Radioactive source localization employing resistive electrode array (REA) detector.

Objective.In this feasibility study, we explore an application of a Resistive Electrode Array (REA) for localization of a radioactive point source. The inverse problem posed by multichannel REA detection is studied from mathematical perspective and involves the questions of the minimal configuration of the conductive leads that can achieve this goal. The basic configuration consists of a circularly shaped REA with four opposite electrical lead-pairs at its perimeter.Approach.A robust mathematical reconstruction method for a 3D radioactive source relative to the REA is presented. The characteristic empirical Green's function for the detector response of the REA is determined by numerically solving Laplace equations with appropriate boundary conditions. Based on this model, Monte Carlo simulations of the inverse problem with Gaussian noise are performed and the overall accuracy of the localization is investigated.Main results.The results show a 3D error distribution of localization which is uniform in the (x,y)-plane of the REA and strongly correlated in the orthogonalz-axis. The overall accuracy decreases with higher distance of the source to the detector which is intuitive due to approximate flux dependence following the inverse square law. Further, a saturation in accuracy regarding the number of electrical leads and a linear dependence of the reconstruction error on the measurement noise level are observed.Significance.A broad range of REA detector configurations and their characteristics are investigated by this study for radioactive source localization allowing diverse practical applications with detector diameters ranging from millimeters to meters.

Stochastic triangulation for prostate positioning during radiotherapy using short CBCT arcs.

BACKGROUND AND PURPOSE: Fast and reliable tumor localization is an important part of today's radiotherapy utilizing new delivery techniques. This proof-of-principle study demonstrates the use of a method called herein 'stochastic triangulation' for this purpose. Stochastic triangulation uses very short imaging arcs and a few projections. MATERIALS AND METHODS: A stochastic Maximum A Posteriori (MAP) estimator is proposed based on an uncertainty-driven model of the acquisition geometry and inter-/intra-fractional deformable anatomy. The application of this method was designed to use the available linac-mounted cone-beam computed tomography (CBCT) and/or electronic portal imaging devices (EPID) for the patient setup based on short imaging arcs. For the proof-of-principle clinical demonstration, the MAP estimator was applied to 5 CBCT scans of a prostate cancer patient with 2 implanted gold markers. Estimation was performed for several (18) very short imaging arcs of 5° with 10 projections resulting in 90 estimations. RESULTS: Short-arc stochastic triangulation led to residual radial errors compared to manual inspection with a mean value of 1.4mm and a standard deviation of 0.9 mm (median 1.2mm, maximum 3.8mm) averaged over imaging directions all around the patient. Furthermore, abrupt intra-fractional motion of up to 10mm resulted in radial errors with a mean value of 1.8mm and a standard deviation of 1.1mm (median 1.5mm, maximum 5.6mm). Slow periodic intra-fractional motions in the range of 12 mm resulted in radial errors with a mean value of 1.8mm and a standard deviation of 1.1mm (median 1.6mm, maximum 4.7 mm). CONCLUSION: Based on this study, the proposed stochastic method is fast, robust and can be used for inter- as well as intra-fractional target localization using current CBCT units.

A stochastic model of cell survival for high-Z nanoparticle radiotherapy.

PURPOSE: The authors present a stochastic framework for the assessment of cell survival in gold nanoparticle radiotherapy. METHODS: The authors derive the equations for the effective macroscopic dose enhancement for a population of cells with nonideal distribution of gold nanoparticles (GNP), allowing different number of GNP per cell and different distances with respect to the cellular target. They use the mixed Poisson distribution formalism to model the impact of the aforementioned physical factors on the effective dose enhancement. RESULTS: The authors show relatively large differences in the estimation of cell survival arising from using approximated formulae. They predict degeneration of the cell killing capacity due to different number of GNP per cell and different distances with respect to the cellular target. CONCLUSIONS: The presented stochastic framework can be used in interpretation of experimental cell survival or tumor control probability studies.