Introduction of external magnetic fields in entropic moment modelling for radiotherapy.

One of the big challenges of the emerging MRI-guided radiotherapy is the prediction of an external magnetic field effect on the deposited dose induced by a beam of charged particles. In this paper, we present the results of the implementation of the Lorentz force in the deterministic M1 model. The validation of our code is performed by comparisons with the Monte-Carlo code FLUKA. The relevant examples show a significant modification of the shape of dose deposition volume induced by the external magnetic field in presence of heterogeneities. A gamma-index analysis 3%/3mm shows a good agreement of our model with FLUKA simulations.

Deterministic model for the transport of energetic particles: Application in the electron radiotherapy.

A new deterministic method for calculating the dose distribution in the electron radiotherapy field is presented. The aim of this work was to validate our model by comparing it with the Monte Carlo simulation toolkit, GEANT4. A comparison of the longitudinal and transverse dose deposition profiles and electron distributions in homogeneous water phantoms showed a good accuracy of our model for electron transport, while reducing the calculation time by a factor of 50. Although the Bremsstrahlung effect is not yet implemented in our model, we propose here a method that solves the Boltzmann kinetic equation and provides a viable and efficient alternative to the expensive Monte Carlo modeling.

A deterministic partial differential equation model for dose calculation in electron radiotherapy.

High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g.Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung, Compton scattering and the production of delta electrons are added to our model, the computation time will only slightly increase. Its margin of error, on the other hand, will decrease and should be within a few per cent of the actual dose. Therefore, the new model has the potential to become useful for dose calculations in clinical practice.

Comparative view of the socioeconomic impact of migraine versus low back pain.

The burden of migraine in terms of cost and impact on socioeconomic indicators is still controversial. In a recent comparative study between migraineurs and controls from the French general population, we show that only general practitioner (GP) consultations and complementary examinations are more frequent in migraineurs. In this paper, we compare the socioeconomic impact of migraine versus another common neurological disease, low back pain, which has similar consequences in term of deficiencies, disabilities, and handicaps. Our study is a subproject of the Gazel cohort study, conducted on 20,000 volunteers working in the "Electricité et Gaz de France" company. The socioeconomic impact was evaluated prospectively by the number of workdays missed between 1989 and 1992 in 436 subjects with migraine but without low back pain (M group), 590 subjects with low back pain but without migraine (L group), 555 subjects with migraine and low back pain (ML group), and in 1005 subjects without headache or low back pain (C group). Moreover, in 1993 all subjects completed a mailed questionnaire on their 6-months' history of use of medical services. The number of workdays missed during this 4-year period was statistically greater in the ML group (58.1 days), followed by the L group (38.4 days), the C group (35.1 days), and the M group (31.8 days) (p = 0.0001). For the use of medical services, the results were different according to the different indicators: GP consultations were more frequent in the ML and M groups, specialist consultations and complementary examinations in the L and C groups. In conclusion, migraine and low back pain seem to have a similar socioeconomic impact. Absenteeism is particularly high when both neurological disorders are present.