An extended Kalman filtering approach for the estimation of human head tissue conductivities by using EEG data: a simulation study.

In this study, we propose an extended Kalman filter approach for the estimation of the human head tissue conductivities in vivo by using electroencephalogram (EEG) data. Since the relationship between the surface potentials and conductivity distribution is nonlinear, the proposed algorithm first linearizes the system and applies extended Kalman filtering. By using a three-compartment realistic head model obtained from the magnetic resonance images of a real subject, a known dipole assumption and 32 electrode positions, the performance of the proposed method is tested in simulation studies and it is shown that the proposed algorithm estimates the tissue conductivities with less than 1% error in noiseless measurements and less than 5% error when the signal-to-noise ratio is 40 dB or higher. We conclude that the proposed extended Kalman filter approach successfully estimates the tissue conductivities in vivo.

Simulating the propagation of spreading cortical depression (SCD) wavefront on human brain surface.

Spreading cortical depression (SCD) is a slowly spreading supression of electroencephalogram (EEG) activity that was first observed in anaesthetized rabbits in 1944. Since then, the spatial properties of propagation have been investigated on numerous animal experiments. In the folded and complex human cortex, both the occurrence of SCD and the relationship between SCD and migraine have been discussed controversially. This study proposes a software tool to simulate the possible wavefront motion on the surface of human brain. The SCD wavefront motion has been simulated up to an affected surface region of roughly 150 cm(2) and validated by clinical experts.

Tissue resistivity estimation in the presence of positional and geometrical uncertainties.

Geometrical uncertainties (organ boundary variation and electrode position uncertainties) are the biggest sources of error in estimating electrical resistivity of tissues from body surface measurements. In this study, in order to decrease estimation errors, the statistically constrained minimum mean squared error estimation algorithm (MiMSEE) is constrained with a priori knowledge of the geometrical uncertainties in addition to the constraints based on geometry, resistivity range, linearization and instrumentation errors. The MiMSEE calculates an optimum inverse matrix, which maps the surface measurements to the unknown resistivity distribution. The required data are obtained from four-electrode impedance measurements, similar to injected-current electrical impedance tomography (EIT). In this study, the surface measurements are simulated by using a numerical thorax model. The data are perturbed with additive instrumentation noise. Simulated surface measurements are then used to estimate the tissue resistivities by using the proposed algorithm. The results are compared with the results of conventional least squares error estimator (LSEE). Depending on the region, the MiMSEE yields an estimation error between 0.42% and 31.3% compared with 7.12% to 2010% for the LSEE. It is shown that the MiMSEE is quite robust even in the case of geometrical uncertainties.

Use of a priori information in estimating tissue resistivities--application to measured data.

A statistically constrained minimum mean squares error estimator (MiMSEE) has been shown to be useful in estimating internal resistivity distribution by the use of simulated data. In this study, the performance of the MiMSEE algorithm is tested by using measured data from resistor phantoms. The MiMSEE uses a priori information on body geometry, electrode position, statistical properties of tissue resistivities, instrumentation noise and linearization error to calculate the optimum inverse matrix which maps the surface potentials to unknown regional resistivities. In this study, the MiMSEE is also constrained with the variance-covariance of the modelling error to improve the estimation accuracy. The data are obtained from two different phantom geometries, namely five-region and thorax. Using the measured data, the estimations are realized and errors are calculated. Then, the results are compared with the results obtained by using a conventional least squares error estimator (LSEE). The five-region model results show similarity with the simulation study results of Baysal and Eyüboglu. On the thorax model, the total estimation error is 34.2% with the MiMSEE compared with 856% with the LSEE. It is concluded that the MiMSEE is more robust than the LSEE and applicable to measured data.

Use of a priori information in estimating tissue resistivities--a simulation study.

Accurate estimation of tissue resistivities in vivo is needed to construct reliable human body volume conductor models in solving forward and inverse bioelectric field problems. The necessary data for the estimation can be obtained by using the four-electrode impedance measurement technique, usually employed in electrical impedance tomography. In this study, a priori geometrical information with statistical properties of regional resistivities and linearization error as well as instrumentation noise has been incorporated into a new resistivity estimation algorithm which is called a statistically constrained minimum mean squares error estimator (MiMSEE) to improve estimation accuracy. MiMSEE intakes geometrical information from the image which is obtained by using a high-resolution imaging modality. This study is an extension of earlier work by Eyüboglu et al and obtains simulated measurements from two numerical models containing five and six regions on a background region. Also, estimations are repeated by using up to eight multiple current electrode pairs, in order to observe the effect of estimation performance while increasing the number of measurements up to 96. The results are compared with a conventional least squares error estimator (LSEE) which is used in one-pass algorithms. It is shown that the MiMSEE estimation error is up to 27 times smaller than the LSEE error which is realized for a small, high-contrast region, for example the aorta. In estimating the regional resistivities, the MiMSEE algorithm requires 25.8 (for the five-region resistivity distribution) and 22.2 (for the six-region resistivity distribution) times more computational time than the LSEE. This gap between the computational times of the two algorithms decreases as the number of regions increases.

Application of electrical impedance tomography in diagnosis of emphysema--a clinical study.

In this paper, electrical impedance tomography (EIT) ventilation images from a group of 12 patients (11 patients with emphysema and one patient with only chronic obstructive pulmonary disease (COPD) (chronic bronchitis) and a group of 15 normal subjects were acquired using a Sheffield mark 1 EIT system, at the levels of second, fourth and sixth intercostal spaces. Patients were diagnosed based on CT scans of the thorax, pulmonary function tests and posteroanterior x-ray graphs. One of the patients with emphysema has also a malignant lung tumour. Ventilation-related conductivity changes at total lung capacity (TLC) relative to residual volume were measured quantitatively in EIT images. These quantitative values demonstrate marked differences compared to those values obtained from the EIT images of 15 normal subjects. The EIT images of the patients were also compared with the CT images. In addition to the visual examination of the EIT images a statistical confidence test is applied to compare the images of the patients with the images of the normal subjects. Prior to statistical analysis all images are normalized with TLC to minimize the effect of mismatch between the TLC of different subjects. A normal mean image is created by averaging the normalized images from the normal subjects, at each intercostal space level. Than a 95% confidence interval is defined for each normal mean image. For each image of the patients, a confidence test image, which represents the deviations from the 95% confidence interval of the normal mean image, is created. The regions with emphysematous bulla and parencyhma are detectable in the confidence test images as regions of positive and negative deviations from the confidence interval of the normal mean, respectively. In the test images, it is possible to differentiate emphysematous parenchyma from emphysematous bulla, tumour structure, and COPD. However, the emphysematous bulla, the tumour structure, and COPD result in the same type of defect in the test images and are therefore indistinguishable from each other. In some case, off-plane contributions in the EIT images may result in underestimation of the defects. EIT may be a useful screening device in detecting emphysema rather than a diagnostic tool.

A method for comparative evaluation of EIT algorithms using a standard data set.

The point spread function (PSF) is the most widely used tool for quantifying the spatial resolution of imaging systems. However, prerequisites for the proper use of this tool are linearity and space invariance. Because EIT is non-linear it is only possible to compare different reconstruction algorithms using a standard data set. In this study, the FEM is used to generate simulation data, which are used to investigate the non-linear behaviour of EIT, the space dependence of its PSF and its capability of resolving nearby objects. It is found that for the case of iterative backprojection (IterB), the full width half maximum (FWHM) values of single-object perturbations for central, intermediate and peripheral high-contrast objects are 27%, 18% and 14% of the imaging region diameter respectively. For the method based on singular value decomposition of the Geselowitz lead sensitivity matrix (GS-SVD), the FWHM is not space dependent and is 12% of the imaging region diameter. Conclusions obtained using single-object PSF studies must also be checked with double-object or more complex perturbations because EIT is non-linear. For example, the GS-SVD method fails to detect two widely separated objects unless the truncation level of SVD is carefully adjusted. With more truncation, however, the resolution of the method is worsened. Based on these and similar observations a set of simulation data, which is proposed for comparative evaluation of different EIT algorithms, is specified and explained in the conclusion section.