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.

Distinguishability analysis of an induced current EIT system using discrete coils.

The distinguishability of a discrete coil induced current electrical impedance tomography system is analysed. The solution methodology of the forward problem of this system is explained. An optimization procedure using this forward problem solution is developed to find optimum currents that maximize the distinguishability. For the concentric inhomogeneity problem, it is shown that the coil currents can be optimized to focus the current density in any desired location, in the field of view. Optimum coil currents under the constraints of limited peak coil currents and limited total power are determined. Examples that demonstrate the performance of the system are presented.

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.

An interleaved drive electrical impedance tomography image reconstruction algorithm.

In this study, a reconstruction algorithm for a 16-electrode interleaved-drive electrical impedance tomography (EIT) system is developed, based on inversion of an analytically calculated sensitivity matrix. The sensitivity matrix is calculated using Geselowitz's lead-sensitivity theorem. Eight interleaved electrodes out of 16 (equally spaced) electrodes are designated as current injection electrodes and the remaining eight electrodes are designated as measurement electrodes. The sensitivity matrix is singular, therefore singular value decomposition (SVD) of the sensitivity matrix, followed by pseudoinversion-with and without truncation-is used to reconstruct images. The algorithm is a single-pass algorithm. Data from a saline filled tank and in vivo data during respiration and the cardiac cycle, acquired by using a Sheffield multifrequency system, are used to reconstruct images. The effect of different truncation levels on the reconstructed images is investigated.

Impedance to defibrillation countershock: does an optimal impedance exist?

Defibrillation is thought to occur because of changes in the transmembrane potential that are caused by current flow through the heart tissue. Impedance to electric countershock is an important parameter because it is determined by the magnitude and distribution of the current that flows for a specific shock voltage. The impedance is comprised of resistive contributions from: (1) extra-tissue sources, which include the defibrillator, leads, and electrodes; (2) tissue sources, which include intracardiac and extra-cardiac tissue; and (3) the interface between electrode and tissue. Tissue sources dominate the impedance and probably contribute to the wide range of impedance values presented to the defibrillation pulse. Because impedance is not constant within or between subjects, defibrillators must be designed to accommodate these differences without compromising patient safety or therapeutic efficacy. Experimental investigations in animals and humans suggest that impedance changes at several different time scales ranging from milliseconds to years. These alterations are believed to be a result of both electrochemical and physiological mechanisms. It is commonly thought that impedance is optimized when it has been decreased to a minimum, since this allows the most current flow for a given voltage shock. However, if the impedance is lowered by changing the location or size of the electrodes in such a way that current flow is decreased in part of the heart even though current flow is increased elsewhere, then the total voltage, current, and energy needed for defibrillation may increase, not decrease, even though impedance is decreased. A simple boundary element computer model suggests that the most even distribution of current flow through the heart is achieved for those electrode locations in which the impedance across the heart is at or near the maximum cardiac impedance for any location of these particular electrodes. Thus, the optimum shock impedance is achieved when impedance is minimized for extra-tissue and extra-cardiac tissue sources and is at or near a maximum for intracardiac tissue sources.

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.

Estimation of tissue resistivities from multiple-electrode impedance measurements.

In order to measure in vivo resistivity of tissues in the thorax, the possibility of combining anatomical data extracted from high-resolution images with multiple-electrode impedance measurements, a priori knowledge of the range of tissue resistivities, and a priori data on the instrumentation noise is assessed in this study. A statistically constrained minimum-mean-square error estimator (MIMSEE) that minimizes the effects of linearization errors and instrumentation noise is developed and compared to the conventional least-squares error estimator (LSEE). The MIMSEE requires a priori signal and noise information. The statistical constraint signal information was obtained from a priori knowledge of the physiologically allowed range of regional resistivities. The noise constraint information was obtained from a priori knowledge of the linearization error and the instrumentation noise. The torso potentials were simulated by employing a three-dimensional canine torso model. The model consists of four different conductivity regions: heart, right lung, left lung, and body. It is demonstrated that the statistically constrained MIMSEE performs significantly better than the LSEE in determining resistivities. The results based on the torso model indicate that regional resistivities can be estimated to within 40% accuracy of their true values by utilizing a statistically constrained MIMSEE, even if the instrumentation noise is comparable to the measured torso potentials. The errors obtained using the LSEE with the same linearized transfer function and level of instrumentation noise were about five times larger than those obtained using the MIMSEE. For larger measurement errors the MIMSEE performs even better when compared to the LSEE.

Comments on distinguishability in electrical impedance imaging.

In Electrical Impedance Imaging (EII), the spatial distribution of electrical resistivity of a volume conductor is reconstructed from measurements of potential which result from an externally applied electric field. The ability of such a system to distinguish a target inhomogeneity and the discussion of several measures of distinguishability has been a subject of a recent study. In this communication a few comments are added to those of. The medical device safety regulations limit the maximum total input current which can be applied to the human thorax. Based on the currently existing safety regulations, if the input current to the thorax is limited and constant, patterns applied between opposite electrodes result in higher distinguishability of a centered target than the cosine current patterns as suggested by.

In vivo imaging of cardiac related impedance changes.

Electrical impedance tomography (EIT) produces cross-sectional images of the electrical resistivity distribution within the body, made from voltage or current measurements through electrodes attached around the body. The authors describe a gated EIT system to image the cardiogenic electrical resistivity variations and the results of in vivo studies on human subjects. It is shown that the sensitivity of EIT to tissue resistivity variations due to blood perfusion is good enough to image blood flow to the lungs; hence, abnormalities in pulmonary perfusion, such as pulmonary embolism, should appear in EIT images. In addition, more valuable information related to the cardiac activity can be gained from EIT images than from impedance cardiography. It is thus likely that a cardiac output index may be calculable from the average resistivity variations over the ventricles, but considerable research is required before the images can be understood in detail.

Methods of cardiac gating applied potential tomography.

Electrical impedance imaging of the heart, pulmonary perfusion and the great blood vessels can only be achieved by synchronising the data collection with cardiac activity. Due to low signal-to-noise ratio, temporal averaging is needed to improve the image quality. In this study several methods of ECG gating are attempted to synchronise the applied potential tomography (APT) serial data collection with the cardiac cycle. They allow us to collect sequential images time-locked with the R-wave of the patient, and hence image the pulsatile movement of blood. Different methods are examined for their sampling speeds, noise levels and ability to image before systole. A method of image data rearrangement in order to provide an apparent increase in speed is also discussed.

Problems of cardiac output determination from electrical impedance tomography scans.

Impedance variations within the thorax related to cardiac activity have been localised using cardiac gated electrical impedance images. Since quantitative measurements of local variations can be made from those images, electrical impedance tomography gives more valuable information than impedance cardiography (ICG). However, because of the three-dimensional (3D) and non-uniform nature of the sensitivity function, localised measurements from electrical impedance tomography (EIT) scans are related to the position and geometry of the regions in which a resistivity change occurs. For accurate determination of volume changes from conductivity variations, the 3D sensitivity distribution needs to be known.

Localisation of cardiac related impedance changes in the thorax.

The existence of variations of normal human thoracic impedance, during the cardiac cycle to high frequency electrical current is well known. Since the impedance variations within the thorax are synchronous with the electrocardiogram (ECG), they are attributed to cardiac activity. They can arise from the change of either the rate of blood flow or the blood volume in the heart chambers, the great blood vessels and the lungs. However, their relative contribution is not known. Many investigators have worked on the non-invasive determination of some cardiac parameters using surface electrode impedance measurements on the thorax. Since the relationships between the measurement results and the pulsatile circulation of blood in various organs inside the chest are not well known, the information determined by surface impedance measurements is not as accurate as the results of invasive techniques. Recent advances in the clinical use of applied potential tomography (APT), or electrical impedance imaging, showed that the APT system gives a good soft-tissue contrast and has good sensitivity to resistivity changes. It is therefore concluded that the origin of thoracic impedance changes related to cardiac activity can be deduced from APT images. Our initial studies of ECG gated dynamic APT images of the thorax show that cardiac related thoracic impedance variations originating from different organs can be separated. Sequential APT images of the thorax during the cardiac cycle are presented. The movement of blood from the ventricles to the lungs and vascular system and back to the ventricles is observable in these images.(ABSTRACT TRUNCATED AT 250 WORDS)