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The correlation between dose-averaged linear energy transfer (LETd) and its therapeutic or adverse effects, especially in carbon-ion radiotherapy (CIRT), remains controversial. This study aimed to investigate the effects of LETd and dose on pelvic insufficiency fractures after CIRT.Among patients who underwent CIRT for uterine carcinoma, 101 who were followed up for 6 months without any other therapy were retrospectively analyzed. The sacrum insufficiency fractures (SIFs) were graded according to the Radiation Therapy Oncology Group/European Organization for Research and Treatment of Cancer toxicity criteria. The correlations between the relative biological effectiveness (RBE)-weighted dose, LETd, physical dose, clinical factors, and SIFs were evaluated. In addition, we analyzed the association of SIF with LETd, physical dose, and clinical factors in cases where the sacrum D50% RBE-weighted dose was above the median dose.At the last follow-up, 19 patients developed SIFs. Receiver operating characteristic curve analysis revealed that the sacrum D50% RBE-weighted dose was a valuable predictor of SIF. Univariate analyses suggested that LETd V10 keV/µm, physical dose V5 Gy, and smoking status were associated with SIF. Cox regression analysis in patients over 50 years of age validated that current smoking habit was the sole risk factor for SIF. Therefore, LETd or physical dose parameters were not associated with SIF prediction.The sacrum D50% RBE-weighted dose was identified as a risk factor for SIF. Additionally, neither LETd nor physical dose parameters were associated with SIF prediction.

Carbon-ions are charged particles with a high linear energy transfer, and therefore, they make a better dose distribution with greater biological effects on the tumors compared with photons and protons. Since prostate cancer, renal cell carcinoma, and retroperitoneal sarcomas such as liposarcoma and leiomyosarcoma are known to be radioresistant tumors, carbon-ion radiotherapy, which provides the advantageous radiobiological properties such as an increasing relative biological effectiveness toward the Bragg peak, a reduced oxygen enhancement ratio, and a reduced dependence on fractionation and cell-cycle stage, has been tested for these urological tumors at the National Institute for Radiological Sciences since 1994. To promote carbon-ion radiotherapy as a standard cancer therapy, the Japan Carbon-ion Radiation Oncology Study Group was established in 2015 to create a registry of all treated patients and conduct multi-institutional prospective studies in cooperation with all the Japanese institutes. Based on accumulating evidence of the efficacy and feasibility of carbon-ion therapy for prostate cancer and retroperitoneal sarcoma, it is now covered by the Japanese health insurance system. On the other hand, carbon-ion radiotherapy for renal cell cancer is not still covered by the insurance system, although the two previous studies showed the efficacy. In this review, we introduce the characteristics, clinical outcomes, and perspectives of carbon-ion radiotherapy and our efforts to disseminate the use of this new technology worldwide.

2021年4月横浜および5月ウェブで、放射線医療関係3学会の合同会議JRC2021の中で学術大会が開催された。特にJRC2021のテーマ「先人たちの功績とその先へ」に即したプログラムが企画された。新型コロナ禍にも関わらず計画通りの全プログラムが実施されて、919名が参加され、うち297名が来場された。

Background and purpose Several studies have focused on increasing the linear energy transfer (LET) within tumours to achieve higher biological effects in carbon-ion radiotherapy (C-ion RT). However, it remains unclear whether LET affects late complications. We assessed whether physical dose and LET distribution can be specific factors for late rectal complications in C-ion RT. Materials and methods Overall, 134 patients with uterine carcinomas were registered and retrospectively analysed. Of 134 patients, 132 who were followed up for >6 months were enrolled. The correlations between the relative biological effectiveness (RBE)-weighted dose based on the Kanai model (the ostensible “clinical dose”), dose-averaged LET (LETd), or physical dose and rectal complications were evaluated. Rectal complications were graded according to the Radiation Therapy Oncology Group/European Organization for Research and Treatment of Cancer criteria. Results Nine patients developed grade 3 or 4 late rectal complications. Linear regression analysis found that D2cc in clinical dose was the sole risk factor for ≥grade 3 late rectal complications (p = 0.012). The receiver operating characteristic analysis found that D2cc of 60.2 Gy (RBE) was a suitable cut-off value for predicting ≥grade 3 late rectal complications. Among 35 patients whose rectal D2cc was ≥60.2 Gy (RBE), no correlations were found between severe rectal toxicities and LETd alone or physical dose per se. Conclusion We demonstrated that severe rectal toxicities were related to the rectal D2cc of the clinical dose in C-ion RT. However, no correlations were found between severe rectal toxicities and LETd alone or physical dose per se.

Background/Aim: The local control rate of chondrosarcomas treated with carbon-ion radiotherapy (CIRT) worsens as tumour size increases, possibly because of the intra-tumoural linear energy transfer (LET) distribution. This study aimed to evaluate the relationship between local recurrence and intra-tumoural LET distribution in chondrosarcomas treated with CIRT. Patients and Methods: Thirty patients treated with CIRT for grade 2 chondrosarcoma were included. Dose-averaged LET (LETd) distribution was calculated by the treatment planning system, and the relationship between LETd distribution in the planning tumour volume (PTV) and local control was evaluated. Results: The mean LETd value in PTV was similar between cases with and without recurrence. Recurrence was not observed in cases where the effective minimum LETd value exceeded 40 keV/μm. Conclusion: LETd distribution in PTV is associated with local control in chondrosarcomas and patients treated with ion beams of higher LETd may have an improved local control rate for unresectable chondrosarcomas.

Background and purpose: Several studies have focused on increasing the linear energy transfer (LET) within tumours to achieve higher biological effects in carbon-ion radiotherapy (C-ion RT). However, it remains unclear whether LET affects late complications. We assessed whether physical dose and LET distribution can be specific factors for late rectal complications in C-ion RT. Materials and methods: Overall, 134 patients with uterine carcinomas were registered and retrospectively analysed. Of 134 patients, 132 who were followed up for >6 months were enrolled. The correlations between the relative biological effectiveness (RBE)-weighted dose based on the Kanai model (the ostensible "clinical dose"), dose-averaged LET (LETd), or physical dose and rectal complications were evaluated. Rectal complications were graded according to the Radiation Therapy Oncology Group/European Organization for Research and Treatment of Cancer criteria. Results: Nine patients developed grade 3 or 4 late rectal complications. Linear regression analysis found that D2cc in clinical dose was the sole risk factor for ≥grade 3 late rectal complications (p = 0.012). The receiver operating characteristic analysis found that D2cc of 60.2 Gy (RBE) was a suitable cut-off value for predicting ≥grade 3 late rectal complications. Among 35 patients whose rectal D2cc was ≥60.2 Gy (RBE), no correlations were found between severe rectal toxicities and LETd alone or physical dose per se. Conclusion: We demonstrated that severe rectal toxicities were related to the rectal D2cc of the clinical dose in C-ion RT. However, no correlations were found between severe rectal toxicities and LETd alone or physical dose per se.

Purpose The purpose is to verify experimentally whether application of magnetic fields longitudinal and perpendicular to a proton beam alters the biological effectiveness of the radiation. Methods and Materials Proton beams with linear energy transfer of 1.1 and 3.3 keV/μm irradiated human cancer and normal cells under a longitudinal (perpendicular) magnetic field of BL (BP) = 0, 0.3, or 0.6 T. Cell survival curves were constructed to evaluate the effects of the magnetic fields on the biological effectiveness. The ratio of dose that would result in a survival fraction of 10% without the magnetic field Dwo to the dose with the magnetic field Dw, R10 = Dwo/Dw, was determined for each cell line and magnetic field. Results For cancer cells exposed to the 1.1- (3.3-) keV/μm proton beams, R10s were increased to 1.10 ± 0.07 (1.11 ± 0.07) and 1.11 ± 0.07 (1.12 ± 0.07) by the longitudinal magnetic fields of BL = 0.3 and 0.6 T, respectively. For normal cells, R10s were increased to 1.13 ± 0.06 (1.17 ± 0.06) and 1.17 ± 0.06 (1.30 ± 0.06) by the BLs. In contrast, R10s were not changed significantly from 1 by the perpendicular magnetic fields of BP = 0.3 and 0.6 T for both cancer and normal cells exposed to 1.1- and 3.3-keV/μm proton beams. Conclusions The biological effectiveness of proton beams was significantly enhanced by longitudinal magnetic fields of BL = 0.3 and 0.6 T, whereas the biological effectiveness was not altered by perpendicular magnetic fields of the same strengths. This enhancement effect should be taken into account in magnetic resonance imaging guided proton therapy with a longitudinal magnetic field.

Background and Purpose The purpose is to verify experimentally whether application of magnetic fields longitudinal and perpendicular to a proton beam alters the biological effectiveness of the radiation. Methods and Materials Proton beams with linear energy transfer (LET) of 1.1 and 3.3 keV/μm were irradiated onto human cancer and normal cells under the longitudinal (perpendicular) magnetic field of BL (BP) = 0, 0.3, or 0.6 T. Cell survival curves were constructed to evaluate the effects of the magnetic fields on the biological effectiveness. The ratio of dose that would result in a survival fraction of 10% without the magnetic field Dwo to the dose with the magnetic field Dw, R10 = Dwo / Dw, was determined for each cell line and magnetic field. Results For cancer cells exposed to the 1.1- (3.3-) keV/μm proton beams, R10s were increased to 1.10±0.07 (1.11±0.07) and 1.11±0.07 (1.12±0.07) by the longitudinal magnetic fields of BL = 0.3 and 0.6 T, respectively. For normal cells, R10s were increased to 1.13±0.06 (1.17±0.06) and 1.17±0.06 (1.30±0.06) by the BLs. In contrast, R10s were not changed significantly from 1 by the perpendicular magnetic fields of BP = 0.3 and 0.6 T for both cancer and normal cells exposed to 1.1- and 3.3-keV/μm proton beams. Conclusions The biological effectiveness of proton beams was significantly enhanced by the longitudinal magnetic fields of BL = 0.3 and 0.6 T, while the biological effectiveness was not altered by the perpendicular magnetic fields of the same strengths. This enhancement effect should be taken into account in MRI guided proton therapy with a longitudinal magnetic field.

Previous studies have revealed application of a magnetic field longitudinal to a carbon-ion beam enhances its biological effectiveness. This communication investigated how timing of the magnetic field application with respect to beam irradiation influenced this effect. Human cancer cells were exposed to carbon-ion beams with linear energy transfer (LET) of 12 and 50 keV/μm. The longitudinal magnetic field of 0.3 T was applied to the cells just before, during, or right after the beam irradiation. The effects of the timing on the biological effectiveness were evaluated by cell survival. The biological effectiveness increased only if the magnetic field was applied during beam irradiation for both LET beams.

The Japan Society of Medical Physics (JSMP) held its 121st semiannual scientific meeting from April 15 to April 18, 2021 in Yokohama, jointly with two other radiological academic societies and radiological industry to constitute Japan Radiology Congress. The congress also included a web-based virtual venue from April 28 to June 3 to provide on-demand services of the same contents. Individual participants, once registered online, were given daily options to participate in either venue. The main theme of the congress was "Milestones and Beyond", which was accidentally ideal for JSMP to commemorate 60th anniversary since its establishment in 1961. Of 121 research presentations collected, 8 were proffered by 7 guest speakers from allied medical physics organizations of India, Bangladesh, Hong Kong, Nepal, and Philippines. The meeting also featured many symposia and lectures on medical physics and interdisciplinary topics. Among them were a special lecture on the history of JSMP with current and past JSMP presidents and an international symposium with distinguished panelists invited from Bangladesh, China, Thailand, Vietnam, and Japan. Of total 919 registrants, 297 participated in the real meeting in Yokohama under the COVID-19 pandemic. Nevertheless, the meeting was perfectly implemented as planned because unvisited speakers had submitted their self-recorded video presentations in advance for onsite viewing in their sessions and many of them remotely participated in real-time discussion over the network. The individual presentations from the speakers, the recorded onsite sessions, and their associated bulletin boards for discussion constituted main contents of the virtual meeting. I would like to express my sincere appreciation to all participants and organizers of this successful meeting. This report supplements the official meeting record including extended abstracts of all presentations, which has been published as the Proceedings of the 121st Scientific Meeting of JSMP (Japanese Journal of Medical Physics Volume 41 Supplement 1, JSMP, Tokyo, April 1, 2021).

For hypo-fractionated multi-ion therapy (HFMIT), the stochastic microdosimetric kinetic (SMK) model had been developed to estimate the biological effectiveness of radiation beams with wide linear energy transfer (LET) and dose ranges. The HFMIT will be applied to radioresistant tumors with oxygen-deficient regions. The response of cells to radiation is strongly dependent on the oxygen condition in addition to radiation type, LET and absorbed dose. This study presents an adaptation of the SMK model to account for oxygen-pressure dependent cell responses, and develops the oxygen-effect-incorporated stochastic microdosimetric kinetic (OSMK) model. In the model, following assumptions were made: the numbers of radiation-induced sublethal lesions (double-strand breaks) are reduced due to lack of oxygen, and the numbers of oxygen-mediated lesions are reduced for radiation with high LET. The model parameters were determined by fitting survival data under aerobic and anoxic conditions for human salivary gland tumor cells and V79 cells exposed to helium-, carbon-, and neon-ion beams over the LET range of 18.5-654.0 keVμm-1. The OSMK model provided good agreement with the experimental survival data of the cells with determination coefficients >0.9. In terms of oxygen enhancement ratio, the OSMK model reproduced the experimental data behavior, including slight dependence on particle type at the same LET. The OSMK model was then implemented into the in-house treatment planning software for the HFMIT to validate its applicability in clinical practice. A treatment plan with helium- and neon-ion beams was made for a pancreatic cancer case assuming an oxygen-deficient region within the tumor. The biological optimization based on the OSMK model preferentially placed the neon-ion beam to the hypoxic region, while it placed both helium- and neon-ion beams to the surrounding normoxic region. The OSMK model offered the accuracy and usability required for hypoxia-based biological optimization in HFMIT treatment planning.

The QST hospital has successfully treated more than 200 patients with choroidal melanoma by broad beam carbon ion radiotherapy (CIRT) with a compensator and a patient-specific collimator since 2001. We decided in 2017 to use scanning carbon ion beam with a rotating gantry for this treatment owing to its flexibilities of dose conformation and beam direction, and then its clinical trial started in April, 2018. In our facility, a commercial 2D ionization chamber array had been employed to verify the 2D dose distribution for any patient specific QA. [1] However, the target volume in choroidal melanoma treatment is typically so small that the 2D array is not appropriate to the verification tool of 2D dose distribution due to its low spatial resolution. Thus, in this clinical trial, we applied new method to the patient specific QA. The method consists of two dosimetric verifications by measurements of depth dose distribution with the Bragg peak chamber and lateral dose distributions at three different depths with the pinpoint chambers, and a verification of beam position at each beam spot with the existing beam position monitor (multi-wire proportional chamber). This method was successfully applied to patient specific QAs for 44 treatment beams of all 22 patients received scanning CIRT for choroidal melanoma in this clinical trial until July, 2019. Here, we provide the summary of the QA results and introduce the current QA procedure based on this clinical trial. [1] T. Furukawa et al., Med. Phys., 40, 121707 (2013)., The 59th Annual Conference of the Particle Therapy Co-Operative Group (PTCOG59)

The National Institute of Radiological Sciences in Japan started clinical studies of carbon-ion radiotherapy (CIRT) in 1994. Due to the high linear energy transfer (LET) of highly charged particles, carbon-ion beams show high relative biological effectiveness in cell killing, especially at the Bragg peak of dose near the beam range, which is controlled to conform to a tumor. Recent technological developments for CIRT include fast pencil-beam scanning, fluoroscopic respiratory motion management, advanced beam modeling for treatment planning, and a superconducting rotating gantry, which have contributed to accuracy, precision, and conformation of dose, operational efficiency, and patient comfort. With technological maturity, CIRT facilities are rapidly increasing in Asia and Europe. Ongoing developments include extension to multiple ion species and facility downsizing to raise the quality and availability of ion-beam therapy in medical care.

Purpose: Our previous study revealed that the application of a magnetic field longitudinal to a carbon-ion beam of 0.1 ≤ B//≤ 0.6 T enhances the biological effectiveness of the radiation. T...

Purpose: A magnetic field longitudinal to an ion beam will potentially affect the biological effectiveness of the radiation. The purpose of this study is to experimentally verify the significance o...

Purpose The QA team of the Japan carbon‐ion radiation oncology study group (J‐CROS) was organized in 2015 to enhance confidence in the accuracy of clinical dosimetry and ensure that the facility QA procedures are adequate. The team conducted onsite dosimetry audits in all the carbon‐ion radiation therapy centers in Japan. Materials and Methods A special phantom was fabricated for the onsite dosimetry audit. Target volumes such as the GTV, CTV, and PTV were contoured to the obtained CT images, and two plans with different isocenter depths were created. The dose at the isocenter was measured by an ionization chamber, in the onsite audit and compared with the calculated dose. Results For all the centers, the average of the percentage ratio between the measured and calculated doses (measured/calculated) was 0.5% (−2.7% to +2.6%) and the standard deviation, 1.7%. In all the centers, the beams were within the set tolerance level of 3%. Conclusions The audit demonstrated that the dose at a single point in the water phantom was within tolerance, but it is a big step to say that all doses are correct. In addition, this external dosimetry audit encouraged centers to improve the quality of their dosimetry systems.

Purpose: The Gold Anchor is a kind of fiducial marker for radiotherapy. There is a trend toward the greater use of it for IGRT because of its great visibility, instant stability and minimal invasive. It has cut-outs in its structure, which allow itself into a ball or placed as a line during implantation. Towards to use of it for prostate cancer with carbon ion radiotherapy, the physical dose perturbation of carbon ion beam was assessed when a Gold Anchor was located proximal to Bragg peak. Methods: The Gold Anchor have two size types, one is φ 0.28 mm × 20 mm and another is φ 0.28 mm × 10 mm, respectively. They were made of 99.5% Au and 0.5% iron. Because of its small and complex structure, dose profiles were calculated by Monte Carlo tool Geant4. A 5 × 5 cm2 field with pristine 350 MeV/u carbon ion beam was irradiated into water, and a Gold Anchor was located around 2 cm proximal to Bragg peak. Several shapes of Gold Anchor, such as curled, zigzag and tadpole shapes, were considered. Results: The differences of depth dose profiles with and without Gold Anchor along beam axis in water were compared. The maximum peak shift was observed with curled 20 mm length Gold Anchor, it was reached around 1 cm. Conclusion: This study recommends the sparser shapes for reducing the dose perturbation., 第121回日本医学物理学会学術大会

A development project for hypo-fractionated multi-ion therapy has been initiated at the National Institute of Radiological Sciences in Japan. In the treatment, helium, carbon, oxygen, and neon ions will be used as primary beams with pencil beam scanning. A ripple filter (RiFi), consisting of a thin plastic or aluminum plate with a fine periodic ridge and groove structure, has been used to broaden the Bragg peak of heavy-ion beams in the beam direction. To sufficiently broaden the Bragg peak of helium-, carbon-, oxygen-, and neon-ion beams with suppressed lateral scattering and surface dose inhomogeneity, in this study, we tested a plate made of a lung substitute material, Gammex LN300, as the RiFi. The planar integrated dose distribution of a 183.5 MeV u−1 neon-ion beam was measured behind a 3 cm thick LN300 plate in water. The Bragg peak of the pristine beam was broadened following the normal distribution with the standard deviation σ value of 1.29 mm, while the range of the beam was reduced by 8.8 mm by the plate. To verify the LN300 performance as the RiFi in multi-ion therapy, we measured the pencil beam data of helium-, carbon-, oxygen- and neon-ion beams penetrating the 3 cm thick LN300 plate. The data were then modeled and used in a treatment planning system to achieve a uniform 10% survival of human undifferentiated carcinoma cells within a cuboid target by the beam for each of the different ion species. The measured survival fractions were reasonably reproduced by the planned ones for all the ion species. No surface dose inhomogeneity was observed for any ion species even when the plate was placed close to the phantom surface. The plate made of lung substitute material, Gammex LN300, is applicable as the RiFi in multi-ion therapy with helium-, carbon-, oxygen- and neon-ion beams.

Background/aim The local control rate of chondrosarcomas treated with carbon-ion radiotherapy (CIRT) worsens as tumour size increases, possibly because of the intra-tumoural linear energy transfer (LET) distribution. This study aimed to evaluate the relationship between local recurrence and intra-tumoural LET distribution in chondrosarcomas treated with CIRT. Patients and methods Thirty patients treated with CIRT for grade 2 chondrosarcoma were included. Dose-averaged LET (LETd) distribution was calculated by the treatment planning system, and the relationship between LETd distribution in the planning tumour volume (PTV) and local control was evaluated. Results The mean LETd value in PTV was similar between cases with and without recurrence. Recurrence was not observed in cases where the effective minimum LETd value exceeded 40 keV/μm. Conclusion LETd distribution in PTV is associated with local control in chondrosarcomas and patients treated with ion beams of higher LETd may have an improved local control rate for unresectable chondrosarcomas.

For hypo-fractionated multi-ion therapy (HFMIT), the stochastic microdosimetric kinetic (SMK) model had been developed to estimate the biological effectiveness of radiation beams with wide linear energy transfer (LET) and dose ranges. The HFMIT will be applied to radioresistant tumors with oxygen-deficient regions. The response of cells to radiation is strongly dependent on the oxygen condition in addition to radiation type, LET and absorbed dose. This study presents an adaptation of the SMK model to account for oxygen-pressure dependent cell responses, and develops the oxygen-effect-incorporated stochastic microdosimetric kinetic (OSMK) model. In the model, following assumptions were made: the numbers of radiation-induced lesions (double-strand breaks and clustered DNA damages) are reduced due to lack of oxygen, and the numbers of oxygen-mediated lesions are reduced for radiation with high LET. The model parameters were determined by fitting survival data under aerobic and anoxic conditions for human salivary gland tumor cells and V79 cells exposed to helium-, carbon-, and neon-ion beams over the LET range of 18.5-654.0 keV/μm. The OSMK model provided good agreement with the experimental survival data of the cells with determination coefficients > 0.9. In terms of oxygen enhancement ratio, the OSMK model reproduced the experimental data behavior, including slight dependence on particle type at the same LET. The OSMK model was then implemented into the in-house treatment planning software for the HFMIT to validate its applicability in clinical practice. A treatment plan with helium- and neon-ion beams was made for a pancreatic cancer case assuming an oxygen-deficient region within the tumor. The biological optimization based on the OSMK model preferentially placed the neon-ion beam to the hypoxic region, while it placed both helium- and neon-ion beams to the surrounding normoxic region. The OSMK model offered the accuracy and usability required for hypoxia-based biological optimization in HFMIT treatment planning.

Purpose To investigate carbon-ion radiotherapy (CIRT) for in-field recurrence of stage I non-small cell lung cancer (NSCLC) initially treated with CIRT. Materials and methods From January 2007 to March 2014, patients initially treated for stage I NSCLC with CIRT and relapsed in-field were candidates. Overall survival (OS) rate, local control (LC) rate, progressive free survival (PFS) rate, dose to the lungs and skin, and adverse effects were analyzed. Results Twenty-nine patients were eligible. Median age at re-irradiation was 74 years (range 53–90). Median observation period from the first day of re-irradiation was 29 months (4–88 months). Median prescribed dose was 46.0 Gy (RBE) as initial treatment and 66.0 Gy (RBE) in 12 fractions as re-irradiation. Two-year OS, LC, and PFS rates after re-irradiation were 69.0% (95% CI: 50.3–83.0), 66.9% (95% CI: 47.5–81.9), and 51.7% (95% CI: 34.1–68.9). Median skin maximum dose was 53.8 Gy (RBE) (range 4.4–103.1) and median of mean lung dose was 7.3 Gy (RBE) (range 2.6–14.0). There were no severer than grade 2 adverse effects except one (3.4%) grade 3 bacterial pneumonia, which was not considered radiation-induced. Conclusion CIRT for stage I NSCLC local recurrence is an acceptable definitive re-treatment.

The HIMAC clinical study has been conducted with a carbon-ion beam since June 1994. Since 2006, as a new treatment research project, NIRS has developed both the accelerator and beam-delivery technologies for the sophisticated heavy-ion radiotherapy, which brings a pencil-beam 3D rescanning technology for both the static and moving-tumor treatments. In this technology, the depth-scanning technique was improved to the full-energy depth scanning by realizing a variable-energy operation of the HIMAC synchrotron itself. At present, a heavy-ion rotating gantry has been developed with the superconducting technology and is in a beam-commissioning stage. As a future plan, we just start a study of a multi-ions irradiation for more sophisticated LET-painting and a design study of a superconducting synchrotron for more compact heavy-ion radiotherapy facility.

The biological effect of charged-particle beams depends on both dose and particle spectrum. As one of the physical quantities describing the particle spectrum of charged-particle beams, we considered the linear energy transfer (LET) throughout this study. We investigated a new therapeutic technique using two or more ion species in one treatment session, which we call an intensity modulated composite particle therapy (IMPACT), for optimizing the physical dose and dose-averaged LET distributions in a patient as its proof of principle. Protons and helium, carbon, and oxygen ions were considered as ion species for IMPACT. For three cubic targets of 4 × 4 × 4, 8 × 8 × 8, and 12 × 12 × 12 cm3, defined at the center of the water phantom of 20 × 20 × 20 cm3, we made IMPACT plans of two composite fields with opposing and orthogonal geometries. The prescribed dose to the target was fixed at 1 Gy, while the prescribed LET to the target was varied from 1 keV µm-1 to 120 keV µm-1 to investigate the range of LET valid for prescription. The minimum and maximum prescribed LETs, (L T_min, L T_max), by the opposing-field geometry, were (3 keV µm-1, 115 keV µm-1), (2 keV µm-1, 84 keV µm-1),and (2 keV µm-1, 66 keV µm-1), while those by the orthogonal-field geometry were (8 keV µm-1, 98 keV µm-1), (7 keV µm-1, 72 keV µm-1), and (8 keV µm-1, 57 keV µm-1) for the three targets, respectively. To show the proof of principle of IMPACT in a clinical situation, we made IMPACT plans for a prostate case. In accordance with the prescriptions, the LETs in prostate, planning target volume (PTV), and rectum could be adjusted at 80 keV µm-1, at 50 keV µm-1, and below 30 keV µm-1, respectively, while keeping the dose to the PTV at 2 Gy uniformly. IMPACT enables the optimization of the dose and the LET distributions in a patient, which will maximize the potential of charged-particle therapy by expanding the therapeutic window. Further studies and developments will enable this therapeutic technique to be used in clinical practice.

4次元治療計画における標的体積に関する概念について記述。

Background and purpose In carbon ion radiotherapy (CIRT), the use of different relative biological effectiveness (RBE) models in the RBE-weighted dose (D RBE ) calculation can lead to deviations in the physical dose (D phy ) delivered to the patient. Our aim is to reduce target D phy deviations by converting prescription dose values. Material and methods Planning data of patients treated at the National Institute of Radiological Sciences (NIRS) were collected, with prescribed doses per fraction ranging from 3.6Gy (RBE) to 4.6Gy (RBE), according to the Japanese semi-empirical model. The D phy was Monte Carlo (MC) re-calculated simulating the NIRS beamline. The local effect model (LEM)_I was then applied to estimate D RBE . Target median D RBE ratios between MC+LEM_I and NIRS plans determined correction factors for the conversion of prescription doses. Plans were re-optimized in a LEM_I-based commercial system, prescribing the NIRS uncorrected and corrected D RBE . Results The MC+LEM_I target median D RBE was respectively 15% and 5% higher than the NIRS reference, for the lowest and highest dose levels. Uncorrected D RBE prescription resulted in significantly lower target D phy in re-optimized plans, with respect to NIRS plans. Conclusions Prescription dose conversion factors could minimize target physical dose variations due to the use of different radiobiological models in the calculation of CIRT RBE-weighted dose.

In the conventional procedure for accurate Monte Carlo simulation of radiotherapy, a CT number given to each pixel of a patient image is directly converted to mass density and elemental composition using their respective functions that have been calibrated specifically for the relevant x-ray CT system. We propose an alternative approach that is a conversion in two steps: the first from CT number to density and the second from density to composition. Based on the latest compilation of standard tissues for reference adult male and female phantoms, we sorted the standard tissues into groups by mass density and defined the representative tissues by averaging the material properties per group. With these representative tissues, we formulated polyline relations between mass density and each of the following; electron density, stopping-power ratio and elemental densities. We also revised a procedure of stoichiometric calibration for CT-number conversion and demonstrated the two-step conversion method for a theoretically emulated CT system with hypothetical 80 keV photons. For the standard tissues, high correlation was generally observed between mass density and the other densities excluding those of C and O for the light spongiosa tissues between 1.0 g cm(-3) and 1.1 g cm(-3) occupying 1% of the human body mass. The polylines fitted to the dominant tissues were generally consistent with similar formulations in the literature. The two-step conversion procedure was demonstrated to be practical and will potentially facilitate Monte Carlo simulation for treatment planning and for retrospective analysis of treatment plans with little impact on the management of planning CT systems.

Purpose The aim of this study was to estimate normal tissue complication probability (NTCP) parameters for late rectal complications after carbon ion radiotherapy (C-ion RT) for prostate cancer. Methods and materials A total of 163 patients were used to derive NTCP parameters. These patients were treated with relative biological effectiveness (RBE)-weighted dose ranging from 57.6Gy (RBE) up to 72Gy (RBE) and included in dose escalation trials. The Lyman–Kutcher–Burman (LKB) model was used and the model parameters were fit to the relation between dose and complication observed after C-ion RT. Results The resulting NTCP parameters were the volume effect parameter; n =0.035 (95% CI: 0.024–0.047), the steepness of the NTCP curve; m =0.10 (0.084–0.13), the tolerance dose associated with 50% probability of complication; TD 50 =63.6Gy (RBE) (61.8–65.4Gy (RBE)) for Grade⩾1, n =0.012 (0.0050–0.023), m =0.046 (0.033–0.062), TD 50 =69.1Gy (RBE) (67.6–70.9Gy (RBE)) for Grade⩾2. Conclusion A new set of rectal NTCP parameters in C-ion RT was determined. The rather small n values suggest that the rectum was consistent with being strictly serial organ. The new derived parameter values facilitate estimation of rectal NTCP in C-ion RT.

In treatment planning for proton radiotherapy, the dose measured in water is applied to the patient dose calculation with density scaling by stopping power ratio [Formula: see text]. Since the body tissues are chemically different from water, this approximation may cause dose calculation errors, especially due to differences in nuclear interactions. We proposed and validated an algorithm for correcting these errors. The dose in water is decomposed into three constituents according to the physical interactions of protons in water: the dose from primary protons continuously slowing down by electromagnetic interactions, the dose from protons scattered by elastic and/or inelastic interactions, and the dose resulting from nonelastic interactions. The proportions of the three dose constituents differ between body tissues and water. We determine correction factors for the proportion of dose constituents with Monte Carlo simulations in various standard body tissues, and formulated them as functions of their [Formula: see text] for patient dose calculation. The influence of nuclear interactions on dose was assessed by comparing the Monte Carlo simulated dose and the uncorrected dose in common phantom materials. The influence around the Bragg peak amounted to -6% for polytetrafluoroethylene and 0.3% for polyethylene. The validity of the correction method was confirmed by comparing the simulated and corrected doses in the materials. The deviation was below 0.8% for all materials. The accuracy of the correction factors derived with Monte Carlo simulations was separately verified through irradiation experiments with a 235 MeV proton beam using common phantom materials. The corrected doses agreed with the measurements within 0.4% for all materials except graphite. The influence on tumor dose was assessed in a prostate case. The dose reduction in the tumor was below 0.5%. Our results verify that this algorithm is practical and accurate for proton radiotherapy treatment planning, and will also be useful in rapidly determining fluence correction factors for non-water phantom dosimetry.

Purpose: In carbon-ion radiotherapy treatment planning, the planar integrated dose (PID) measured in water is applied to the patient dose calculation with density scaling using the stopping power ratio. Since body tissues are chemically different from water, this dose calculation can be subject to errors, particularly due to differences in inelastic nuclear interactions. In recent studies, the authors proposed and validated a PID correction method for these errors. In the present study, the authors used this correction method to assess the influence of these nuclear interactions in body tissues on tumordose in various clinical cases. Methods: Using 10–20 cases each of prostate, head and neck (HN), bone and soft tissue (BS), lung,liver, pancreas, and uterine neoplasms, the authors first used treatment plans for carbon-ion radiotherapy without nuclear interaction correction to derive uncorrected dose distributions. The authors then compared these distributions with recalculated distributions using the nuclear interaction correction (corrected dose distributions). Results: Median (25%/75% quartiles) differences between the target mean uncorrected doses and corrected doses were 0.2% (0.1%/0.2%), 0.0% (0.0%/0.0%), −0.3% (−0.4%/−0.2%), −0.1% (−0.2%/−0.1%), −0.1% (−0.2%/0.0%), −0.4% (−0.5%/−0.1%), and −0.3% (−0.4%/0.0%) for the prostate, HN, BS, lung,liver, pancreas, and uterine cases, respectively. The largest difference of −1.6% in target mean and −2.5% at maximum were observed in a uterine case. Conclusions: For most clinical cases, dose calculation errors due to the water nonequivalence of the tissues in nuclear interactions would be marginal compared to intrinsic uncertainties in treatment planning, patient setup, beam delivery, and clinical response. In some extreme cases, however, these errors can be substantial. Accordingly, this correction method should be routinely applied to treatment planning in clinical practice.

The National Institute of Radiological Sciences (NIRS) has initiated a development project for hypo-fractionated multi-ion therapy. In the treatment, heavy ions up to neon ions will be used as a primary beam, which is a high linear energy transfer (LET) radiation. The fractionated dose of the treatment will be 10 Gy or more. The microdosimetric kinetic (MK) model overestimates the biological effectiveness of high-LET and high-dose radiations. To address this issue, the stochastic microdosimetric kinetic (SMK) model has been developed as an extension of the MK model. By taking the stochastic nature of domain-specific and cell nucleus-specific energies into account, the SMK model could estimate the biological effectiveness of radiations with wide LET and dose ranges. Previously, the accuracy of the SMK model was examined by comparison of estimated and reported survival fractions of human cells exposed to pristine helium-, carbon-, and neon-ion beams. In this study, we verified the SMK model in treatment planning of scanned helium-, carbon-, oxygen-, and neon-ion beams as well as their combinations through the irradiations of human undifferentiated carcinoma and human pancreatic cancer cells. Treatment plans were made with the ion-species beams to achieve a uniform 10% survival of the cells within a cuboid target. The planned survival fractions were reasonably reproduced by the measured survival fractions in the whole region from the plateau to the fragment tail for all planned irradiations. The SMK model offers the accuracy and simplicity required in hypo-fractionated multi-ion therapy treatment planning.

The National Institute of Radiological Sciences (NIRS) has initiated a development project for hypo-fractionated multi-ion therapy. In the treatment, heavy ions up to neon ions will be used as a primary beam, which is a high linear energy transfer (LET) radiation. The fractionated dose of the treatment will be 10 Gy or more. The microdosimetric kinetic (MK) model overestimates the biological effectiveness of high-LET and high-dose radiations. To address this issue, the stochastic microdosimetric kinetic (SMK) model has been developed as an extension of the MK model. By taking the stochastic nature of domain-specific and cell nucleus-specific energies into account, the SMK model could estimate the biological effectiveness of radiations with wide LET and dose ranges. Previously, the accuracy of the SMK model was examined by comparison of estimated and reported survival fractions of human cells exposed to pristine helium-, carbon-, and neon-ion beams. In this study, we verified the SMK model in treatment planning of scanned helium-, carbon-, oxygen-, and neon-ion beams as well as their combinations through the irradiations of human undifferentiated carcinoma and human pancreatic cancer cells. Treatment plans were made with the ion-species beams to achieve a uniform 10% survival of the cells within a cuboid target. The planned survival fractions were reasonably reproduced by the measured survival fractions in the whole region from the plateau to the fragment tail for all planned irradiations. The SMK model offers the accuracy and simplicity required in hypo-fractionated multi-ion therapy treatment planning.

In charged-particle therapy treatment planning, the patient is conventionally modeled as variable-density water, i.e. stopping effective density ρ S, and the planar integrated dose distribution measured in water (PID) is applied for patient dose calculation based on path length scaling with the ρ S. This approximation assures the range accuracy of charged-particle beams. However, it causes dose calculation errors due to water nonequivalence of body tissues in nuclear interactions originating from compositional differences. We had previously proposed and validated a PID correction method for the errors in carbon-ion radiotherapy. In the present study, we verify the PID correction method for helium-, oxygen-, and neon-ion beams. The one-to-one relationships between ρ S and the nuclear effective density ρ N of body tissues were constructed for helium-, carbon-, oxygen-, and neon-ion beams, and were used to correct the PIDs to account for the dose calculation errors in patient. The correction method was tested for non-water materials with un-scanned and scanned ion beams. In un-scanned beams penetrating the materials, the dose calculation errors of up to 5.9% were observed at the Bragg peak region, while they were reduced to ⩽0.9% by the PID correction method. In scanned beams penetrating olive oil, the dose calculation errors of up to 2.7% averaged over the spread-out Bragg peak were observed, while they were reduced to ⩽0.4% by the correction method. To investigate the influence of water nonequivalence of body tissues on tumor dose, we carried out a treatment planning study for prostate and uterine cases. The tumor over-doses of 0.9%, 1.8%, 2.0%, and 2.2% were observed in the uterine case for the helium-, carbon-, oxygen-, and neon-ion beams, respectively. These dose errors could be diminished by the PID correction method. The present results verify that the PID correction method is simple, practical, and accurate for treatment planning of these four ion species.

In charged-particle therapy treatment planning, the patient is conventionally modeled as variable-density water, i.e., stopping effective density ρS, and the planar integrated dose distribution measured in water (PID) is applied for patient dose calculation based on path length scaling with the ρS. This approximation assures the range accuracy of charged-particle beams. However, it causes dose calculation errors due to water nonequivalence of body tissues in nuclear interactions originating from compositional differences. We had previously proposed and validated a PID correction method for the errors in carbon-ion radiotherapy. In the present study, we verify the PID correction method for helium-, oxygen-, and neon-ion beams. The one-to-one relationships between ρS and the nuclear effective density ρN of body tissues were constructed for helium-, carbon-, oxygen-, and neon-ion beams, and were used to correct the PIDs to account for the dose calculation errors in patient. The correction method was tested for non-water materials with un-scanned and scanned ion beams. In un-scanned beams penetrating the materials, the dose calculation errors of up to 5.9% were observed at the Bragg peak region, while they were reduced to ≤ 0.9% by the PID correction method. In scanned beams penetrating olive oil, the dose calculation errors of up to 2.7% averaged over the spread-out Bragg peak were observed, while they were reduced to ≤ 0.4% by the correction method. To investigate the influence of water nonequivalence of body tissues on tumor dose, we carried out a treatment planning study for prostate and uterine cases. The tumor over-doses of 0.9%, 1.8%, 2.0%, and 2.2% were observed in the uterine case for the helium-, carbon-, oxygen-, and neon-ion beams, respectively. These dose errors could be diminished by the PID correction method. The present results verify that the PID correction method is simple, practical, and accurate for treatment planning of these four ion species.

Purpose: This is a theoretical simulation study for proof of concept of radiochromic film dosimetry to measure physical and biological doses without plan-based quenching correction for patient-specific quality assurance of carbon-ion radiotherapy. Methods: We took a layer-stacking carbon-ion beam comprised of range-shifted beamlets. The dosimeter response was simulated according to an experimental quenching model. The beam model followed a treatment planning system. The beam was decomposed into finely arranged beamlets with weights estimated by deconvolution of longitudinal dosimeter responses. The distributions of physical and biological doses were reconstructed from the estimated weights, and were compared with the plan. We also evaluated the sensitivity to measurement errors and to erratic delivery with an undelivered beamlet. Results: The reconstructed physical and biological doses accurately reproduced the simulated delivery with errors approximately corresponding to the measurement errors. The erratic beam delivery was easily detectable by comparison of biological dose distribution to the plan. Conclusions: We have developed a method to measure physical and biological doses by longitudinal dosimetry of quenched response without using plan data. The method only involves a general optimization algorithm, a radiobiology model, and experimental beamlet data, and requires no extra corrections. Theoretically, this approach is applicable to various dosimeters and to proton and ion beams of any delivery method, regardless of quenching or biological effectiveness.

In light ion therapy, the dose concentration is highly sensitive to setup and range errors. Here we propose a method for evaluating the effects of these errors by using the correlation between fractions on tumour control probability (TCP) in carbon-ion therapy. This method incorporates the concept of equivalent stochastic dose (Cranmer-Sargison and Zavgorodni 2005 Phys. Med. Biol. 50 4097-109), which was defined as a dose that gives the mean expected survival fraction (SF) for the stochastically variable dose. The mean expected SFs were calculated while considering the correlation between fractions for setup and range errors. By using this SF, equivalent stochastic clinical doses (ESCD), which are weighted by relative biological effectiveness, of lung and prostate cases with varying errors were derived. To account for spatial dose heterogeneity, equivalent uniform stochastic clinical doses (EUSCD) were obtained by using the mean expected SF in the volume of interest. TCP curves were calculated for each assumed error considering inter-patient sensitivity variation with a fractionation effect. ESCD distributions, EUSCD, and TCP curves were affected by the inter-fraction correlation and the contribution of setup and range errors. Irradiated areas that could be affected by these errors can be visualized quantitatively by using the ESCD distribution. TCP curves for the errors of various conditions converged around the TCP curve in nominal conditions by using the EUSCD. EUSCD correlated well with TCP in setup and range errors when the errors were not large and was comparatively stably insensitive to uncertain biological parameters. The proposed evaluation method with EUSCD and TCP calculations will be useful to indicate tumour doses to improve realistic dose distributions in carbon-ion therapy.

At the National Institute of Radiological Sciences (NIRS), more than 8,000 patients have been treated for various tumors with carbon-ion (C-ion) radiotherapy in the past 20 years based on a radiobiologically defined clinical-dose system. Through clinical experience, including extensive dose escalation studies, optimum dose-fractionation protocols have been established for respective tumors, which may be considered as the standards in C-ion radiotherapy. Although the therapeutic appropriateness of the clinical-dose system has been widely demonstrated by clinical results, the system incorporates several oversimplifications such as dose-independent relative biological effectiveness (RBE), empirical nuclear fragmentation model, and use of dose-averaged linear energy transfer to represent the spectrum of particles. We took the opportunity to update the clinical-dose system at the time we started clinical treatment with pencil beam scanning, a new beam delivery method, in 2011. The requirements for the updated system were to correct the oversimplifications made in the original system, while harmonizing with the original system to maintain the established dose-fractionation protocols. In the updated system, the radiation quality of the therapeutic C-ion beam was derived with Monte Carlo simulations, and its biological effectiveness was predicted with a theoretical model. We selected the most used C-ion beam with αr = 0.764 Gy(-1) and β = 0.0615 Gy(-2) as reference radiation for RBE. The C-equivalent biological dose distribution is designed to allow the prescribed survival of tumor cells of the human salivary gland (HSG) in entire spread-out Bragg peak (SOBP) region, with consideration to the dose dependence of the RBE. This C-equivalent biological dose distribution is scaled to a clinical dose distribution to harmonize with our clinical experiences with C-ion radiotherapy. Treatment plans were made with the original and the updated clinical-dose systems, and both physical and clinical dose distributions were compared with regard to the prescribed dose level, beam energy, and SOBP width. Both systems provided uniform clinical dose distributions within the targets consistent with the prescriptions. The mean physical doses delivered to targets by the updated system agreed with the doses by the original system within ± 1.5% for all tested conditions. The updated system reflects the physical and biological characteristics of the therapeutic C-ion beam more accurately than the original system, while at the same time allowing the continued use of the dose-fractionation protocols established with the original system at NIRS.

In scanned carbon-ion (C-ion) radiotherapy, some primary C-ions undergo nuclear reactions before reaching the target and the resulting particles deliver doses to regions at a significant distance from the central axis of the beam. The effects of these particles on physical dose distribution are accounted for in treatment planning by representing the transverse profile of the scanned C-ion beam as the superposition of three Gaussian distributions. In the calculation of biological dose distribution, however, the radiation quality of the scanned C-ion beam has been assumed to be uniform over its cross-section, taking the average value over the plane at a given depth (monochrome model). Since these particles, which have relatively low radiation quality, spread widely compared to the primary C-ions, the radiation quality of the beam should vary with radial distance from the central beam axis. To represent its transverse distribution, we propose a trichrome beam model in which primary C-ions, heavy fragments with atomic number Z ≥ 3, and light fragments with Z ≤ 2 are assigned to the first, second, and third Gaussian components, respectively. Assuming a realistic beam-delivery system, we performed computer simulations using Geant4 Monte Carlo code for analytical beam modeling of the monochrome and trichrome models. The analytical beam models were integrated into a treatment planning system for scanned C-ion radiotherapy. A target volume of 20 × 20 × 40 mm(3) was defined within a water phantom. A uniform biological dose of 2.65 Gy (RBE) was planned for the target with the two beam models based on the microdosimetric kinetic model (MKM). The plans were recalculated with Geant4, and the recalculated biological dose distributions were compared with the planned distributions. The mean target dose of the recalculated distribution with the monochrome model was 2.72 Gy (RBE), while the dose with the trichrome model was 2.64 Gy (RBE). The monochrome model underestimated the RBE within the target due to the assumption of no radial variations in radiation quality. Conversely, the trichrome model accurately predicted the RBE even in a small target. Our results verify the applicability of the trichrome model for clinical use in C-ion radiotherapy treatment planning.

A calibration method for CT-number to stopping-power-ratio conversion was recently proposed as a revision of the Japanese de facto standard method that has been used at particle therapy centers in Japan for over a decade. The revised method deals with 11 representative tissues of specific elemental composition and density, based on a latest compilation of standard tissue data. We report here how the revision was actually implemented into clinical practice. We applied the revised method to 7 CT-scanning conditions currently in use for treatment planning. For each condition, we derived CT numbers and stopping-power ratios of the representative tissues to constitute a polyline conversion function. We analyzed the change of target water-equivalent depth by the revision for 38 beams in treatment plans for 13 randomly sampled patients. The revision caused a mean change of +0.3 mm with a standard deviation of 0.4 mm. The maximum change was +1.2 mm or +0.5% of the depth, which may be clinically insignificant. The transition to the revised method was straightforward and would slightly improve the accuracy of the beam range in particle therapy.

In carbon-ion radiotherapy, single-beam delivery each day in alternate directions has been commonly practiced for operational efficiency, taking advantage of the Bragg peak and the relative biological effectiveness (RBE) for uniform dose conformation to a tumor. The treatment plans are usually evaluated with total RBE-weighted dose, which is however deficient in relevance to the biological effect in the linear-quadratic model due to its quadratic-dose term, or the dose-fractionation effect. In this study, we reformulate the extrapolated response dose (ERD), or synonymously BED, which normalizes the dose-fractionation and cell-repopulation effects as well as the RBE of treating radiation, based on inactivation of a single model cell system and a typical treating radiation in carbon-ion RT. The ERD distribution virtually represents the biological effect of the treatment regardless of radiation modality or fractionation scheme. We applied the ERD formulation to simplistic model treatments and to a preclinical survey for hypofractionation based on an actual prostate-cancer treatment of carbon-ion radiotherapy. The proposed formulation was demonstrated to be practical and to offer theoretical implications. In the prostate-cancer case, the ERD distribution was very similar to the RBE-weighted-dose distribution of the actual treatment in 12 fractions. With hypofractionation, while the RBE-weighted-dose distribution varied significantly, the ERD distribution was nearly invariant, implying that the carbon-ion radiotherapy would be insensitive to fractionation. However, treatment evaluation with simplistic biological dose is intrinsically limited and must be complemented in practice somehow by clinical experiences and biology experiments.

Carbon-ion radiotherapy (CIRT) is generally evaluated with the dose weighted by relative biological effectiveness (RBE), while the radiation quality varying in the body of each patient is ignored for lack of such distribution. In this study, we attempted to develop a method to estimate linear energy transfer (LET) for a treatment planning system that only handled physical and RBE-weighted doses. The LET taken from a database of clinical broad beams was related to the RBE per energy with two polyline fitting functions for spread-out Bragg peak (SOBP) and for entrance depths, which would be selected by RBE threshold per energy per modulation. The LET estimation was consistent with the original calculation typically within a few keV/{\mu}m except for the overkill at the distal end of SOBP. The CIRT treatments can thus be related to the knowledge obtained in radiobiology experiments that used LET to represent radiation quality., Comment: 6 pages, 2 tables, 5 figures

Challenging issues in treatment planning for scanned carbon-ion (C-ion) therapy are (i) accurate calculation of dose distribution, including the contribution of large angle-scattered fragments, (ii) reduction in the memory space required to store the dose kernel of individual pencil beams and (iii) shortening of computation time for dose optimization and calculation. To calculate the dose contribution from fragments, we modeled the transverse dose profile of the scanned C-ion beam with the superposition of three Gaussian distributions. The development of pencil beams belonging to the first Gaussian component was calculated analytically based on the Fermi-Eyges theory, while those belonging to the second and third components were transported empirically using the measured beam widths in a water phantom. To reduce the memory space for the kernels, we stored doses only in the regions of interest considered in the dose optimization. For the final dose calculation within the patient's whole body, we applied a pencil beam redefinition algorithm. With these techniques, the triple Gaussian beam model can be applied not only to final dose calculation but also to dose optimization in treatment planning for scanned C-ion therapy. To verify the model, we made treatment plans for a homogeneous water phantom and a heterogeneous head phantom. The planned doses agreed with the measurements within ±2% of the target dose in both phantoms, except for the doses at the periphery of the target with a high dose gradient. To estimate the memory space and computation time reduction with these techniques, we made a treatment plan for a bone sarcoma case with a target volume of 1.94 l. The memory space for the kernel and the computation time for final dose calculation were reduced to 1/22 and 1/100 of those without the techniques, respectively. Computation with the triple Gaussian beam model using the proposed techniques is rapid, accurate and applicable to dose optimization and calculation in treatment planning for scanned C-ion therapy.