Creating a spread-out Bragg peak in proton beams

The model of Bortfeld and Schlegel (1996 Phys. Med. Biol. 41 1331-9) for determining the weights of proton beams required to create a spread-out Bragg peak (SOBP) gives a significantly tilted SOBP. However, by arbitrarily varying its parameter p, which relates the range of protons to their energy, we have been able to create satisfactory SOBPs. MCNPX Monte Carlo calculations have been carried out to determine p, demonstrating the success of this modification. Optimal values of p are tabulated for various combinations of maximum beam energy E(0) (50, 100, 150, 200 and 250 MeV) and SOBP width χ (15%, 20%, 25%, 30%, 35% and 40%), as well as for a correction factor needed to calculate the SOBP dose. An example shows the application of these results to analyzing the dose deposited by deuterons and alpha particles in broad proton beams.     

Radiobiological significance of beamline dependent proton energy distributions in a spread-out Bragg peak

Similar target doses can be achieved with different mixed radiation fields, i.e., particle energy distributions, produced by a practical proton beam and a range modulator. The dose delivered in particle therapy can be described as the integral of fluence times the total mass stopping power over the particle energy distributions. We employed Monte Carlo simulations to explore the influence on the relative biological effectiveness (RBE) of the energy and the energy spread of the proton beam incident on a range modulator system. Using different beams, the conditions of beam delivery were adjusted so that similar spread out Bragg peak (SOBP) doses were delivered to a simulated water phantom. We calculated the RBE for inactivation of three different cell lines using the track structure model. The RBE depends on the details of the dose deposition and the biological characteristics of the irradiated tissue. Our calculations show that, for differing beam conditions, the corresponding differences in the total mass stopping power distributions are reflected in differences in the RBE. However, these differences are remarkable only at the very distal edge of the SOBP, for low doses, and/or for large differences in beam setup.     

Optimization of current modulation function for proton spread-out Bragg peak fields

Proton treatments with spread-out Bragg peak (SOBP) fields often use a rotating modulation wheel of varying thickness to modulate the pristine Bragg peak in depth and intensity. The technique of modulating also the beam current independently over the wheel rotation provides an additional control over the intensities of the pulled-back Bragg peaks. As a result, a single wheel can be used over a large range of energies and SOBP parameters and field-specific wheels are no longer necessary. An essential task in commissioning a particular treatment depth is the determination of this current modulation function. We have developed a method for the optimization of the current modulation function. The basic idea is to treat the entire beam nozzle, housing the various beam scattering and modulating components, as a whole and to characterize its effect as a transformation from a modulating beam current to a depth-dose distribution. While this transformation is difficult to calculate theoretically due to the complex scattering paths in the nozzle and the phantom, it can, however, be determined by time-resolved dose measurements. Using this transformation, we can calculate SOBP depth-dose distributions for any current modulation function and optimize it by a simple numerical optimization. We have applied the new method to a number of proton beams with satisfactory results.     

Monte Carlo simulation and analysis of proton energy-deposition patterns in the Bragg peak

The spatial pattern of energy depositions is crucial for understanding the mechanisms that modify the relative biological effectiveness of different radiation qualities. In this paper, we present data on energy-deposition properties of mono-energetic protons (1-20 MeV) and their secondary electrons in liquid water. Proton-impact ionization was described by means of the Hansen-Kocbach-Stolterfoht doubly differential cross section (DDCS), thus modelling both the initial energy and angle of the emitted electron. Excitation by proton impact was included to account for the contribution of this interaction channel to the electronic stopping power of the projectile. Proton transport was implemented assuming track-segment conditions, whereas electrons were followed down to 50 eV by the Monte Carlo code PENELOPE. Electron intra-track energy-deposition properties, such as slowing-down and energy-imparted spectra of electrons, were calculated. Furthermore, the use of DDCSs enabled the scoring of electron inter-track properties. We present novel results for 1, 5 and 20 MeV single-proton-track frequencies of distances between the nearest inter- (e(-)-e(-), e(-)-H+) and intra-track (e(-)-e(-), e(-)-H+, H+-H+) energy-deposition events. By setting a threshold energy of 17.5 eV, commonly employed as a surrogate to discriminate for elementary damage in the DNA, the variation in these frequencies was studied as well. The energy deposited directly by the proton represents a large amount of the total energy deposited along the track, but when an energy threshold is adopted the relative contribution of the secondary electrons becomes larger for increasing energy of the projectile. We found that the frequencies of closest energy-deposition events per nanometre decrease with proton energy, i.e. for lower proton energies a denser ionization occurs, following the trend of the characteristic LET curves. In conclusion, considering the energy depositions due to the delta electrons and at the core of the track, 1 MeV protons have an intrinsic capability of generating about five times more dual depositions within the characteristic 2 nm of the DNA-chain structure than 20 MeV protons.     

Bragg peak prediction from quantitative proton computed tomography using different path estimates

This paper characterizes the performance of the straight-line path (SLP) and cubic spline path (CSP) as path estimates used in reconstruction of proton computed tomography (pCT). The GEANT4 Monte Carlo simulation toolkit is employed to simulate the imaging phantom and proton projections. SLP, CSP and the most-probable path (MPP) are constructed based on the entrance and exit information of each proton. The physical deviations of SLP, CSP and MPP from the real path are calculated. Using a conditional proton path probability map, the relative probability of SLP, CSP and MPP are calculated and compared. The depth dose and Bragg peak are predicted on the pCT images reconstructed using SLP, CSP, and MPP and compared with the simulation result. The root-mean-square physical deviations and the cumulative distribution of the physical deviations show that the performance of CSP is comparable to MPP while SLP is slightly inferior. About 90% of the SLP pixels and 99% of the CSP pixels lie in the 99% relative probability envelope of the MPP. Even at an imaging dose of ～0.1 mGy the proton Bragg peak for a given incoming energy can be predicted on the pCT image reconstructed using SLP, CSP, or MPP with 1 mm accuracy. This study shows that SLP and CSP, like MPP, are adequate path estimates for pCT reconstruction, and therefore can be chosen as the path estimation method for pCT reconstruction, which can aid the treatment planning and range prediction of proton radiation therapy.     

The prediction of output factors for spread-out proton Bragg peak fields in clinical practice

The reliable prediction of output factors for spread-out proton Bragg peak (SOBP) fields in clinical practice remained unrealized due to a lack of a consistent theoretical framework and the great number of variables introduced by the mechanical devices necessary for the production of such fields. These limitations necessitated an almost exclusive reliance on manual calibration for individual fields and empirical, ad hoc, models. We recently reported on a theoretical framework for the prediction of output factors for such fields. In this work, we describe the implementation of this framework in our clinical practice. In our practice, we use a treatment delivery nozzle that uses a limited, and constant, set of mechanical devices to produce SOBP fields over the full extent of clinical penetration depths, or ranges, and modulation widths. This use of a limited set of mechanical devices allows us to unfold the physical effects that affect the output factor. We describe these effects and their incorporation into the theoretical framework. We describe the calibration and protocol for SOBP fields, the effects of apertures and range-compensators and the use of output factors in the treatment planning process.     

A compact ridge filter for spread out Bragg peak production in pulsed proton clinical beams

A number of designs have been proposed for ridge filters and range modulators used in proton therapy to modify the beam in order to spread out the Bragg peak. Despite the variety of solutions, no simple design capable of providing large fields and easy variation of the spread out Bragg peak (SOBP) length in a pulsed beam has been developed. We propose a compact ridge filter that can be used in a proton beam of any time structure. It allows the production of depth dose distributions that meet the requirements of therapy dose fields.     

Degradation of the Bragg peak due to inhomogeneities

The rapid fall-off of dose at the end of range of heavy charged particle beams has the potential in therapeutic applications of sparing critical structures just distal to the target volume. Here we explored the effects of highly inhomogeneous regions on this desirable depth-dose characteristic. The proton depth-dose distribution behind a lucite-air interface parallel to the beam was bimodal, indicating the presence of two groups of protons with different residual ranges, creating a step-like depth-dose distribution at the end of range. The residual ranges became more spread out as the interface was angled at 3 degrees, and still more at 6 degrees, to the direction of the beam. A second experiment showed little significant effect on the distal depth-dose of protons having passed through a mosaic of teflon and lucite. Anatomic studies demonstrated significant effects of complex fine inhomogeneities on the end of range characteristics. Monoenergetic protons passing through the petrous ridges and mastoid air cells in the base of skull showed a dramatic degradation of the distal Bragg peak. In beams with spread out Bragg peaks passing through regions of the base of skull, the distal fall-off from 90 to 20% dose was increased from its nominal 6 to well over 32 mm. Heavy ions showed a corresponding degradation in their ends of range. In the worst case in the base of skull region, a monoenergetic neon beam showed a broadening of the full width at half maximum of the Bragg peak to over 15 mm (compared with 4 mm in a homogeneous unit density medium). A similar effect was found with carbon ions in the abdomen, where the full width at half maximum of the Bragg peak (nominally 5.5 mm) was found to be greater than 25 mm behind gas-soft-tissue interfaces. We address the implications of these data for dose computation with heavy charged particles.     

An analytical solution for improved HIFU SAR estimation

Accurate determination of the specific absorption rates (SARs) present during high intensity focused ultrasound (HIFU) experiments and treatments provides a solid physical basis for scientific comparison of results among HIFU studies and is necessary to validate and improve SAR predictive software, which will improve patient treatment planning, control and evaluation. This study develops and tests an analytical solution that significantly improves the accuracy of SAR values obtained from HIFU temperature data. SAR estimates are obtained by fitting the analytical temperature solution for a one-dimensional radial Gaussian heating pattern to the temperature versus time data following a step in applied power and evaluating the initial slope of the analytical solution. The analytical method is evaluated in multiple parametric simulations for which it consistently (except at high perfusions) yields maximum errors of less than 10% at the center of the focal zone compared with errors up to 90% and 55% for the commonly used linear method and an exponential method, respectively. For high perfusion, an extension of the analytical method estimates SAR with less than 10% error. The analytical method is validated experimentally by showing that the temperature elevations predicted using the analytical method's SAR values determined for the entire 3D focal region agree well with the experimental temperature elevations in a HIFU-heated tissue-mimicking phantom.     

Feasibility of MRI guided proton therapy: magnetic field dose effects

Many methods exist to improve treatment outcome in radiotherapy. Two of these are image-guided radiotherapy (IGRT) and proton therapy. IGRT aims at a more precise delivery of the radiation, while proton therapy is able to achieve more conformal dose distributions. In order to maximally exploit the sharp dose gradients from proton therapy it has to be combined with soft-tissue based IGRT. MRI-guided photon therapy (currently under development) offers unequalled soft-tissue contrast and real-time image guidance. A hybrid MRI proton therapy system would combine these advantages with the advantageous dose steering capacity of proton therapy. This paper addresses a first technical feasibility issue of this concept, namely the impact of a 0.5 T magnetic field on the dose distribution from a 90 MeV proton beam. In contrast to photon therapy, for MR-guided proton therapy the impact of the magnetic field on the dose distribution is very small. At tissue-air interfaces no effect of the magnetic field on the dose distribution can be detected. This is due to the low-energy of the secondary electrons released by the heavy protons.     

Carbon-13 and proton magnetic resonance studies of poly(N-vinylcarbazole) in solution

Spin-lattice relaxation times T₁ of individual carbons and protons were measured by the partially relaxed Fourier transform (PRFT) method for poly(N-vinylcarbazole) in solution. The ¹³C-T₁ value of the methylene carbon is about one-half of that of the methine carbon, and the carbazolyl CH carbons have T₁ values close to that of the skeletal CH carbons. The effective correlation time for the skeletal carbon is estimated as ca. 0,95 ns on the basis of the measured T₁ and ¹³C-¹H nuclear Overhauser effect (NOE) factor. Moreover, the ¹³C normal Fourier transformation (NFT) spectrum and proton T₁ indicate strong steric interactions between the pendant carbazolyl groups in the polymer. The results demonstrate that the polymer in solution has a rigid local structure with hindered internal rotation of the bulky side-chain groups.     

Density heterogeneities and the influence of multiple Coulomb and nuclear scatterings on the Bragg peak distal edge of proton therapy beams

Density heterogeneities in the path of proton beams are known to cause degradation of the Bragg peak and, thus, widening of its distal fall-off. Inadequate accounting for this effect may lead to unwanted dose delivered to normal tissue distal to the target volume. In low-density regions, such as the thorax, this may lead to large volumes of healthy tissue receiving unnecessary dose. Although it is known that multiple Coulomb scattering within the density heterogeneities is the main cause of Bragg peak degradation, no systematic attempt has been made to quantify the contribution of multiple Coulomb scattering and nuclear scattering. Through a systematic study using a 220 MeV proton beam, we show that nuclear scattering contributes to about 5% of the distal fall-off width and is only slightly dependent on heterogeneity complexity. Furthermore, we also show that the energy spectra of the proton fluence downstream of various heterogeneity volumes are well correlated with the Bragg peak distal fall-off widths. Based on this correlation, a novel method for predicting distal fall-offs is suggested. This method is tested for three clinical setups of a voxelized model of a human head based on computer tomography data. Results are within 3% of the distal fall-off values obtained using Monte Carlo simulations.     

Head tilt in rats during exposure to a high magnetic field

During exposure to high strength static magnetic fields, humans report vestibular symptoms such as vertigo, apparent motion, and nausea. Rodents also show signs of vestibular perturbation after magnetic field exposure at 7 tesla (T) and above, such as locomotor circling, activation of vestibular nuclei, and acquisition of conditioned taste aversions. We hypothesized that the acute effects of the magnetic field might be seen as changes in head position during exposure within the magnet. Using a yoked restraint tube that allowed movement of the head and neck, we found that rats showed an immediate and persistent deviation of the head during exposure to a static 14.1 T magnetic field. The direction of the head tilt was dependent on the orientation of the rat in the magnetic field (B), such that rats oriented head-up (snout towards B+) showed a rightward tilt of the head, while rats oriented head-down (snout towards B-) showed a leftward tilt of the head. The tilt of the head during magnet exposure was opposite to the direction of locomotor circling immediately after exposure observed previously. Rats exposed in the yoked restraint tube showed significantly more locomotor circling compared to rats exposed with the head restrained. There was little difference in CTA magnitude or extinction rate, however. The deviation of the head was seen when the rats were motionless within the homogenous static field; movement through the field or exposure to the steep gradients of the field was not necessary to elicit the apparent vestibulo-collic reflex.     

Circular swimming in mice after exposure to a high magnetic field

There is increasing evidence that exposure to high magnetic fields of 4 T and above perturbs the vestibular system of rodents and humans. Performance in a swim test is a sensitive test of vestibular function. In order to determine the effect of magnet field exposure on swimming in mice, mice were exposed for 30 min within a 14.1 T superconducting magnet and then tested at different times after exposure in a 2-min swim test. As previously observed in open field tests, mice swam in tight counter-clockwise circles when tested immediately after magnet exposure. The counter-clockwise orientation persisted throughout the 2-min swim test. The tendency to circle was transient, because no significant circling was observed when mice were tested at 3 min or later after magnet exposure. However, mice did show a decrease in total distance swum when tested between 3 and 40 min after magnet exposure. The decrease in swimming distance was accompanied by a pronounced postural change involving a counter-clockwise twist of the pelvis and hindlimbs that was particularly severe in the first 15 s of the swim test. Finally, no persistent difference from sham-exposed mice was seen in the swimming of magnet-exposed mice when tested 60 min, 24 h, or 96 h after magnet exposure. This suggests that there is no long-lasting effect of magnet exposure on the ability of mice to orient or swim. The transient deficits in swimming and posture seen shortly after magnet exposure are consistent with an acute perturbation of the vestibular system by the high magnetic field.     

Benchmarking analytical calculations of proton doses in heterogeneous matter

A proton dose computational algorithm, performing an analytical superposition of infinitely narrow proton beamlets (ASPB) is introduced. The algorithm uses the standard pencil beam technique of laterally distributing the central axis broad beam doses according to the Moliere scattering theory extended to slablike varying density media. The purpose of this study was to determine the accuracy of our computational tool by comparing it with experimental and Monte Carlo (MC) simulation data as benchmarks. In the tests, parallel wide beams of protons were scattered in water phantoms containing embedded air and bone materials with simple geometrical forms and spatial dimensions of a few centimeters. For homogeneous water and bone phantoms, the proton doses we calculated with the ASPB algorithm were found very comparable to experimental and MC data. For layered bone slab inhomogeneity in water, the comparison between our analytical calculation and the MC simulation showed reasonable agreement, even when the inhomogeneity was placed at the Bragg peak depth. There also was reasonable agreement for the parallelepiped bone block inhomogeneity placed at various depths, except for cases in which the bone was located in the region of the Bragg peak, when discrepancies were as large as more than 10%. When the inhomogeneity was in the form of abutting air-bone slabs, discrepancies of as much as 8% occurred in the lateral dose profiles on the air cavity side of the phantom. Additionally, the analytical depth-dose calculations disagreed with the MC calculations within 3% of the Bragg peak dose, at the entry and midway depths in the phantom. The distal depth-dose 20%-80% fall-off widths and ranges calculated with our algorithm and the MC simulation were generally within 0.1 cm of agreement. The analytical lateral-dose profile calculations showed smaller (by less than 0.1 cm) 20%-80% penumbra widths and shorter fall-off tails than did those calculated by the MC simulations. Overall, this work validates the usefulness of our ASPB algorithm as a reasonably fast and accurate tool for quality assurance in planning wide beam proton therapy treatment of clinical sites either composed of homogeneous materials or containing laterally extended inhomogeneities that are comparable in density and located away from the Bragg peak depths.     

A method for achieving variable widths of the spread-out Bragg peak using a ridge filter

A method for designing a variable-SOBP (spread-out Bragg peak) ridge filter has been proposed. First, ridge filter parameters are determined by using a Monte Carlo calculation followed by a fast two-step iterative optimization. Then, tilting the ridge filter results in continuous variation of the SOBP width. Monte Carlo calculations show that depth dose uniformity changes from +/- 1.3% to +/- 1.6% for SOBP widths ranging from 10.3 cm to 14.5 cm. Advantages of the proposed tilting ridge filter include a capability of continuous SOBP variation and cost-effective installation for a given SOBP width range.     

Real-time correction of magnetic field inhomogeneity-induced image distortions for MRI-guided conventional and proton radiotherapy

Image-guided radiotherapy has the potential to increase the success of treatment by decreasing uncertainties concerning tumour position and shape. We pursue integrated diagnostic quality MRI functionality with radiotherapy systems to boost the possibilities of image guidance by providing images with superior soft-tissue contrast during treatment. However, the use of MR images in radiotherapy can be hindered by geometrical distortions due to magnetic field inhomogeneity problems. A method for fast correction of these distortions is presented and implemented. Using a 20 cm square phantom containing a regular grid, a measure of residual deformation after correction is established. At very low gradient strength (which leads to large deformations) a maximum displacement of 2.9 mm is shown to be reduced to 0.63 mm. Next, the method is applied in vivo to the case of pelvic body contour extraction for prostate radiotherapy treatment planning. Here, again with low gradient strengths, distortions of up to 6 mm can be reduced to 2 mm. All results are provided within a lag time of 8 ms. We discuss implications of image distortions for MRI-guided photon and proton radiotherapy separately, since the dose-depth curves in these treatments are very different. We argue that, although field inhomogeneities cannot be prevented from occurring, distortion correction is not always necessary in practice. This work opens new possibilities for investigating on-line MRI-based plan adaptations and ultimately MRI-based treatment planning.     

A blood-oxygenation-dependent increase in blood viscosity due to a static magnetic field

As the magnetic field of widely used MR scanners is one of the strongest magnetic fields to which people are exposed, the biological influence of the static magnetic field of MR scanners is of great concern. One magnetic interaction in biological subjects is the magnetic torque on the magnetic moment induced by biomagnetic substances. The red blood cell is a major biomagnetic substance, and the blood flow may be influenced by the magnetic field. However, the underlying mechanisms have been poorly understood. To examine the mechanisms of the magnetic influence on blood viscosity, we measured the time for blood to fall through a glass capillary inside and outside a 1.5 T MR scanner. Our in vitro results showed that the blood viscosity significantly increased in a 1.5 T MR scanner, and also clarified the mechanism of the interaction between red blood cells and the external magnetic field. Notably, the blood viscosity increased depending on blood oxygenation and the shear rate of the blood flow. Thus, our findings suggest that even a 1.5 T magnetic field may modulate blood flow.