Grid structure impact in sparse point representation of derivatives

In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.

The use of non-standard CT conversion ramps for Monte Carlo verification of 6 MV prostate IMRT plans

Monte Carlo (MC) dose calculation algorithms have been widely used to verify the accuracy of intensity-modulated radiotherapy (IMRT) dose distributions computed by conventional algorithms due to the ability to precisely account for the effects of tissue inhomogeneities and multileaf collimator characteristics. Both algorithms present, however, a particular difference in terms of dose calculation and report. Whereas dose from conventional methods is traditionally computed and reported as the water-equivalent dose (Dw), MC dose algorithms calculate and report dose to medium (Dm). In order to compare consistently both methods, the conversion of MC Dm into Dw is therefore necessary. This study aims to assess the effect of applying the conversion of MC-based Dm distributions to Dw for prostate IMRT plans generated for 6 MV photon beams. MC phantoms were created from the patient CT images using three different ramps to convert CT numbers into material and mass density: a conventional four material ramp (CTCREATE) and two simplified CT conversion ramps: (1) air and water with variable densities and (2) air and water with unit density. MC simulations were performed using the BEAMnrc code for the treatment head simulation and the DOSXYZnrc code for the patient dose calculation. The conversion of Dm to Dw by scaling with the stopping power ratios of water to medium was also performed in a post-MC calculation process. The comparison of MC dose distributions calculated in conventional and simplified (water with variable densities) phantoms showed that the effect of material composition on dose-volume histograms (DVH) was less than 1% for soft tissue and about 2.5% near and inside bone structures. The effect of material density on DVH was less than 1% for all tissues through the comparison of MC distributions performed in the two simplified phantoms considering water. Additionally, MC dose distributions were compared with the predictions from an Eclipse treatment planning system (TPS), which employed a pencil beam convolution (PBC) algorithm with Modified Batho Power Law heterogeneity correction. Eclipse PBC and MC calculations (conventional and simplified phantoms) agreed well (<1%) for soft tissues. For femoral heads, differences up to 3% were observed between the DVH for Eclipse PBC and MC calculated in conventional phantoms. The use of the CT conversion ramp of water with variable densities for MC simulations showed no dose discrepancies (0.5%) with the PBC algorithm. Moreover, converting Dm to Dw using mass stopping power ratios resulted in a significant shift (up to 6%) in the DVH for the femoral heads compared to the Eclipse PBC one. Our results show that, for prostate IMRT plans delivered with 6 MV photon beams, no conversion of MC dose from medium to water using stopping power ratio is needed. In contrast, MC dose calculations using water with variable density may be a simple way to solve the problem found using the dose conversion method based on the stopping power ratio.

Estudo comparativo entre o tonómetro de aplanação de Goldmann e o tonómetro de não contacto em pacientes com glaucoma primário de ângulo aberto

Mestrado em Gestão e Avaliação de Tecnologias em Saúde