Electrical impedance tomography imaging using a priori ultrasound data

Improved resolution of D-bar images of ventilation using a Schur complement property and an anatomical atlas

BACKGROUND

Electrical impedance tomography (EIT) is a nonionizing imaging technique for real-time imaging of ventilation of patients with respiratory distress. Cross-sectional dynamic images are formed by reconstructing the conductivity distribution from measured voltage data arising from applied alternating currents on electrodes placed circumferentially around the chest. Since the conductivity of lung tissue depends on air content, blood flow, and the presence of pathology, the dynamic images provide regional information about ventilation, pulsatile perfusion, and abnormalities. However, due to the ill-posedness of the inverse conductivity problem, EIT images have a coarse spatial resolution. One method of improving the resolution is to include prior information in the reconstruction.

PURPOSE

In this work, we propose a technique in which a statistical prior built from an anatomical atlas is used to postprocess EIT reconstructions of human chest data. The effectiveness of the method is demonstrated on data from two patients with cystic fibrosis.

METHODS

A direct reconstruction algorithm known as the D-bar method was used to compute a two-dimensional reconstruction of the conductivity distribution in the plane of the electrodes. Reconstructions using one step in an iterative (regularized) Newton's method were also computed for comparison. An anatomical atlas consisting of 1589 synthetic EIT images computed from X-ray computed tomography (CT) scans of 74 adult male subjects was computed for use as a statistical prior. The resolution of the D-bar images was then improved by maximizing the conditional probability density function of an image that is consistent with the a priori information and the statistical model. A new method to evaluate the accuracy of the EIT images using CT scans of the imaged patient as ground truth is presented. The novel approach is tested on data from two patients with cystic fibrosis.

RESULTS AND CONCLUSIONS

The D-bar images resulted in better structural similarity index measures (SSIM) and multiscale (MS) SSIM measures for both subjects using the mask or amplitude evaluation approach than the one-step (regularized) Newton's method. Further improvement was achieved using the Schur complement (SC) approach, with MS-SSIM values of 0.718 and 0.682 using SC evaluated with the mask and amplitude approach, respectively, for Patient 1, and MS-SSIM values of 0.726 and 0.692 using SC evaluated with the mask and amplitude approach, respectively, for Patient 2. The results from applying an anatomical atlas and statistical prior to EIT data from two patients with cystic fibrosis suggest that the spatial resolution of the EIT image can be improved to reveal pathology that may be difficult to discern in the original EIT image. The novel metric of evaluation is consistent with the appearance of improved spatial resolution and provides a new way to evaluate the accuracy of EIT reconstructions when a CT scan is available.

Complementary use of priors for pulmonary imaging with electrical impedance and ultrasound computed tomography

For medical professionals caring for patients undergoing mechanical ventilation due to respiratory failure, the ability to quickly and safely obtain images of pulmonary function at the patient's bedside would be highly desirable. Such images could be used to provide early warnings of developing pulmonary pathologies in real time, thereby reducing the incidence of complications and improving patient outcomes. Electrical impedance tomography (EIT) and low-frequency ultrasound computed tomography (USCT) are two imaging techniques with the potential to provide real-time non-ionizing pulmonary monitoring in the ICU setting, and each method has its own unique advantages as well as drawbacks. In this work, we describe a new algorithm for a system in which the strengths of the two modalities are combined in a complementary fashion. Specifically, preliminary reconstructions from each modality are used as priors to stabilize subsequent reconstructions, providing improved spatial resolution, sharper organ boundaries, and enhanced appearance of pathologies and other features. Results are validated using three numerically simulated thoracic phantoms representing pulmonary pathologies.

Retrieval of the conductivity spectrum of tissuesin vitrowith novel multimodal tomography

OBJECTIVE

Imaging of tissue engineered three-dimensional (3D) specimens is challenging due to their thickness. We propose a novel multimodal imaging technique to obtain multi-physical 3D images and the electrical conductivity spectrum of tissue engineered specimensin vitro.

APPROACH

We combine simultaneous recording of rotational multifrequency electrical impedance tomography (R-mfEIT) with optical projection tomography (OPT). Structural details of the specimen provided by OPT are used here as geometrical priors for R-mfEIT.

MAIN RESULTS

This data fusion enables accurate retrieval of the conductivity spectrum of the specimen. We demonstrate experimentally the feasibility of the proposed technique using a potato phantom, adipose and liver tissues, and stem cells in biomaterial spheroids. The results indicate that the proposed technique can distinguish between viable and dead tissues and detect the presence of stem cells.

SIGNIFICANCE

This technique is expected to become a valuable tool for monitoring tissue engineered specimens' growth and viabilityin vitro.

Calderón's Method with a Spatial Prior for 2-D EIT Imaging of Ventilation and Perfusion

Bedside imaging of ventilation and perfusion is a leading application of 2-D medical electrical impedance tomography (EIT), in which dynamic cross-sectional images of the torso are created by numerically solving the inverse problem of computing the conductivity from voltage measurements arising on electrodes due to currents applied on electrodes on the surface. Methods of reconstruction may be direct or iterative. Calderón’s method is a direct reconstruction method based on complex geometrical optics solutions to Laplace’s equation capable of providing real-time reconstructions in a region of interest. In this paper, the importance of accurate modeling of the electrode location on the body is demonstrated on simulated and experimental data, and a method of including a priori spatial information in dynamic human subject data is presented. The results of accurate electrode modeling and a spatial prior are shown to improve detection of inhomogeneities not included in the prior and to improve the resolution of ventilation and perfusion images in a human subject.

Comparison of Electrical Impedance Tomography and Ultrasonography for Determination of Solid and Cystic Lesion Resembling Breast Tumor Embedded in Chicken Phantom

Ultrasonography (US) and Electrical Impedance Tomography (EIT) can be used to detect breast cancer. Ultrasonography is based on non-ionizing radiations without adverse biological effects. A set of electrodes was placed around the torso and a small alternating current (AC) was injected via two of the electrodes into the object. This study aimed to acquire preliminary data to evaluate the EIT method for differentiation of artificial solid and cystic tumors in comparison to standard US. This study used a phantom made from chicken meat. In order to obtain the image of the solid tumor, an olive with carrot insertion was done, and the cystic tumor was created by filling a small balloon with water. GE Logic C5 ultrasound was performed with a 12 MHz linear transducer. For EIT measurement, 16 ECG electrodes and 32 ECG electrodes were placed. Data processing was done using the Graz consensus Reconstruction algorithm for EIT (GREIT) and Newton's One Step Error Reconstructor (NOSER) methods. The artificial solid tumor produced an ultrasound image of an oval, inhomogeneous lesions. The GREIT method with 16 electrodes of artificial solid tumor did not show a match between the reconstructed image and the original object containing 2 anomalies, but a match was found with 32 electrodes. In the NOSER method, both 16 and 32 electrodes showed a match. Ultrasound of the artificial cystic tumor showed an oval, circumscribed, anechoic with posterior enhancement. Both the GREIT and NOSER methods using the artificial cystic tumor showed a match between the reconstructed image and the original object containing two anomalies. EIT has a lower imaging resolution in comparison to ultrasonography, but is progressively maturing as a tool for monitoring and imaging. The solid and cystic anomalies on the phantoms were visualized by the GREIT and NOSER methods except for the solid anomaly with the GREIT 16 electrodes.

Introduction of Sample Based Prior into the D-Bar Method Through a Schur Complement Property

Electrical impedance tomography (EIT) is a non-invasive medical imaging technique in which images of the conductivity in a region of interest in the body are computed from measurements of voltages on electrodes arising from low-frequency, low-amplitude applied currents. Mathematically, the inverse conductivity problem is nonlinear and ill-posed, and the reconstructions have characteristically low spatial resolution. One approach to improve the spatial resolution of EIT images is to include anatomically and physiologically-based prior information in the reconstruction algorithm. Statistical inversion theory provides a means of including prior information from a representative sample population. In this paper, a method is proposed to introduce statistical prior information into the D-bar method based on Schur complement properties. The method presents an improvement of the image obtained by the D-bar method by maximizing the conditional probability density function of an image that is consistent with a prior information and the model, given a D-bar image computed from the voltage measurements. Experimental phantoms show an improved spatial resolution by the use of the proposed method for the D-bar image reconstructions.

A second order Calderón's method with a correction term and a priori information

Calderón's method is a direct linearized reconstruction method for the inverse conductivity problem with the attribute that it can provide absolute images of both conductivity and permittivity with no need for forward modeling. In this work, an explicit relationship between Calderón's method and the D-bar method is provided, facilitating a "higher-order" Calderón's method in which a correction term is included, derived from the relationship to the D-bar method. Furthermore, a method of including a spatial prior is provided. These advances are demonstrated on simulated data and on tank data collected with the ACE1 EIT system.

DYNAMIC OPTIMIZED PRIORS FOR D-BAR RECONSTRUCTIONS OF HUMAN VENTILATION USING ELECTRICAL IMPEDANCE TOMOGRAPHY

A method of including dynamic spatial priors in the 2-D D-bar reconstruction algorithm is presented for use on time-difference reconstructions of human subject thoracic data. The conductivity values for the prior are updated at each frame in the reconstruction using an optimization method applied to the scattering transform. The updates of the dynamic spatial priors are guided by a principle component analysis of the data to determine the timepoint in the ventilatory (or cardiac) cycle. The effectiveness of the method is demonstrated on human subject ventilatory data.

A Statistical Shape-Constrained Reconstruction Framework for Electrical Impedance Tomography

A statistical shape-constrained reconstruction (SSCR) framework is presented to incorporate the statistical prior information of human lung shapes for lung electrical impedance tomography. The prior information is extracted from 8000 chest-computed tomography scans across 800 patients. The reconstruction framework is implemented with two approaches-a one-step SSCR and an iterative SSCR in lung imaging. The one-step SSCR provides fast and high accurate reconstructions of healthy lungs, whereas the iterative SSCR allows to simultaneously estimate the pre-injured lung and the injury lung part. The approaches are evaluated with the simulated examples of thorax imaging and also with the experimental data from a laboratory setting, with difference imaging considered in both the approaches. It is demonstrated that the accuracy of lung shape reconstruction is significantly improved. In addition, the proposed approaches are proved to be robust against measurement noise, modeling error caused by inaccurately known domain boundary, and the selection of the regularization parameters.

A novel time-difference electrical impedance tomography algorithm using multi-frequency information

BACKGROUND

Electrical impedance tomography (EIT) is a noninvasive, radiation-free, and low-cost imaging modality for monitoring the conductivity distribution inside a patient. Nowadays, time-difference EIT (tdEIT) is used extensively as it has fast imaging speed and can reflect the dynamic changes of diseases, which make it attractive for a number of medical applications. Moreover, modeling errors are compensated to some extent by subtraction of voltage measurements collected before and after the change. However, tissue conductivity varies with frequency and tdEIT does not efficiently exploit multi-frequency information as it only uses measurements associated with a single frequency.

METHODS

This paper proposes a tdEIT algorithm that imposes spectral constraints on the framework of the linear least squares problem. Simulation and phantom experiments are conducted to compare the proposed spectral constraints algorithm (SC) with the damped least squares algorithm (DLS), which is a stable tdEIT algorithm used in clinical practice. The condition number and rank of the matrices needing inverses are analyzed, and image quality is evaluated using four indexes. The possibility of multi-tissue imaging and the influence of spectral errors are also explored.

RESULTS

Significant performance improvement is achieved by combining multi-frequency and time-difference information. The simulation results show that, in one-step iteration, both algorithms have the same condition number and rank, but SC effectively reduces image noise by 20.25% compared to DLS. In addition, deformation error and position error are reduced by 8.37% and 7.86%, respectively. In two-step iteration, the rank of SC is greatly increased, which suggests that more information is employed in image reconstruction. Image noise is further reduced by an average of 32.58%, and deformation error and position error are also reduced by 20.20% and 31.36%, respectively. The phantom results also indicate that SC has stronger noise suppression and target identification abilities, and this advantage is more obvious with iteration. The results of multi-tissue imaging show that SC has the unique advantage of automatically extracting a single tissue to image.

CONCLUSIONS

SC enables tdEIT to utilize multi-frequency information in cases where the spectral constraints are known and then provides higher quality images for applications.

EIT Imaging of admittivities with a D-bar method and spatial prior: experimental results for absolute and difference imaging

Electrical impedance tomography (EIT) is an emerging imaging modality that uses harmless electrical measurements taken on electrodes at a body's surface to recover information about the internal electrical conductivity and or permittivity. The image reconstruction task of EIT is a highly nonlinear inverse problem that is sensitive to noise and modeling errors making the image reconstruction task challenging. D-bar methods solve the nonlinear problem directly, bypassing the need for detailed and time-intensive forward models, to provide absolute (static) as well as time-difference EIT images. Coupling the D-bar methodology with the inclusion of high confidence a priori data results in a noise-robust regularized image reconstruction method. In this work, the a priori D-bar method for complex admittivities is demonstrated effective on experimental tank data for absolute imaging for the first time. Additionally, the method is adjusted for, and tested on, time-difference imaging scenarios. The ability of the method to be used for conductivity, permittivity, absolute as well as time-difference imaging provides the user with great flexibility without a high computational cost.

Incorporating a Spatial Prior into Nonlinear D-Bar EIT Imaging for Complex Admittivities

Electrical Impedance Tomography (EIT) aims to recover the internal conductivity and permittivity distributions of a body from electrical measurements taken on electrodes on the surface of the body. The reconstruction task is a severely ill-posed nonlinear inverse problem that is highly sensitive to measurement noise and modeling errors. Regularized D-bar methods have shown great promise in producing noise-robust algorithms by employing a low-pass filtering of nonlinear (nonphysical) Fourier transform data specific to the EIT problem. Including prior data with the approximate locations of major organ boundaries in the scattering transform provides a means of extending the radius of the low-pass filter to include higher frequency components in the reconstruction, in particular, features that are known with high confidence. This information is additionally included in the system of D-bar equations with an independent regularization parameter from that of the extended scattering transform. In this paper, this approach is used in the 2-D D-bar method for admittivity (conductivity as well as permittivity) EIT imaging. Noise-robust reconstructions are presented for simulated EIT data on chest-shaped phantoms with a simulated pneumothorax and pleural effusion. No assumption of the pathology is used in the construction of the prior, yet the method still produces significant enhancements of the underlying pathology (pneumothorax or pleural effusion) even in the presence of strong noise.

Sparse regularization for EIT reconstruction incorporating structural information derived from medical imaging

Electrical impedance tomography (EIT) reconstructs the conductivity distribution of a domain using electrical data on its boundary. This is an ill-posed inverse problem usually solved on a finite element mesh. For this article, a special regularization method incorporating structural information of the targeted domain is proposed and evaluated. Structural information was obtained either from computed tomography images or from preliminary EIT reconstructions by a modified k-means clustering. The proposed regularization method integrates this structural information into the reconstruction as a soft constraint preferring sparsity in group level. A first evaluation with Monte Carlo simulations indicated that the proposed solver is more robust to noise and the resulting images show fewer artifacts. This finding is supported by real data analysis. The structure based regularization has the potential to balance structural a priori information with data driven reconstruction. It is robust to noise, reduces artifacts and produces images that reflect anatomy and are thus easier to interpret for physicians.

Sensitivity study of an ultrasound coupled transrectal electrical impedance tomography system for prostate imaging

In 2009, prostate cancer ranked as the most common cancer and the second most fatal cancer in men in the United States. Unfortunately, the current clinical diagnostic methods (e.g. prostate-specific antigen (PSA), digital rectal examination, endorectal MRI, transrectal ultrasound, biopsy) used for detecting and staging prostate cancer are limited. It has been shown that cancerous prostate tissue has significantly different electrical properties when compared to benign tissues. Based on these electrical property findings, a transrectal electrical impedance tomography (TREIT) system is proposed as a novel prostate imaging modality. The TREIT system comprises an array of electrodes interfaced with a clinical transrectal ultrasound (TRUS) probe. We evaluate this imaging system through a series of phantom imaging experiments to assess the system's ability to image high and low contrast objects at various positions. We found that the TREIT system can easily discern high contrast inclusions of 1 cm in diameter at distances centered at two times the radius of the TREIT probe away from the probe surface. Furthermore, this technology's ability to detect low contrast inclusions suggests that it has the potential to successfully detect prostate cancer.

A bio-electromechanical imaging technique with combined electrical impedance and ultrasound tomography

Electrical impedance tomography (EIT) seeks to image the electrical conductivity of an object using electrical impedance measurement data at its periphery. Ultrasound reflection tomography (URT) is an imaging modality that is able to generate images of mechanical properties of the object in terms of acoustic impedance changes. Both URT and EIT have the potential to be used in various medical applications. In this paper we focus on breast tumour detection. Both URT and EIT belong to soft field tomography and suffer from the small amounts of available data and the inherently ill-posed nature of the inverse problems. These facts result in limited achievable reconstruction accuracy and resolution. A dual bio-electromechanical tomography system using ultrasound and electrical tomography is proposed in this paper to improve the detection of the small-size tumour. Data fusion techniques are implemented to combine the EIT/URT data. Based on simulations, we demonstrate the improvement of detection of small size anomalies and improved depth detection compared to single modality soft field tomography.