A simplified analytical random walk model for proton dose calculation

Technical note: Determination of proton linear energy transfer from the integral depth dose

BACKGROUND

Proton linear energy transfer (LET) is associated with the relative biological effectiveness of radiation on tissues. Monte Carlo (MC) simulations have been known to be the preferred method to calculate LET. Detectors have also been built to measure LET, but they need to be calibrated with MC simulations.

PURPOSE

To propose and test a MC-free method for determining LET from the measured integral depth dose (LFI) of the protons of interest.

METHOD AND MATERIALS

LFI consists of three steps: (1) IDD measurements, (2) extraction of energy spectrum (ES) from the IDD, and (3) LET determination from the extracted ES and the stopping power of each energy. To validate the accuracy of the extraction of ES, we use Gaussian ES to synthesize IDD, extract ES from the synthesized IDD, and then compare the original (ground truth) and extracted ES. LETs calculated from the original and extracted ES are also compared. To obtain the LET of protons of interest, we measure IDDs by a large-area plane-parallel ionization chamber in water. Finally, TOPAS MC is employed to simulate IDDs, ES, and LETs. From the simulated IDD, the extracted ES and LET are compared with the simulations from TOPAS MC.

RESULTS

From the synthesized IDDs, the LETs agreed excellently when the peak energies ≥10 and 1.25 MeV with depth resolutions 0.1 and 0.01 mm, respectively. For energy <1.25 MeV, even higher depth resolution than 0.01 mm is required. From the MC simulated IDDs, our track-averaged LET excellently agreed with MC simulation, but not the LETd. Our LETd was smaller than MC simulated LETd in the shallow region but larger in the distal Bragg peak region.

CONCLUSION

LET can be accurately determined from the IDD. This method can be used in the clinic to commission or validate LETs from other measurement methods or a treatment planning system.

Technical note: Extraction of proton pencil beam energy spectrum from measured integral depth dose in a cyclotron proton beam system

PURPOSE

Proton pencil beam energy spectrum is an essential parameter for calculations of dose and linear energy transfer. We extract the energy spectrum from measured integral depth dose (IDD).

METHODS

A measured IDD (measIDD) in water is decomposed into many IDDs of mono-energetic pencil beams (monoIDDs) in water. A simultaneous iterative technique is used to do the decomposition that extracts the energy spectrum of protons from the measIDD. The monoIDDs are generated by our analytic random walk model-based proton dose calculation algorithm. The linear independence of the monoIDDs is considered and high spatial resolution monoIDDs are used to improve their linear independence. To validate the extraction, first we use synthesized IDDs (synIDD) with Gaussian energy spectrum and compare the extracted energy spectrum with the Gaussian; second, for the energy spectrum extracted from measIDDs, the accuracy of the extraction is validated by comparing the calculated IDD from the energy spectrum with the measIDD. The measIDDs are derived from commissioning of a cyclotron proton pencil beam system with a Bragg peak ionization chamber. The nominal energy of the pencil beams is from 70 to 245 MeV. The monoIDDs are generated for energies from 0.05 to 275 MeV in steps of 0.05 MeV with a spatial resolution of 1 mm.

RESULTS

The difference of the extracted and original Gaussian energy spectrum peaked at 75 and 80 MeV was <1%. As the energy decreased, the difference increased but was reduced by using 0.1-mm monoIDDs. The difference was not sensitive to the energy interval of monoIDDs when the interval increased from 0.05 to 1 MeV. For the energy spectrum extraction from measIDDs, there was a main peak near the nominal energy but the spectrum was not in Gaussian distribution. In three example cases (70, 160, and 245 MeV), the relative differences of the measIDDs and calculated IDDs were within 3.4%, 2.9%, and 4.7% of the Bragg peak value, respectively. Fitting the spectrum by Gaussian distribution, we had σ = 0.87, 1.51, and 0.86 MeV, respectively, for these three examples, and the relative differences of the resultant calculated IDDs from the measIDDs were within 4.7%, 7.4%, and 4.5%, respectively.

CONCLUSIONS

Our algorithm accurately extracted the energy spectrum from the synIDDs and measIDDs. High-resolution monoIDDs are necessary to extract low-energy spectrum. Energy spectrum extraction from measIDD reveals important information for beam modeling.

Validation and application of a fast Monte Carlo algorithm for assessing the clinical impact of approximations in analytical dose calculations for pencil beam scanning proton therapy

PURPOSE

Monte Carlo (MC) dose calculation is generally superior to analytical dose calculation (ADC) used in commercial TPS to model the dose distribution especially for heterogeneous sites, such as lung and head/neck patients. The purpose of this study was to provide a validated, fast, and open-source MC code, MCsquare, to assess the impact of approximations in ADC on clinical pencil beam scanning (PBS) plans covering various sites.

METHODS

First, MCsquare was validated using tissue-mimicking IROC lung phantom measurements as well as benchmarked with the general purpose Monte Carlo TOPAS for patient dose calculation. Then a comparative analysis between MCsquare and ADC was performed for a total of 50 patients with 10 patients per site (including liver, pelvis, brain, head-and-neck, and lung). Differences among TOPAS, MCsquare, and ADC were evaluated using four dosimetric indices based on the dose-volume histogram (target Dmean, D95, homogeneity index, V95), a 3D gamma index analysis (using 3%/3 mm criteria), and estimations of tumor control probability (TCP).

RESULTS

Comparison between MCsquare and TOPAS showed less than 1.8% difference for all of the dosimetric indices/TCP values and resulted in a 3D gamma index passing rate for voxels within the target in excess of 99%. When comparing ADC and MCsquare, the variances of all the indices were found to increase as the degree of tissue heterogeneity increased. In the case of lung, the D95s for ADC were found to differ by as much as 6.5% from the corresponding MCsquare statistic. The median gamma index passing rate for voxels within the target volume decreased from 99.3% for liver to 75.8% for lung. Resulting TCP differences can be large for lung (≤10.5%) and head-and-neck (≤6.2%), while smaller for brain, pelvis and liver (≤1.5%).

CONCLUSIONS

Given the differences found in the analysis, accurate dose calculation algorithms such as Monte Carlo simulations are needed for proton therapy, especially for disease sites with high heterogeneity, such as head-and-neck and lung. The establishment of MCsquare can facilitate patient plan reviews at any institution and can potentially provide unbiased comparison in clinical trials given its accuracy, speed and open-source availability.

Feasibility study of range-based registration using daily cone beam CT for intensity-modulated proton therapy

PURPOSE

Proton dose coverage is sensitive to proton beam range. The current practice of CT number-based registration for patient positioning focuses on matching the target and is not sufficient for proton therapy because the proton range depends on the medium traversed by the beam. Patient body deformations and anatomical changes result in range deviation in the target. We propose proton range-based registration to minimize the range deviation.

METHODS

The range was calculated from cone beam-computed tomography (CBCT) of the patient on couch, and the range deviation was the difference of the calculated range from that on the initial (day 1) CBCT. In the investigated prostate cases in which the main cause of range deviation was the rotation of femur bones, and in the investigated abdomen cases in which the main cause of range deviation was body growth and anatomic change, our range-based registration was used to obtain the optimal beam angle by minimizing the range deviation. The new angle was limited to be ±5° from that planned to prevent potentially increased dose to the organs at risk. To demonstrate the benefit of range-based registration, we investigated the range at the voxels on the surface of the target volume. The calculation error of range deviation due to CBCT scatter was investigated by using solid water phantoms with different thicknesses. Range-based registration using both CBCTs and CTs was performed in cases of two patients with pelvic rhabdomyosarcoma and one patient with upper abdominal tumor. The range was represented by the water-equivalent thickness to shorten the computation for online application purposes.

RESULTS

In the phantom study, the calculation error of range deviation due to CBCT scatter was within 2 mm for a 1-cm thickness change (the mean range deviation was 0.8 mm). In the CT study of the prostate cases, the range deviation (mean ± root-mean-square deviation) on the contour in each slice was efficiently reduced from 3.6 ± 2.8 mm to 2.1 ± 1.4 mm, with most slices being within 3 mm; in the CT study of the abdomen cases, the range deviation of the whole set was reduced from 4.4 ± 1.9 mm to 3.5 ± 2.1 mm. Both the mean and root-mean-square deviation of the range deviation on each treatment day were decreased. The dose coverage on the target was improved and the dose on the OARs was only slightly changed.

CONCLUSION

Range-based registration can efficiently mitigate range deviation due to patient positioning and anatomical changes. It can shorten patient positioning time and reduce the patient's dose from CBCT.

A correction scheme for a simplified analytical random walk model algorithm of proton dose calculation in distal Bragg peak regions

The lateral homogeneity assumption is used in most analytical algorithms for proton dose, such as the pencil-beam algorithms and our simplified analytical random walk model. To improve the dose calculation in the distal fall-off region in heterogeneous media, we analyzed primary proton fluence near heterogeneous media and propose to calculate the lateral fluence with voxel-specific Gaussian distributions. The lateral fluence from a beamlet is no longer expressed by a single Gaussian for all the lateral voxels, but by a specific Gaussian for each lateral voxel. The voxel-specific Gaussian for the beamlet of interest is calculated by re-initializing the fluence deviation on an effective surface where the proton energies of the beamlet of interest and the beamlet passing the voxel are the same. The dose improvement from the correction scheme was demonstrated by the dose distributions in two sets of heterogeneous phantoms consisting of cortical bone, lung, and water and by evaluating distributions in example patients with a head-and-neck tumor and metal spinal implants. The dose distributions from Monte Carlo simulations were used as the reference. The correction scheme effectively improved the dose calculation accuracy in the distal fall-off region and increased the gamma test pass rate. The extra computation for the correction was about 20% of that for the original algorithm but is dependent upon patient geometry.