Choice Of Mixing Scheme Research Articles

On mixed electron-photon radiation therapy optimization using the column generation approach.

Despite considerable increase in the number of degrees of freedom handled by recent radiotherapy optimisation algorithms, treatments are still typically delivered using a single modality. Column generation is an iterative method for solving large optimisation problems. It is well suited for mixed-modality (e.g., photon-electron) optimisation as the aperture shaping and modality selection problem can be solved rapidly, and the performance of the algorithm scales favourably with increasing degrees of freedom. We demonstrate that the column generation method applied to mixed photon-electron planning can efficiently generate treatment plans and investigate its behaviour under different aperture addition schemes. Column generation was applied to the problem of mixed-modality treatment planning for a chest wall case and a leg sarcoma case. 6MV beamlets (100cm SAD) were generated for the photon components along with 5 energies for electron beamlets (6, 9, 12, 16 and 20MeV), simulated as shortened-SAD (80cm) beams collimated with a photon MLC. For the chest wall case, IMRT-only, modulated electron radiation therapy (MERT)-only, and mixed electron-photon (MBRT) treatment plans were created using the same planning criteria. For the sarcoma case, MBRT and MERT plans were created to study the behaviour of the algorithm under two different sets of planning criteria designed to favour specific modalities. Finally, the efficiency and plan quality of four different aperture addition schemes was analysed by creating chest wall MBRT treatment plans which incorporate more than a single aperture per iteration of the column generation loop based on a heuristic aperture ranking scheme. MBRT plans produced superior target coverage and homogeneity relative to IMRT and MERT plans created using the same optimisation criteria, all the while preserving the normal tissue-sparing advantages of electron therapy. Adjusting the planning criteria to favour a specific modality in the sarcoma case resulted in the algorithm correctly emphasizing the appropriate modality. As expected, adding a single aperture per iteration yielded the lowest (best) cost function value per aperture included in the treatment plan. However, a greedier scheme was able to converge to approximately the same cost function after 125 apertures in one third of the running time. Electron apertures were on average 50-100% larger than photon apertures for all aperture addition schemes. The distribution of intensities among the available modalities followed a similar trend for all schemes, with the dominant modalities being 6MV photons along with 6, 9 and 20MeV electrons. The column generation method applied to mixed modality treatment planning was able to produce clinically realistic treatment plans and combined the advantages of photon and electron radiotherapy. The running time of the algorithm depended heavily on the choice of mixing scheme. Adding the highest ranked aperture for each modality provided the best trade-off between running time and plan quality for a fixed number of apertures. This work contributes an efficient methodology for the planning of mixed electron-photon treatments.

Effects of Precipitation on the Upper-Ocean Response to a Hurricane

Abstract The effect of precipitation on the upper-ocean response during a tropical cyclone passage is investigated using a numerical model in this paper. For realistic wind forcing and empirical rain rates based on satellite climatology, numerical simulations are performed with and without precipitation forcing to delineate the effects of freshwater forcing on the upper-ocean heat and salt budgets. Additionally, the performance of five mixing parameterizations is also examined for the two forcing conditions to understand the sensitivity of simulated ocean response. Overall, results from 15 numerical experiments are analyzed to quantify the precipitation effects on the oceanic mixed layer and the upper ocean. Simulated fields for the same mixing scheme with and without precipitation indicate a decrease in the upper-ocean cooling of about 0.2°–0.5°C. This is mainly due to reduced mixing of colder water from below induced by the increased stability of the added freshwater. The cooler rainwater contributes a maximum of approximately 10% to the total surface heat loss from the ocean. The rate of freshening due to precipitation exceeds the rate of mixing of the more saline water from below, leading to a change in sign of the mixed layer salinity response. As seen in earlier studies, large uncertainty exists in the simulated upper-ocean response due to the choice of mixing parameterization. Although the nature of simulated response remains similar for all the mixing schemes, the magnitude of freshening and cooling varies by as much as 0.5 psu and 1°C between the schemes to the right of the storm track. While changes in the mixed layer and in the top 100 m of heat and salt budgets are strongly influenced by the choice of mixing scheme, integrated budgets in the top 200 m are seen to be affected more by advection and surface fluxes. However, since the estimated surface fluxes depend upon the simulated sea surface temperature, the choice of mixing scheme is crucial for realistic coupled predictive models.

Solar neutrino problem within the left-right model.

Limiting ourselves to the two flavor approximation within the SU(2){sub {ital L}}{times}SU(2){sub {ital R}}{times}U(1){sub {ital B}}{minus}{ital L} gauge model the motion of the neutrino flux in solar matter is considered. For the neutrino system described by the eight-component wave function {Psi}{sup {ital T}}=({nu}{sub {ital eL}},{nu}{sub {ital XL}},{ital N}{sub {ital eR}},{ital N}{sub {ital XR}} ,{bar {nu}}{sub {ital eR}},{bar {nu}}{sub {ital XL}},{bar {ital N}}{sub {ital eR}},{bar {ital N}}{sub {ital XR}}), where {ital X}={mu},{tau}, an evolution equation in a Schr{umlt o}dinger-like form is found. It is shown that the number of possible resonance transitions for the flux of solar {nu}{sub {ital eL}} is defined both by the mass hierarchy within the system {nu}{sub {ital eL}},{nu}{sub {ital XL}},{ital N}{sub {ital eR}},{ital N}{sub {ital XL}}, and by the choice of mixing scheme. Factors influencing the neutrino flux crossing a region of solar flares are defined. {copyright} {ital 1996 The American Physical Society.}