Yves D'Asseler

Review on solving the forward problem in EEG source analysis

BackgroundThe aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes.MethodsWhile other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field.ResultsIt starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poissons differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter). In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poissons equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM), the finite element method (FEM) and the finite difference method (FDM). In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poissons equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative methods are required to solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method.ConclusionSolving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem.

Iterative reconstruction algorithms in nuclear medicine

Iterative reconstruction algorithms produce accurate images without streak artifacts as in filtered backprojection. They allow improved incorporation of important corrections for image degrading effects, such as attenuation, scatter and depth-dependent resolution. Only some corrections, which are important for accurate reconstruction in positron emission tomography and single photon emission computed tomography, can be applied to the data before filtered backprojection. The main limitation for introducing iterative algorithms in nuclear medicine has been computation time, which is much longer for iterative techniques than for filtered backprojection. Modern algorithms make use of acceleration techniques to speed up the reconstruction. These acceleration techniques and the development in computer processors have introduced iterative reconstruction in daily nuclear medicine routine. We give an overview of the most important iterative techniques and discuss the different corrections that can be incorporated to improve the image quality.

Monte Carlo simulations of a scintillation camera using GATE: validation and application modelling

Geant4 application for tomographic emission (GATE) is a recently developed simulation platform based on Geant4, specifically designed for PET and SPECT studies. In this paper we present validation results of GATE based on the comparison of simulations against experimental data, acquired with a standard SPECT camera. The most important components of the scintillation camera were modelled. The photoelectric effect. Compton and Rayleigh scatter are included in the gamma transport process. Special attention was paid to the processes involved in the collimator: scatter, penetration and lead fluorescence. A LEHR and a MEGP collimator were modelled as closely as possible to their shape and dimensions. In the validation study, we compared the simulated and measured energy spectra of different isotopes: 99mTc, 22Na, 57Co and 67Ga. The sensitivity was evaluated by using sources at varying distances from the detector surface. Scatter component analysis was performed in different energy windows at different distances from the detector and for different attenuation geometries. Spatial resolution was evaluated using a 99mTc source at various distances. Overall results showed very good agreement between the acquisitions and the simulations. The clinical usefulness of GATE depends on its ability to use voxelized datasets. Therefore, a clinical extension was written so that digital patient data can be read in by the simulator as a source distribution or as an attenuating geometry. Following this validation we modelled two additional camera designs: the Beacon transmission device for attenuation correction and the Solstice scanner prototype with a rotating collimator. For the first setup a scatter analysis was performed and for the latter design. the simulated sensitivity results were compared against theoretical predictions. Both case studies demonstrated the flexibility and accuracy of GATE and exemplified its potential benefits in protocol optimization and in system design.

A finite difference method with reciprocity used to incorporate anisotropy in electroencephalogram dipole source localization

Many implementations of electroencephalogram (EEG) dipole source localization neglect the anisotropical conductivities inherent to brain tissues, such as the skull and white matter anisotropy. An examination of dipole localization errors is made in EEG source analysis, due to not incorporating the anisotropic properties of the conductivity of the skull and white matter. First, simulations were performed in a 5 shell spherical head model using the analytical formula. Test dipoles were placed in three orthogonal planes in the spherical head model. Neglecting the skull anisotropy results in a dipole localization error of, on average, 13.73 mm with a maximum of 24.51 mm. For white matter anisotropy these values are 11.21 mm and 26.3 mm, respectively. Next, a finite difference method (FDM), presented by Saleheen and Kwong (1997 IEEE Trans. Biomed. Eng. 44 800-9), is used to incorporate the anisotropy of the skull and white matter. The FDM method has been validated for EEG dipole source localization in head models with all compartments isotropic as well as in a head model with white matter anisotropy. In a head model with skull anisotropy the numerical method could only be validated if the 3D lattice was chosen very fine (grid size < or = 2 mm).

Dynamic PET Reconstruction Using Wavelet Regularization With Adapted Basis Functions

Tomographic reconstruction from positron emission tomography (PET) data is an ill-posed problem that requires regularization. An attractive approach is to impose an lscr1-regularization constraint, which favors sparse solutions in the wavelet domain. This can be achieved quite efficiently thanks to the iterative algorithm developed by Daubechies et al., 2004. In this paper, we apply this technique and extend it for the reconstruction of dynamic (spatio-temporal) PET data. Moreover, instead of using classical wavelets in the temporal dimension, we introduce exponential-spline wavelets (E-spline wavelets) that are specially tailored to model time activity curves (TACs) in PET. We show that the exponential-spline wavelets naturally arise from the compartmental description of the dynamics of the tracer distribution. We address the issue of the selection of the ldquooptimalrdquo E-spline parameters (poles and zeros) and we investigate their effect on reconstruction quality. We demonstrate the usefulness of spatio-temporal regularization and the superior performance of E-spline wavelets over conventional Battle-Lemarie wavelets in a series of experiments: the 1-D fitting of TACs, and the tomographic reconstruction of both simulated and clinical data. We find that the E-spline wavelets outperform the conventional wavelets in terms of the reconstructed signal-to-noise ratio (SNR) and the sparsity of the wavelet coefficients. Based on our simulations, we conclude that replacing the conventional wavelets with E-spline wavelets leads to equal reconstruction quality for a 40% reduction of detected coincidences, meaning an improved image quality for the same number of counts or equivalently a reduced exposure to the patient for the same image quality.

A three-dimensional theoretical model incorporating spatial detection uncertainty in continuous detector PET.

In this paper, we will describe a theoretical model of the spatial uncertainty for a line of response, due to the imperfect localization of events on the detector heads of a positron emission tomography (PET) camera. The forward acquisition problem is modelled by a Gaussian distribution of the position of interaction on a detector head, centred at the measured position. The a posteriori probability that an event originates from a certain point in the field of view (FOV) is calculated by integrating all the possible lines of response (LORs) through this point, weighted with the Gaussian detection likelihood at the LORs end points. We have calculated these a posteriori probabilities both for perpendicular and oblique coincidences. For the oblique coincidence case it was necessary to incorporate the effect of the crystal thickness in the calculations. We found in the perpendicular incidence case as well as in the oblique incidence case that the probability density function cannot be analytically expressed in a closed form, and it was thus calculated by means of numerical integration. A Gaussian was fit to the transversal profiles of this function for a given distance to the detectors. From these fits, we can conclude that the profiles can be accurately approximated by a Gaussian, both for perpendicular and oblique coincidences. The FWHM reaches a maximum at the detector heads, and decreases towards the centre of the FOV, as was expected. Afterwards we extended this two-dimensional model to three dimensions, thus incorporating the spatial uncertainty in both transversal directions. This theoretical model was then evaluated and a very good agreement was found with theoretical calculations and with geometric Monte Carlo simulations. Possible improvements for the above-described incorporation of crystal thickness are discussed. Therefore a detailed Monte Carlo study has been performed in order to investigate the interaction probability of photons of different energies along their path in several detector materials dedicated to PET. Finally two approaches for the incorporation of this theoretical model in reconstruction algorithms are outlined.

99Tcm labelled HL91 versus computed tomography and biopsy for the visualization of tumour recurrence of squamous head and neck carcinoma

This phase I pilot study reports on (1) the safety and feasibility of 99Tcm-HL91, an amine oxime core radioligand that has shown oxygen dependent binding, and imaging; and (2) its usefulness for the visualization of local tumour recurrence of a biopsy proven squamous cell carcinoma of the head and neck (SCCHN) as compared to spiral computed tomogaphy (CT) and biopsy. Nine men (mean age 33 years, range 34-74 years) were prospectively included. For safety measurements, vital signs were recorded and serum chemical analysis carried out, with a complete blood cell count and urine analysis, and an ECG was performed prior to injection of 99Tcm-HL91 and repeated during the investigation. Single photon emission computed tomography (SPECT) scans of the head and neck, and of a standard, were performed at 2 h and 4 h post-injection of 740 MBq 99Tcm-HL91. Tumour-to-normal tissue background (T/N) ratios and percentage uptake were measured for all 99Tcm-HL91 scans. Spiral CT scans were obtained using a Somaton 4+ Siemens scanner within 1 week from the 99Tcm-HL91 scans. Based on CT and the 99Tcm-HL91 scan findings guided biopsies were performed. No adverse or subjective side effects were noticed. Vital signs, ECG findings, clinical laboratory, blood and urine assays remained stable in all patients. Spiral CT suggested local recurrence in 5/9 patients accompanied by nodal involvement in three, all of which proved positive on biopsy. 99Tcm-HL91 scintigraphy was false positive in one patient and true positive (TP) in 3/5 local recurrences and two out of three sites of lymph node involvement depicted by spiral CT. The mean T/N ratios at 2 h and 4 h in TPs were 1.28 (range 1.1-1.66) and 1.40 (range 1.0-1.6), respectively. The corresponding absolute percentages of 99Tcm-HL91 lesional uptake at 2 h and 4 h were μ = 0.05% (SD = 0.03%) and μ = 0.048% (SD = 0.035%). The findings suggest 99Tcm-HL91 is a safe radioligand and that metabolic binding in a large fraction but not all of local SCCHN recurrences may be expected. The inference that tumour 99Tcm-HL91 avidity could be a non-invasive measure of tumour hypoxia deserves however independent confirmation with needle oximetry.

Coincidence camera FDG imaging for the diagnosis of chronic orthopedic infections: a feasibility study.

Purpose Results of dedicated [18F]fluoro-2-deoxy-d-glucose (FDG) PET imaging in patients with suspected orthopedic infections are promising. This study evaluates the feasibility of dual-head gamma-camera coincidence (DHC) imaging in this population. Method Twenty-four patients, referred for the confirmation or exclusion of orthopedic infection, were prospectively studied with consecutive FDG-dedicated PET and FDG DHC imaging. Images were read by two blinded readers experienced with FDG PET and compared with the final diagnosis, obtained by microbiologic proof in 11 patients and clinical follow-up of at least 9 months in 13 patients. Results Nine patients had osseous infection on final diagnosis. Sensitivity, specificity, and accuracy in this limited series were (Reader 1/Reader 2), respectively, 100/100, 86/86, and 92/92% for FDG-dedicated PET and 89/89, 100/93, and 96/92% for FDG DHC imaging. Conclusion Despite lower image quality for FDG DHC imaging, results in this limited series were comparable with the results of FDG-dedicated PET. Further studies are needed to confirm the utility of FDG DHC imaging in suspected chronic orthopedic infections in larger patient groups.

Absolute quantification of carnosine in human calf muscle by proton magnetic resonance spectroscopy

Carnosine has been shown to be present in the skeletal muscle and in the brain of a variety of animals and humans. Despite the various physiological functions assigned to this metabolite, its exact role remains unclear. It has been suggested that carnosine plays a role in buffering in the intracellular physiological pHi range in skeletal muscle as a result of accepting hydrogen ions released in the development of fatigue during intensive exercise. It is thus postulated that the concentration of carnosine is an indicator for the extent of the buffering capacity. However, the determination of the concentration of this metabolite has only been performed by means of muscle biopsy, which is an invasive procedure. In this paper, we utilized proton magnetic resonance spectroscopy (1H MRS) in order to perform absolute quantification of carnosine in vivo non-invasively. The method was verified by phantom experiments and in vivo measurements in the calf muscles of athletes and untrained volunteers. The measured mean concentrations in the soleus and the gastrocnemius muscles were found to be 2.81 +/- 0.57/4.8 +/- 1.59 mM (mean +/- SD) for athletes and 2.58 +/- 0.65/3.3 +/- 0.32 mM for untrained volunteers, respectively. These values are in agreement with previously reported biopsy-based results. Our results suggest that 1H MRS can provide an alternative method for non-invasively determining carnosine concentration in human calf muscle in vivo.

Iterative list mode reconstruction for coincidence data of gamma camera

The 3D acquisition data from positron coincidence detection on a gamma camera, can be stored in list-mode or histogram format. The standard processing of the list mode-data is Single Slice Rebinning (with a maximum acceptance angle) to 2D histogrammed projections followed by Ordered Subsets Expectation Maximization reconstruction. This method has several disadvantages: sampling accuracy is lost by histogramming events, axial resolution degrades with increasing distance from the center of rotation and useful events, with angle bigger than the acceptance angle, are not included in the reconstruction. Therefore an iterative reconstruction algorithm, operating directly on list-mode data, has been implemented. The 2D and 3D version of this iterative list-mode algorithm have been compared with the aforementioned standard reconstruction method. A higher number of events is used in the reconstruction, which results in a lower standard deviation. Resolution is fairly constant over the Field of View. The use of a fast projector and backprojector reduces the reconstruction time to clinical acceptable times.