Analysis of a novel X-ray lens for converging beam radiotherapy.

We describe the development and analysis of a new teletherapy modality that, through a novel approach to targeted radiation delivery, has the potential to provide greater conformality than conventional photon-based treatments. The proposed system uses an X-ray lens to reflect photons from a conventional X-ray tube toward a focal spot. The resulting dose distributions have a highly localized peak dose, with lower doses in the converging radiation cone. Physical principles governing the design of this system are presented, along with a series of measurements analyzing various characteristics of the converging beam. The beam was designed to be nearly monoenergetic (~ 59 keV), with an energy bandwidth of approximately 10 keV allowing for treatment energies lower than conventional therapies. The focal spot was measured to be approximately 2.5 cm long and 4 mm wide. Mounting the proposed X-ray delivery system on a robotic arm would allow sub-millimeter accuracy in focal spot positioning, resulting in highly conformal dose distribution via the optimal placement of individual focal spots within the target volume. Aspects of this novel radiation beam are discussed considering their possible clinical application as a treatment approach that takes maximum advantage of the unique properties afforded by converging X-ray beam therapy.

Mixed Effect Modeling of Dose and Linear Energy Transfer Correlations With Brain Image Changes After Intensity Modulated Proton Therapy for Skull Base Head and Neck Cancer.

PURPOSE: Intensity modulated proton therapy (IMPT) could yield high linear energy transfer (LET) in critical structures and increased biological effect. For head and neck cancers at the skull base this could potentially result in radiation-associated brain image change (RAIC). The purpose of the current study was to investigate voxel-wise dose and LET correlations with RAIC after IMPT. METHODS AND MATERIALS: For 15 patients with RAIC after IMPT, contrast enhancement observed on T1-weighted magnetic resonance imaging was contoured and coregistered to the planning computed tomography. Monte Carlo calculated dose and dose-averaged LET (LETd) distributions were extracted at voxel level and associations with RAIC were modelled using uni- and multivariate mixed effect logistic regression. Model performance was evaluated using the area under the receiver operating characteristic curve and precision-recall curve. RESULTS: An overall statistically significant RAIC association with dose and LETd was found in both the uni- and multivariate analysis. Patient heterogeneity was considerable, with standard deviation of the random effects of 1.81 (1.30-2.72) for dose and 2.68 (1.93-4.93) for LETd, respectively. Area under the receiver operating characteristic curve was 0.93 and 0.95 for the univariate dose-response model and multivariate model, respectively. Analysis of the LETd effect demonstrated increased risk of RAIC with increasing LETd for the majority of patients. Estimated probability of RAIC with LETd = 1 keV/µm was 4% (95% confidence interval, 0%, 0.44%) and 29% (95% confidence interval, 0.01%, 0.92%) for 60 and 70 Gy, respectively. The TD15 were estimated to be 63.6 and 50.1 Gy with LETd equal to 2 and 5 keV/µm, respectively. CONCLUSIONS: Our results suggest that the LETd effect could be of clinical significance for some patients; LETd assessment in clinical treatment plans should therefore be taken into consideration.

A framework for voxel-based assessment of biological effect after proton radiotherapy in pediatric brain cancer patients using multi-modal imaging.

INTRODUCTION: The exact dependence of biological effect on dose and linear energy transfer (LET) in human tissue when delivering proton therapy is unknown. In this study, we propose a framework for measuring this dependency using multi-modal image-based assays with deformable registrations within imaging sessions and across time. MATERIALS AND METHODS: 3T MRI scans were prospectively collected from 6 pediatric brain cancer patients before they underwent proton therapy treatment, and every 3 months for a year after treatment. Scans included T1-weighted with contrast enhancement (T1), T2-FLAIR (T2) and fractional anisotropy (FA) images. In addition, the planning CT, dose distributions and Monte Carlo-calculated LET distributions were collected. A multi-modal deformable image registration framework was used to create a dataset of dose, LET and imaging intensities at baseline and follow-up on a voxel-by-voxel basis. We modelled the biological effect of dose and LET from proton therapy using imaging changes over time as a surrogate for biological effect. We investigated various models to show the feasibility of the framework to model imaging changes. To account for interpatient and intrapatient variations, we used a nested generalized linear mixed regression model. The models were applied to predict imaging changes over time as a function of dose and LET for each modality. RESULTS: Using the nested models to predict imaging changes, we saw a decrease in the FA signal as a function of dose; however, the signal increased with increasing LET. Similarly, we saw an increase in T2 signal as a function of dose, but a decrease in signal with LET. We saw no changes in T1 voxel values as a function of either dose or LET. CONCLUSIONS: The imaging changes could successfully model biological effect as a function of dose and LET using our proposed framework. Due to the low number of patients, the imaging changes observed for FA and T2 scans were not marked enough to draw any firm conclusions.

Comparison of Monte Carlo and analytical dose computations for intensity modulated proton therapy.

To evaluate the effect of approximations in clinical analytical calculations performed by a treatment planning system (TPS) on dosimetric indices in intensity modulated proton therapy. TPS calculated dose distributions were compared with dose distributions as estimated by Monte Carlo (MC) simulations, calculated with the fast dose calculator (FDC) a system previously benchmarked to full MC. This study analyzed a total of 525 patients for four treatment sites (brain, head-and-neck, thorax and prostate). Dosimetric indices (D02, D05, D20, D50, D95, D98, EUD and Mean Dose) and a gamma-index analysis were utilized to evaluate the differences. The gamma-index passing rates for a 3%/3 mm criterion for voxels with a dose larger than 10% of the maximum dose had a median larger than 98% for all sites. The median difference for all dosimetric indices for target volumes was less than 2% for all cases. However, differences for target volumes as large as 10% were found for 2% of the thoracic patients. For organs at risk (OARs), the median absolute dose difference was smaller than 2 Gy for all indices and cohorts. However, absolute dose differences as large as 10 Gy were found for some small volume organs in brain and head-and-neck patients. This analysis concludes that for a fraction of the patients studied, TPS may overestimate the dose in the target by as much as 10%, while for some OARs the dose could be underestimated by as much as 10 Gy. Monte Carlo dose calculations may be needed to ensure more accurate dose computations to improve target coverage and sparing of OARs in proton therapy.

Clinical evidence of variable proton biological effectiveness in pediatric patients treated for ependymoma.

BACKGROUND AND PURPOSE: A constant relative biological effectiveness (RBE) is used for clinical proton therapy; however, experimental evidence indicates that RBE can vary. We analyzed pediatric ependymoma patients who received proton therapy to determine if areas of normal tissue damage indicated by post-treatment image changes were associated with increased biological dose effectiveness. MATERIAL AND METHODS: Fourteen of 34 children showed T2-FLAIR hyperintensity on post-treatment magnetic resonance (MR) images. We delineated regions of treatment-related change and calculated dose and linear energy transfer (LET) distributions with Monte Carlo. Voxel-level image change data were fit to a generalized linear model incorporating dose and LET. Cross-validation was used to determine model parameters and for receiver operating characteristic curve analysis. Tolerance dose (TD50; dose at which 50% of patients would experience toxicity) was interpolated from the model. RESULTS: Image changes showed dependence on increasing LET and dose. TD50 decreased with increasing LET, indicating an increase in biological dose effectiveness. The cross-validated area under the curve for the model was 0.91 (95% confidence interval 0.88-0.94). CONCLUSIONS: Our correlation of changes on MR images after proton therapy with increased LET constitutes the first clinical evidence of variable proton biological effectiveness.

Monte Carlo simulations of ³He ion physical characteristics in a water phantom and evaluation of radiobiological effectiveness.

PURPOSE: (3)He ions may hold great potential for clinical therapy because of both their physical and biological properties. In this study, the authors investigated the physical properties, i.e., the depth-dose curves from primary and secondary particles, and the energy distributions of helium ((3)He) ions. A relative biological effectiveness (RBE) model was applied to assess the biological effectiveness on survival of multiple cell lines. METHODS: In light of the lack of experimental measurements and cross sections, the authors used Monte Carlo methods to study the energy deposition of (3)He ions. The transport of (3)He ions in water was simulated by using three Monte Carlo codes-FLUKA, GEANT4, and MCNPX-for incident beams with Gaussian energy distributions with average energies of 527 and 699 MeV and a full width at half maximum of 3.3 MeV in both cases. The RBE of each was evaluated by using the repair-misrepair-fixation model. In all of the simulations with each of the three Monte Carlo codes, the same geometry and primary beam parameters were used. RESULTS: Energy deposition as a function of depth and energy spectra with high resolution was calculated on the central axis of the beam. Secondary proton dose from the primary (3)He beams was predicted quite differently by the three Monte Carlo systems. The predictions differed by as much as a factor of 2. Microdosimetric parameters such as dose mean lineal energy (y(D)), frequency mean lineal energy (y(F)), and frequency mean specific energy (z(F)) were used to characterize the radiation beam quality at four depths of the Bragg curve. Calculated RBE values were close to 1 at the entrance, reached on average 1.8 and 1.6 for prostate and head and neck cancer cell lines at the Bragg peak for both energies, but showed some variations between the different Monte Carlo codes. CONCLUSIONS: Although the Monte Carlo codes provided different results in energy deposition and especially in secondary particle production (most of the differences between the three codes were observed close to the Bragg peak, where the energy spectrum broadens), the results in terms of RBE were generally similar.

Analysis of the track- and dose-averaged LET and LET spectra in proton therapy using the geant4 Monte Carlo code.

PURPOSE: The motivation of this study was to find and eliminate the cause of errors in dose-averaged linear energy transfer (LET) calculations from therapeutic protons in small targets, such as biological cell layers, calculated using the geant 4 Monte Carlo code. Furthermore, the purpose was also to provide a recommendation to select an appropriate LET quantity from geant 4 simulations to correlate with biological effectiveness of therapeutic protons. METHODS: The authors developed a particle tracking step based strategy to calculate the average LET quantities (track-averaged LET, LETt and dose-averaged LET, LETd) using geant 4 for different tracking step size limits. A step size limit refers to the maximally allowable tracking step length. The authors investigated how the tracking step size limit influenced the calculated LETt and LETd of protons with six different step limits ranging from 1 to 500 µm in a water phantom irradiated by a 79.7-MeV clinical proton beam. In addition, the authors analyzed the detailed stochastic energy deposition information including fluence spectra and dose spectra of the energy-deposition-per-step of protons. As a reference, the authors also calculated the averaged LET and analyzed the LET spectra combining the Monte Carlo method and the deterministic method. Relative biological effectiveness (RBE) calculations were performed to illustrate the impact of different LET calculation methods on the RBE-weighted dose. RESULTS: Simulation results showed that the step limit effect was small for LETt but significant for LETd. This resulted from differences in the energy-deposition-per-step between the fluence spectra and dose spectra at different depths in the phantom. Using the Monte Carlo particle tracking method in geant 4 can result in incorrect LETd calculation results in the dose plateau region for small step limits. The erroneous LETd results can be attributed to the algorithm to determine fluctuations in energy deposition along the tracking step in geant 4. The incorrect LETd values lead to substantial differences in the calculated RBE. CONCLUSIONS: When the geant 4 particle tracking method is used to calculate the average LET values within targets with a small step limit, such as smaller than 500 µm, the authors recommend the use of LETt in the dose plateau region and LETd around the Bragg peak. For a large step limit, i.e., 500 µm, LETd is recommended along the whole Bragg curve. The transition point depends on beam parameters and can be found by determining the location where the gradient of the ratio of LETd and LETt becomes positive.

Spatial mapping of the biologic effectiveness of scanned particle beams: towards biologically optimized particle therapy.

The physical properties of particles used in radiation therapy, such as protons, have been well characterized, and their dose distributions are superior to photon-based treatments. However, proton therapy may also have inherent biologic advantages that have not been capitalized on. Unlike photon beams, the linear energy transfer (LET) and hence biologic effectiveness of particle beams varies along the beam path. Selective placement of areas of high effectiveness could enhance tumor cell kill and simultaneously spare normal tissues. However, previous methods for mapping spatial variations in biologic effectiveness are time-consuming and often yield inconsistent results with large uncertainties. Thus the data needed to accurately model relative biological effectiveness to guide novel treatment planning approaches are limited. We used Monte Carlo modeling and high-content automated clonogenic survival assays to spatially map the biologic effectiveness of scanned proton beams with high accuracy and throughput while minimizing biological uncertainties. We found that the relationship between cell kill, dose, and LET, is complex and non-unique. Measured biologic effects were substantially greater than in most previous reports, and non-linear surviving fraction response was observed even for the highest LET values. Extension of this approach could generate data needed to optimize proton therapy plans incorporating variable RBE.

Quenching correction for volumetric scintillation dosimetry of proton beams.

Volumetric scintillation dosimetry has the potential to provide fast, high-resolution, three-dimensional radiation dosimetry. However, scintillators exhibit a nonlinear response at the high linear energy transfer (LET) values characteristic of proton Bragg peaks. The purpose of this study was to develop a quenching correction method for volumetric scintillation dosimetry of proton beams. Scintillation light from a miniature liquid scintillator detector was measured along the central axis of a 161.6 MeV proton pencil beam. Three-dimensional dose and LET distributions were calculated for 85.6, 100.9, 144.9 and 161.6 MeV beams using a validated Monte Carlo model. LET values were also calculated using an analytical formula. A least-squares fit to the data established the empirical parameters of a quenching correction model. The light distribution in a tank of liquid scintillator was measured with a CCD camera at all four beam energies. The quenching model and LET data were used to correct the measured light distribution. The calculated and measured Bragg peak heights agreed within ±3% for all energies except 85.6 MeV, where the agreement was within ±10%. The quality of the quenching correction was poorer for sharp low-energy Bragg peaks because of blurring and detector size effects. The corrections performed using analytical LET values resulted in doses within 1% of those obtained using Monte Carlo LET values. The proposed method can correct for quenching with sufficient accuracy for dosimetric purposes. The required LET values may be computed effectively using Monte Carlo or analytical methods. Future detectors should improve blurring correction methods and optimize the pixel size to improve accuracy for low-energy Bragg peaks.

ADVANTAGES OF MCNPX-BASED LATTICE TALLY OVER MESH TALLY IN HIGH-SPEED MONTE CARLO DOSE RECONSTRUCTION FOR PROTON RADIOTHERAPY.

Monte Carlo simulations are increasingly used to reconstruct dose distributions in radiotherapy research studies. Many studies have used the MCNPX Monte Carlo code with a mesh tally for dose reconstructions. However, when the number of voxels in the simulated patient anatomy is large, the computation time for a mesh tally can become prohibitively long. The purpose of this work was to test the feasibility of using lattice tally instead of mesh tally for whole-body dose reconstructions. We did this by comparing the dosimetric accuracy and computation time of lattice tallies with those of mesh tallies for craniospinal proton irradiation. The two tally methods generated nearly identical dosimetric results, within 1% in dose and within 1 mm distance-to-agreement for 99% of the voxels. For a typical craniospinal proton treatment field, simulation speed was 4 to 17 times faster using the lattice tally than using the mesh tally, depending on the numbers of proton histories and voxels. We conclude that the lattice tally is an acceptable substitute for the mesh tally in dose reconstruction, making it a suitable potential candidate for clinical treatment planning.

Predicted risks of second malignant neoplasm incidence and mortality due to secondary neutrons in a girl and boy receiving proton craniospinal irradiation.

The purpose of this study was to compare the predicted risks of second malignant neoplasm (SMN) incidence and mortality from secondary neutrons for a 9-year-old girl and a 10-year-old boy who received proton craniospinal irradiation (CSI). SMN incidence and mortality from neutrons were predicted from equivalent doses to radiosensitive organs for cranial, spinal and intracranial boost fields. Therapeutic proton absorbed dose and equivalent dose from neutrons were calculated using Monte Carlo simulations. Risks of SMN incidence and mortality in most organs and tissues were predicted by applying risks models from the National Research Council of the National Academies to the equivalent dose from neutrons; for non-melanoma skin cancer, risk models from the International Commission on Radiological Protection were applied. The lifetime absolute risks of SMN incidence due to neutrons were 14.8% and 8.5%, for the girl and boy, respectively. The risks of a fatal SMN were 5.3% and 3.4% for the girl and boy, respectively. The girl had a greater risk for any SMN except colon and liver cancers, indicating that the girl's higher risks were not attributable solely to greater susceptibility to breast cancer. Lung cancer predominated the risk of SMN mortality for both patients. This study suggests that the risks of SMN incidence and mortality from neutrons may be greater for girls than for boys treated with proton CSI.

A GPU implementation of a track-repeating algorithm for proton radiotherapy dose calculations.

An essential component in proton radiotherapy is the algorithm to calculate the radiation dose to be delivered to the patient. The most common dose algorithms are fast but they are approximate analytical approaches. However their level of accuracy is not always satisfactory, especially for heterogeneous anatomical areas, like the thorax. Monte Carlo techniques provide superior accuracy; however, they often require large computation resources, which render them impractical for routine clinical use. Track-repeating algorithms, for example the fast dose calculator, have shown promise for achieving the accuracy of Monte Carlo simulations for proton radiotherapy dose calculations in a fraction of the computation time. We report on the implementation of the fast dose calculator for proton radiotherapy on a card equipped with graphics processor units (GPUs) rather than on a central processing unit architecture. This implementation reproduces the full Monte Carlo and CPU-based track-repeating dose calculations within 2%, while achieving a statistical uncertainty of 2% in less than 1 min utilizing one single GPU card, which should allow real-time accurate dose calculations.

Adjustment of the lateral and longitudinal size of scanned proton beam spots using a pre-absorber to optimize penumbrae and delivery efficiency.

In scanned-beam proton therapy, the beam spot properties, such as the lateral and longitudinal size and the minimum achievable range, are influenced by beam optics, scattering media and drift spaces in the treatment unit. Currently available spot scanning systems offer few options for adjusting these properties. We investigated a method for adjusting the lateral and longitudinal spot size that utilizes downstream plastic pre-absorbers located near a water phantom. The spot size adjustment was characterized using Monte Carlo simulations of a modified commercial scanned-beam treatment head. Our results revealed that the pre-absorbers can be used to reduce the lateral full width at half maximum (FWHM) of dose spots in water by up to 14 mm, and to increase the longitudinal extent from about 1 mm to 5 mm at residual ranges of 4 cm and less. A large factor in manipulating the lateral spot sizes is the drift space between the pre-absorber and the water phantom. Increasing the drift space from 0 cm to 15 cm leads to an increase in the lateral FWHM from 2.15 cm to 2.87 cm, at a water-equivalent depth of 1 cm. These findings suggest that this spot adjustment method may improve the quality of spot-scanned proton treatments.

An MCNPX Monte Carlo model of a discrete spot scanning proton beam therapy nozzle.

PURPOSE: The purposes of this study were to validate a discrete spot scanning proton beam nozzle using the Monte Carlo (MC) code MCNPX and use the MC validated model to investigate the effects of a low-dose envelope, which surrounds the beam's central axis, on measurements of integral depth dose (IDD) profiles. METHODS: An accurate model of the discrete spot scanning beam nozzle from The University of Texas M. D. Anderson Cancer Center (Houston, Texas) was developed on the basis of blueprints provided by the manufacturer of the nozzle. The authors performed simulations of single proton pencil beams of various energies using the standard multiple Coulomb scattering (MCS) algorithm within the MCNPX source code and a new MCS algorithm, which was implemented in the MCNPX source code. The MC models were validated by comparing calculated in-air and in-water lateral profiles and percentage depth dose profiles for single pencil beams with their corresponding measured values. The models were then further tested by comparing the calculated and measured three-dimensional (3-D) dose distributions. Finally, an IDD profile was calculated with different scoring radii to determine the limitations on the use of commercially available plane-parallel ionization chambers to measure IDD. RESULTS: The distance to agreement, defined as the distance between the nearest positions of two equivalent distributions with the same value of dose, between measured and simulated ranges was within 0.13 cm for both MCS algorithms. For low and intermediate pencil beam energies, the MC simulations using the standard MCS algorithm were in better agreement with measurements. Conversely, the new MCS algorithm produced better results for high-energy single pencil beams. The IDD profile calculated with cylindrical tallies with an area equivalent to the area of the largest commercially available ionization chamber showed up to 7.8% underestimation of the integral dose in certain depths of the IDD profile. CONCLUSIONS: The authors conclude that a combination of MCS algorithms is required to accurately reproduce experimental data of single pencil beams and 3-D dose distributions for the scanning beam nozzle. In addition, the MC simulations showed that because of the low-dose envelope, ionization chambers with radii as large as 4.08 cm are insufficient to accurately measure IDD profiles for a 221.8 MeV pencil beam in the scanning beam nozzle.

Monte Carlo investigation of the low-dose envelope from scanned proton pencil beams.

Scanned proton pencil beams carry a low-dose envelope that extends several centimeters from the individual beam's central axis. Thus, the total delivered dose depends on the size of the target volume and the corresponding number and intensity of beams necessary to cover the target volume uniformly. This dependence must be considered in dose calculation algorithms used by treatment planning systems. In this work, we investigated the sources of particles contributing to the low-dose envelope using the Monte Carlo technique. We used a validated model of our institution's scanning beam line to determine the contributions to the low-dose envelope from secondary particles created in a water phantom and particles scattered in beam line components. Our results suggested that, for high-energy beams, secondary particles produced by nuclear interactions in the water phantom are the major contributors to the low-dose envelope. For low-energy beams, the low-dose envelope is dominated by particles undergoing multiple Coulomb scattering in the beam line components and water phantom. Clearly, in the latter situation, the low-dose envelope depends directly on beam line design features. Finally, we investigated the dosimetric consequences of the low-dose envelope. Our results showed that if not modeled properly the low-dose envelope may cause clinically relevant dose disturbance in the target volume. This work suggested that this low-dose envelope is beam line specific for low-energy beams, should be thoroughly experimentally characterized and validated during commissioning of the treatment planning system, and therefore is of great concern for accurate delivery of proton scanning beam doses.

The risk of developing a second cancer after receiving craniospinal proton irradiation.

The purpose of this work was to compare the risk of developing a second cancer after craniospinal irradiation using photon versus proton radiotherapy by means of simulation studies designed to account for the effects of neutron exposures. Craniospinal irradiation of a male phantom was calculated for passively-scattered and scanned-beam proton treatment units. Organ doses were estimated from treatment plans; for the proton treatments, the amount of stray radiation was calculated separately using the Monte Carlo method. The organ doses were converted to risk of cancer incidence using a standard formalism developed for radiation protection purposes. The total lifetime risk of second cancer due exclusively to stray radiation was 1.5% for the passively scattered treatment versus 0.8% for the scanned proton beam treatment. Taking into account the therapeutic and stray radiation fields, the risk of second cancer from intensity-modulated radiation therapy and conventional radiotherapy photon treatments were 7 and 12 times higher than the risk associated with scanned-beam proton therapy, respectively, and 6 and 11 times higher than with passively scattered proton therapy, respectively. Simulations revealed that both passively scattered and scanned-beam proton therapies confer significantly lower risks of second cancers than 6 MV conventional and intensity-modulated photon therapies.

Stray radiation dose and second cancer risk for a pediatric patient receiving craniospinal irradiation with proton beams.

Proton beam radiotherapy unavoidably exposes healthy tissue to stray radiation emanating from the treatment unit and secondary radiation produced within the patient. These exposures provide no known benefit and may increase a patient's risk of developing a radiogenic cancer. The aims of this study were to calculate doses to major organs and tissues and to estimate second cancer risk from stray radiation following craniospinal irradiation (CSI) with proton therapy. This was accomplished using detailed Monte Carlo simulations of a passive-scattering proton treatment unit and a voxelized phantom to represent the patient. Equivalent doses, effective dose and corresponding risk for developing a fatal second cancer were calculated for a 10-year-old boy who received proton therapy. The proton treatment comprised CSI at 30.6 Gy plus a boost of 23.4 Gy to the clinical target volume. The predicted effective dose from stray radiation was 418 mSv, of which 344 mSv was from neutrons originating outside the patient; the remaining 74 mSv was caused by neutrons originating within the patient. This effective dose corresponds to an attributable lifetime risk of a fatal second cancer of 3.4%. The equivalent doses that predominated the effective dose from stray radiation were in the lungs, stomach and colon. These results establish a baseline estimate of the stray radiation dose and corresponding risk for a pediatric patient undergoing proton CSI and support the suitability of passively-scattered proton beams for the treatment of central nervous system tumors in pediatric patients.

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.