A vector derivation useful in impedance plethysmographic field calculations

Posterior Approximate Clustering-Based Sensitivity Matrix Decomposition for Electrical Impedance Tomography

This paper introduces a sensitivity matrix decomposition regularization (SMDR) method for electric impedance tomography (EIT). Using k-means clustering, the EIT-reconstructed image can be divided into four clusters, derived based on image features, representing posterior information. The sensitivity matrix is then decomposed into distinct work areas based on these clusters. The elimination of smooth edge effects is achieved through differentiation of the images from the decomposed sensitivity matrix and further post-processing reliant on image features. The algorithm ensures low computational complexity and avoids introducing extra parameters. Numerical simulations and experimental data verification highlight the effectiveness of SMDR. The proposed SMDR algorithm demonstrates higher accuracy and robustness compared to the typical Tikhonov regularization and the iterative penalty term-based regularization method (with an improvement of up to 0.1156 in correlation coefficient). Moreover, SMDR achieves a harmonious balance between image fidelity and sparsity, effectively addressing practical application requirements.

Arts of electrical impedance tomographic sensing

This paper reviews governing theorems in electrical impedance sensing for analysing the relationships of boundary voltages obtained from different sensing strategies. It reports that both the boundary voltage values and the associated sensitivity matrix of an alternative sensing strategy can be derived from a set of full independent measurements and sensitivity matrix obtained from other sensing strategy. A new sensing method for regional imaging with limited measurements is reported. It also proves that the sensitivity coefficient back-projection algorithm does not always work for all sensing strategies, unless the diagonal elements of the transformed matrix, A(T)A, have significant values and can be approximate to a diagonal matrix. Imaging capabilities of few sensing strategies were verified with static set-ups, which suggest the adjacent electrode pair sensing strategy displays better performance compared with the diametrically opposite protocol, with both the back-projection and multi-step image reconstruction methods. An application of electrical impedance tomography for sensing gas in water two-phase flows is demonstrated. This article is part of the themed issue 'Supersensing through industrial process tomography'.

Analysis of the spatial sensitivity of conductance/admittance catheter ventricular volume estimation

Conductance catheters are known to have a nonuniform spatial sensitivity due to the distribution of the electric field. The Geselowitz relation is applied to murine and multisegment conductance catheters using finite element models to determine the spatial sensitivity in a uniform medium and simplified left ventricle models. A new formulation is proposed that allows determination of the spatial sensitivity to admittance. Analysis of FEM numerical modeling results using the Geselowitz relation provides a true measure of parallel conductance in simplified left ventricle models for assessment of the admittance method and hypertonic saline techniques. The spatial sensitivity of blood conductance (Gb) is determined throughout the cardiac cycle. Gb is converted to volume using Wei's equation to determine if the presence of myocardium alters the nonlinear relationship through changes to the electric field. Results show that muscle conductance (Gm) from the admittance method matches results from the Geselowitz relation and that the relationship between Gb and volume is accurately fit using Wei's equation. Single-segment admittance measurements in large animals result in a more evenly distributed sensitivity to the LV blood pool. The hypertonic saline method overestimates parallel conductance throughout the cardiac cycle in both murine and multisegment conductance catheters.

Application of the Geselowitz relationship to the murine conductance catheter

Conductance catheters are known to have a nonuniform spatial sensitivity due to the distribution of the electric field. The Geselowitz relation is applied to the murine conductance catheter using a finite element model to determine catheter's spatial sensitivity in uniform media. Further analysis of FEM numerical modeling results using the Geselowitz relation provides a true measure of parallel conductance in a simplified murine left ventricle for assessment of the admittance method and hypertonic saline techniques. The spatial sensitivity of blood conductance (G(b)) is determined throughout the cardiac cycle. G(b) is converted to volume using Wei's equation to determine if the presence of myocardium alters the nonlinear relationship through changes to the electric field shape. Results show that the admittance method correctly calculates G(b) in comparison to the Geselowitz relation, and that the relationship between G(b) and volume is accurately fit using Wei's equation.

Electrode configurations for detection of intraventricular haemorrhage in the premature neonate

Intraventricular haemorrhage is a common cause of death in premature human infants. As preventative measures and treatments become available, a method for monitoring and detection is required. Electrical impedance tomography (EIT) is a viable monitoring method compared to modalities such as ultrasound, MRI or CT because of its low cost and contrast sensitivity to blood. However, its sensitivity to blood may be obscured by the low conductivity skull, high conductivity cerebrospinal fluid (CSF) and shape changes in the head and body. We estimated the sensitivity of three 16-electrode and impedance measurement configurations to bleeding using both idealized spherical and realistic geometry three-dimensional finite element models of the neonatal head. Sensitivity distribution responses to alterations in skull composition as well as introduction of conductivity anomalies were determined. Of the three patterns tested, a measurement scheme that employed electrodes at locations based on the 10-20 EEG layout, and impedance measurements involving current return over the anterior fontanelle produced superior distinguishabilities in regions near the lateral ventricles. This configuration also showed strongly improved sensitivities and selectivities when skull composition was varied to include the anterior fontanelle. A pattern using electrodes placed in a ring about the equator of the model had similar sensitivities but performed worse than the EEG layout in terms of selectivity. The third pattern performed worse than either the Ring or EEG-based patterns in terms of sensitivity. The overall performance of the EEG-based pattern on a spherical homogeneous model was maintained in a sensitivity matrix calculated using a homogeneous realistic geometry model.

Electrical impedance tomography with an optimized calculable square sensor

Electrical impedance tomography is a technique that reconstructs the medium distribution in a region of interest through electrical measurements on its boundary. In this paper, an optimized square sensor was designed for electrical impedance tomography in order to obtain maximum information over the cross section of interest, e.g., circulating fluidized beds, in the sense of Shannon information entropy. An analytical model of the sensor was obtained using the conformal transformation. The model indicates that the square sensor possesses calculable property, which allows the calculation of standard values of the sensor directly from a single dimensional measurement that can be made traceable to the SI unit of length. Based on the model, the sensitivity maps and electrical field lines can be calculated in less than a second. Two model based algorithms for image reconstruction, i.e., back projection algorithm based on electrical field lines and iterative Lavrentiev regularization algorithm based on the sensitivity map, were introduced. Simulated results and experimental results validate the feasibility of the algorithms.

Imaging and quantification of anomaly volume using an eight-electrode 'hemiarray' EIT reconstruction method

Electrical impedance tomography (EIT) is particularly well-suited to applications where its portability, rapid acquisition speed and sensitivity give it a practical advantage over other monitoring or imaging systems. An EIT system's patient interface can potentially be adapted to match the target environment, and thereby increase its utility. It may thus be appropriate to use different electrode positions from those conventionally used in EIT in these cases. One application that may require this is the use of EIT on emergency medicine patients; in particular those who have suffered blunt abdominal trauma. In patients who have suffered major trauma, it is desirable to minimize the risk of spinal cord injury by avoiding lifting them. To adapt EIT to this requirement, we devised and evaluated a new electrode topology (the 'hemiarray') which comprises a set of eight electrodes placed only on the subject's anterior surface. Images were obtained using a two-dimensional sensitivity matrix and weighted singular value decomposition reconstruction. The hemiarray method's ability to quantify bleeding was evaluated by comparing its performance with conventional 2D reconstruction methods using data gathered from a saline phantom. We found that without applying corrections to reconstructed images it was possible to estimate blood volume in a two-dimensional hemiarray case with an uncertainty of around 27 ml. In an approximately 3D hemiarray case, volume prediction was possible with a maximum uncertainty of around 38 ml in the centre of the electrode plane. After application of a QI normalizing filter, average uncertainties in a two-dimensional hemiarray case were reduced to about 15 ml. Uncertainties in the approximate 3D case were reduced to about 30 ml.

The contribution of the lungs to thoracic impedance measurements: a simulation study based on a high resolution finite difference model

A high resolution electrical finite difference model of the human thorax based on a 43 slice MRI data set along with lead field theory was used to examine the contribution of the lungs to the total impedance for a typical mid-thoracic 2D EIT eight and sixteen electrode configuration. Regional analysis of the thoracic sources of impedance revealed that the maximum contribution of lungs to the total impedance was approximately 22% for the eight electrode array and 25% for the sixteen electrode array. Analysis of impedance distribution of the lungs using a mid-thoracic application showed that the contribution of impedance of each slice followed closely the volume of the lungs in the given slice. This suggests that the mid-thoracic application gives results reflecting the entire lung. The contributions of the lung impedance for the various electrode positions showed that the eight electrode configuration had a more smooth change between adjacent electrodes compared to the 16 electrode arrangement.

Analytical solutions of electric potential and impedance for a multilayered spherical volume conductor excited by time-harmonic electric current source: application in brain EIT

A model of a multilayered spherical volume conductor with four electrodes is built. In this model, a time-harmonic electric current is injected into the sphere through a pair of drive electrodes, and electric potential is measured by the other pair of measurement electrodes. By solving the boundary value problem of the electromagnetic field, the analytical solutions of electric potential and impedance in the whole conduction region are derived. The theoretical values of electric potential on the surface of the sphere are in good accordance with the experimental results. The analytical solutions are then applied to the simulation of the forward problem of brain electrical impedance tomography (EIT). The results show that, for a real human head, the imaginary part of the electric potential is not small enough to be ignored at above 20 kHz, and there exists an approximate linear relationship between the real and imaginary parts of the electric potential when the electromagnetic parameters of the innermost layer keep unchanged. Increase in the conductivity of the innermost layer leads to a decrease of the magnitude of both real and imaginary parts of the electric potential on the scalp. However, the increase of permittivity makes the magnitude of the imaginary part of the electric potential increase while that of the real part decreases, and vice versa.

The Contribution of Blood-Flow-Induced Conductivity Changes to Measured Impedance

The paper considers the contribution of conductivity changes undergone in an anisotropical medium to measured resistance. This was achieved by extending the relationship proposed by Geselowitz to anisotropical materials described, therefore, by a conductivity tensor. It was found that each element of a conductivity change tensor contributed to the measured resistance only if a corresponding component of the electrical field was nonzero. Numerical calculations were performed for blood-flow-associated conductivity changes. A special experiment stand was developed which allowed experiments to be performed proving the theoretical results. It was found that the absolute value of resistance change measured in the direction perpendicular to the vessel axis was much smaller than that measured along the vessel axis. The results obtained may explain the fact that the actual change of measured resistance created by changes of conductivity induced by aortic blood flow is lower than expected from simplified models.

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.

Regional head tissue conductivity estimation for improved EEG analysis

We develop a method for estimating regional head tissue conductivities in vivo, by injecting small (1-10 microA) electric currents into the scalp, and measuring the potentials at the remaining electrodes of a dense-array electroencephalography net. We first derive analytic expressions for the potentials generated by scalp current injection in a four-sphere model of the human head. We then use a multistart downhill simplex algorithm to find regional tissue conductivities which minimize the error between measured and computed scalp potentials. Two error functions are studied, with similar results. The results show that, despite the low skull conductivity and expected shunting by the scalp, all four regional conductivities can be determined to within a few percent error. The method is robust to the noise levels expected in practice. To obtain accurate results the cerebrospinal fluid must be included in the forward solution, but may be treated as a known parameter in the inverse solution.

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.