Claudio H. Sibata

Discrete analytical hyperplanes

This paper presents the properties of the discrete analytical hyperplanes. They are defined analytically in the discrete domain by Diophantine equations. We show that the discrete hyperplane is a generalization of the classical digital hyperplanes. We present original properties such as exact point localization and space tiling. The main result is the links made between the arithmetical thickness of a hyperplane and its topology.

Deconvolution of detector size effect for small field measurement

Parametrization of the small fields employed in stereotactic applications is a painstaking process involving extensive film dosimetry to achieve acceptable beam edge definition. Use of cylindrical or spherical detectors for profile measurements would simplify data acquisition but add a volume averaging artifact to beam edge definition. We demonstrate a simple approach to unfolding the chamber size artifact from measured small beam profiles using typical cylindrical chambers. In comparison with film measurements we have found good agreement when the detector response function is deconvoluted from the measured profiles, although the amount of correction needed is fairly minimal for the detectors studied.

A patient-specific in vivo tumor model

A significant body of research, spanning approximately the last 25 years, has focused upon the task of developing a better understanding of tumor growth through the use of in vitro mathematical models. Although such models are useful for simulation, in vivo growth differs in significant ways due to the variety of competing biological, biochemical, and mechanical factors present in a living biological system. An in vivo, macroscopic, primary brain tumor growth model is developed, incorporating previous in vitro growth pattern research as well as scientific investigations into the biological and biochemical factors that affect in vivo neoplastic growth. The tumor growth potential model presents an integrated, universal framework that can be employed to predict the direction and extent of spread of a primary brain tumor with respect to time for a specific patient. This framework may be extended as necessary to include the results of current and future research into parameters affecting neoplastic proliferation. The patient-specific primary brain tumor growth model is expected to have multiple clinical uses, including: predictive modeling, tumor boundary delineation, growth pattern research, improved radiation surgery planning, and expert diagnostic assistance.

Supercover 3D polygons

A new discrete 3D polygon called Supercover Polygon is introduced. The polygon is a tunnel free plane segment defined by vertices and edges. An edge is a 3D line segment. Two different polygons can share a common edge and if they do, the union of both polygons is tunnel free. This is definition of discrete polygons that has the “most” properties in common with the continuous polygon. It seems particularly interesting for modelization of discrete scenes by way of digitization.

Two new parallel-plate ionization chambers for electron beam dosimetry

Abstract Two parallel-plate ionization chambers were projected, constructed and evauated for use in high energy electron beams. They were constructed using the two plastic materials recommended for clinical dosimetry protocols, i.e. acrylic and polystyrene. Both chambers have cylindrical shape with entrance windows in aluminized Mylar and they are open to the air. The acrylic chamber has a 2 mm air gap and the polystyrene chamber has a 1 mm air gap. Pre- and post-irradiation leakage, repeatability and long term stability were determined for these two ionization chambers. The ionic recombination and polarity effects, besides angular and energy dependencies, were also verified. The results obtained are within values recommended by IEC (1982) [Medical electrical equipment: dosimeters with ioniz chamber as used in radiotherapy. IEC, Geneva (IEC-731-82)] for this kind of ionization chamber. The ionization chambers were calibrated in a 20 MeV electron beam and gamma radiation of cobalt-60. The wall correction factors for the gamma radiation for cobalt-60 were 1.014 and 1.000 for the acrylic and polystyrene chambers, respectively. The ionization chambers do not present the energy dependence for the 6–20 MeV electron beam range. These results are comparable to commercially available ionization chambers.

Accuracy of the point source approximation to high dose-rate Ir-192 sources

The accuracy of the point source approximation used in dose calculations for an implant comprised of multiple high dose rate (HDR) Ir-192 source dwell positions is investigated. First, a single dwell position implant is modeled. The exposure rate about the source is calculated using both the point source approximation and the more rigorous line source formalism. A comparison of these calculated exposure rates is made. It is found that for each HDR Ir-192 source dwell position, the point source approximation results in a dose overestimation of 1% at a distance of 1 cm on the source transverse axis, while dose underestimations of more than 2% can be found at a distance of 1 cm on the source longitudinal axis. Even larger errors occur closer to the source. The results of this academic study are then extended to two clinical cases--an endobronchial treatment and a tandem and ovoids setup, both involving multiple source dwell positions. Since clinical HDR Ir-192 implants are comprised of many individual source dwell positions, there will be inaccuracy in the calculated overall dose distribution leading to dose delivery errors. For example, the dose delivered to a prescription point located 0.5 cm from an endobronchial applicator will be 3% lower than prescribed. Similar errors are produced in gynecologic implants. To decrease below 0.5% the dose delivery error resulting from the point source approximation, prescription points should be at a distance of at least 1 cm from any applicator. Since the dosimetry error is a direct result of the choice of model used to describe the source, the use of anisotropy factors accounting for the variation of photon fluence around the HDR Ir-192 source will not completely correct the calculation.

Patient-specific tumor prognosis prediction via multimodality imaging

This paper proposes an approach to advance the utility of physical modeling techniques for medical applications by correlating finite element based models with the mechanical anatomy characteristic of a clinical patient. A methodology is presented to model the patient-specific mechanical response of brain tissue in vivo. The resultant model is parameterized in terms of clinical CT and MRI imaging sequences acquired for each patient. Applications of the proposed technique to the areas of brain tumor growth modeling and predicting tissue shifts during stereotactic neurosurgery, are described. Results are presented for an implementation of our approach to the problem of predictive brain tumor modeling.

Fractal-based characterization of structural changes in biomedical images

In the present work, distinct structures appearing in biomedical images are modeled as fractals. Within an image, the relevant structures are associated to a fractal dimension. Changes in the dimension values, as a function of time, reflect alterations of structural properties. Accurate and robust estimation of this dimension, leads to a precise characterization of changes undergone by the structure. The Continuous Pyramidal Alternating Sequential Filter method is proposed as a robust and accurate fractal dimension estimator. A study on bedrest data of human subjects was conducted. Bedrest is an accepted model for the study of osteoporosis. Here the spine is modeled as a fractal structure. Fractal model were also applied towards analysis of breast cancer and brain tumors. Results from these different studies confirm that fractals can suitably model a variety of biological structures. These studies also suggest that fractal models can be effectively utilized to detect temporal changes undergone by the structures.

New methods in oblique slice generation

In this paper, we present a new approach to the generation and manipulation of oblique slices of MR/CT or any voxel space images. We consider the result of the voxel space as if it would be cut by a scalpel, simulating the action of a surgeon. With the intervention of a new definition of discrete 3D voxel plane, we show that this can be done in a highly efficient way and that there are very few computations to do. It is shown that the supercover of the continuous oblique plane is a 6-connected discrete plane that has many very interesting properties that can be usefully exploited. For instance, geometrical considerations avoid much of the intersection computations and once one oblique slice is generated, all the other parallel oblique slices can be generated with few further computations. These results are applied to improve the existing algorithms and provide some ideas for new ones. It should also improve the handling possibilities of oblique slices, indeed, almost all that can be done on a sagittal or axial slice can then also be done on oblique slices. An extension to 4D oblique slices is possible.

Rational bitmap scaling

Abstract A simple mathematical approach is presented for scaling a bitmap image by a rational factor without interpolation. The transformation is reversible. As application of these results, we present a step-by-step scaling algorithm.