Complex conductivity reconstruction in multiple frequency electrical impedance tomography for fabric-based pressure sensor

This paper presents a pure element-free Galerkin method (EFGM) forward model for image reconstruction in 2D and 3D electrical impedance tomography (EIT) using an adaptive current injection method. In EIT systems with the adapting current injection method, both static and dynamic images can be reconstructed; however, determination of electrode contact impedances in the complete electrode model is difficult and the Gap model is used. In this paper, in the EIT forward problem a weak form functional based on the Gap model and a pure EFGM approach are developed, and in the EIT inverse problem, Jacobian matrix is computed by the EFGM, and a fast integration technique is introduced to calculate the entries of the Jacobian matrix within an adequate computation time. The influence of increasing the density of nodes at and near the electrodes with steep electric potential gradients on the accuracy of FEM and EFGM forward solutions is investigated, and the performance of the image reconstruction algorithm with the proposed fast integration technique is examined. The numerical results reveal that the proposed EFGM forward model with the fast integration technique has an efficient performance both in terms of mean relative imaging errors and computational time.

Objective. Currently no efficient and reliable technique exists to routinely assess surgical margins during a radical prostatectomy. Electrical impedance spectroscopy (EIS) has been reported as a potential technique to provide surgeons with real-time intraoperative margin assessment. In addition to providing a quantified measure of margin status, a co-registered electrical impedance tomography (EIT) image presented on a surgeon’s workstation could add value to the margin assessment process. Approach. To investigate this, we conducted a comparative study between EIS and EIT to evaluate the potential these technologies might have for margin assessment. EIS and EIT data was acquired from ex vivo human prostates using a multi-electrode endoscopic impedance acquisition probe. Main results. EIS and EIT show good predictive performance with a 0.76 and 0.80 area-under-curve (AUC), respectively, when considering discrete frequencies only. A machine learning (ML) algorithm is implemented to combine features, which improves the AUCs of EIS and EIT to 0.84 and 0.85, respectively. Single-step EIT takes significantly less time to reconstruct than multi-step EIT, yet provides similarly accurate classification results, making the single-step approach a potential candidate for real-time margin assessment. While the ML-based approach clearly exhibits benefits as compared to the single feature assessment, the decision to use EIS versus EIT is unclear since each approach performs better for different subsets of tissue classifications. Significance. The results presented in this paper corroborate our previous studies and present the strongest evidence yet that an intraoperative-capable impedance probe can be used to distinguish benign from malignant prostate tissues. An in vivo study with a large cohort will be necessary to definitively determine the preferred approach and to show the clinical effectiveness of using this technology for margin assessment.

A real-time EIT imaging system based on the split augmented Lagrangian shrinkage algorithm

This study evaluates the potential of complex 3D Electrical Impedance Tomography (EIT) for intraoperative surgical margin assessment (SMA) using an ex vivo bovine model. A custom electrode array was used to collect impedance data across multiple frequencies (100 Hz-1 MHz) from 57 tissue samples. An optimal pressure range was identified to ensure proper electrode contact with minimal tissue deformation (2 kPa to 5 kPa) and a saline calibration was used to minimize model-data mismatch. A novel best fit factor, β, was introduced to scale the reference data of difference EIT and initial guess for absolute EIT to eliminate inversions in permittivity. The accuracy of complex EIT reconstructions were investigated using pixel-based tissue classification. Experimental difference EIT, particularly for conductivity (σ) at 100 Hz, achieved high sensitivity (0.92) and specificity (0.90) with fast reconstruction speeds of 1.67 seconds. While absolute EIT performed slightly better in quantitative metrics for σ imaging (AUC = 0.90, Accuracy = 0.86), difference EIT was found to be more suitable for real-time applications due to its faster processing time. Simulations suggested that permittivity (ϵ) has sufficient contrast for classifying muscle and adipose tissue. However, experimental ϵ reconstructions exhibited lower performance, suggesting the need for hardware improvements. Difference EIT is the most promising method for real-time applications, balancing high accuracy with reconstruction speeds. Absolute EIT, while slightly more accurate, is less feasible due to longer processing times (150.6 seconds). This study advances the potential for real-time intraoperative SMA using a novel complex EIT reconstruction method.

Image reconstruction in electrical impedance tomography using the sensitivity theorem is generally based on the assumption that the initial conductivity distribution of the body being imaged is uniform. The technique of image reconstruction using this method is described and reconstructed images are presented. Improvements in image quality and accuracy are demonstrated when accurate a priori `anatomical' information, in the form of a model of the distribution of conductivity within the region to be imaged, is used to construct the sensitivity matrix. In practice correct a priori information is not available, for example the conductivity values within the various anatomical regions will not be known. An iterative algorithm is presented which allows the conductivity parameters of the a priori model to be determined during reconstruction. Keywords: electrical impedance tomography, image reconstruction, a priori information

This paper introduces a new method of simultaneous acquisition of electrocardiogram (ECG) signals and electrical impedance tomography (EIT) measurements on active electrodes, i.e. electrodes that are applying current, in an EIT system. Howland noise reduction followed by an integrate-and-dump filter and adaptive filtering are used to extract the ECG signal without loss of amplitude. Results of simultaneous ECG signals and EIT reconstructions on human subjects are shown. It is also demonstrated that the recovered ECG waveforms from 32 electrodes can be used to reconstruct the heart current source vectors during a cardiac cycle, yielding an approximate solution to the inverse problem of electrocardiography. Acquiring ECG signals from all electrodes attached to the body simultaneously with EIT data acquisition eliminates the need for a separate system to collect ECG signals. Time-aligned ECG signals are helpful in interpreting pulsatile perfusion images by providing exact timing of each image in relation to the cardiac cycle. Additionally, collecting ECG signals from many or all of the EIT electrodes enables reconstruction of the heart's moving dipole moment at the same time as the EIT images.

Contact pressure sensing and pressure mapping are commonly used in many automotive, healthcare, industrial, and robotics applications. Many commercially available pressure mapping solutions use a dense array of transducers embedded in a pad. However, the pad is relatively thick with noticeable rigid components, and high-resolution pressure mapping systems can be complex, cumbersome, bulky, expensive, and not portable. Thus, the objective of this study was to validate pressure mapping using a commercial Smartfoam interrogated using an electrical impedance tomography (EIT) measurement strategy and algorithm. In addition, the sensitivity of the Smartfoam was enhanced by depositing on its surface a piezoresistive carbon nanotube-based thin film. EIT electrodes were installed along the foam boundaries, thereby eliminating the need for any electrodes or rigid objects on the foam and pressure mapping surface. A custom data acquisition system was employed to apply electrical current excitations while measuring the boundary voltage response across pairs of boundary electrodes. The boundary voltage datasets were used for solving the EIT inverse problem to reconstruct the conductivity distribution of the specimen. Controlled pressure mapping tests were performed by placing different weights of varying contact areas on different positions of the nanocomposite Smartfoam. The EIT results confirmed that the nanocomposite Smartfoam could resolve pressure hotspots at different locations, as well as different magnitudes of contact pressure applied. Real-time pressure mapping was successfully demonstrated, while pressure mapping resolution and accuracy were also characterized. Overall, the system is lightweight, low-profile, and does not use rigid components on the foam surface. Future work will align this method for targeted consumer and healthcare applications.

Magnetic induction tomography (MIT) of biological tissue is used for the reconstruction of the complex conductivity distribution κ inside the object under investigation. It is based on the perturbation of an alternating magnetic field caused by the object and can be used in all applications of electrical impedance tomography (EIT) such as functional lung monitoring and assessment of tissue fluids. In contrast to EIT, MIT does not require electrodes and magnetic fields can also penetrate non-conducting barriers such as the skull. As in EIT, the reconstruction of absolute conductivity values is very difficult because of the method's sensitivity to numerical errors and noise. To overcome this problem, image reconstruction in EIT is often done differentially. Analogously, this concept has been adopted for MIT. Two different methods for differential imaging are applicable. The first one is state-differential, for example when the conductivity change between inspiration and expiration in the lung regions is being detected. The second one is frequency-differential, which is of high interest in motionless organs like the brain, where a state-differential method cannot be applied. An equation for frequency-differential MIT was derived taking into consideration the frequency dependence of the sensitivity matrix. This formula is valid if we can assume that only small conductivity changes occur. In this way, the non-linear inverse problem of MIT can be approximated by a linear one (depending only on the frequency), similar to in EIT. Keeping this limitation in mind, the conductivity changes between one or more reference frequencies and several measurement frequencies were reconstructed, yielding normalized conductivity spectra. Due to the differential character of the method, these spectra do not provide absolute conductivities but preserve the shape of the spectrum. The validity of the method was tested with artificial data generated with a spherical perturbation within a conducting cylinder as well as for real measurement data. The measurement data were obtained from a potato immersed in saline. The resulting spectra were compared with reference measurements and the preservation of the shape of the spectra was analyzed.

Impact of the Radial Basis Function Spread Factor onto Image Reconstruction in Electrical Impedance Tomography

This paper establishes for the first time that a coupled ultrasound (US) and electrical impedance tomography (EIT) system can serve as a non-invasive, spatially localized approach to extract clinically relevant muscle properties. The US/EIT system represents a potential enhancement to electrical impedance myography (EIM), which has shown promise as a non-invasive technology that may have important clinical use in indicating neuromuscular disease status and as a diagnostic tool. A 2.5D EIT algorithm evaluated on simulation, measured phantoms, and measured patient data was studied to evaluate US/EIT's ability to distinguish different aspects of muscle tissue. Simulated and phantom experiments revealed the depths of distinguishability of 3.2 and 4.2 mm in simulation for 10% and 20% changes in muscle properties, respectively, and 3.6 mm in measured phantom experiments assuming a 12% muscle conductivity change. Reconstructions from the patient data established that there were consistent differences 1) between longitudinal (along) and transverse (across) muscle conductivity reconstructions at frequencies of 40 and 80 kHz and 2) side-by-side comparison between healthy and diseased tissue in terms of conductivity, permittivity, and phase at 40 and 80 kHz. Comparisons were made between the EIT reconstructed values and electrical impedance spectroscopy (EIS) measurements (an available surrogate in place of standard EIM measurements) made with the US/EIT system, wherein 1) EIS and EIT show similar sensitivity to longitudinal and transverse differences and 2) EIT showed a more consistent ability to differentiate healthy and diseased tissue. These results suggest that US/EIT appears very promising for non-invasive and spatially localized diagnosis of muscle health.

Resistivity reconstruction of practical phantoms is studied with Projection Error Propagation-based Regularization (PEPR) method to improve the image quality in Electrical Impedance Tomography (EIT). PEPR method calculates the regularization parameter as a function of the projection error produced due to the mismatch between experimental measurements and the calculated data. The regularization parameter in the reconstruction algorithm automatically adjusts its magnitude depending on the noise level present in measured data as well as the ill-posedness of the Hessian matrix. Resistivity images are reconstructed from the practical phantom data using the Electrical Impedance Diffuse Optical Reconstruction Software (EIDORS). The resistivity images reconstructed with PEPR method are compared with the Single step Tikhonov Regularization (STR) and Modified Levenberg Regularization (LMR) techniques. The results show that, the PEPR technique reduces the reconstruction errors in each iteration and improves the reconstructed images with better contrast to noise ratio (CNR), percentage of contrast recovery (PCR), coefficient of contrast (COC) and diametric resistivity profile (DRP).KeywordsElectrical Impedance Tomography (EIT)Projection Error Propagation-based Regularization (PEPR)Practical PhantomsBoundary potentialsEIDORSResistivity reconstructionSTRLMR

Image reconstruction in electrical impedance tomography (EIT) deals with an ill-posed and non-linear inverse problem. It has the objective of minimizing the difference between simulated (virtual) object data and electric voltage measurements performed on a non-simulated (real) object. In this paper, a new approach to the simulated annealing method applied to the reconstruction of EIT images is described. The main advantage of this approach is that all conductivity parameters are updated simultaneously. Most methods that employ simulated annealing to the problem of EIT usually evaluate each conductivity parameter individually resulting in high computational cost. The algorithm was tested both with computationally generated data and with measurements performed on a physical tank. In both cases, the method was able to make data inversion, determining the position, the dimensions and the conductivity of materials in an opaque object plane.

Image reconstruction in electrical impedance tomography (EIT) is a non-linear inverse problem. The linear model is always used in most of the reconstruction algorithm in dynamic EIT, which causes large errors of image reconstruction. In this paper, we proposed a new image reconstruction method in dynamic EIT. In the method the artificial neural network based on the error back propagation algorithm (BP ANN) is used to express the non-linear relation between the impedance change position inside the measured object and the voltage change value measured on the surface of the object. Thus, the location ofthe impedance change can be decided by the measured voltage change on the surface, and then the impedance change image will be reconstructed with linear approximated method. The reconstructed error will be decreased largely, because the impedance change position can be detected precisely by our proposed method. The experimental results indicate that the precision of the reconstructed image with our method is greatly higher than that with the back projection method.

Purpose:Clinically, there exists a need to develop a non‐invasive technique for monitoring salivary activity. In this study, we investigate the feasibility of a using the electrical conductivity information from Electrical Impedance Tomography (EIT) to monitor salivary flow activity.Methods:To acquire EIT data, eight Ag/AgCl ECG electrodes were placed around the mandible of the subject. An EIT scan was obtained by injecting current at 50 KHz, 0.4 mA through each pair of electrodes and recording voltage across other electrode pairs. The functional conductivity image was obtained through reconstruction of the voltage data, using Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software (EIDORS) in Matlab. In using EIDORS, forward solution was obtained using a user‐defined finite element model shape and inverse solution was obtained using one‐step Gaussian solver. EIT scans of volunteer research team members were acquired for three different physiological states: pre‐stimulation, stimulation and post‐stimulation. For pre‐stimulation phase, data were collected in intervals of 5 minutes for 15 minutes. The salivary glands were then stimulated in the subject using lemon and the data were collected immediately. Post‐stimulation data were collected at 4 different timings after stimulation.Results:Variations were observed in the electrical conductivity patterns near parotid regions between the pre‐ and post‐stimulation stages. The three images acquired during the 15 minute pre‐stimulation phase showed no major changes in the conductivity. Immediately after stimulation, electrical conductivity increased near parotid regions and 15 minutes later slowly returned to pre‐stimulation level.Conclusion:In the present study involving human subjects, the change in electrical conductivity pattern shown in the EIT images, acquired at different times with and without stimulation of salivary glands, appeared to be consistent with the change in salivary gland activity. The conductivity changes imaged through EIT are potentially useful for the purpose of salivary monitoring.

We have recently built and tested a 32 channel, multi-frequency (1 kHz to 1 MHz) voltage mode system to investigate electrical impedance spectroscopy (EIS) imaging. We completed a series of phantom experiments to define the baseline imaging performance of our system. Our phantom consisted of a plastic circular tank (20 cm diameter) filled with 0.9% aqueous NaCl solution. Conductors and nonconductors of decreasing width (W5: 3.4 cm, W4: 2.54 cm, W3: 0.95 cm, W2: 0.64 cm and W1: 0.32 cm) were positioned at various distances from the tank edge (1 cm, 2 cm, 4 cm and 8 cm). The results suggest that the detection of objects less than 1 cm in width is limited to the first 1 to 2 cm from the tank edge for absolute images, but this depth can extend to 8 cm in difference images. Larger 3.4 cm wide objects can be detected in absolute images at depths up to 8 cm from the tank edge. Generally, conductor images were clearer than their nonconductor counterparts. Not only did electrode artefacts lessen as the frequency increased, but the system's maximum resolution was attained at the highest operating frequencies. Although the system recovered the value of the electrical conductivity at the correct order of magnitude, it tended to smooth out large property discontinuities. The calculated electrical permittivity in these phantom studies was inconclusive due to the presence of electrode artefacts.