Hiroyuki Date

A Mathematical Study to Select Fractionation Regimen Based on Physical Dose Distribution and the Linear–Quadratic Model

PURPOSE Hypofractionated irradiation is often used in precise radiotherapy instead of conventional multifractionated irradiation. We propose a novel mathematical method for selecting a hypofractionated or multifractionated irradiation regimen based on physical dose distribution adding to biologic consideration. METHODS AND MATERIALS The linear-quadratic model was used for the radiation effects on tumor and normal tissues, especially organs at risk (OARs). On the basis of the assumption that the OAR receives a fraction of the dose intended for the tumor, the minimization problem for the damage effect on the OAR was treated under the constraint that the radiation effect on the tumor is fixed. RESULTS For an N-time fractionated irradiation regimen, the constraint of tumor lethality was described by an N-dimensional hypersphere. The total dose of the fractionated irradiations was considered for minimizing the damage effect on the OAR under the hypersphere condition. It was found that the advantage of hypofractionated or multifractionated irradiation therapies depends on the magnitude of the ratio of α/β parameters for the OAR and tumor in the linear-quadratic model and the ratio of the dose for the OAR and tumor. CONCLUSIONS Our mathematical method shows that multifractionated irradiation with a constant dose is better if the ratio of α/β for the OAR and tumor is less than the ratio of the dose for the OAR and tumor, whereas hypofractionated irradiation is better otherwise.

The drift velocity and longitudinal diffusion coefficient of electrons in nitrogen and carbon dioxide from 20 to 1000 Td

The distribution of arrival time spectra (ATS) of electrons in nitrogen and carbon dioxide has been measured over the range of E/N from 20 to 1000 Td (1 ) at room temperature by a double-shutter drift tube. The drift velocity of electrons in and was evaluated from these distributions by the ATS method. Moreover, the ratio of the longitudinal diffusion coefficient to the electron mobility was measured. The values of and in and were in good agreement with experimental and theoretical values obtained by previous investigators except for a few of the earlier studies.

Electron swarm parameters in water vapour

Electron swarm parameters, such as the drift velocity and the ionization coefficient, in water vapour have been measured for relatively wide ranges in reduced electric fields (E/N) at room temperature. The drift velocity (Wm) was obtained based upon the arrival-time spectra of electrons by using a double-shutter drift tube for the E/N from 60 to 1000 Td, while the first and second ionization coefficients (α and γ) were determined by the steady-state Townsend method from 50 to 3000 Td. A comparison between the results and other data in the literature shows that our results for both the drift velocity and the effective ionization coefficient are lower than those of the other data in the above ranges.

A multi-term Boltzmann equation analysis of electron swarms in gases-the time-of-flight parameters

An accurate and efficient method for solving the Boltzmann equation is presented. Using a multi-term expansion technique, the time-of-flight (TOF) electron swarm parameters (such as the centre-of-mass drift velocity Wr, the longitudinal DL and transverse DT diffusion coefficients) can be evaluated. The method utilizes an amalgamation of the conventional two-term expansion and the Galerkin method. The first two terms of the Legendre polynomial expansion of the electron energy distribution are obtained by the two-term method, while the third-order and higher-order terms are deduced by the Galerkin method. The present technique is applied to determine the electron energy distribution using Fourier components to solve the Boltzmann equation and TOF swarm parameters in methane gas. Good agreement with Monte Carlo simulation is obtained and the method is also applied to a previously described model gas.

Model for a large area multi‐frequency multiplanar coil inductively coupled plasma source

A model for a large area multifrequency multiplanar coil inductively coupled plasma (ICP) source is presented. Typical ICP sources employ a single coil that is engineered to provide optimum plasma uniformity for large area processing. Pulsed sources have also been developed to improve etch selectivity via increased radical generation and lower net ion densities. The source described here potentially achieves a combined pulsed mode and the capability of moving the plasma source from inner to outer radii in a controlled fashion (raster mode) for very large area applications. The model consists of a coupled steady‐state two‐dimensional ambipolar diffusion model, an electromagnetics model, and a lumped parameter circuit model. While stable operation is possible, the model shows that the scheme is found to be very sensitive to coil‐to‐coil coupling and to the ordering of the phases and frequencies of the coils. Examples of stable operation of a three coil set device are presented. Results suggest that frequenc...

Quantitative estimation of DNA damage by photon irradiation based on the microdosimetric-kinetic model

The microdosimetric-kinetic (MK) model is one of the models that can describe the fraction of cells surviving after exposure to ionizing radiation. In the MK model, there are specific parameters, k and yD, where k is an inherent parameter to represent the number of potentially lethal lesions (PLLs) and yD indicates the dose-mean lineal energy in keV/μm. Assuming the PLLs to be DNA double-strand breaks (DSBs), the rate equations are derived for evaluating the DSB number in the cell nucleus. In this study, we estimated the ratio of DSBs for two types of photon irradiation (6 MV and 200 kVp X-rays) in Chinese hamster ovary (CHO-K1) cells and human non-small cell lung cancer (H1299) cells by observing the surviving fraction. The estimated ratio was then compared with the ratio of γ-H2AX foci using immunofluorescent staining. For making a comparison of the number of DSBs among a variety of radiation energy cases, we next utilized the survival data in the literature for both cells exposed to other photon types, such as 60Co γ-rays, 137Cs γ-rays and 100 kVp X-rays. The ratio of DSBs based on the MK model with conventional data was consistent with the ratio of γ-H2AX foci numbers, confirming that the γ-H2AX focus is indicative of DSBs. It was also shown that the larger yD is, the larger the DSB number is. These results suggest that k and yD represent the characteristics of the surviving fraction and the biological effects for photon irradiation.

Investigation of the change in marker geometry during respiration motion: a preliminary study for dynamic-multi-leaf real-time tumor tracking

BackgroundThe use of stereotactic body radiotherapy (SBRT) is rapidly increasing. Presently, the most accurate method uses fiducial markers implanted near the tumor. A shortcoming of this method is that the beams turn off during the majority of the respiratory cycle, resulting in a prolonged treatment time. Recent advances in collimation technology have enabled continuous irradiation to a moving tumor. However, the lung is a dynamic organ characterized by inhalation exhalation cycles, during which marker/tumor geometry may change (i.e., misalignment), resulting in under-dosing to the tumor.FindingsEight patients with lung cancer who were candidates for stereotactic radiotherapy were examined with 4D high-resolution CT. As a marker surrogate, virtual bronchoscopy using the pulmonary artery (VBPA) was conducted. To detect possible marker/tumor misalignment during the respiration cycle, the distance between the peripheral bronchus, where a marker could be implanted, and the center of gravity of a tumor were calculated for each respiratory phase. When the respiration cycle was divided into 10 phases, the median value was significantly larger for the 30%-70% respiratory phases compared to that for the 10% respiratory phase (P<0.05, Mann–Whitney U-test).ConclusionsThese results demonstrate that physiological aspect must be considered when continuous tumor tracking is applied to a moving tumor. To minimize an “additional” internal target volume (ITV) margin, a marker should be placed approximately 2.5 cm from the tumor.

Electron collision processes in gaseous xenon

Abstract In this study, we investigate electron transport properties in xenon gas by using a Monte Carlo technique for electrons with energies below 10 keV. First, we construct a set of electron collision cross sections with xenon by looking up cross section data taken from several publications. Secondly, the W value and the Fano factor for electrons in gaseous xenon are computed by Monte Carlo simulation on the assumption that electrons undergo single collision events including elastic, excitation and ionization processes. Finally, we obtain the production rate of excited atoms, which may contribute to an estimation of scintillation efficiency. Accuracy of the calculation from a viewpoint of the collision cross sections is also discussed.

A Simulation Study of the Radiation-Induced Bystander Effect : Modeling with Stochastically Defined Signal Reemission

The radiation-induced bystander effect (RIBE) has been experimentally observed for different types of radiation, cell types, and cell culture conditions. However, the behavior of signal transmission between unirradiated and irradiated cells is not well known. In this study, we have developed a new model for RIBE based on the diffusion of soluble factors in cell cultures using a Monte Carlo technique. The model involves the signal emission probability from bystander cells following Poisson statistics. Simulations with this model show that the spatial configuration of the bystander cells agrees well with that of corresponding experiments, where the optimal emission probability is estimated through a large number of simulation runs. It was suggested that the most likely probability falls within 0.63–0.92 for mean number of the emission signals ranging from 1.0 to 2.5.

SPATIAL CHARACTERISTICS OF ELECTRON SWARM PARAMETERS IN GASES

The results of a Monte Carlo simulation study focusing on the spatial characteristics of swarm parameters in an isolated electron swarm and the distribution of the electron density and flux taking into account the anode boundary are presented. The spatial variation of the swarm parameters is interpreted using conventional swarm theory, and potential problems with the measurement of arrival-time spectra of electrons are considered.