27.1-27.2: Basic Physics & Radiobiology
- Protons that traverse through a medium can interact by inelastic collisions or elastic scattering.
- Inelastic collisions refer to an interaction either by ionization and excitation, or by bremsstrahlung. A head-on collision with a nuclei can produce a nuclear reaction which can result in short-lived radioisotopes such as C-11, N-13, and O-15.
- Elastic scattering refers to an interaction without energy loss.
- Stopping power refers to the average rate of energy loss per unit path length by a particle as it traverses through a medium.
- Linear stopping power (MeV/cm) can also be expressed as linear energy transfer (LET), and the LET, i.e. the rate of energy transfer to the surrounding, will increase as a proton approaches the end of its range.
- This concept can be thought of by a marble that is flicked into a sea of marbles. The marble that is flicked possesses high velocity, relative to the still marbles of the sea, when it initially interacts with marbles of the sea.
- These interactions will be brief compared to when the marble approaches a stop, as these interactions become lengthier and more pronounced.
- Thus, as the velocity of the proton decreases, the rate of energy loss will increase. The rate of energy loss of a proton is proportional to the square of the particle charge and inversely proportional to the square of its velocity.
- Linear stopping power (MeV/cm) can also be expressed as linear energy transfer (LET), and the LET, i.e. the rate of energy transfer to the surrounding, will increase as a proton approaches the end of its range.
- This phenomenon can be seen on a PDD curve where the curve exhibits a sharp increase in dose deposition near the end of the proton’s range which is referred to as the Bragg peak.
- However, the Bragg peak of a monoenergetic proton beam (pristine peak) is too narrow to envelope a target volume. As a result, additional proton beams of varying energies are used to stagger their Bragg peaks to create a plateau region of full uniform dose called a spread-out Bragg peak (SOBP).
- The Bragg peak is followed by a steep dose drop off to nearly zero dose and is a significant advantage to using protons over photons.
- However, the full potential of the steep distal dose gradient of the SOBP is not utilized in practice due to a combination of the following uncertainties: accuracy of dose calculation algorithms, organ motion during treatment, varying patient setup, and subjective target delineation.
- Multiple isocentric beams are used to reduce the uncertainty from a statistical standpoint.
- Different radiation (e.g. type, quality, and fractionation) possess different cell damaging capacities, and so the relative biologic effectiveness (RBE) is used as a frame of reference.
- The RBE is the ratio of 250 kVp x-rays required to produce a specified biological effect (e.g. cell killing, tissue damage, mutation, etc.) divided by the dose of the radiation in question required to produce the same biological effect.
- The RBE is directly proportional to the LET.
- The LET of a proton continuously changes with depth, and so an averaged value of 1.1 has been assigned for the RBE of a proton beam which is relative to the RBE of megavoltage beam which is 1.0.
27.2, 27.3, & 27.6: Proton Accelerators, Beam Delivery Systems, & Treatment Planning
- Cyclotrons and synchrotrons are used to accelerate proton beams for clinical use.
- A cyclotron is made up of two semicircles (dees) that are parallel and separated by a gap. An electric field is applied across the gap, and a magnetic field is applied that is perpendicular to the dees. When a proton is injected into the center of the cyclotron, it will move towards the negative dee. The direction of the electric field will reverse everytime the proton passes over the gap, and thus, the proton will accelerate in orbit until it reaches the maximum energy.
- Cyclotrons can only produce a proton beam of a fixed energy and will require energy degradors of varying thickness to reduce the proton beam range for SOBP and/or superficial treatments.
- Energy degraders have the following drawbacks: produce greater neutron contamination, require greater shielding around beam-generating equipment, and exhibit higher radioactivity in the metal collimators energy-degrading system following treatment.
- A synchrotron receives protons of 3 to 7 MeV from a paired linear accelerator and circulates the protons along a narrow tube ring. The proton beam is accelerated to desired energies by radiofrequency cavities and are kept in circulation by magnets lining the tube ring.
- Synchrotrons can vary the proton beam range and will not require energy degraders.
- A cyclotron is made up of two semicircles (dees) that are parallel and separated by a gap. An electric field is applied across the gap, and a magnetic field is applied that is perpendicular to the dees. When a proton is injected into the center of the cyclotron, it will move towards the negative dee. The direction of the electric field will reverse everytime the proton passes over the gap, and thus, the proton will accelerate in orbit until it reaches the maximum energy.
- A single accelerator can provide proton beams to multiple treatment rooms. The proton beam is transported from the accelerator to the treatment rooms by bending magnets with a minor loss of beam intensity. The small proton beam is spread in the nozzle or treatment head by passive beam scattering or by pencil beam scanning.
- Passive beam spreading uses a high-Z scattering foil to scatter a proton beam to a useful field size.
- High-Z materials result in less energy degradation of the beam.
- Mass stopping power, i.e energy loss in a unit distance per unit density, increases as the Z of the material decreases because low-Z materials have a more electrons per gram of material. The difference can be seen by a comparison between aluminum and tungsten:
- 1 Al atom = 26.98 amu and 13 electrons.
- 26.98 amu * 1.66 * 10^-24 g/amu = 4.48 * 10^-23 g.
- 13 electrons / 4.48 * 10^-23 g = 2.90 * 10^23 electrons/g of Al.
- 1 W atom = 183.84 amu and 74 electrons.
- 183.84 * 1.66 * 10^-24 g/amu = 3.05 * 10^-22 g.
- 74 electrons / 3.05 * 10^-22 g = 2.42 * 10^23 electrons/g of W.
- (2.90 * 10^23 electrons/g of Al) / (2.42 * 10^23 electrons/g of W) = 1.20 or 20% more electrons/g in Al than in that of W.
- Thus, using high-Z materials will result in less energy degradation of the beam.
- 1 Al atom = 26.98 amu and 13 electrons.
- Mass stopping power, i.e energy loss in a unit distance per unit density, increases as the Z of the material decreases because low-Z materials have a more electrons per gram of material. The difference can be seen by a comparison between aluminum and tungsten:
- High-Z materials scatter protons through wider angles.
- Compared to an electron beam, proton beams will inherently scatter through small angles as protons are heavier particles, and will exhibit a sharper lateral distribution than that of electron and even photon beams.
- High-Z materials result in less energy degradation of the beam.
- To achieve a uniform dose distribution across the field (excluding the penumbral region), the beam is collimated such that the lateral profile is within 5% of the central area.
- For treatments requiring large field sizes, dual scattering foils are used to achieve at least 5% uniformity across the field.
- The first foil is of uniform thickness for the purpose of spreading the beam to a large enough size.
- The second foil is of varying thickness, and the thickness at a given point is dependent on the amount of intensity modulation that will be required to achieve a uniform distribution.
- For treatments requiring large field sizes, dual scattering foils are used to achieve at least 5% uniformity across the field.
- Patient-specific field apertures are used to shape the field and are placed close to the phantom surface (small air gap) to reduce scatter in air and the penumbra region.
- The energy of the proton beam that will provide adequate coverage to the distal shape of the target volume is initially determined.
- The range and intensity of the proton beam will then be reduced to pull back the Bragg peak, and this reduction is repeated until the Bragg peak encompasses the extent of the target volume.
- The SOBP is achievable by a rotating range-modulator wheel (propeller) that inserts successively thicker layers of plastic or varying angular widths in the path of the beam. The range is dependent on the thickness of segment, and the intensity is based on the beam-on time with the segment that correlates to its angular width.
- The SOBP is specified by its modulation width and range. The modulation width is the distance between the proximal 90% PDD and the distal 90% PDD, and the range is the distance to the distal 90% PDD from the surface.
- Furthermore, range compensators of low Z materials such as plastic or wax can be placed on the phantom surface to compensate for an irregular surface, tissue heterogeneity, and the shape of the distal PTV surface.
- The uncertainty of patient setup, patient and/or internal organ motion, and the uncertainty of PTV and/or OAR localization is taken into account in the design of the compensator.
- In proton planning, it is important to take into account the uncertainty resulting from water-equivalent depths, calculated beam ranges, patient setup, and target localization and motion.
- Thus, dose distribution may be computed at the upper and lower ends of these uncertainties and/or corrective techniques such as “smearing” are incorporated into the planning system algorithm.
- Smearing involves adjusting a range compensator to account for the “worst” case scenario and the margin of coverage at the distal edge of the target volume will increase.
- This precaution is at the expense of target volume conformality and more dose beyond the distal edge of the target volume.
- Thus, dose distribution may be computed at the upper and lower ends of these uncertainties and/or corrective techniques such as “smearing” are incorporated into the planning system algorithm.
- The beam energy, SOBP range and modulation, angle compensator, field aperture, and dose distribution are designed during treatment planning.
- Pencil beam scanning is the magnetic scanning of narrow beams of proton to place Bragg peaks in the voxels of the tissue region of interest to deliver a uniform dose to the target volume.
- The beam scanning system will control the beam intensity, field size, depth, and beam position. A single treatment port is made up of thousands of individually weighted pencil beams calculated for by an optimization process.
- The beam scanning system does not degrade the beam energy (loss of treatment range) due to the absence of a scattering foil.
- Custom field blocking and range compensators become unnecessary as magnetic scanning can define the field size and determine the beam range and intensity.
- The beam scanning system will control the beam intensity, field size, depth, and beam position. A single treatment port is made up of thousands of individually weighted pencil beams calculated for by an optimization process.
- Beam scanning can used in intensity-modulated proton therapy (IMPT) by using multiple treatment ports of varying proton fluence distribution that will deliver a homogeneous dose to the target volume when summed.
- IMPT is more susceptible to organ motion as the slight movement of an organ into or out of the beam path can result in an over/underdose of the target and/or the normal structures surrounding. This issue is more pronounced for protons than for photons due to the PDD of a proton, and the following strategies can be utilized to combat the organ motion problem:
- Tracking the tumor during treatment by imaging and gating.
- Synchronizing beam delivery with a patient’s breathing cycle by a 4DCT.
- Repainting the dose multiple times over the target volume during the organ motion period to achieve an average dose distribution.
- Increasing the scanning speed to increase the number of repaintings for the same delivery time.
27.5: Dosimetry
- The International Atomic Energy Agency (IAEA) report is a protocol for the absorbed dose calibration of proton beams between the energy range of 50 to 250 MeV.
- The equation to calculate absorbed dose in water (D) that is irradiated by a proton beam (z) is given by: D = M * N * k.
- M is the dosimeter reading that is corrected for temperature and pressure, electrometer calibration, polarity effect, and ion recombination.
- N is the ion chamber calibration factor that converts the dosimeter reading to absorbed dose.
- k is the beam quality factor which is the correction for chamber response for a beam quality different than that of the reference quality. More specifically, it is the ratio of calibration factors between the beams of quality Q and Q_0 for the given ion chamber. k_Q,Q_0 = N_Q / N_Q_0.
- Ideally, the beam quality factor would be obtained by the direct measurement of absorbed dose at the beam qualities of Q and Q_0, but as there are no primary standards of absorbed dose to water available for proton beams, it has been calculated by the following equation: k_Q,Q_0 = (S_Q * W_Q * P_Q) / (S_Q_0 * W_Q_0 * P_Q_0).
- S is the Spencer-Attix water/air stopping power ratio.
- W is the mean energy required to create in air.
- P is the chamber perturbation factor that accounts for air cavity, displacement factor, chamber wall, and central electrode.
- Co-60 is used as the reference beam quality.
- Ideally, the beam quality factor would be obtained by the direct measurement of absorbed dose at the beam qualities of Q and Q_0, but as there are no primary standards of absorbed dose to water available for proton beams, it has been calculated by the following equation: k_Q,Q_0 = (S_Q * W_Q * P_Q) / (S_Q_0 * W_Q_0 * P_Q_0).
- The equation to calculate absorbed dose in water (D) that is irradiated by a proton beam (z) is given by: D = M * N * k.
- The IAEA protocol specifies the quality of a proton beam based on its effective energy.
- The effective energy is about the maximum energy used for a SOPB, and is defined as the energy of a monoenergetic proton beam that has the same residual range as that of the SOPB.
- The residual range (R_es) is obtained by the equation: R_es = R_p – z_r.
- R_p is the practical range (the depth beyond the SOBP where the dose falls to 10% of its maximum value.
- z_r is the depth at which is the midpoint of the SOBP.
- The residual range (R_es) is obtained by the equation: R_es = R_p – z_r.
- The effective energy is about the maximum energy used for a SOPB, and is defined as the energy of a monoenergetic proton beam that has the same residual range as that of the SOPB.
Related Content:
| Planning Technique Guides: |
| Notes on Proton Planning |
| Miscellaneous: |
| Khan Chapter 1 Summary |
| Khan Chapter 2 Summary |
| Khan Chapter 3 Summary |
| Khan Chapter 4.5 Summary |
| Khan Chapter 5 Summary |
| Khan Chapter 7 Summary |
