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Some biological model is needed to establish radiation therapy with helium-ions.
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A biological model used for carbon-ion radiotherapy was investigated.
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A ridge filter was designed and fabricated using the model to form a biologically uniform spread-out Bragg peak.
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Biological experiments were performed in the spread-out Bragg peak.
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It was found that the model could be applicable by some modification.
Abstract
Purpose
To evaluate the applicability of microdosimetric kinetic model (MKM) to helium-ion therapy by forming a spread-out Bragg peak (SOBP) of a helium-ion beam using the MKM developed for carbon-ion radiotherapy and confirming the predictions in biological experiments.
Methods
Using a ridge filter, a 90-mm wide SOBP for a 210 MeV/u helium-ion beam was created in a broad beam delivery system. The ridge filter was designed such that a uniform biological response was achieved with a cell survival rate of 7% over the SOBP region. Biological experiments were then performed using the SOBP beam in a human salivary gland (HSG) cell line to measure the cell survival rates.
Results
The biological responses were uniform in the SOBP region, as expected by the MKM; however, the mean of the measured cell survival rates was (11.2 ± 0.6) % in the SOBP region, which was 60% higher than the designed rate. When investigating the biological parameters of the HSG cell line used in the experiments, we found that they were altered slightly from the MKM parameters used for carbon-ion radiotherapy. The new β parameter reproduced the measured survival rates within 6.5% in the SOBP region.
Conclusion
We produced biologically uniform SOBP using MKM for carbon-ion radiotherapy. The measured survival rates in the SOBP region were higher than expected, and the survival rates were reproduced by modifying the MKM parameter. This study was limited to one SOBP, and further investigations are required to prove that MKM is generally applicable to helium-ion radiotherapy.
Long-term Results of the UCSF-LBNL Randomized Trial: Charged Particle With Helium Ion Versus Iodine-125 Plaque Therapy for Choroidal and Ciliary Body Melanoma.
]. However, treatments using helium ions have not been performed since 1992. A promising dosimetric comparison of protons and helium ions in pediatric patients has also been reported [
]. Heidelberg Ion-Beam Therapy Center (HIT) launched the first European clinical program using therapeutic helium-ion beams and the clinical application of raster-scanning helium-ion therapy [
The linear energy transfer (LET) of helium ions is approximately 10 keV/μm in the plateau region, similar to that of protons, whereas the LET in the last few millimeters of the Bragg peak is above 20 keV/μm [
]. Therefore, the relative biological effectiveness (RBE) of a helium-ion beam changes with depth, particularly near the Bragg peak. Thus, variations in the RBE should be considered for the delivery of biologically uniform doses to patients.
Intensity-modulated particle therapy (IMPT) has been developed with several clinical advantages [
]. IMPT reduces the doses to organs at risk by optimizing multiple radiation fields. A biological model should consider the RBE during field optimization for particles heavier than protons. In carbon-ion radiotherapy, two methods have been proposed for RBE in a treatment planning system: the local effect model developed at Gesellschaft fur Schwerionenforschung GmbH (GSI) [
Carante MP, Embriaco A, Aricò G, Ferrari A, Mairani A, Mein S, et al. Biological effectiveness of He-3 and He-4 ion beams for cancer hadrontherapy: a study based on the BIANCA biophysical model. Phys Med Biol. 202; 66: 195009.
]. The MKM has already been applied to treatments using helium-ion beams at HIT, although the treatment has not yet been systematically practiced. The MKM is also considered for use in calculating of the RBE of proton beams [
This study aims to investigate whether the MKM can be applied to the calculation of biological responses in a helium-ion beam. The applicability was verified by forming a biologically uniform spread-out Bragg peak (SOBP) using the MKM and measuring biological responses through experiments with a human salivary gland (HSG) cell line. The SOBP was formed using a range modulator in a helium-ion beam spread laterally by a wobbling system.
2. Materials and methods
2.1 MKM
The MKM is briefly described below. The survival rate of a cell line , can be expressed as , where is the average number of lethal lesions in the cell nucleus. Based on Kase et al. [
where and are parameters in the linear–quadratic (LQ) model in the limit LET = 0 and is the absorbed dose. The saturation-corrected dose-mean specific energy in a single event, , is given as [
where is the probability density of deposited by a single energy-deposition event of a domain (the subnuclear volume defined in the MKM), and is the saturation-corrected specific energy, expressed as
(3)
is the saturation coefficient, expressed as
(4)
where and are the radii of the cell nucleus and the domain, respectively.
2.2 Formation of an SOBP
In a laterally broad helium-ion beam, an SOBP is formed by modulating the energy using a range modulator. The depth–dose distribution of the SOBP was calculated by superimposing pristine Bragg curves. The physical dose of an SOBP at a depth of is expressed as , where is the weight of the kth Bragg curve and is the depth–dose curve of the kth pristine Bragg curve for which a beam passes through a certain thickness of the range modulator, . is written as
(5)
where is the planar integrated depth–dose curve in water (IDD) of a helium-ion beam and is the factor that converts the physical thickness to water-equivalent thickness, which is obtained from the ratio of the material stopping power to that of water. The IDDs for various thicknesses of the range modulator were obtained from , which was calculated using a Monte Carlo simulation toolkit, PTSim [
]. The details of the derivation of , are described in the Appendix. Here, is the fan-beam correction to consider the effect that the beam intensity is inversely proportional to the square of the distance, and it is given by:
(6)
where and are the distances from the wobbling x-magnet and y-magnet to the isocenter, respectively. is the distance from the surface of the water phantom used for the dose profile measurements to the isocenter. This correction was necessary when the water phantom was placed at a fixed position during measurement. The last term of Eq. (5) represents the reduction of helium ions owing to inelastic nuclear interactions. The range modulator used in this study is made of aluminum, and is the attenuation coefficient of aluminum, which is calculated as 3.93 × 10-3 mm using the inelastic cross sections of helium ions to aluminum. The cross-section of 652 mb at an energy of 210 MeV/u was obtained from Tripathi99 parameterization [
]. Tripathi99 is one of the best parameterizations that reproduces past experiments for measuring the cross-section of aluminum. The attenuation coefficient was treated as a constant in this study because the variation of the cross-section by Tripathi99 was less than 0.3% between 150 and 210 MeV/u of energy.
The saturation-corrected specific energy (referred to as the specific energy below) was also obtained using PTSim. The specific energy of a particle with kinetic energy and energy deposition, , was calculated using Eq. (2). The specific energy was averaged over all particles with doses at depth , and the dose-mean specific energy, , was obtained by
(7)
where is the dose of particle at a depth of . The dose-mean specific energy of the SOBP at depth , , is calculated as follows:
(8)
The kth dose-mean specific energy, , was obtained by inferring from (see the Appendix). The survival rate of the SOBP was calculated using Eq. (1), where and at depth are given by:
(9)
The MKM parameters used in the SOBP formation in this study are summarized in Table 1. in Eq. (1) can be written as using Eq. (9). The dose of the SOBP at a cell survival rate of at a depth of , , is obtained by solving for the dose as
(10)
The RBE is then calculated by , where is the dose of a reference radiation, which is usually a photon, at a cell survival rate of . The RBE-weighted dose at a depth of is then obtained by
(11)
Table 1MKM parameters used for the SOBP formation. The parameters were obtained from the report of Inaniwa et al.
The number of Bragg curves used to form the SOBP was manually determined to obtain a smooth SOBP curve. The range modulator was designed by optimizing the weights in Eq. (11) such that the RBE-weighted doses in the SOBP region become uniform.
2.3 Experimental apparatus and procedure
A series of experiments were performed in the Research and Development (RD) room equipped with a horizontal beam line at the Hyogo Ion Beam Medical Center (HIBMC). The accelerator complex of HIBMC was composed of two electron cyclotron resonance (ECR) ion sources, a linear-accelerator system composed of radiofrequency quadrupole linac (RFQ) and drift-tube linac (DTL), a 30 m-diameter synchrotron, and a high-energy beam transport (HEBT) system. This complex can produce proton, helium-ion, and carbon-ion beams. The beams were transported through the HEBT system to the treatment and experimental rooms. A schematic of the beam delivery system in the RD room is shown in Fig. 1. A 210 MeV/u helium-ion beam was spread laterally using wobbling magnets and a scatterer composed of tantalum. The wobbling radius and scatterer thickness were determined to form a laterally uniform field at the isocenter. The uniformity was within ±3% for a diameter of 160 mm. A 90 mm SOBP was formed using a ridge filter made of aluminum. The ridge filter consisted of 50 bars lined up at 5 mm intervals. The length of each bar was 25 cm and it had a ridge shape, as shown in Fig. 2. The ridge filter was manufactured with a numerically controlled machine by Mitsubishi Electric Corporation (Tokyo, Japan). A dose monitor was placed upstream of the ridge filter to control the delivered dose.
Fig. 1Schematic of the beam delivery devices in the Research and Development room at HIBMC.
The lateral and depth–dose profiles were measured using a water phantom MP3-P (PTW Freiburg, Germany). The depth–dose profiles were measured using a parallel-plate ionization chamber ROOS (34001, PTW Freiburg, Germany), while the lateral profiles were measured using a pinpoint ionization chamber (31016, PTW Freiburg, Germany). The absolute absorbed dose was measured in the middle of the SOBP at the isocenter using a parallel-plate ionization chamber Advanced Markus (34045, PTW Freiburg, Germany). The chamber was calibrated using a standard Japanese dosimetry protocol [
]. A colony formation assay was used to measure the cell survival rates over the beam range and fragmentation tail. Cells were incubated in Eagle’s minimum essential medium (Sigma-Aldrich Co., St. Louis, MO) supplemented with 5% fetal bovine serum under standard conditions (at 37.8 ℃, in a humid atmosphere of 5% CO2 in the air). A 25 cm2 plastic flask (Nalge Nunc International, Rochester, NY) on which cells in logarithmic growth were seeded was placed at the isocenter to be irradiated by the SOBP beam. A polyethylene (PE) block with a cross-sectional area of 200 × 200 mm2 was placed in front of the flask to degrade the SOBP beam energy. Ten flasks were irradiated with the SOBP beam by changing the water-equivalent thickness of the block to 77, 117, 157, 177, 197, 217, 237, 257, 277, and 317 mm. The physical thickness of the PE block was calculated using the stopping-power table of ICRU49 [
] such that the water-equivalent thickness of the PE block becomes the thickness used in the experiment. The density of PE was assumed as 0.94 g/cm3, but it can vary from 0.94 to 0.97 g/cm3. The uncertainty of the stopping power can be up to 3%. The cells in each flask were trypsinized immediately after irradiation and plated on five plastic dishes (diameter: 60 mm) at the appropriate densities for clonogenic assays. Fixation with 10% formalin solution and staining with 1% methylene blue solution of colonies was performed after 14 days of incubation. Colonies consisting of more than 50 cells were considered viable. This experiment was independently performed three times on three different days.
3. Results
Fig. 3 shows the measured SOBP depth–dose curve in water with the designed curve. The designed RBE-weighted depth–dose curve is also shown. These curves were normalized in the middle of the SOBP. The dose at the middle of the SOBP was estimated to be 4.59 Gy at a cell survival rate of 7% using Eq. (10). The calculated depth–dose curve reproduced the measured dose curve within a root mean square of 5% over the measured depth.
Fig. 3Depth–dose curves of the SOBP in water for the designed physical doses (solid line), designed RBE-weighted doses (dashed line) and measured physical doses (closed circles). The doses are normalized at the middle of the SOBP to 1.
The cell survival rates were measured at 10 depth points thrice, as mentioned in Section 2.3. Fig. 4 shows the results along with the expected cell survival rates as a function of depth. The cell survival rate at each point was the mean of the number of colonies on the five plates, and the uncertainty of each point was estimated using the standard deviation. The mean cell survival rate over the SOBP region was (11.2 ± 0.6) %, which was higher than the expected rate of 7%. The root mean square deviation from expectation was more than 60% [=(11.2–7.0)/7.0 × 100].
Fig. 4Measured survival rates at 10 depth points, represented by the open symbols. Each symbol, circle, triangle, and square, represents three experiments performed independently. The red solid line depicts the cell survival rate curve calculated by the MKM using the parameters in Table 1, while the red dotted line depicts the cell survival rate curve calculated using β = 0.0457 Gy−2 (described in Section 4). The green dashed-dotted line was calculated using the parameters by Kase et al., and the blue dashed line using the parameters by Lee et al. (see also Section 4). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
The 90 mm SOBP of the 210 MeV/u helium-ion beam was created using the MKM and ridge filter in the broad beam spread laterally by the wobbling system. Biological responses in the SOBP beam were measured using the HSG cell line using a colony formation assay.
As expected, biological responses in the SOBP region were uniform. However, the cell survival rate was 60% higher than that expected. One possible reason for this discrepancy is the alteration in the HSG cell line used in this study. Cell sensitivity has been known to vary over time; for example, the passage number affects a cell line’s characteristics. To investigate the alteration of the HSG cell line, the cell survival dose curves were measured at a depth of 25 mm in the plateau region of the Bragg curve of the 210 MeV/u monoenergetic helium-ion beam. The results, along with the MKM estimation, are shown in Fig. 5. The dose-mean specific energy at a depth of 25 mm was approximately 0.5 Gy. The measurements were not reproduced by the MKM using the parameters listed in Table 1. Although Inaniwa et al. [
] adjusted parameter to reproduce their biological experiments, we could not reproduce the experimental results by modifying the parameter . Meanwhile, the MKM estimation using = 0.0457 Gy−2 was consistent with the experimental results, as shown by the dashed line in Fig. 5. The adjustment was made by minimizing the variance between the measurements and the survival curve by fixing and . The depth-cell survival curve of the SOBP was then recalculated using = 0.0457 Gy−2. The results are shown as dashed lines in Fig. 4. The cell survival rates over the SOBP region, recalculated using = 0.0457 Gy−2, were consistent with the measured values. The root mean square of the deviations between the measurement and expectation, with = 0.0457 Gy−2, was within 6.5%.
Fig. 5Cell survival rates of the HSG cell line as a function of the dose of the 210 MeV/u monoenergetic beam at a depth of 25 mm in the plastic block phantom. The open symbols represent the measured data, the solid line represents the cell survival rates calculated by the MKM using = 0.0615 Gy−2, and the dashed line represents those calculated using = 0.0457 Gy−2.
Lee SH, Mizushima K, Yonai S, Matsumoto S, Mizuno H, Nakaji T, et al. T. Predicting the Biological Effects of Human Salivary Gland Tumour Cells for Scanned 4He-, 12C-, 16O-, and 20Ne-Ion Beams Using an SOI Microdosimeter. Appl Sci 2022; 12(12), 6148.
]. These parameters, summarized in Table 2, were applied in this study, and the results are shown in Fig. 4. The survival rates obtained using Lee’s parameter set were higher than those measured. The survival rates obtained by Kase reproduced the measurements well in the plateau region, whereas those in the SOBP region were higher than the measurements. None of these could reproduce the measured survival rates in the SOBP region.
Lee SH, Mizushima K, Yonai S, Matsumoto S, Mizuno H, Nakaji T, et al. T. Predicting the Biological Effects of Human Salivary Gland Tumour Cells for Scanned 4He-, 12C-, 16O-, and 20Ne-Ion Beams Using an SOI Microdosimeter. Appl Sci 2022; 12(12), 6148.
A slight difference in the depth–dose curve of the SOBP between the calculation and the measurement is shown in Fig. 3. One possible reason for this is the difference in the pristine Bragg curve of the 210 MeV/u beam between the calculation and measurement, as seen in Fig. A1 in Appendix. The peak-plateau ratio of the measurement was not reproduced well by Geant4. Possible reasons for this difference could be the model of the range straggling and/or the cross section of the helium ions for the water implemented in Geant4. The difference in doses between the calculation and measured values may lead differences in the survival rate, as the difference affects the calculation of the dose-mean saturation-corrected specific energy, . Reproducing the physical behaviors of helium ions by the code is therefore very important to calculate accurate RBEs. We should use a Monte Carlo code or a related code which reproduces the physical behaviors to accurately calculate the dose-mean saturation-corrected specific energy curves, , for clinical use.
5. Conclusion
A 90-mm wide SOBP of a 210 MeV/u helium-ion beam was created using the MKM, a biological model for particle beams. The SOBP was formed by using a ridge filter in a laterally spread beam. Biologically uniform responses were successfully obtained in the SOBP region as expected; however, the measured cell survival rate at the SOBP was 60% higher than the expected value. With the new parameter, MKM could reproduce the measured cell survival rates, and the measurements were in agreement with the expectation within 6.5%. The conclusions drawn in this study are limited to one SOBP, and further investigation of the MKM parameters and physical characteristics of helium ions is required to prove that MKM is generally applicable to helium-ion radiotherapy.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
We would like to thank Editage (www.editage.com) for English language editing.
Appendix A. Modeling of Bragg curves and dose-mean curves
An SOBP curve was formed by superimposing several pristine Bragg curves in different ranges. Therefore, Bragg curves with different ranges were necessary to calculate the depth–dose curve of the SOBP. Additionally, the dose-mean saturation-corrected specific energy, , curves corresponding to the Bragg curves were also necessary to calculate the biological response of the SOBP. In this study, the Bragg curve and dose-mean curve of a helium-ion beam were inferred from those of the beam used for the formation of the SOBP, that is, the 210 MeV/u beam in this study.
The planer integrated depth–dose curve of the 210 MeV/u beam and the corresponding dose-mean curve were calculated by dividing into the primary and secondary parts using the Monte Carlo simulation toolkit PTSim. In PTSim, a phantom with dimensions of 300 × 300 × 500 mm3 was constructed by stacking 500 tallies with a thickness of 1 mm. Monoenergetic helium ions were impinged at the center of the phantom. The Bragg curve of the 210 MeV/u beam is shown in Fig. A1 with the measurements.
Fig. A1Comparison of the depth–dose curves of the 210 MeV/u beam between the measurement (closed circles) and the calculation (solid line). The calculated depth–dose curve was obtained from the IDD with the fan-beam correction of Eq. (6). The doses are normalized at the shallowest depth of the measurement.
The primary and secondary parts of the planer integrated depth–dose curve (IDD) with a shorter beam range by than the 210 MeV/u beam are modeled as follows:
(A1)
where and are the primary and secondary parts of the IDD of the 210 MeV/u beam, respectively. is the beam range of the 210 MeV/u beam, which is defined at an 80% dose level. corresponds to the water-equivalent thickness at a point on the range modulator through which the beam passes. The total IDD was given by .
The primary and secondary parts of the dose-mean curve (Z1D) are modeled in a similar way to the IDD, as follows:
(A2)
where and are the primary and secondary parts of the Z1D of the 210 MeV/u beam, respectively. The total Z1D was given by .
The modeling factors –, were determined such that IDDs and Z1Ds with various ranges were reproduced well, where the IDDs and Z1Ds were also obtained by PTSim. The functional forms of are
(A3)
The modeling was performed using IDDs and Z1Ds of 160, 170, 180, 190, and 200 MeV/u beams calculated using PTSim. The energy fluctuation for each beam was determined to reproduce the Bragg peak width of the 210 MeV/u beam. The 210 MeV/u beam was degraded by a range modulator and impinged in water, whereas in the PTSim, the beams were directly impinged into the phantom. The energy fluctuation in the range moderator should be considered when calculating IDDs and Z1Ds. The results of the model are presented in Fig. A2. IDDs and Z1Ds were reproduced well for the primary beam, while slight differences for the secondary beam were seen in a slightly shallower region than the beam range, especially for lower energies. However, the contribution of the secondary beam to the total is small, and the inference and the actual agree within 4% for IDDs and 5% for Z1Ds in the shallower region than the beam range.
Fig. A2Comparison of IDDs and Z1Ds with different ranges between inferred curves from the 210 MeV/u beam (solid lines) and calculated curves using PTSim (dash lines), where (a) is IDDs for the primary, (b) is IDDs for the secondary, (c) is Z1Ds for the primary, and (d) is Z1Ds for the secondary.
Long-term Results of the UCSF-LBNL Randomized Trial: Charged Particle With Helium Ion Versus Iodine-125 Plaque Therapy for Choroidal and Ciliary Body Melanoma.
Carante MP, Embriaco A, Aricò G, Ferrari A, Mairani A, Mein S, et al. Biological effectiveness of He-3 and He-4 ion beams for cancer hadrontherapy: a study based on the BIANCA biophysical model. Phys Med Biol. 202; 66: 195009.
Lee SH, Mizushima K, Yonai S, Matsumoto S, Mizuno H, Nakaji T, et al. T. Predicting the Biological Effects of Human Salivary Gland Tumour Cells for Scanned 4He-, 12C-, 16O-, and 20Ne-Ion Beams Using an SOI Microdosimeter. Appl Sci 2022; 12(12), 6148.
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