The dependence of EIT images on the assumed initial conductivity distribution: a study of pelvic imaging

A New Meshless Method for Solving 3D Inverse Conductivity Issues of Highly Nonlinear Elliptic Equations

In this research, the 3D inverse conductivity issues of highly nonlinear elliptic partial differential equations (PDEs) are investigated numerically. Even some researchers have utilized several schemes to overcome these multi-dimensional forward issues of those PDEs; nevertheless, an effective numerical algorithm to solve these 3D inverse conductivity issues of highly nonlinear elliptic PDEs is still not available. We apply two sets of single-parameter homogenization functions as the foundations for the answer and conductivity function to cope with the 3D inverse conductivity issue of highly nonlinear PDEs. The unknown conductivity function can be retrieved by working out another linear system produced from the governing equation by collocation skill, while the answer is acquired by dealing with a linear system to gratify over-specified Neumann boundary condition on a fractional border. As this new computational approach is based on a concrete theoretical foundation, it can result in a deeper understanding of 3D inverse conductivity issues with symmetry and asymmetry geometries. The homogenization functions method is rather stable, effective, and accurate in revealing the conductivity function when the over-specified Neumann data with a large level of noise of 28%.

A 3D visualization method for bladder filling examination based on EIT

As the researches of electric impedance tomography (EIT) applications in medical examinations deepen, we attempt to produce the visualization of 3D images of human bladder. In this paper, a planar electrode array system will be introduced as the measuring platform and a series of feasible methods are proposed to evaluate the simulated volume of bladder to avoid overfilling. The combined regularization algorithm enhances the spatial resolution and presents distinguishable sketch of disturbances from the background, which provides us with reliable data from inverse problem to carry on to the three-dimensional reconstruction. By detecting the edge elements and tracking down the lost information, we extract quantitative morphological features of the object from the noises and background. Preliminary measurements were conducted and the results showed that the proposed algorithm overcomes the defects of holes, protrusions, and debris in reconstruction. In addition, the targets' location in space and roughly volume could be calculated according to the grid of finite element of the model, and this feature was never achievable for the previous 2D imaging.

Quantification of intraventricular hemorrhage with electrical impedance tomography using a spherical model

We have developed a robust EEG-based current pattern which shows promise for the detection of intraventricular hemorrhage (IVH) in neonates. Our reconstructions to date are based on a layered spherical head model. In this study, the current pattern was used to gather data from three realistic-shaped neonatal head models and a physical phantom based on one of these models. We found that a sensitivity matrix calculated from a spherical model gave us satisfactory reconstructions in terms of both image quality and quantification. Incorporating correct geometry information into the forward model improved image quality. However, it did not improve quantification accuracy. The results indicate that using a spherical matrix may be a more practical choice for monitoring IVH volumes in neonates for whom patient-specific models are not available.

A robust current pattern for the detection of intraventricular hemorrhage in neonates using electrical impedance tomography

We compared two 16-electrode electrical impedance tomography (EIT) current patterns on their ability to reconstruct and quantify small amounts of bleeding inside a neonatal human head using both simulated and phantom data. The current patterns used were an adjacent injection RING pattern (with electrodes located equidistantly on the equator of a sphere) and an EEG current pattern based on the 10-20 EEG electrode layout. Structures mimicking electrically important structures in the infant skull were included in a spherical numerical forward model and their effects on reconstructions were determined. The EEG pattern was found to be a better topology to localize and quantify anomalies within lateral ventricular regions. The RING electrode pattern could not reconstruct anomaly location well, as it could not distinguish different axial positions. The quantification accuracy of the RING pattern was as good as the EEG pattern in noise-free environments. However, the EEG pattern showed better quantification ability than the RING pattern when noise was added. The performance of the EEG pattern improved further with respect to the RING pattern when a fontanel was included in forward models. Significantly better resolution and contrast of reconstructed anomalies was achieved when generated from a model containing such an opening and 50 dB added noise. The EEG method was further applied to reconstruct data from a realistic neonatal head model. Overall, acceptable reconstructions and quantification results were obtained using this model and the homogeneous spherical forward model.

Normalization of a spatially variant image reconstruction problem in electrical impedance tomography using system blurring properties

The electrical impedance tomography (EIT) image reconstruction problem is ill posed and spatially variant. Because of the problem's ill-posed nature, small amounts of measurement noise can corrupt reconstructed images. The problem must be regularized to reduce image artifacts. In this paper, we focus on the spatially variant characteristics of the problem. Correcting errors due to spatial variance should improve reconstruction accuracy. In this paper, we present methods to normalize the spatially variant image reconstruction problem by equalizing the point spread function (PSF). In order to equalize the PSF, we used the reconstruction blurring properties obtained from the sensitivity matrix. We compared three mathematical normalization schemes: pixel-wise scaling (PWS), weighted pseudo-inversion (WPI) and weighted minimum norm method (WMNM) to equalize images. The quantity index (QI), defined as the integral of pixel values of an EIT conductivity image, was considered in investigating spatial variance. The QI values along with reconstructed images are presented for cases of two-dimensional full array and hemiarray electrode topologies. We found that a spatially invariant QI could be obtained by applying normalization methods based on equalization of the PSF using conventional regularized reconstruction methods such as truncated singular value decomposition (TSVD) and WMNM. We found that WMNM normalization applied to WMNM regularized reconstruction was the best of the methods tested overall, for both hemiarray and full array electrode topologies.

Weighted regularization in electrical impedance tomography with applications to acute cerebral stroke

We apply electrical impedance tomography to detect and localize brain impedance changes associated with stroke. Forward solutions are computed using the finite-element method in two dimensions. We assume that baseline conductivity values are known for the major head tissues, and focus on changes in the brain compartment only. We use singular-value decomposition (SVD) to show that different impedance measurement patterns, which are theoretically equivalent by the reciprocity theorem, have different sensitivities to the brain compartment in the presence of measurement noise. The inverse problem is solved in part by standard means, using iterated SVD, and regularizing by truncation. To improve regularization we introduce a weighting scheme which normalizes the sensitivity matrix for voxels at different depths. This increases the number of linearly independent components which contribute to the solution, and forces the different measurement patterns to have similar sensitivity. When applied to stroke, this weighted regularization improves image quality overall.

Electrical impedance tomography reconstruction algorithm based on general inversion theory and finite element method

A strict EIT reconstruction algorithm, the general inversion algorithm (GIA) is presented. To improve the noise performance, the algorithm is modified by attenuating the condition number of the forward matrix F and implemented using an improved FEM scheme, to obtain the 2D image of impedance change (dynamic image). This modified general inversion algorithm (MGIA) can be used on a larger dimension FEM model (248 elements) and is more practical than the GIA. When implementing this algorithm in computer simulation and in a physical phantom, it is found that the MGIA has a smaller reconstruction error than the currently used algorithms (equipotential-back-projection algorithm and filtered spectral expansion algorithm). With 0.1% white noise in the data, the algorithm can still reconstruct images of a complicated model. Further improvements are also discussed.

Nonlinear reconstruction constrained by image properties in electrical impedance tomography

It is proposed that image quality, for example the degree of roughness, in electrical impedance tomography is the essential measure required to regularize nonlinear reconstruction. Most previously published work has addressed efficiency, stabilization and speed of reconstruction and has overlooked the targeted image qualities. The measure of quality adopted is the mean square gradient of the logarithm of resistivity which, in combination with the chi2 statistic as a measure of the fit to the data, is minimized by iteration until convergence to a stable image is achieved. This penalty function is invariant to the scale of the resistivity and to the interchange of resistivity and conductivity. The algorithm is tested on computer simulated data and on measurements from a cylindrical tank of electrolyte. The results demonstrate the increased image definition that it would be possible to achieve as data acquisition systems are improved. The images show how a reduction in resolution can be traded for reduced noise artefacts, by selecting an appropriate target chi2.

Optimal filtering of EIT data in spectral expansion analysis

The signal-to-noise rations for some EIT measurements are very low, and for in vivo EIT measurements these are dependent on the electrode positioning and the distance from the current drive. The effect of removing noisy measurements to produce higher-fidelity images was investigated for the case of gastric emptying data. A consequence of this filtering was the reduction in the size of the sensitivity matrix and its subsequent singular-value decomposition. Several different filters were tested and for each of these spectral expansion regularization filter was optimized using a chi 2 test. Filtering out the measurement made by the spinal electrode, where the spinal bone barrier lies directly in the current path to the stomach, produced improved images by reducing the artefact content in the spinal sector of the conductivity map. For stomach imaging little useful information is produced by the spinal electrode, and the benefits of filtering dominate. However artefact images may be generated. In contrast consistent small improvements were produced by filtering out some of the weakest signals.

EIT data noise evaluation in the clinical environment

In the clinical environment the reliable interpretation of EIT images depends on the quality of the data. In the electrically noisy hospital environment the system performance needs to be assessed for each clinical investigation. From the model of noise presented, a figure of merit for comparisons of system performance with a known standard, or with previous studies, can be generated. The method depends on calculating the variances of the differences in reciprocity measurements as a function of the distance between the current drive electrodes and the receive voltage electrodes. These measurements fit the noise model, with minimal interference from physiological variability, and permit a figure of merit to be calculated which is a representation of the noise at the point to the system. Typical figures of merit are 7.36 +/- 0.03 microV for a test card and 10.50 +/- 16 microV for subject data.