David Jette

Integrating a MRI scanner with a 6 MV radiotherapy accelerator: dose deposition in a transverse magnetic field

Integrating magnetic resonance imaging (MRI) functionality with a radiotherapy accelerator can facilitate on-line, soft-tissue based, position verification. A technical feasibility study, in collaboration with Elekta Oncology Systems and Philips Medical Systems, led to the preliminary design specifications of a MRI accelerator. Basically the design is a 6 MV accelerator rotating around a 1.5 T MRI system. Several technical issues and the clinical rational are currently under investigation. The aim of this paper is to determine the impact of the transverse 1.5 T magnetic field on the dose deposition. Monte Carlo simulations were used to calculate the dose deposition kernel in the presence of 1.5 T. This kernel in turn was used to determine the dose deposition for larger fields. Also simulations and measurements were done in the presence of 1.1 T. The pencil beam dose deposition is asymmetric. For larger fields the asymmetry persists but decreases. For the latter the distance to dose maximum is reduced by approximately 5 mm, the penumbra is increased by approximately 1 mm, and the 50% isodose line is shifted approximately 1 mm. The dose deposition in the presence of 1.5 T is affected, but the effect can be taken into account in a conventional treatment planning procedure. The impact of the altered dose deposition for clinical IMRT treatments is the topic of further research.

Electron dose calculation using multiple‐scattering theory. A. Gaussian multiple‐scattering theory

This article is the first in a series on the calculation of electron dose using multiple-scattering theory. In it we develop a unified theory, which we term Gaussian multiple-scattering theory, starting from a number of contributions already in the literature: the Fermi-Eyges multiple-scattering theory, the Yang path length distribution, the second-order multiple-scattering theory of Jette [Med. Phys. 12, 178 (1985)], and the diffusion theory of Bethe et al. [Proc. Am. Philos. Soc. 78, 573 (1938)]. After examining in detail the ramifications and limitations of Gaussian multiple-scattering theory, we derive basic formulas generalizing the Fermi-Eyges theory, for use in subsequent articles. We also find explicit, accurate expressions for incorporating the scattering power into the theory.

Electron dose calculation using multiple‐scattering theory: A new theory of multiple scattering

Starting from the Boltzmann-Fokker-Planck transport equation, we have developed a new theory of multiple scattering which incorporates the advances already made with our Gaussian multiple-scattering theory for electron dose calculation. This incorporation has been accomplished in a natural way, by modifying the scattering power T and by adding a convolution term to the distribution-function equation of the Gaussian theory. Our previous results concerning increasing the accuracy of the small-angle approximation used and dealing with localized tissue inhomogeneities have thus been maintained, and we have arrived at a complete distribution function in both transverse spatial and angular variables. When integrated over the transverse angular variables, for a first-order small-angle approximation this distribution function for a pencil beam is essentially the same as the Moliere multiple-scattering distribution, which includes large-angle single scattering. For a water phantom, we have used comparisons with EGS4 Monte Carlo calculations to demonstrate the greatly increased accuracy of our new multiple-scattering theory over the Gaussian theory, which includes the usual Fermi-Eyges theory. We have also presented a fairly accurate Gaussian approximation to the pencil-beam dose profiles given by our new theory, which can be used in order to maintain the mathematical simplicity of the predictions of the Fermi-Eyges theory.

The application of multiple scattering theory to therapeutic electron dosimetry.

Fermi–Eyges multiple scatteringtheory for electrons is explained, and a general three‐dimensional formalism is developed for its application to problems of therapeutic electron dosimetry. The formalism is illustrated by a number of elementary examples: a rectangular beam, an isotropic point source, and a scanning line source.

Electron dose calculation using multiple-scattering theory: second-order multiple-scattering theory

This article is part of a series on the calculation of electron dose using multiple-scattering theory. It presents systematically the second-order multiple-scattering theory which is a generalization of the (first-order) Fermi-Eyges theory, outlining its derivation and giving explicit formulas for its defining functions. The predictions of the Fermi-Eyges theory and of the second-order theory are compared with modified Monte Carlo calculations, demonstrating the increased accuracy of the latter multiple-scattering theory. We derive and compare broad-beam angular distributions for the two theories, and note the effect of large-angle scattering upon dose profiles. Finally, we present the second-order theory in Fourier-transformed space, which is appropriate to a high-speed dose-calculation algorithm using the fast Fourier transform (FFT) technique.

Magnetic fields with photon beams: Monte Carlo calculations for a model magnetic field.

Strong transverse magnetic fields can produce very large dose enhancements and reductions in localized regions of a patient under irradiation by a photon beam. We have suggested a model magnetic field which can be expected to produce such large dose enhancements and reductions, and we have carried out EGS4 Monte Carlo calculations to examine this effect for a 6x6 cm2 photon beam of energy 15, 30, or 45 MV penetrating a water phantom. Our model magnetic field has a nominal (center) strength B0 ranging between 1 and 5 T, and a maximum strength within the geometric beam which is 2.2xB0. For all three beam energies, there is significant dose enhancement for B0 = 2 T which increases greatly for B0 = 3 T, but stronger magnetic fields increase the enhancement further only for the 45-MV beam. Correspondingly, there is major reduction in the dose just distal to this region of large dose enhancement, resulting from secondary electrons and positrons originating upstream which are depositing energy in the dose-enhancement region rather than continuing further into the patient. The dose peak region is fairly narrow (in depth), but the magnetic field can be shifted along the longitudinal axis to produce a flat peak region of medium width (approximately 2 cm) or of large width (approximately 4 cm), with rapid dose dropoffs on either side. For the 30-MV beam with B0 = 3 T, we found a dose enhancement of 55% for the narrow-width configuration, 32% for the medium-width configuration, and 23% for the large-width configuration; for the 45-MV beam with B0 = 3 T, the enhancements were quite similar, but for the 15-MV beam they were considerably less. For all of these 30-MV configurations, the dose reductions were approximately 30%, and they were approximately 40% for the 45-MV configurations.

On the possibility of determining an effective energy spectrum of clinical electron beams from percentage depth dose (PDD) data of broad beams

Experiments have already shown that obvious differences exist between the dose distribution of electron beams of a clinical accelerator in a water phantom and the dose distribution of monoenergetic electrons of nominal energy of the clinical accelerator in water, because the electron beams which reach the water surface travelling through the collimation system of the accelerator are no longer monoenergetic. It is evident that, while calculating precisely the dose distribution of any incident electron beams, the energy spectrum of the incident electron beam must be taken into consideration. In this note we shall present a method for determining an effective energy spectrum of clinical electron beams from PDD data (percentage depth dose data). It is well known that there is an integral equation of the first kind which links the energy spectrum of an incident electron beam with PDD through the dose distribution of monoenergetic electrons in the medium, as a kernel function in the integral equation. In this note, the integral equation of the first kind will be solved by using the regularization method. The bipartition model of electron transport will be used to calculate the kernel function, namely the energy deposition due to monoenergetic electron beams in the medium.

Electron dose calculation using multiple-scattering theory : localized inhomogeneities : a new theory

In this fourth article in a series on the calculation of electron dose using multiple-scattering theory, we deal with localized inhomogeneities by solving the Fermi equation for scattering power which is an arbitrary function of position. In fact, we go further, by solving the second-order multiple-scattering equation which supersedes the (first-order) Fermi equation, again for scattering power which is an arbitrary function of position. Thus, we are no longer restricted to a horizontally layered medium, as is the case with the Fermi-Eyges theory. Our general solution is in the form of a perturbation series which evidently converges rapidly enough that only its first two or three terms need be taken for accurate dose calculation. Regarding the energy directly deposited by the primary electrons, the formulas developed in this article give very good agreement with Monte Carlo calculations for the thick half-slab configuration, as will be seen in the next article in this series. Moreover, our first-rank, second-order formulas, when expressed in Fourier-transformed space, are simple enough to be implemented in a treatment planning system providing full three-dimensional electron dose calculation for arbitrary configurations of inhomogeneities.

Magnetic fields with photon beams: use of circular current loops.

Strong transverse magnetic fields can produce very large dose enhancements and reductions in localized regions of a patient under irradiation by a photon beam. Through EGS4 Monte Carlo simulations, we have examined the effects of applying a magnetic field produced by a pair of circular current loops to a photon beam penetrating a water phantom of finite thickness. We have indeed found very substantial localized dose enhancements, albeit with no corresponding dose reduction just distal to the region of dose enhancement. (However, dose reduction does occur near the distal end of the phantom.) We have also observed two phenomena to be concerned with, for this configuration: significant broadening of the penumbra close to the current loop, and narrowness of the enhanced dose region in a plane parallel to the planes of the loops. We have also examined the use of a single current loop to produce the magnetic field, and have found great asymmetry in the dose distribution; this asymmetry appears to make it impossible to treat with a single circular magnet a tumor of large dimension extending below the application surface.

Electron dose calculation using multiple‐scattering theory: Energy distribution due to multiple scattering

In 1951, Yang derived formulas for computing the pathlength distribution of particles traversing foils, considering only the multiple-scattering process. We here improve upon the accuracy of that work, by using our second-order small-angle approximation. We derive the general solution for a broad parallel beam, and find simple formulas for Yangs two special cases: the pathlength distribution of all the particles at a particular point, taken together; and the pathlength distribution at a particular point of only those particles with zero net angular deflection. From the pathlength (or excess pathlength) distribution, residual range and energy distributions can immediately be deduced. All this work assumes relatively small energy loss, and we consider 5 MeV electrons penetrating lead, which provides considerable scattering without major energy loss. The second-order energy distribution is found to differ considerably from the (first-order) Yang energy distribution, and to agree more closely with EGS4 Monte Carlo calculations.