Patient-specific deep learning for 3D protoacoustic image reconstruction and dose verification in proton therapy

BACKGROUND

Protoacoustic (PA) imaging has the potential to provide real-time 3D dose verification of proton therapy. However, PA images are susceptible to severe distortion due to limited angle acquisition. Our previous studies showed the potential of using deep learning to enhance PA images. As the model was trained using a limited number of patients' data, its efficacy was limited when applied to individual patients.

PURPOSE

In this study, we developed a patient-specific deep learning method for protoacoustic imaging to improve the reconstruction quality of protoacoustic imaging and the accuracy of dose verification for individual patients.

METHODS

Our method consists of two stages: in the first stage, a group model is trained from a diverse training set containing all patients, where a novel deep learning network is employed to directly reconstruct the initial pressure maps from the radiofrequency (RF) signals; in the second stage, we apply transfer learning on the pre-trained group model using patient-specific dataset derived from a novel data augmentation method to tune it into a patient-specific model. Raw PA signals were simulated based on computed tomography (CT) images and the pressure map derived from the planned dose. The reconstructed PA images were evaluated against the ground truth by using the root mean squared errors (RMSE), structural similarity index measure (SSIM) and gamma index on 10 specific prostate cancer patients. The significance level was evaluated by t-test with the p-value threshold of 0.05 compared with the results from the group model.

RESULTS

The patient-specific model achieved an average RMSE of 0.014 (p < 0.05 ${{{p}}}<{0.05}$ ), and an average SSIM of 0.981 (p < 0.05 ${{{p}}}<{0.05}$ ), out-performing the group model. Qualitative results also demonstrated that our patient-specific approach acquired better imaging quality with more details reconstructed when comparing with the group model. Dose verification achieved an average RMSE of 0.011 (p < 0.05 ${{{p}}}<{0.05}$ ), and an average SSIM of 0.995 (p < 0.05 ${{{p}}}<{0.05}$ ). Gamma index evaluation demonstrated a high agreement (97.4% [p < 0.05 ${{{p}}}<{0.05}$ ] and 97.9% [p < 0.05 ${{{p}}}<{0.05}$ ] for 1%/3  and 1%/5 mm) between the predicted and the ground truth dose maps. Our approach approximately took 6 s to reconstruct PA images for each patient, demonstrating its feasibility for online 3D dose verification for prostate proton therapy.

CONCLUSIONS

Our method demonstrated the feasibility of achieving 3D high-precision PA-based dose verification using patient-specific deep-learning approaches, which can potentially be used to guide the treatment to mitigate the impact of range uncertainty and improve the precision. Further studies are needed to validate the clinical impact of the technique.

Hybrid-supervised deep learning for domain transfer 3D protoacoustic image reconstruction

Objective. Protoacoustic imaging showed great promise in providing real-time 3D dose verification of proton therapy. However, the limited acquisition angle in protoacoustic imaging induces severe artifacts, which impairs its accuracy for dose verification. In this study, we developed a hybrid-supervised deep learning method for protoacoustic imaging to address the limited view issue.Approach. We proposed a Recon-Enhance two-stage deep learning method. In the Recon-stage, a transformer-based network was developed to reconstruct initial pressure maps from raw acoustic signals. The network is trained in a hybrid-supervised approach, where it is first trained using supervision by the iteratively reconstructed pressure map and then fine-tuned using transfer learning and self-supervision based on the data fidelity constraint. In the enhance-stage, a 3D U-net is applied to further enhance the image quality with supervision from the ground truth pressure map. The final protoacoustic images are then converted to dose for proton verification.Main results. The results evaluated on a dataset of 126 prostate cancer patients achieved an average root mean squared errors (RMSE) of 0.0292, and an average structural similarity index measure (SSIM) of 0.9618, out-performing related start-of-the-art methods. Qualitative results also demonstrated that our approach addressed the limit-view issue with more details reconstructed. Dose verification achieved an average RMSE of 0.018, and an average SSIM of 0.9891. Gamma index evaluation demonstrated a high agreement (94.7% and 95.7% for 1%/3 mm and 1%/5 mm) between the predicted and the ground truth dose maps. Notably, the processing time was reduced to 6 s, demonstrating its feasibility for online 3D dose verification for prostate proton therapy.Significance. Our study achieved start-of-the-art performance in the challenging task of direct reconstruction from radiofrequency signals, demonstrating the great promise of PA imaging as a highly efficient and accurate tool forinvivo3D proton dose verification to minimize the range uncertainties of proton therapy to improve its precision and outcomes.

3Din vivodose verification in prostate proton therapy with deep learning-based proton-acoustic imaging

Dose delivery uncertainty is a major concern in proton therapy, adversely affecting the treatment precision and outcome. Recently, a promising technique, proton-acoustic (PA) imaging, has been developed to provide real-timein vivo3D dose verification. However, its dosimetry accuracy is limited due to the limited-angle view of the ultrasound transducer. In this study, we developed a deep learning-based method to address the limited-view issue in the PA reconstruction. A deep cascaded convolutional neural network (DC-CNN) was proposed to reconstruct 3D high-quality radiation-induced pressures using PA signals detected by a matrix array, and then derive precise 3D dosimetry from pressures for dose verification in proton therapy. To validate its performance, we collected 81 prostate cancer patients' proton therapy treatment plans. Dose was calculated using the commercial software RayStation and was normalized to the maximum dose. The PA simulation was performed using the open-source k-wave package. A matrix ultrasound array with 64 × 64 sensors and 500 kHz central frequency was simulated near the perineum to acquire radiofrequency (RF) signals during dose delivery. For realistic acoustic simulations, tissue heterogeneity and attenuation were considered, and Gaussian white noise was added to the acquired RF signals. The proposed DC-CNN was trained on 204 samples from 69 patients and tested on 26 samples from 12 other patients. Predicted 3D pressures and dose maps were compared against the ground truth qualitatively and quantitatively using root-mean-squared-error (RMSE), gamma-index (GI), and dice coefficient of isodose lines. Results demonstrated that the proposed method considerably improved the limited-view PA image quality, reconstructing pressures with clear and accurate structures and deriving doses with a high agreement with the ground truth. Quantitatively, the pressure accuracy achieved an RMSE of 0.061, and the dose accuracy achieved an RMSE of 0.044, GI (3%/3 mm) of 93.71%, and 90%-isodose line dice of 0.922. The proposed method demonstrates the feasibility of achieving high-quality quantitative 3D dosimetry in PA imaging using a matrix array, which potentially enables the online 3D dose verification for prostate proton therapy.

Quantitative assessment of radionuclide production yields in in-beam and offline PET measurements at different proton irradiation facilities

Objective. Reliable radionuclide production yield data are a prerequisite for positron-emission-tomography (PET) based in vivo proton treatment verification. In this context, activation data acquired at two different treatment facilities with different imaging systems were analyzed to provide experimentally determined radionuclide yields in thick targets and were compared with each other to investigate the impact of the respective imaging technique. Approach. Homogeneous thick targets (PMMA, gelatine, and graphite) were irradiated with mono-energetic proton pencil-beams at two distinct energies. Material activation was measured (i) in-beam during and after beam delivery with a double-head prototype PET camera and (ii) offline shortly after beam delivery with a commercial full-ring PET/CT scanner. Integral as well as depth-resolved β +-emitter yields were determined for the dominant positron-emitting radionuclides 11C, 15O, 13N and (in-beam only) 10C. In-beam data were used to investigate the qualitative impact of different monitoring time schemes on activity depth profiles and their quantitative impact on count rates and total activity. Main results. Production yields measured with the in-beam camera were comparable to or higher compared to respective offline results. Depth profiles of radionuclide-specific yields obtained from the double-head camera showed qualitative differences to data acquired with the full-ring camera with a more convex profile shape. Considerable impact of the imaging timing scheme on the activity profile was observed for gelatine only with a range variation of up to 3.5 mm. Evaluation of the coincidence rate and the total number of observed events in the considered workflows confirmed a strongly decreasing rate in targets with a large oxygen fraction. Significance. The observed quantitative and qualitative differences between the datasets underline the importance of a thorough system commissioning. Due to the lack of reliable cross-section data, in-house phantom measurements are still considered a gold standard for careful characterization of the system response and to ensure a reliable beam range verification.

Technical Design Report for a Carbon-11 Treatment Facility

Particle therapy relies on the advantageous dose deposition which permits to highly conform the dose to the target and better spare the surrounding healthy tissues and organs at risk with respect to conventional radiotherapy. In the case of treatments with heavier ions (like carbon ions already clinically used), another advantage is the enhanced radiobiological effectiveness due to high linear energy transfer radiation. These particle therapy advantages are unfortunately not thoroughly exploited due to particle range uncertainties. The possibility to monitor the compliance between the ongoing and prescribed dose distribution is a crucial step toward new optimizations in treatment planning and adaptive therapy. The Positron Emission Tomography (PET) is an established quantitative 3D imaging technique for particle treatment verification and, among the isotopes used for PET imaging, the 11C has gained more attention from the scientific and clinical communities for its application as new radioactive projectile for particle therapy. This is an interesting option clinically because of an enhanced imaging potential, without dosimetry drawbacks; technically, because the stable isotope 12C is successfully already in use in clinics. The MEDICIS-Promed network led an initiative to study the possible technical solutions for the implementation of 11C radioisotopes in an accelerator-based particle therapy center. We present here the result of this study, consisting in a Technical Design Report for a 11C Treatment Facility. The clinical usefulness is reviewed based on existing experimental data, complemented by Monte Carlo simulations using the FLUKA code. The technical analysis starts from reviewing the layout and results of the facilities which produced 11C beams in the past, for testing purposes. It then focuses on the elaboration of the feasible upgrades of an existing 12C particle therapy center, to accommodate the production of 11C beams for therapy. The analysis covers the options to produce the 11C atoms in sufficient amounts (as required for therapy), to ionize them as required by the existing accelerator layouts, to accelerate and transport them to the irradiation rooms. The results of the analysis and the identified challenges define the possible implementation scenario and timeline.

Use of short-lived positron emitters for in-beam and real-time β+ range monitoring in proton therapy

AIM

The purpose of this work is to evaluate the precision with which the GEANT4 toolkit simulates the production of β⁺ emitters relevant for in-beam and real-time PET in proton therapy.

BACKGROUND

An important evolution in proton therapy is the implementation of in-beam and real-time verification of the range of protons by measuring the correlation between the activity of β⁺ and dose deposition. For that purpose, it is important that the simulation of the various β⁺ emitters be sufficiently realistic, in particular for the ¹²N short-lived emitter that is required for efficient in-beam and real-time monitoring.

METHODS

The GEANT4 toolkit was used to simulate positron emitter production for a proton beam of 55 MeV in a cubic PMMA target and results are compared to experimental data.

RESULTS

The three β⁺ emitters with the highest production rates in the experimental data (¹¹C, ¹⁵O and ¹²N) are also those with the highest production rate in the simulation. Production rates differ by 8% to 174%. For the ¹²N isotope, the β⁺ spatial distribution in the simulation shows major deviations from the data. The effect of the long range (of the order of 20 mm) of the β⁺ originating from ¹²N is also shown and discussed.

CONCLUSIONS

At first order, the GEANT4 simulation of the β⁺ activity presents significant deviations from the data. The need for precise cross-section measurements versus energy below 30 MeV is of first priority in order to evaluate the feasibility of in-beam and real-time PET.

Offline imaging of positron emitters induced by therapeutic helium, carbon and oxygen ion beams with a full-ring PET/CT scanner: experiments in reference targets

In vivo verification of light ion therapy based on positron-emission tomography (PET) imaging of irradiation induced patient activation relies on activity predictions from Monte-Carlo (MC) or analytical computational engines for comparison to the measurements. In order to achieve the necessary accuracy, experimental data are indispensable for the validation of the calculation models. For this we irradiated thick reference targets with mono-energetic helium, carbon and oxygen ion beams and measured the resulting material activation offline with a commercial full-ring PET/CT scanner located nearby the treatment room. Acquired PET data were analysed over time to separate the activity contribution of different radionuclides. Determined production yields were compared to published findings obtained from in-beam activation measurements with a limited-angle double-head PET camera. In addition, we investigated the time-dependence of the measured radionuclide-specific contributions and of the distal activity range, as well as the lateral spread of the activity signal as a function of beam penetration depth. We present radionuclide-specific depth-resolved activity distributions and production yields for the radionuclides [Formula: see text], [Formula: see text] and [Formula: see text], dominating irradiation-induced patient activation. We observe systematically lower production yields with a ratio between the dual-head and our full-ring PET measurements of, on average, 1.7 and 1.3 for the oxygen and carbon beam irradiations, and 1.7 (2.1) for the high (low) energy helium beam irradiations. Findings on the temporal development of the activity range confirm the expectation, with the oxygen beam induced signal being the most sensitive scenario. The experimental data reported in this work, acquired with a state-of-the-art full ring PET scanner, provide a comprehensive and consistent basis for the benchmarking of PET signal calculation engines. In particular, they can support a fine-tuning of the underlying physics models used by the respective implementation and therefore improve the accuracy of PET-based therapy verifications at current and future treatment facilities.

Simulation of positron emitters for monitoring of dose distribution in proton therapy

AIM

The purpose of this work was to estimate the dependency between the produced positron emitters and the proton dose distribution as well as the dependency between points of annihilation and the proton dose distribution.

BACKGROUND

One important feature of proton therapy is that, through the non-elastic nuclear interaction of protons with the target nuclei such as ¹²C, ¹⁴N and ¹⁶O, it produces a small number of positron-emitting radioisotopes along the beam-path. These radioisotopes allow imaging the Bragg peak position which is related to the proton dose distribution by using positron emission tomography.

METHODS

In this study, the GEANT4 toolkit was applied to simulate a soft and bone tissue phantom in proton therapy to evaluate the positron emitter productions and the actual annihilation points of β⁺. Simulation was done by delivering pencil and spread-out Bragg peak (SOBP) proton beams.

RESULTS

The findings showed that (¹⁵O, ¹¹C, ¹³N) and (¹¹C, ¹⁵O, ³⁸K, ³⁰P, ³⁹Ca, ¹³N) are the most suitable positron emitters in the soft and bone tissue respectively. By increasing the proton energy, the distance between the peak of annihilation profile and Bragg peak is almost constant, but the distance between the Bragg peak position and positron annihilation point peak in bone tissue is smaller than that in the soft tissue. The peak of β⁺ activity distribution becomes sharper at higher proton energies.

CONCLUSIONS

There is a good relationship between the positions of positron annihilation profile and positron emitters radioactive decay. Also, GEANT4 is a powerful and suitable tool for simulation of nuclear interactions and positron emitters in tissues.

Solution Radioactivated by Hadron Radiation Can Increase Sister Chromatid Exchanges

When energetic particles irradiate matter, it becomes activated by nuclear reactions. Radioactivation induced cellular effects are not clearly understood, but it could be a part of bystander effects. This investigation is aimed at understanding the biological effects from radioactivation in solution induced by hadron radiation. Water or phosphate buffered saline was activated by being exposed to hadron radiation including protons, carbon- and iron-ions. 1 mL of radioactivated solution was transferred to flasks with Chinese hamster ovary (CHO) cells cultured in 5 mL of complete media. The induction of sister chromatid exchanges (SCE) was used to observe any increase in DNA damage responses. The energy spectrum and the half-lives of the radioactivation were analyzed by NaI scintillation detector in order to identify generated radionuclides. In the radioactivated solution, 511 keV gamma-rays were observed, and their half-lives were approximately 2 min, 10 min, and 20 min. They respectively correspond to the beta+ decay of 15O, 13N, and 11C. The SCE frequencies in CHO cells increased depending on the amount of radioactivation in the solution. These were suppressed with a 2-hour delayed solution transfer or pretreatment with dimethyl sulfoxide (DMSO). Our results suggest that the SCE induction by radioactivated solution was mediated by free radicals produced by the annihilated gamma-rays. Since the SCE induction and DMSO modulation are also reported in radiation-induced bystander effects, our results imply that radioactivation of the solution may have some contribution to the bystander effects from hadron radiation. Further investigations are required to assess if radioactivation effects would attribute an additional level of cancer risk of the hadron radiation therapy itself.

Short-lived positron emitters in beam-on PET imaging during proton therapy

The only method for in vivo dose delivery verification in proton beam radiotherapy in clinical use today is positron emission tomography (PET) of the positron emitters produced in the patient during irradiation. PET imaging while the beam is on (so called beam-on PET) is an attractive option, providing the largest number of counts, the least biological washout and the fastest feedback. In this implementation, all nuclides, independent of their half-life, will contribute. As a first step towards assessing the relevance of short-lived nuclides (half-life shorter than that of (10)C, T1/2  =  19 s) for in vivo dose delivery verification using beam-on PET, we measured their production in the stopping of 55 MeV protons in water, carbon, phosphorus and calcium The most copiously produced short-lived nuclides and their production rates relative to the relevant long-lived nuclides are: (12)N (T1/2  =  11 ms) on carbon (9% of (11)C), (29)P (T1/2  =  4.1 s) on phosphorus (20% of (30)P) and (38m)K (T1/2  =  0.92 s) on calcium (113% of (38g)K). No short-lived nuclides are produced on oxygen. The number of decays integrated from the start of an irradiation as a function of time during the irradiation of PMMA and 4 tissue materials has been determined. For (carbon-rich) adipose tissue, (12)N dominates up to 70 s. On bone tissue, (12)N dominates over (15)O during the first 8-15 s (depending on carbon-to-oxygen ratio). The short-lived nuclides created on phosphorus and calcium provide 2.5 times more beam-on PET counts than the long-lived ones produced on these elements during a 70 s irradiation. From the estimated number of (12)N PET counts, we conclude that, for any tissue, (12)N PET imaging potentially provides equal to superior proton range information compared to prompt gamma imaging with an optimized knife-edge slit camera. The practical implementation of (12)N PET imaging is discussed.

Mapping (15)O production rate for proton therapy verification

PURPOSE

This work was a proof-of-principle study for the evaluation of oxygen-15 ((15)O) production as an imaging target through the use of positron emission tomography (PET), to improve verification of proton treatment plans and to study the effects of perfusion.

METHODS AND MATERIALS

Dynamic PET measurements of irradiation-produced isotopes were made for a phantom and rabbit thigh muscles. The rabbit muscle was irradiated and imaged under both live and dead conditions. A differential equation was fitted to phantom and in vivo data, yielding estimates of (15)O production and clearance rates, which were compared to live versus dead rates for the rabbit and to Monte Carlo predictions.

RESULTS

PET clearance rates agreed with decay constants of the dominant radionuclide species in 3 different phantom materials. In 2 oxygen-rich materials, the ratio of (15)O production rates agreed with the expected ratio. In the dead rabbit thighs, the dynamic PET concentration histories were accurately described using (15)O decay constant, whereas the live thigh activity decayed faster. Most importantly, the (15)O production rates agreed within 2% (P>.5) between conditions.

CONCLUSIONS

We developed a new method for quantitative measurement of (15)O production and clearance rates in the period immediately following proton therapy. Measurements in the phantom and rabbits were well described in terms of (15)O production and clearance rates, plus a correction for other isotopes. These proof-of-principle results support the feasibility of detailed verification of proton therapy treatment delivery. In addition, (15)O clearance rates may be useful in monitoring permeability changes due to therapy.

Application of activity pencil beam algorithm using measured distribution data of positron emitter nuclei for therapeutic SOBP proton beam

PURPOSE

Recently, much research on imaging the clinical proton-irradiated volume using positron emitter nuclei based on target nuclear fragment reaction has been carried out. The purpose of this study is to develop an activity pencil beam (APB) algorithm for a simulation system for proton-activated positron-emitting imaging in clinical proton therapy using spread-out Bragg peak (SOBP) beams.

METHODS

The target nuclei of activity distribution calculations are (12)C nuclei, (16)O nuclei, and (40)Ca nuclei, which are the main elements in a human body. Depth activity distributions with SOBP beam irradiations were obtained from the material information of ridge filter (RF) and depth activity distributions of compounds of the three target nuclei measured by BOLPs-RGp (beam ON-LINE PET system mounted on a rotating gantry port) with mono-energetic Bragg peak (MONO) beam irradiations. The calculated data of depth activity distributions with SOBP beam irradiations were sorted in terms of kind of nucleus, energy of proton beam, SOBP width, and thickness of fine degrader (FD), which were verified. The calculated depth activity distributions with SOBP beam irradiations were compared with the measured ones. APB kernels were made from the calculated depth activity distributions with SOBP beam irradiations to construct a simulation system using the APB algorithm for SOBP beams.

RESULTS

The depth activity distributions were prepared using the material information of RF and the measured depth activity distributions with MONO beam irradiations for clinical therapy using SOBP beams. With the SOBP width widening, the distal fall-offs of depth activity distributions and the difference from the depth dose distributions were large. The shapes of the calculated depth activity distributions nearly agreed with those of the measured ones upon comparison between the two. The APB kernels of SOBP beams were prepared by making use of the data on depth activity distributions with SOBP beam irradiations that were made from the depth activity distributions with MONO beam irradiations and sorted in terms of energy, SOBP width, and thickness of FD. The data on APB kernels of SOBP beams were determined as installment data for the simulation system using the APB algorithm for SOBP beam irradiations.

CONCLUSIONS

A method of obtaining the depth activity distributions and the APB algorithm for clinical use of SOBP beams have been developed. It is suggested that the simulation system for imaging the clinical irradiated volume with the APB algorithm can be used in clinical proton therapy using SOBP beams by preparing and investigating the data on APB kernels of SOBP beams.

Proton therapy verification with PET imaging

Proton therapy is very sensitive to uncertainties introduced during treatment planning and dose delivery. PET imaging of proton induced positron emitter distributions is the only practical approach for in vivo, in situ verification of proton therapy. This article reviews the current status of proton therapy verification with PET imaging. The different data detecting systems (in-beam, in-room and off-line PET), calculation methods for the prediction of proton induced PET activity distributions, and approaches for data evaluation are discussed.

In vivo proton range verification: a review

Protons are an interesting modality for radiotherapy because of their well defined range and favourable depth dose characteristics. On the other hand, these same characteristics lead to added uncertainties in their delivery. This is particularly the case at the distal end of proton dose distributions, where the dose gradient can be extremely steep. In practice however, this gradient is rarely used to spare critical normal tissues due to such worries about its exact position in the patient. Reasons for this uncertainty are inaccuracies and non-uniqueness of the calibration from CT Hounsfield units to proton stopping powers, imaging artefacts (e.g. due to metal implants) and anatomical changes of the patient during treatment. In order to improve the precision of proton therapy therefore, it would be extremely desirable to verify proton range in vivo, either prior to, during, or after therapy. In this review, we describe and compare state-of-the art in vivo proton range verification methods currently being proposed, developed or clinically implemented.

Development of activity pencil beam algorithm using measured distribution data of positron emitter nuclei generated by proton irradiation of targets containing (12)C, (16)O, and (40)Ca nuclei in preparation of clinical application

PURPOSE

The purpose of this study is to develop a new calculation algorithm that is satisfactory in terms of the requirements for both accuracy and calculation time for a simulation of imaging of the proton-irradiated volume in a patient body in clinical proton therapy.

METHODS

The activity pencil beam algorithm (APB algorithm), which is a new technique to apply the pencil beam algorithm generally used for proton dose calculations in proton therapy to the calculation of activity distributions, was developed as a calculation algorithm of the activity distributions formed by positron emitter nuclei generated from target nuclear fragment reactions. In the APB algorithm, activity distributions are calculated using an activity pencil beam kernel. In addition, the activity pencil beam kernel is constructed using measured activity distributions in the depth direction and calculations in the lateral direction. (12)C, (16)O, and (40)Ca nuclei were determined as the major target nuclei that constitute a human body that are of relevance for calculation of activity distributions. In this study, "virtual positron emitter nuclei" was defined as the integral yield of various positron emitter nuclei generated from each target nucleus by target nuclear fragment reactions with irradiated proton beam. Compounds, namely, polyethylene, water (including some gelatin) and calcium oxide, which contain plenty of the target nuclei, were irradiated using a proton beam. In addition, depth activity distributions of virtual positron emitter nuclei generated in each compound from target nuclear fragment reactions were measured using a beam ON-LINE PET system mounted a rotating gantry port (BOLPs-RGp). The measured activity distributions depend on depth or, in other words, energy. The irradiated proton beam energies were 138, 179, and 223 MeV, and measurement time was about 5 h until the measured activity reached the background level. Furthermore, the activity pencil beam data were made using the activity pencil beam kernel, which was composed of the measured depth data and the lateral data including multiple Coulomb scattering approximated by the Gaussian function, and were used for calculating activity distributions.

RESULTS

The data of measured depth activity distributions for every target nucleus by proton beam energy were obtained using BOLPs-RGp. The form of the depth activity distribution was verified, and the data were made in consideration of the time-dependent change of the form. Time dependence of an activity distribution form could be represented by two half-lives. Gaussian form of the lateral distribution of the activity pencil beam kernel was decided by the effect of multiple Coulomb scattering. Thus, the data of activity pencil beam involving time dependence could be obtained in this study.

CONCLUSIONS

The simulation of imaging of the proton-irradiated volume in a patient body using target nuclear fragment reactions was feasible with the developed APB algorithm taking time dependence into account. With the use of the APB algorithm, it was suggested that a system of simulation of activity distributions that has levels of both accuracy and calculation time appropriate for clinical use can be constructed.