Deep heating of pelvic tumours with electromagnetic phased arrays has recently been reported to improve local tumour control when combined with radiotherapy in a randomized clinical trial despite the fact that rather modest elevations in tumour temperatures were achieved. It is reasonable to surmise that improvements in temperature elevation could lead to even better tumour response rates, motivating studies which attempt to explore the parameter space associated with heating rate delivery in the pelvis. Computational models which are based on detailed three-dimensional patient anatomy are readily available and lend themselves to this type of investigation. In this paper, volume average SAR is optimized in a predefined target volume subject to a maximum allowable volume average SAR outside this zone. Variables under study include the position of the target zone, the number and distribution of radiators and the applicator operating frequency. The results show a clear preference for increasing frequency beyond 100 MHz, which is typically applied clinically, especially as the number of antennae increases. Increasing both the number of antennae per circumferential distance around the patient, as well as the number of independently functioning antenna bands along the patient length, is important in this regard, although improvements were found to be more significant with increasing circumferential antenna density. However, there is considerable site specific variation and cases occur where lower numbers of antennae spread out over multiple longitudinal bands are more advantageous. The results presented here have been normalized relative to an optimized set of antenna array amplitudes and phases operating at 100 MHz which is a common clinical configuration. The intent is to provide some indications of avenues for improving the heating rate distributions achievable with current technology.
Weak forms are derived for Maxwell's equations which are suitable for implementation on conventional C O elements with scalar bases. The governing equations are %xpressed in terms of general vector and scalar potentials for E. Gauge theory is invoked to close the system and dictates the continuity requirements for the potentials at material interfaces as well as the blend of boundary conditions at exterior boundaries. Two specific gauges are presented, both of which lead to Helmholtz weak forms which are parasite-free and enjoy simple, physically meaningful boundary conditions. The extended weak form introduced by Lynch and Paulsen along with associated boundary conditions, is recovered in greater generality from the first gauge considered, where the vector potential is discontinuous at material interfaces and when the scalar potential vanishes. The second and preferred gauge allows the use of continuous vector and scalar potentials at the expense of introducing coupling among the two potentials. A general and numerically efficient procedure for enforcing the jump discontinuities on the normal components of vector fields at dielectric interfaces and boundary conditions on curved surfaces is given in the Appendix.
We present a formalism for obtaining the subsurface velocity configuration directly from reflection seismic data. Our approach is to apply the results obtained for inverse problems in quantum scattering theory to the reflection seismic problem. In particular, we extend the results of Moses (1956) for inverse quantum scattering and Razavy (1975) for the one‐dimensional (1-D) identification of the acoustic wave equation to the problem of identifying the velocity in the three‐dimensional (3-D) acoustic wave equation from boundary value measurements. No a priori knowledge of the subsurface velocity is assumed and all refraction, diffraction, and multiple reflection phenomena are taken into account. In addition, we explain how the idea of slant stack in processing seismic data is an important part of the proposed 3-D inverse scattering formalism.
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