Ignace Lemahieu

The Validation of the Finite Difference Method and Reciprocity for Solving the Inverse Problem in EEG Dipole Source Analysis

The performance of the finite difference reciprocity method (FDRM) to solve the inverse problem in EEG dipole source analysis is investigated in the analytically solvable three-shell spherical head model for a large set of test dipoles. The location error for a grid with 2 mm and 3 mm node spacing is in general, not larger than twice the internode distance, hence 4 mm and 6 mm, respectively. Increasing the number of scalp electrodes from 27 to 44 only marginally improves the location error. The orientation error is always smaller than 4° for all the test dipoles considered. We have also compared the sensitivity to noise using FDRM in EEG dipole source analysis with the sensitivity to noise using the analytical expression for the forward problem. FDRM is not more sensitive to noise than the method using the analytical expression.

Comparison of performance of spherical and realistic head models in dipole localization from noisy EEG

The performance of a three-shell spherical head model versus the performance of a realistic head model is investigated when solving the inverse problem with a single dipole, in the presence of noise. This is evaluated by calculating the average dipole location error for 1000 noisy scalp potential sets, originating from the same test dipole and having the same noise level. The average location errors are obtained utilizing a local linearization, which is validated with a Monte-Carlo simulation. When the difference between the average location error utilizing a spherical and a realistic head model, represented by deltaR, is large for a large number of test dipoles, then it is worth using the more computationally demanding realistic head model. However, if deltaR is small for a large number of test dipoles, then it does not matter which model is used. For 27 electrodes, an electroencephalogram (EEG) epoch of one time sample and spatially white Gaussian noise, we found that the importance of the realistic head model over the spherical head model reduces by increasing the noise level. We further found that increasing the number of scalp electrodes from 27 to 44 has limited impact on the importance of the realistic head model over the spherical head model in EEG dipole source analysis. By increasing the number of time samples to six, the performance of the realistic head model in the inverse calculation gains importance compared with the three-shell spherical head model. Finally, we used spatially and temporally correlated background EEG instead of Gaussian noise. The advantage of the realistic head model over the spherical head model is reduced when applying correlated noise compared to Gaussian noise.

Degradation of myocardial perfusion SPECT images caused by contaminants in thallous (201Tl) chloride

PurposeThallous (201Tl) chloride is a single-photon emission computed tomography (SPECT) tracer mainly used for assessing perfusion and viability of myocardial tissue. 201Tl emits X-rays around 72xa0keV and gammas at 167xa0keV, and has a half-life of 73xa0h. Regulations allow an intrinsic contamination up to 3-5%, which is mainly caused by 200Tl (368xa0keV; 26xa0h) and by 202Tl (439xa0keV; 12.2xa0days). Contra-intuitive to the low-level percentages in which these contaminants are present, their impact may be significant because of much higher gamma camera sensitivity for these high-energy photon emissions. Therefore, we investigate the effects of the contaminants in terms of detected fractions of photons in projections and contrast degradation in reconstructed images.MethodsAcquisitions of a digital thorax phantom filled with thallous (201Tl) chloride were simulated with a validated Monte Carlo tool, thereby, modelling 1% of contamination by 200Tl and 202Tl each. In addition, measurements of a thorax phantom on a dual-headed gamma camera were performed. The product used was contaminated by 0.17% of 200Tl and 0.24% of 202Tl at activity reference time (ART). This ART is specified by the manufacturer, thereby, accounting for the difference in half-lives of 201Tl and its contaminants. These measurements were repeated at different dates associated with various contamination levels.ResultsSimulations showed that, with 1% of 200Tl and 202Tl, the total contamination in the 72xa0keV window can rise up to one out of three detected photons. For the 167keV window, the contamination is even more pronounced: more than four out of five detections in this photopeak window originate from contaminants. Measurements indicate that cold lesion contrast in myocardial perfusion SPECT imaging is at maximum close to ART. In addition to a higher noise level, relative contrast decreases 15% 2xa0days early to ART, which is explained by an increase in 200Tl contamination. After ART, contrast decreased by 16% when the 202Tl contamination increased to the maximal allowed limit.ConclusionsContra-intuitive to the low-level percentages in which they are typically present, penetration and downscatter of high-energy photons from 200Tl and 202Tl significantly contribute to thallous (201Tl) chloride images, thereby, reducing contrast and adding noise. These findings may prompt for improved production methods, for updated policies with regard to timing of usage, and they also render the usefulness of adding the high photopeak window (167xa0keV) questionable. A window-based correction method for this contamination is advisable.

A Mathematica™ Package for Symbolic Bayesian Calculations

A package, BayesCalc, is presented that extends the standard possibilities of Mathematica. The implemented extensions allow the automatic, symbolic calculation of many operations needed in the daily application of Bayesian theory. The main feature of the package is the symbolic calculation of posterior probabilities.

Evolution review of Bayescalc, a MATHEMATICA package for doing bayesian calculations

The application of Bayesian probability theory requires only a few rules: the sum rule, the product rule and the marginalization procedure. However, in practice Bayesian computations can become tedious. The package BayesCalc implements the rules governing Bayesian probability theory in a Mathematica framework. Consequently BayesCalc can help introduce Bayesian theory to newcomers and facilitate computations for regular Bayesians.

PARALLEL MAXIMUM ENTROPY RECONSTRUCTION OF PET IMAGES

The application of a maximum entropy reconstruction method to PET images requires a long computation time. To overcome this problem multiprocessor machines could be used. In this paper we present a parallelization method for the Green expectation maximization method.

A Multicriterion Evaluation of the MemSys5 Program for PET

In Positron Emission Tomography (PET) images have to be reconstructed from noisy projection data. The noise on the PET data can be modeled by a Poisson distribution.