e., neutron absorption leads to the emission of a gamma ray. H (nth, γ) 2H 1 Eγ = 2.22 MeV This reaction occurs in hydrogenous shielding materials such as polyethylene and concrete. For shielding maze doors, borated polyethylene is used instead of polyethylene, because the cross section for capture in boron is ten times higher. B (nth, α) 7Li 10 Eγ = 0.48 MeV Intermediate neutrons lose energy by scattering and are absorbed. Fast neutrons Fast neutrons include evaporation neutrons and neutrons from specific nuclear reactions such as (p, n) reactions. They interact with matter mainly through a series of elastic and inelastic scattering. Inelastic scattering is the dominant process in all materials at neutron energies above 10 MeV. Elastic scattering dominates at lower energies. Below 1 MeV, neutrons may be transparent to the nonhydrogenous material. Therefore in high-Z materials as energy is decreasing the elastic scattering dominates and increase the travelled length but also the opportunities for an inelastic and (n, 2n) reactions to occur. As energy is reduced neutrons are captured by hydrogenous materials (concrete, PET) elastic Pb H (n, n) 1 MeV inelastic (n, nγ) 7 MeV 10 MeV non elastic (n,2n) 20 MeV H (nth, γ) 2H 1 2.22 MeV Relativistic neutrons The high-energy component of the cascade with neutron energies above 100 MeV propagates the neutrons through the shielding; and continuously regenerates lower-energy neutrons and charged particles at all depths in the shield via inelastic reactions with the shielding material. Neutrons with energies above ~100 MeV produce copious amounts of neutrons through spallation. Neutron yields increase with increasing proton energy because the thresholds for neutron production in the target material are exceeded. Neutron yields increase with the mass number (not atomic number, Z). The reactions occur in three stages for neutrons with energies between 50 and 100 MeV. For neutrons < 50 MeV, only the 2. and 3. stages are assumed to be operative. 1. In the first stage, an intranuclear cascade develops, where the incident high-energy neutron interacts with an individual nucleon in the nucleus. 2. In the second stage, the residual nucleus is left in an excited state and evaporates particles such as alpha particles and other nucleons. 3. In the third stage, after particle emission is no longer energetically possible, the remaining excitation energy is emitted in the form of gamma rays. The de-excited nucleus may be radioactive. Neutron spectra High energy The high-energy neutrons are anisotropic and forward peaked, but the evaporation neutrons are isotropic. Relativistic Fast Unshielded neutron spectra for neutrons at various emission angles, produced by 250-MeV protons incident on a thick iron target (without any concrete shielding). Monte Carlo simulations 1. Incident proton with a certain energy distribution and spatial distribution 2. EM losses, statistical fluctuations (energy straggling) 3. Multiple Coulomb scattering treated as aggregated interaction, angular spreading 1 3 2 4. Hard scatter, energy and angular spread. Creation of a second particle? Follow it? high computation time but can be parallelised Follow each event rolling the dice 4 Monte Carlo simulations Advantages Physics modelled in steps, one event at time Use of experimental data for cross sections and stopping power Full environment simulation Experimental set up modelling and evaluation for data comparison To speed up Combined events Energy and particles cut-off Magnification of rare events Monte Carlo simulated proton fluence as a function of depth for a 160 MeV proton beam. The dose is shown as dashed line, while the solid and dotted lines illustrate the primary proton and the total (primary and secondary) proton fluence. Examples Proton tracks steered though a magnet with a specific field strength as modeled within Geant4. Simulation done with TOPAS. Monte Carlo model of a contoured scatterer used in a double-scattering system (a; mesh-type image) and a modulator wheel based [(b) showing the transparent steps of the wheel and (c) showing actual simulated proton tracks] at the Francis H Burr Proton Therapy Center at the Massachusetts General Hospital, Boston. Simulation done with TOPAS. Examples Frontal views of patient-dependent pediatric female phantoms at a specific targeted standing height and at their 10th, 25th, 15th, 75th, and 19th percentile body masses. Also shown are lateral views for different targeted standing heights. Simulated fluence profiles of a 230 MeV pencil beam scored at treatment head exit. (a) Primary protons and electrons, (b) secondary protons and neutrons. The simulations are plotted in units of Gy(RBE) mm2 Gp−1 and the measurements are normalized to the maximum dose (dashed) and neutrons from nuclear interactions (dotted). (c) Monte Carlo simulated Bragg curves (blue lines) compared with measurements (red stars). Conclusions Primary protons are the main responsible of the biological damage on the patient However several secondary particles and produced and must be shielded Modelling can be performed to design the treatment Errors can be treated in the modelling but accuracy depends on experimental data Università degli Studi di Padova Course Proton Therapy Physics part Lesson 4 – Particle Therapy Facilities Prof. Alessandro Patelli [email protected] Dept Physics and Astronomy 049 827 7039 – Room 108, via Marzolo 8 The facility bending degrader cyclotron fixed gantry Inside Seattle Cancer Care Alliance’s Proton Therapy Center Accelerators Synchrotron Cyclotron Synchro Cyclotron Beam accelerated along a fixed track by RF cavities. Exit energy can be changed. Beam accelerated with a fixed potential to a fixed energy in a constant magnetic field. To change energy need a degrader and therefore loss of proton flux to maintain monochromaticity. Beam accelerated with a fixed potential to a fixed energy as in cyclotron but in a shaped magnetic field to correct relativistic effects. Treatment - Dose spreading in Depth Change depth —> Change energy Synchrotron —> OK Energy spread —> ADD Energy Selection system Cyclotron —> ADD Degrader —> Lateral spread —> ADD Collimator fluence reduction neutrons production Beam transport and monitoring depends on proton energy, therefore must be adjusted accordingly. Degrader can be also close to patient (range shifter, ridge filter, wheel modulator ) but difficult to correct energy straggling and shield neutrons production. In this respect, relevant parameters of the accelerator choice and the beam transport system design are: the needed speed of the energy change the accuracy of the obtained energy (range) the effect on beam parameters such as intensity, energy spread, and beam broadening the background dose to the patient from neutrons created by proton interactions with materials, for example, in collimators. Treatment - Lateral dose spreading Beam spreading in lateral direction is necessary because the typical 0.5-1 cm size of a proton beam is much smaller than typical tumor dimensions. To irradiate target volumes of sizes between a few centimeters (e.g., eye treatments) up to 30–40 cm (e.g., sarcoma), one needs dedicated beam spreading systems adapted to the needed size. Passive Scattering Multiple scattering of the protons in a (set of) foil(s) or thin plate(s) and collimated just before the patient (usually Double Scattering). When crossing the scatter foil, the beam will also lose a few MeV. When specifying the accelerator energy, one should be aware of this energy loss. Also one should keep in mind that, if no dedicated beam focusing measures are taken, up to 90% of the intensity can be lost at the collimator(s) in the nozzle, which will generate neutrons. To widen further Beam wobbling Bema rastering Treatment - Lateral dose spreading Beam spreading in lateral direction is necessary because the typical 0.5-1 cm size of a proton beam is much smaller than typical tumor dimensions. To irradiate target volumes of sizes between a few centimeters (e.g., eye treatments) up to 30–40 cm (e.g., sarcoma), one needs dedicated beam spreading systems adapted to the needed size. Pencil Beam Scanning Fast steering magnets (scanning magnets) are used to aim a narrow beam at the volume elements (voxels) in the target volume sequentially. At each voxel, a specific dose is deposited. Spot scanning At each voxel, a specific dose is deposited. This is usually being done on a discrete grid, using a “step and shoot” method, in which the beam is only switched “on” if the pencil beam is aimed at the correct voxel Continuous scanning The pencil beam moves along a certain trajectory within the target volume. The beam is kept “on” continuously. The dose is set by the controlling the pencil-beam intensity and scanning speed. Time driven Event driven Cyclotrons Modern cyclotrons dedicated for proton therapy accelerate protons to a fixed energy of 230 or 250 MeV. These machines are rather compact with a magnet height of approximately 1.5 m and a typical diameter between 3.5 m (100 tons) and 5 m (200 tons), when equipped with superconducting coils or with room temperature coils, respectively. Usually, some extra space is needed above and/or below the cyclotron for the support devices of the ion source, eventual liquid helium supply, and space for access and equipment to open the machine. ACCEL Continous beam Intensity can be adjusted quickly Beam energy by means of fast degraders Simple system — > easy maintenance IBA Cyclotron components The major components of a typical compact cyclotron are an RF system, which provides oscillating strong electric fields by which the protons are accelerated, a strong magnet of few Tesla, confining the particle trajectories into a spirally shaped orbit, so that they can be accelerated repeatedly by the RF voltage in the order of 30– 100 kV, a proton source in the center of the cyclotron, in which hydrogen gas is ionized and from which the protons are extracted, an extraction system that guides the particles that have reached their maximum energy out of the cyclotron’s magnetic field into a beam transport system. A Charged Particle in Crossed E and B Fields For any particular combination of electric and magnetic fields, the two forces are balanced only for one particular particle speed, since the magnetic force is velocity-dependent, but the electric force is not. The velocity that gives zero net force can be found from: → = → → → → → → + × = ( + × ) The intensity of the magnetic field is measured in Tesla or in Gauss = 104 = 10000 𝐵 𝑣 𝐸 𝑞 𝐵 𝐺 𝑣 𝑞 𝐺 𝐸 𝑡 𝑒 𝑞 𝑇 𝐹 𝑛 1 Lorentz Force The first cyclotron was built in 1932 by Lawrence. The fundamental elements of the cyclotron are a source S of ions located at the center of the accelerator, two regions (D) of space, bounded by conductive surfaces, inside which there is a vacuum. Perpendicular to the plane in which the motion of the ions takes place, there exists a uniform and outgoing magnetic field from the sheet. 𝑠 𝑡 𝑙 𝑜 𝑣 𝑉 𝑉 A ∆ is applied between the two D's. ∆ of 4 the order of 0 = 10. Positive ions produced by the source S enter the first D, in whose interior there is no electric field, but only a magnetic field; as a consequence the ions are deflected and follow a circular trajectory whose radius depends on , ∆ and. Once out of the first D, the ion is an electric field that accelerates it towards the second D. 𝑉 𝑉 𝐵 𝑣 𝐵 Cyclotrons Cyclotrons So that at each passage between the D the ion finds an accelerating field that increases its energy, the value of the electric field between the two D must vary over time with the same frequency with which the ions move in the magnetic field (cyclotron pulsation), therefore = = and After half a turn the polarity of the D was reversed. At each jump between the D the radius of the trajectory increases, while remains constant. When one arrives at the edge of the D (radius of the trajectory ) and ion velocity equal to , the ion beam is extracted. You will have = = 𝐵 𝑋 𝐴 𝑞 𝑣 𝑅 𝑡 𝑋 𝐴 𝐵 𝑚 𝑞 𝑀 𝜔 𝑋 𝑉 𝐴 𝑽 𝑀 𝐵 𝑅 𝜔 𝑀 𝑚 𝑞 𝑚 We note that the kinetic energy T does not depend on the ∆ 𝑣 𝜔𝑅𝑣 𝑉 0sin Do not depend on ion speed 2 1 2 1q 2 (BR) T = mvMAX = 2 2 m among the D. How it works Magnets are designed to have only small gaps: magnetic field more intense and uniform. The magnetic field must be correct within approximately 10–5. The magnetic field strength in the commercially available cyclotrons is between 2 and 3.5 T. The RF power is applied in a resonant cavity in order to reduce the required power. The RF currents float along the inner surface of the cavity and can be on the order of kA. A lot of power (60–120 kW) dissipates as small components in the Dees and in the transfer lines, making the RF system usually one of the most vulnerable subsystems of a cyclotron. Relativistic correction The magnetic field in the cyclotron should be homogeneous. However, when the energy of the protons becomes larger than 20–30 MeV, their velocity becomes a considerable fraction of the speed of light c (β = v/c = 0.2 at 20 MeV). Due to relativistic effects, this yields an increase of the proton mass m with respect to its rest mass m0: the gap between the magnet poles is decreasing with radius m(r) = γ (r) m0 = since Saturated iron + coil field qB ω= m (r) 1 2 1 − v (r) /c 2 m0 B (r) = γ (r) B0 To maintain ω constant Synchro Cyclotron Beam focusing Improving Beam Vertical stability Focusing magnetic field Change in B-field —> change in radius Defocusing magnetic field Proton source Free electrons are created by heating a filament or, in case of a “cold-cathode source,” by spontaneous emission from the cathode in the strong electric field between cathode and ground or by emissions after impact of a proton at the cathode. In the electric field between cathode and ground, the electrons are accelerated and will ionize the gas. They are confined along the magnetic field lines and bounce up and down between the cathodes, thus increasing the ionization of the gas. Arc current regulate beam intensity Ions that diffuse to a little hole in the chimney wall will experience electric field from the nearest Dee (the puller). When the Dee is at a negative potential, protons that escape from the plasma will accelerate towards the Dee. If they arrive at the right phase, they will cross the distance to the puller and will be further accelerated Synchrotron All machines provide protons between 70 and 250 MeV. For proton therapy, synchrotrons and cyclotrons are quite competitive, but for heavy ion therapy, synchrotrons are currently the only machines in operation. Recognized advantages of a synchrotron: 1. the protons are accelerated until the desired energy, 2. almost no radioactivity is created due to beam losses 3. low-energy protons have the same intensity as high-energy protons, since there is no transmission loss in a degrader Synchrotron The acceleration process in a synchrotron is in cycles (spills), each consisting of filling of the ring with a bunch of 2 × 1010 protons of 2 MeV (Loma Linda) or 1011 protons of 7 MeV by an injector (Hitachi, Mitsubishi), acceleration in a ring until the desired energy between 70 and 250 MeV, slow extraction of the protons into the beam line, finally followed by ramping down to the initial situation, eventually with deceleration and dumping unused protons at low energy. In general, this sequence takes rather long to be useful for energy modulation, so the energy to be extracted is chosen for each gantry angle and equal to the maximum energy needed at that angle. If the spill repetition rate is considered too slow, energy modulation is done in the nozzle by means of a modulator wheel or ridge filters. Ion Source and Injector Proton ion sources typically based on ionization by microwaves in a special configuration of coils or permanent magnet to confine the electrons up to 2-3 MeV RF quadrupole (RFQ) An RFQ consists of four rods parallel to the beam direction. Each rod is shaped as a wave-like structure along its length. The rods are mounted in a resonant cavity such that the pairs of opposing rods have 180° phase shift of the RF voltage with respect to the orthogonal pair. The component of the electric field along the beam direction provides the acceleration and the radial components provide focus. from 3 to 7 MeV Drift Tube Linac (DTL) The operation of a DTL is based on electromagnetic oscillations in tuned structures. The structures support a traveling wave of alternating voltages on cylindrical electrodes, between which the protons are accelerated. The electrode lengths increase along the tube, in accordance with the velocity of the accelerated particles. Acceleration in the Ring acceleration phase —> 0.5 s and 106 turns Induction cavity with magnetic cores The cavity is not resonant and the frequency must remain synchronous to the increasing revolution frequency ( 1→8 MHz) and increases (nonlinearly) in time. The electric current through the coil is driven with the RF frequency and induces an RF magnetic field in the ferrite ring. On its turn, this varying field induces an electric current in the beam pipe, which acts as inner conductor. An outer conductor surrounding the cores is closing the loop for this driven current. However, in the center of the device, the inner conductor is interrupted. Across this gap, an RF voltage of a few hundred Volts is built up by the RF current, so that the protons that cross the gap at the correct RF phase will be accelerated. Gantry Bending magnets bend the proton tracks with a curvature radius of approximately 1.5 m. Typically, a distance of at least 2 m is needed to distribute the beam over a sufficiently large field size. Also between the last magnet and the patient, space is needed for additional equipment, such as scanning magnets, dose monitors, range shifter, and collimation systems. Therefore, a typical diameter of these 100–200 ton gantries is 10–12 m, both for scattered beams and for scanned beams. Proton dose delivery Spread-Out Bragg Peaks (SOBP) Same beam direction different energy To obtain the desired depth-dose distribution throughout the target volume for the rationale discussed earlier, one must build a superposition of many Bragg peaks with proper intensities and locations. 1. it delivers a near-uniform dose distribution in depth along the target volume. 2. it preserves the sharp distal fall of the Bragg peak. 3. the total entrance dose has increased from about 30% due to the deepest Bragg peak along to nearly 80% due to the additional shallower peaks. and lateral beam features? Thicker the SOBP higher the entrance dose Scattering system Pencil beam scanning Scattering systems Scatterers are specially designed such that the beam has uniform penetration and uniform intensity across the scattered area specified for clinical use. The energy of the beam is modulated to spread out the location of the Bragg peaks over the target volume in depth. Mechanical range shifting devices such as ridge filters and range modulator wheels are used and are configured to produce a homogeneous dose distribution with the same penetration across the beam. For patient treatment, the beam is collimated by an aperture to match the target volume. A range compensator (usually, a Lucite block with varying thicknesses) to “pull back” the most distant Bragg peaks to conform to the distal surface of the target volume Single Scattering The scatters are made of high-Z materials, like lead or tantalum, providing that largest amount of scattering for the lowest energy (range) loss. same ΔE increased field, no ripples same ΔE increased field but ripples Blocks protons no ΔE increased field, no ripples Contoured scatterer Energy compensated scatterer high-Z materials, like lead or tantalum, providing that largest amount of scattering + Low-Z materials, like PE, provide energy loss with less scattering Achromatic energy loss Range modulator wheel Range modulator wheel combining three range modulation tracks as installed in the IBA universal nozzle. Two modulator wheel blocks (left) determining the modulation width for an RM wheel (right) in the IBA eyeline. Range modulator wheel used at the Harvard Cyclotron Laboratory. Ridge filters To avoid the dependence of the SOBP shape on lateral position, the ridge is made small enough that the incident proton angular diffusion and scattering in the ridge filter smooth out any positional dependence. The width of the ridges is typically 5 mm in systems that have the ridge filter downstream of the second scatterer Traditionally, ridge filters are made of high-Z materials, like brass, that can be machined accurately. Bar ridge filter designed to modulate the beam to a 6 cm SOBP. On the right hand side the cross section of a ridge is shown Aperture and range compensator aperture range compensator Because of the large geometric source size of a protonscattering system, it is important to bring the aperture close to the patient. Large air gaps inflate the lateral penumbra undesirably. Aperture and range compensator are mounted together on a snout. It should be pointed out that such an aperture will completely stop the beam. Due to the finite range of protons, the chance is zero that a primary proton will traverse the complete aperture. Unlike X-ray therapy, leakage of primary protons through the aperture does not exist. The aperture and snout are the largest contributors of neutrons to the patient. The energy loss in the high-density structure in the figure is compensated for by removing more material from the compensator. The full scattering system Schematic layout of the IBA universal nozzle. Schematic representation of the IBA eye line that applies single scattering to spread the beam. Pencil Beam Scanning Beam scanning is quite a general technique, and while it has acquired many acronyms such as particle beam scanning (PBS), intensity-modulated proton therapy (IMPT), and spot scanning (SS), coming from specific implementations of the technology and limitations of accelerator beam properties Pencil Beam Scanning There is full freedom to put any amount of dose, anywhere within the target. In the depth-dose direction, the most clinically relevant beam characterization is the Bragg peak. In the lateral direction, the most clinically relevant beam characteristics include the beam width (usually specified in terms of the sigma (σ) parameter of a Gaussian curve representing the beam and lateral falloff. Effects of σ on treated tissue The distance between the target and this critical structure has to be at least 0.85σ. This sets the scale of the beam size needed for different treatment sites. For example, if the target and organ at risk are separated by 5 mm, then the beam sigma should be smaller than approximately 6 mm. Optimisation by intensity modulation (a) A superposition of equally space and equal amplitude Gaussian beams. (b) A nonuniformly spaced and modulated dose distribution resulting in an acceptable uniform overall dose with a sharper penumbra Depth modulation have to be considered as well as proximal energy release in the different spots. Continuous Scanning constant beam deflection speed The beam intensity is modulated to adjust the dose per voxel. The constant beam deflection rate translates into benign requirements for the deflection magnet power supply (essentially a constant voltage). constant beam intensity The dose per voxel is controlled by the time the beam spends on each spot. Between spots, the beam is deflected as fast as possible by applying the maximum power supply voltage to the deflection magnet. This is not used in practice yet. Scanning Hardware Energy: accelerated beam energy or using a degrader system Size: intrinsic emittance of the beam + quadrupoles The equipment used to deflect and measure the beam for the MGH/IBA system. Target position: magnetic field in the scanning dipoles will determine the final beam path angle Scanning patterns: constant frequencies along X and Y axes lead to Lissajous pattern, α = fY /fX The beam deflections resulting from the magnetic fields. Dose rate:The speed with which one can detect and turn off the beam limits the dose rate Cyclortons and synchrotrons compared cyclotron Time structure synchrotron continuous/pulsed pulsed Mono-energetic pulse-to-pulse Activation degrader Requires shielding No shielding required Intensity Can be very high Limited, per spill Intensity stability 3-5% 15-20% Size ∅ 3.5 (p) 6(p)-25 m (C) Energy changes Scattering ok ok Spot scanning ok ok Fast continuous scanning ok difficult Lateral penumbra Lateral penumbra of photon slightly increases with depth, while for protons the beam laterally widen due to MCS At more than 15 cm usually the photon beams have smaller lateral penumbra than proton beams. Conclusions High localisation of the treatment requires high accuracy. Careful treatment planning to match clinical needs is mandatory. Treatment and set up customised to the patient. Calibration and planning simulations are needed. PBS facilities are the more usually installed now Still fix beams and scattering may optimise cost and efficiency for some tutors Università degli Studi di Padova Course Proton Therapy Physics part Lesson 5 – Detectors Prof. Alessandro Patelli [email protected] Dept Physics and Astronomy 049 827 7039 – Room 108, via Marzolo 8 Detectors requirements Sensitive to what? Dose? Fluency? Spatial information? Size and set-up accuracy precision resolution limit of detections linearity Response Time depends on Energy depends on Dose Rate Respect to water? Ionisation Chambers Air-filled plane-parallel ionization chambers (PPIC’s) are commonly used to measure incident beam current, to monitor accumulated dose and terminate irradiation at the prescribed dose, or to scan the transverse dose distribution for QA. Small PPIC’s (‘Markus’ chamber) are used in water phantoms to measure the depth-dose, as are small thimble chambers. For beam QA we frequently use PPIC’s whose electrodes are segmented to provide, in one shot, a complete transverse scan. As a case study, we’ll describe a large segmented air PPIC that was used at HCL, both to monitor dose to the patient and to measure transverse dose flatness in a beam steering loop. Plane-Parallel IC (Beam Monitor) signal out vent Window: should be slack (so P will equal the ambient value), conductive to complete the electrostatic shield, and impermeable to humidity. Aluminized Mylar is good. baseplate flange signal standoff HV plane HV standoff window signal pad guard vent Signal pad: normally should either be larger than the beam (integral chamber) or much smaller (dose sampling chamber). Output is harder to interpret for in-between sizes Guard: this conducting ring serves three purposes. It makes the electric field uniform at the edge of the signal pad. It intercepts surface current paths from HV to signal. Finally, it defines the potential of the unused part of the signal plate. Signal standoff: connects to the grounded baseplate, not the HV plane. That would create a surface path between HV and signal. HV in Output Current Beam traverses the IC, ionizing atoms to produce positive ions and free electrons. The electrons rapidly attach themselves to other atoms, so after a short time the current at any given point consists of + ions drifting towards the – electrode and – ions drifting towards the + electrode. (The rapid attachment of electrons is usually beneficial in a beam line environment because ions are much less susceptible to the influence of stray magnetic fields.) The current from the IC is where A is the effective area, d is the gap and q is the charge liberated per unit volume per second by the radiation. ξ is a measure of the ions lost to recombination, which we’ll ignore for the moment (ξ2 = 0). q is given by where e = 1.602 × 10-19 C is the quantum of charge, ρ = 0.00129 g/cm3 is the density of standard air, W ≈ 34.3 eV is · the average energy expended per ion pair and D is the dose rate. Output Current · Combining these equations and values, assuming A = 1 cm2, d = 1 cm, D = 1 Gy/sec and working through the conversions we find, in practical units This form is useful if the dose rate is essentially constant over A (a small PPIC in a big beam). If on the other hand we assume a beam that is uniform over A and zero elsewhere we obtain for the current multiplication of the PPIC, with d in cm and S/ρ in MeV/(g/cm2). Absent recombination, this holds whatever the shape of the beam as long as it is fully contained in A. If there is recombination it will be worse, the smaller the beam. Case Study: Combined Dose and Flatness Monitor Padded 8” IC real time monitor An Alternative: Strips The segmented IC in the standard IBA nozzle uses 32 strips instead of pads, with another 32 orthogonal. MultiLayer Ionization Chambers In the 1980’s and early 90’s a multi-layer ionization chamber (MLIC) was used as a range verifier at HCL. Only the measured range mattered. It is much harder to build an MLIC that measures an entire SOBP to a clinical level of accuracy. In scattered beam QA the potential time savings, compared to scans with a single dosimeter in a water tank, are modest: seconds compared to a few minutes. By contrast, in scanned or laminated beams the time saved is enormous because, otherwise, the entire sequence has to be repeated for each point of a depth scan. Identical PC boards with a signal pad on one side, and a (larger) HV pad on the other, form an array of small PPIC’s. Example 65 identical PC boards, fabricated with standard commercial technology, are mounted 1 mm apart in a rigid frame. Collimation is provided by the eye treatment line. The defining aperture or natural beam size must be much smaller than the hole shown. Otherwise, the connections are bathed in ionized air and contribute garbage signal. Faraday Cups A Faraday cup (FC) is a shielded insulated block thick enough to stop the beam. We measure the charge accumulated on the block. Since the proton’s charge is very well known (+1.602 × 10-19 C) we are effectively counting protons. Therefore the FC is a fluence meter (protons/area) if the cross sectional area of the incident beam is known. The art of designing FC’s consists of making sure that all the charge is counted and that no spurious charge is picked up, either by the FC itself or in the charge measuring device (current integrator). The FC is not a dose meter. However, dose = fluence × mass stopping power, so the FC can be used to determine the dose at a point in a beam line if the mass stopping power of the protons is also known. To look up the mass stopping power we need to know the beam energy. Happily, the FC can also be used to measure that or, strictly speaking, the mean proton range in some well characterized material such as aluminum. Faraday Cups Schematic diagram of a reference dosimetry-level Faraday cup with internal vacuum. Shown are: the collecting electrode the guard electrode (which is at negative potential with respect to the collecting electrode) the entrance window the windings creating a magnetic field, B, to suppress the loss of electrons generated in the collecting electrode. Measuring Proton Range Proton range can be measured adding and removing absorber layers MultiLayer Faraday Cups (MLFC’s) The MLFC is simply a stack of conducting sheets separated by insulating sheets. Either may be regarded as the ‘active’ element. The conducting sheets are connected to an integrator array of the sort described in connection with MLIC’s. The current to be detected is fairly large (nA, not pA) so demands on the integrator are lower. Even though it is known that secondary electrons are emitted at each interface between conductor and insulator, and even though protons stop in insulator as well as conductor, the MLFC measures the total charge entering, as well as its range distribution, perfectly. MLFC’s are usually used as range verifiers. Even a relatively crude device can detect changes as small as 0.1mm H2O equivalent. How it works Why the device works so well is explained by simple electrostatics. C B A A) Proton knocks an electron out of Kapton before stopping. Electron is essentially ‘bound’ to the positive vacancy left behind, so does not contribute to measured current. B) Proton stops in Kapton. It induces a mirror charge in the facing conductor, so it is counted anyway. C) Proton has a nuclear reaction. Net charge in MLFC still +e. Therefore the MLFC counts all the charge entering and only the charge entering. ‘Internal’ processes in insulator and conductors have no effect. Alanine detectors The L-isomer of alpha-alanine, a natural amino acid, is used in crystalline powder form as a dosimeter. Free radicals formed by ionization remain in a stable position in the crystal, and the number of radicals present in a sample of alanine can be quantified by electron spin resonance. NIST EPR spectra of alanine irradiated with a 10 Gy dose along with the Bruker Cr reference (at 3523 gauss) with its position in the resonator adjusted so that its intensity is comparable to that of the alanine, but with the opposite phase, recorded with microwave powers of (a) 0.35 mW and (b) 5 mW. Semiconductor devices Scintillators Scintillating detectors are based on the detection of prompt light emission due to molecular or crystalline transitions after ionization. Organic scintillators can be embedded in a polymer matrix but can also be available in liquid form or gaseous phase, making the application of these detectors as online dosimeters very versatile. Gaseous scintillators in a gas electron multiplier system, and scintillating screens have been developed as a 2D detector for beam profile monitoring. Microdosimetry The pattern of energy (dose) deposition by a particle, not just the total energy deposited, is very important in determining the biological effect. Low Linear Energy Transfer (LET) particles (γ’s, protons) produce single hits in many cells. Neutrons (via low energy protons from glancing collisions) produce multiple hits in fewer cells. These are difficult for the cell to repair, leading to a larger biological effect. Microdosimetry is the art of measuring not just average dose but the pattern of dose deposition at the cellular scale. Macroscopic counters mimic the cellular scale by using tissueequivalent gas as the detection medium. One detects single events (beam intensity must be reduced) and logs the energy deposited in each event using a pulse-height analyzer. Unlike moderated counters and ionization chambers, which are relatively easy to use, LET counters and their associated data logging and analysis require considerable care and are best left to experts. Microdosimetry The SOI (Silicon-On-Insulator) microdosimeter. Here the fiducial volume actually is of μm dimensions. A large array (4800 30×30×10 μm cells) is used to get enough signal. Even so, the whole detector is small enough to be embedded in a phantom. A ½ mm polyethylene converter in front of the array converts neutrons to recoil protons. Neutrons detectors Fluence Moderated detectors A neutron moderator which slows neutrons to thermal energy (0.025 eV, 2 km/s) surrounds a small detecting element which has a very high cross section for thermal neutrons. The simplest moderator is a polyethylene (CH2) sphere. Three possible detecting reactions are: 6 3 (4.787 MeV) Li6 I(Eu) scintillator (somewhat obsolete) 3Li (n,α) 1H 10(n,α) Li7 B (2.78 MeV) BF3 gas proportional counter 5 3 3(n,p) H3 3 gas proportional counter He (0.764 MeV) He 2 1 A modern neutron survey meter (Ludlum Model 12-4). The moderator is a 9″ diameter cadmium-loaded polyethylene sphere and the detector is a He3 gas proportional counter. In a modern proton therapy center a number of such meters will be mounted at various locations, feeding data to a central point where it is recorded, to monitor neutron dose to staff and the general public. Neutron detectors Dose Bubble dosimeter Inside the detector, tiny droplet of superheated liquid are dispersed through a clear polymer. When a neutron strikes a droplet, the droplet immediately vaporises, forming a visible gas bubble trapped in the gel. The number of droplets provides a direct measurement of the tissue equivalent neutron dose. Neutrons detectors Dose CR-39 Track Etch Detectors CR-39 is a near tissue-equivalent thermosetting polymer sensitive to charged particles of LET ≥ 5 keV/μm (50 MeV/cm, corresponding to a ~10 MeV proton in water). An ion traversing the CR-39 breaks chemical bonds in the polymer, producing latent damage along the trajectory. After exposure, the detector is etched in 6.25 N NaOH at 50°C, converting the damage trails to conical pits which can be measured with an optical microscope. The size of the elliptical opening of each track is proportional to the LET of the charged particle that produced it. By measuring many tracks one can infer an LET spectrum and therefore, dose and dose equivalent. CR-39 is used in commercial dosimetry systems or, sometimes, by experts in in-house experiments. Commercial dosimeters use a polyethylene converter to produce proton recoils from fast neutrons and/or a borated converter to produce α’s from thermal neutrons. Solution Number of decays for unit time The activity (7.4E8 Bq) together with the half-life (6.0 h) enable us to calculate the number of 99mTc nuclei. N = N0e − τt dN R0 = − dt 0 N0 − t = e τ τ 0 N0 = τ Then we can determine how many photons are absorbed in the body; multiplying the number of photons absorbed by the energy of each photon (143 keV) gives the total radiation energy absorbed. AbsDose The absorbed dose is the radiation energy absorbed per unit mass of tissue. The biologically equivalent dose is the absorbed dose times the relative biological effectiveness. RBE BED Typical Values of Relative Biological Effectiveness RBE of therapy protons is generally 1-1.1 Particle therapy facilities in the world (update: June 2023) proton C-ion INFN-LNS, Catania (p) CNAO, Pavia (p, C) APSS, Trento (p) 2018 Humanitas, Milano (p) Istituto Europeo Oncologia, Milano (p) CRO, Aviano (p) data taken from: www.ptcog.ch Particle therapy facilities in the world (update: June 2023) Synchrotron proton Cyclotron C-ion Synchro-Cyclotron INFN-LNS, Catania (p) CNAO, Pavia (p, C) APSS, Trento (p) Humanitas, Milano (p) Istituto Europeo Oncologia, Milano (p) CRO, Aviano (p) data taken from: www.ptcog.ch Particle therapy facilities in the world Synchrotron (CNAO, Pavia) Particle facilities are complex facilities Facilities Structure - Making a useful beam Source Accelerator gas/target RF plasma Synchrotron Cyclotron Isochronous Cyclotron Beam line Lenses Degrader Beam monitors Gantry Range modula on Aperture, range compensator Beam ga ng, beam current modula on Beam monitors Scattered beam basic physics single sca ering double sca ering ti ti stopping sca ering nuclear interac ons high-Z/low-Z ti ti ti tt tt ti ti tt ti tt ti Nozzle con: neutron dose Scanned beam scanning magnets pro: be er conforma on, no wasted energy or protons, no pa ent hardware con: complexity, sensi ve to beam me structure and organ mo on Facilities Structure Degrader Conventional Gantry Framework of the IBA gantry. This is a massive structure, three stories high. It carries the final section of the beam line and the beam spreading ‘nozzle’ so that beam can be directed at the patient from any direction. It strives for sub-mm accuracy in the center of rotation, a major challenge to the mechanical engineer. What the patient sees: gantry room at the Midwest Proton Radiotherapy Institute (MPRI). This is a modified IBA gantry. Also visible are an industrial robot adapted to serve as the patient couch, the proton ‘snout’ which carries the aperture and range compensator, and an X-ray imaging plate used during patient alignment. Compact Gantry (Paul Scherrer Institute, PSI) (sweeping magnet) X scanning Z scanning (degraders) Y scanning (couch motion) One scanning dimension is provided by a sweeping magnet just before the 90º bend The second (depth) by degraders just upstream of the patient The third by couch motion The system, operating since 1996, is used for variable modulation or for IMPT. Stopping In matter, protons slow down and stop by millions of collisions with atomic electrons. If we measure range by mass traversed rather than distance, the range in air is similar to water. nuclear reactions range If we place a stack of material just upstream of a charge collector we find that protons of a definite energy have a characteristic range, defined as the halfway point of the steep falloff. However, even that has some width: the protons do not all stop at exactly the same depth. This range straggling spread is roughly 1.2% of the range itself and depends very little on the stopping material. The slow falloff is caused by loss of primary protons to nuclear reactions. The upper curve obtains if we move the Faraday Cup closer, allowing it to catch more of the wide-angle charged nuclear secondaries. Stopping Theory A very successful theory of stopping was developed by Bethe and others in the 1930’s. However, the stopping power of each material depends on an empirical parameter, the mean ionization energy I for that material. Because I is difficult to choose, we usually rely on standard tables such as ICRU Report 49 instead of computing stopping power directly from the theory. It turns out that range is nearly proportional to energy on a log-log plot (above) which implies an approximate power law R ≈ aTb The energy range of clinical relevance for protons is 3-300 MeV. T = particle kinetic energy Multiple scattering L x0 θ0 MP When protons pass through a slab of material they suffer millions of EM collisions with atomic nuclei. The statistical resultant is a multiple scattering angle whose distribution is approximately Gaussian. For protons, this angle is always small so the projected displacement in any measuring plane (MP) is also Gaussian. The width parameter of the angular distribution is θ0. The corresponding displacement x0 can easily be measured by scanning a dosimeter across the MP. The task of multiple scattering theory is to predict θ0 given the scattering material, thickness and incident proton energy. Multiple Scattering Theory The definitive theory of multiple Coulomb scattering was published by G. Molière in 1947. It has no empirical parameters and (very important for proton therapy design) covers arbitrarily thick scatterers (that is, the effect of energy loss) as well as compounds and mixtures. gaussian 1 θ4 The angular distribution at large angles falls off roughly as 1/θ4 but is nearly Gaussian for small angles, a good enough approximation for most proton therapy calculations. θ0 , the width parameter of the Gaussian, is given by Molière theory as shown by this figure (Gottschalk et al. NIM 74 (1993) 467). The points are experimental. Nuclear Reactions proton About 20% of 160 MeV protons stopping in water have a non-elastic nuclear reaction where the primary proton is seriously degraded and secondary protons, neutrons and nuclear fragments appear. This figure (M. Berger, NISTIR 5226 (1993)) shows the effect on the Bragg peak. Dose from the EM peak shifts upstream, lowering the peak and flattening the entrance region especially at high proton energy. High-Z/Low-Z Energy loss and multiple scattering beam: 160 MeV protons target: 1 g/cm2 of various materials LR ≡ radiation length. For scattering with minimum energy loss, use lead. To reduce energy with minimum scattering, use beryllium. Choice of Energy Degrader Material Beam Transmission Beryllium slab Lighter materials allow to decrease beam energy with higher transmission and lower beam energy and lateral spreading Carbon stepped wedge Single Scattering scattered beam configuration The simplest treatment beam. 5mm 100 mm With enough scatterer, we can make the Gaussian at the target wide enough so it is sufficiently flat (say 5% or ±2.5%) over the required radius. Unfortunately, only 5% of the protons will fall within that radius. Also, the scatterer uses up a lot of the proton energy. dE dx To treat large or deep fields we need something better. Single scattering is used for targets, like the eye, which are small and shallow. x Range Shifter and Modulator At a fixed energy machine we may need some extra material to bring the dose forward to the desired distal depth. Also, if the target has significant extent in depth we can use a modulator wheel of different thicknesses of plastic to sweep the proton endpoint back and forth. The dwell time of each step in the beam is carefully computed so the resulting spread out Bragg peak (SOBP) will be flat. dE dx x Double Scattering Stronger scattering in the center Double scattering: for better efficiency (up to 45%) and less energy loss A flat first scatterer S1 produces a Gaussian on the second scatterer S2, which is stronger in the center to scatter those protons more. With careful design the transverse dose at the target is flat. Modulator wheel First Scatter Second Scatter A complementary plastic plate is used to compensate energy loss across S2. The first scatterer can be a simple sheet, or it can be a modulator wheel as shown. Patient specific hardware Having made a large uniform cylindrical dose field, we shape it as required for that particular target. The patient aperture AP blocks protons outside the target cross section. A range compensator RC shapes the distal dose surface and can also compensate for inhomogeneities is the patient. The snout SN holds this hardware while blocking unwanted large-angle protons. A therapy center should have snouts of several sizes. Range Shifter and Modulator range compensator patient aperture Modulator wheel Simulations - Montecarlo Although we can design scattering systems accurately from first principles the math is complicated and we need special programs. This run shows an experimental test of the first ‘upstream modulator’ double scattering system ca. 1990 at the Harvard Cyclotron Lab. Except for the transverse width the data agree rather well. Limitations Passive beam spreading is limited by the fact that nature does not provide perfect scatterers (no energy loss) or degraders (no scattering). The limits are best visualized by graphing the attainable field radius vs. maximum treatment depth. In this case we assume 230 MeV protons, a throw of 250 cm and S2 placed at 50 cm. The relative modulation (mod/depth) obtainable at each point is indicated by the degree of filling of the point. Solid means full modulation or anything less. A larger throw would yield deeper fields for the same energy. Unwanted Neutron Dose In addition to unwanted proton dose patients receive some neutron dose: unavoidable internal neutrons from therapy protons interacting in the target plus external neutrons from the beam spreading system. Neutrons originate wherever a lot of protons lose a lot of energy. In a well designed scattering system the main source is the patient collimator, so we should match the open field size to the target, and the external neutron dose is comparable to the internal dose. Many studies show that both are on the order of 1mSv/Gy. The attributable lifetime risk of a fatal cancer is