Multi-frequency electrical impedance tomography of the breast: new clinical results

Electrical impedance tomography (EIT) has been used in the recent past for a number of clinical applications. In this work we present recent tomographic and spectroscopic findings for breast imaging from clinical exams completed at Dartmouth. The results presented here are based on 18 normal and 24 abnormal subjects. The participants were classified as normal or abnormal using the American College of Radiology (ACR) indexing system for mammograms. The EIT data were collected for ten discrete frequencies in the range 10 kHz-1 MHz using a single array of 16 electrodes. The finite element method was used to reconstruct the images. The images were examined visually and were compared with mammograms. The results were also analyzed based on zonal averages of property values and breast tissue radiodensities. Statistical analysis showed a significance difference between the mean conductivity and permittivity values of normal and abnormal subjects for various zones defined on the reconstructed images. Tissues with high radiodensity also had increased conductivity and permittivity.     

A real-time volumetric visualization system for electrical impedance tomography

Three dimensional (3D) electrical impedance tomography (EIT) presents many additional challenges over and above those associated with two dimensional EIT systems. With present two dimensional (2D) systems, tomographs can be reconstructed and displayed on a PC with a standard computer monitor. In addition, using appropriate data acquisition hardware and simple image reconstruction algorithms, it is possible to collect, reconstruct and display volumetric EIT images in real time using parallel processing architectures. The advantages of this 'real-time' capability are many and include the ability to immediately assess the correct functioning of the system and the ability to track patient events and the effect of procedures in real time. Whilst 3D EIT boundary datasets can be collected in real time, their real-time image reconstruction and display presents some computational challenges. This explains why, to date, no real-time solutions have been presented. In addition the use of a standard computer monitor to display 3D volumes is unsatisfactory since not all depth cues are preserved when using this type of 2D display device. We present a system which is capable of displaying 3D EIT datasets in real time and allows interactive modification of the user's viewpoint. This allows the user to fly around (and through) the EIT volumetric dataset.     

Breast EIT using a new projected image reconstruction method with multi-frequency measurements

We propose a new method to produce admittivity images of the breast for the diagnosis of breast cancer using electrical impedance tomography(EIT). Considering the anatomical structure of the breast, we designed an electrode configuration where current-injection and voltage-sensing electrodes are separated in such a way that internal current pathways are approximately along the tangential direction of an array of voltage-sensing electrodes. Unlike conventional EIT imaging methods where the number of injected currents is maximized to increase the total amount of measured data, current is injected only twice between two pairs of current-injection electrodes attached along the circumferential side of the breast. For each current injection, the induced voltages are measured from the front surface of the breast using as many voltage-sensing electrodes as possible. Although this electrode configurational lows us to measure induced voltages only on the front surface of the breast,they are more sensitive to an anomaly inside the breast since such an injected current tends to produce a more uniform internal current density distribution. Furthermore, the sensitivity of a measured boundary voltage between two equipotential lines on the front surface of the breast is improved since those equipotential lines are perpendicular to the primary direction of internal current streamlines. One should note that this novel data collection method is different from those of other frontal plane techniques such as the x-ray projection and T-scan imaging methods because we do not get any data on the plane that is perpendicular to the current flow. To reconstruct admittivity images using two measured voltage data sets, a new projected image reconstruction algorithm is developed. Numerical simulations demonstrate the frequency-difference EIT imaging of the breast. The results show that the new method is promising to accurately detect and localize small anomalies inside the breast.     

Excitation patterns in three-dimensional electrical impedance tomography

Electrical impedance tomography (EIT) is a non-invasive technique that aims to reconstruct images of internal electrical properties of a domain, based on electrical measurements on the periphery. Improvements in instrumentation and numerical modeling have led to three-dimensional (3D) imaging. The availability of 3D modeling and imaging raises the question of identifying the best possible excitation patterns that will yield to data, which can be used to produce the best image reconstruction of internal properties. In this work, we describe our 3D finite element model of EIT. Through singular value decomposition as well as examples of reconstructed images, we show that for a homogenous female breast model with four layers of electrodes, a driving pattern where each excitation plane is a sinusoidal pattern out-of-phase with its neighboring plane produces better qualitative images. However, in terms of quantitative imaging an excitation pattern where all electrode layers are in phase produces better results.     

Using the GRID to improve the computation speed of electrical impedance tomography (EIT) reconstruction algorithms

In our group at University College London, we have been developing electrical impedance tomography (EIT) of brain function. We have attempted to improve image quality by the use of realistic anatomical meshes and, more recently, non-linear reconstruction methods. Reconstruction with linear methods, with pre-processing, may take up to a few minutes per image for even detailed meshes. However, iterative non-linear reconstruction methods require much more computational resources, and reconstruction with detailed meshes was taking far too long for clinical use. We present a solution to this timing bottleneck, using the resources of the GRID, the development of coordinated computing resources over the internet that are not subject to centralized control using standard, open, general-purpose protocols and are transparent to the user. Optimization was performed by splitting reconstruction of image series into individual jobs of one image each; no parallelization was attempted. Using the GRID middleware 'Condor' and a cluster of 920 nodes, reconstruction of EIT images of the human head with a non-linear algorithm was speeded up by 25-40 times compared to serial processing of each image. This distributed method is of direct practical value in applications such as EIT of epileptic seizures where hundreds of images are collected over the few minutes of a seizure and will be of value to clinical data collection with similar requirements. In the future, the same resources could be employed for the more ambitious task of parallelized code.     

An optimized strategy for real-time hemorrhage monitoring with electrical impedance tomography

Delayed detection of an internal hemorrhage may result in serious disabilities and possibly death for a patient. Currently, there are no portable medical imaging instruments that are suitable for long-term monitoring of patients at risk of internal hemorrhage. Electrical impedance tomography (EIT) has the potential to monitor patients continuously as a novel functional image modality and instantly detect the occurrence of an internal hemorrhage. However, the low spatial resolution and high sensitivity to noise of this technique have limited its application in clinics. In addition, due to the circular boundary display mode used in current EIT images, it is difficult for clinicians to identify precisely which organ is bleeding using this technique. The aim of this study was to propose an optimized strategy for EIT reconstruction to promote the use of EIT for clinical studies, which mainly includes the use of anatomically accurate boundary shapes, rapid selection of optimal regularization parameters and image fusion of EIT and computed tomography images. The method was evaluated on retroperitoneal and intraperitoneal bleeding piglet data. Both traditional backprojection images and optimized images among different boundary shapes were reconstructed and compared. The experimental results demonstrated that EIT images with precise anatomical information can be reconstructed in which the image resolution and resistance to noise can be improved effectively.     

Frequency-difference electrical impedance tomography (fdEIT): algorithm development and feasibility study

Frequency-difference electrical impedance tomography (fdEIT) has been proposed to deal with technical difficulties of a conventional static EIT imaging method caused by unknown boundary geometry, uncertainty in electrode positions and other systematic measurement artifacts. In fdEIT, we try to produce images showing changes of a complex conductivity distribution with respect to frequency. Simultaneously injecting currents with at least two frequencies, we find differences of measured boundary voltages between those frequencies. In most previous studies, real parts of frequency-difference voltage data were used to reconstruct conductivity changes and imaginary parts to reconstruct permittivity changes. This conventional approach neglects the interplay of conductivity and permittivity upon measured boundary voltage data. In this paper, we propose an improved fdEIT image reconstruction algorithm that properly handles the interaction. It uses weighted frequency differences of complex voltage data and a complex sensitivity matrix to reconstruct frequency-difference images of complex conductivity distributions. We found that there are two major sources of image contrast in fdEIT. The first is a contrast in complex conductivity values between an anomaly and background. The second is a frequency dependence of a complex conductivity distribution to be imaged. We note that even for the case where conductivity and permittivity do not change with frequency, the fdEIT algorithm may show a contrast in frequency-difference images of complex conductivity distributions. On the other hand, even if conductivity and permittivity values significantly change with frequency, there is an example where we cannot find any contrast. The performance of the proposed method is demonstrated by using computer simulations to validate its feasibility in future experimental studies.     

Reconstruction of conductivity changes and electrode movements based on EIT temporal sequences

Electrical impedance tomography (EIT) reconstructs a conductivity change image within a body from electrical measurements on the body surface; while it has relatively low spatial resolution, it has a high temporal resolution. One key difficulty with EIT measurements is due to the movement and position uncertainty of the electrodes, especially due to breathing and posture change. In this paper, we develop an approach to reconstruct both the conductivity change image and the electrode movements from the temporal sequence of EIT measurements. Since both the conductivity change and electrode movement are slow with respect to the data frame rate, there are significant temporal correlations which we formulate as priors for the regularized image reconstruction model. Image reconstruction is posed in terms of a regularization matrix and a Jacobian matrix which are augmented for the conductivity change and electrode movement, and then further augmented to concatenate the d previous and future frames. Results are shown for simulation, phantom and human data, and show that the proposed algorithm yields improved resolution and noise performance in comparison to a conventional one-step reconstruction method.     

Imaging of conductivity changes and electrode movement in EIT

Electrical impedance tomography (EIT) attempts to reconstruct the internal impedance distribution in a medium from electrical measurements at electrodes on the medium surface. One key difficulty with EIT measurements is due to the position uncertainty of the electrodes, especially for medical applications, in which the body surface moves during breathing and posture change. In this paper, we develop a new approach which directly reconstructs both electrode movements and internal conductivity changes for difference EIT. The reconstruction problem is formulated in terms of a regularized inverse, using an augmented Jacobian, sensitive to impedance change and electrode movement. A reconstruction prior term is computed to impose a smoothness constraint on both the spatial distribution of impedance change and electrode movement. A one-step regularized imaging algorithm is then implemented based on the augmented Jacobian and smoothness constraint. Images were reconstructed using the algorithm of this paper with data from simulated 2D and 3D conductivity changes and electrode movements, and from saline phantom measurements. Results showed good reconstruction of the actual electrode movements, as well as a dramatic reduction in image artefacts compared to images from the standard algorithm, which did not account for electrode movement.     

Evaluation of an EIT reconstruction algorithm using finite difference human thorax models as phantoms

A finite difference model of the human thorax with 113,400 control volumes (nodes) based on ECG gated MRI images was used to evaluate the Sheffield DAS-01P EIT system. Sixteen simulated electrode positions equally spaced around the thorax model at approximately the fourth intercostals space level were selected. Pairs of adjacent positions were excited sequentially by injecting current in a manner similar to that used by the Sheffield DAS-01P EIT system. The resulting voltages on the non-excited electrode positions were calculated and used to reconstruct the image using the Sheffield filtered back projection algorithm. By changing the resistivities of the lungs, the ventricles and the atria over a range of 1% to 40%, the resulting changes in the images were quantified by measuring the average resistivity change over a region defined automatically by two thresholds, 40% or 80% of the average of the first four pixels with the largest change. The results show that the changes observed in the images are consistently less than the changes in the model, but changed in a nearly linear manner as a function of resistivity in the model. For 40% resistivity changes in the model for right lung, right ventricle and right atrium, the observed resistivity changes in the region of interest (ROI, defined by the 80% threshold) of the images are 32% for the right lung, 11% for the right ventricle and 5.5% for the right atrium, which suggests strong volume dependence of EIT imaging. The effect of structural (size) change between end diastole and end systole was also studied, which showed large resistivity changes caused in the heart region of the constructed image. The study demonstrates that the Sheffield DAS-01P EIT reconstruction algorithm tracks the change occurring in the lungs most closely and with proper scaling may be used to observe physiological changes.     

Accounting for hardware imperfections in EIT image reconstruction algorithms

Electrical impedance tomography (EIT) is a non-invasive technique for imaging the conductivity distribution of a body section. Different types of EIT images can be reconstructed: absolute, time difference and frequency difference. Reconstruction algorithms are sensitive to many errors which translate into image artefacts. These errors generally result from incorrect modelling or inaccurate measurements. Every reconstruction algorithm incorporates a model of the physical set-up which must be as accurate as possible since any discrepancy with the actual set-up will cause image artefacts. Several methods have been proposed in the literature to improve the model realism, such as creating anatomical-shaped meshes, adding a complete electrode model and tracking changes in electrode contact impedances and positions. Absolute and frequency difference reconstruction algorithms are particularly sensitive to measurement errors and generally assume that measurements are made with an ideal EIT system. Real EIT systems have hardware imperfections that cause measurement errors. These errors translate into image artefacts since the reconstruction algorithm cannot properly discriminate genuine measurement variations produced by the medium under study from those caused by hardware imperfections. We therefore propose a method for eliminating these artefacts by integrating a model of the system hardware imperfections into the reconstruction algorithms. The effectiveness of the method has been evaluated by reconstructing absolute, time difference and frequency difference images with and without the hardware model from data acquired on a resistor mesh phantom. Results have shown that artefacts are smaller for images reconstructed with the model, especially for frequency difference imaging.     

A motion-compensated cone-beam CT using electrical impedance tomography imaging

Cone-beam CT (CBCT) is an imaging technique used in conjunction with radiation therapy. For example CBCT is used to verify the position of lung cancer tumours just prior to radiation treatment. The accuracy of the radiation treatment of thoracic and upper abdominal structures is heavily affected by respiratory movement. Such movement typically blurs the CBCT reconstruction and ideally should be removed. Hence motion-compensated CBCT has recently been researched for correcting image artefacts due to breathing motion. This paper presents a new dual-modality approach where CBCT is aided by using electrical impedance tomography (EIT) for motion compensation. EIT can generate images of contrasts in electrical properties. The main advantage of using EIT is its high temporal resolution. In this paper motion information is extracted from EIT images and incorporated directly in the CBCT reconstruction. In this study synthetic moving data are generated using simulated and experimental phantoms. The paper demonstrates that image blur, created as a result of motion, can be reduced through motion compensation with EIT.     

Optical breast shape capture and finite-element mesh generation for electrical impedance tomography

X-ray mammography is the standard for breast cancer screening. The development of alternative imaging modalities is desirable because mammograms expose patients to ionizing radiation. Electrical impedance tomography (EIT) may be used to determine tissue conductivity, a property which is an indicator of cancer presence. EIT is also a low-cost imaging solution and does not involve ionizing radiation. In breast EIT, impedance measurements are made using electrodes placed on the surface of the patient's breast. The complex conductivity of the volume of the breast is estimated by a reconstruction algorithm. EIT reconstruction is a severely ill-posed inverse problem. As a result, noisy instrumentation and incorrect modelling of the electrodes and domain shape produce significant image artefacts. In this paper, we propose a method that has the potential to reduce these errors by accurately modelling the patient breast shape. A 3D hand-held optical scanner is used to acquire the breast geometry and electrode positions. We develop methods for processing the data from the scanner and producing volume meshes accurately matching the breast surface and electrode locations, which can be used for image reconstruction. We demonstrate this method for a plaster breast phantom and a human subject. Using this approach will allow patient-specific finite-element meshes to be generated which has the potential to improve the clinical value of EIT for breast cancer diagnosis.     

Electrical impedance tomography of human brain function using reconstruction algorithms based on the finite element method

Electrical impedance tomography (EIT) is a recently developed technique which enables the internal conductivity of an object to be imaged using rings of external electrodes. In a recent study, EIT during cortical evoked responses showed encouraging changes in the raw impedance measurements, but reconstructed images were noisy. A simplified reconstruction algorithm was used which modelled the head as a homogeneous sphere. In the current study, the development and validation of an improved reconstruction algorithm are described in which realistic geometry and conductivity distributions have been incorporated using the finite element method. Data from computer simulations and spherical or head-shaped saline-filled tank phantoms, in which the skull was represented by a concentric shell of plaster of Paris or a real human skull, have been reconstructed into images. There were significant improvements in image quality as a result of the incorporation of accurate geometry and extracerebral layers in the reconstruction algorithm. Image quality, assessed by blinded subjective expert observers, also improved significantly when data from the previous evoked response study were reanalysed with the new algorithm. In preliminary images collected during epileptic seizures, the new algorithm generated EIT conductivity changes which were consistent with the electrographic ictal activity. Incorporation of realistic geometry and conductivity into the reconstruction algorithm significantly improves the quality of EIT images and lends encouragement to the belief that EIT may provide a low-cost, portable functional neuroimaging system in the foreseeable future.     

Use of statistical parametric mapping (SPM) to enhance electrical impedance tomography (EIT) image sets

Use of statistical parametric mapping (SPM), which is widely used in analysis of neuroimaging studies with fMRI and PET, has the potential to improve quality of EIT images for clinical use. Minimal modification to SPM is needed, but statistical analysis based on height, not extent thresholds, should be employed, due to the 20-80% variation of the point spread function, across EIT images. SPM was assessed in EIT images reconstructed with a linear time difference algorithm utilizing an anatomically realistic finite element model of the human head. Images of the average of data sets were compared with those produced using SPM over 10-40 individual image data sets without averaging. For a point disturbance, a sponge 15% of the diameter of an anatomically realistic saline-filled tank including a skull, with a contrast of 15%, and for visual evoked response data in 14 normal human volunteers, images produced with SPM were less noisy than the average images. For the human data, no consistent physiologically realistic changes were seen with either SPM or direct reconstruction; however, only a small data set was available, limiting the power of the SPM analysis. SPM may be used on EIT images and has the potential to extract improved images from clinical data series with a low signal-to-noise ratio.     

Direct EIT Jacobian calculations for conductivity change and electrode movement

Electrical impedance tomography (EIT) is very sensitive to deformations of the medium boundary shape. For lung imaging, breathing and changes in posture move the electrodes and change the chest shape, resulting in image artefacts. Several approaches have been proposed to improve the reconstructed images; most methods reconstruct both the boundary deformation and conductivity change from the measured data. These techniques require the calculation of the 'movement Jacobian', reflecting measurement changes due to the boundary deformation. Previous papers have calculated this Jacobian using perturbation techniques, which are slow (requiring multiple solutions of the forward problem) and become inaccurate with increasing finite element model size. This effect has limited reconstruction algorithms for deformable media to mostly 2D. To address this problem, we propose a direct method to calculate the Jacobian, based on a formulation of the derivatives of the finite element system matrix with respect to geometry changes. An illustrative example of these calculations is given, as well as a comparison between the proposed method and a perturbation method. Results show this method is approximately 300 times faster; and for larger model sizes, the perturbation method begins to diverge from those from the direct method proposed.     

Temporal image reconstruction in electrical impedance tomography

Electrical impedance tomography (EIT) calculates images of the body from body impedance measurements. While the spatial resolution of these images is relatively low, the temporal resolution of EIT data can be high. Most EIT reconstruction algorithms solve each data frame independently, although Kalman filter algorithms track the image changes across frames. This paper proposes a new approach which directly accounts for correlations between images in successive data frames. Image reconstruction is posed in terms of an augmented image x and measurement vector y, which concatenate the values from the d previous and future frames. Image reconstruction is then based on an augmented regularization matrix R, which accounts for a model of both the spatial and temporal correlations between image elements. Results are compared for reconstruction algorithms based on independent frames, Kalman filters and the proposed approach. For low values of the regularization hyperparameter, the proposed approach performs similarly to independent frames, but for higher hyperparameter values, it uses adjacent frame data to reduce reconstructed image noise.     

Numerical modelling errors in electrical impedance tomography

Electrical impedance tomography (EIT) is a non-invasive technique that aims to reconstruct images of internal impedance values of a volume of interest, based on measurements taken on the external boundary. Since most reconstruction algorithms rely on model-based approximations, it is important to ensure numerical accuracy for the model being used. This work demonstrates and highlights the importance of accurate modelling in terms of model discretization (meshing) and shows that although the predicted boundary data from a forward model may be within an accepted error, the calculated internal field, which is often used for image reconstruction, may contain errors, based on the mesh quality that will result in image artefacts.     

Imaging cardiac activity by the D-bar method for electrical impedance tomography

A practical D-bar algorithm for reconstructing conductivity changes from EIT data taken on electrodes in a 2D geometry is described. The algorithm is based on the global uniqueness proof of Nachman (1996 Ann. Math. 143 71-96) for the 2D inverse conductivity problem. Results are shown for reconstructions from data collected on electrodes placed around the circumference of a human chest to reconstruct a 2D cross-section of the torso. The images show changes in conductivity during a cardiac cycle.     

基于电阻抗成像技术的脑病变组织检测仿真研究

目的 采用电阻抗成像技术重建三维头部模型的阻抗分布图像,检测组织是否发生病变。方法 在有限元球头模型和真实头部模型两种三维组织模型上进行仿真,采用微分进化算法重构组织图像,有效定位阻抗突变区域,检测病变组织部位。结果 该算法能够精确重建组织图像,成功检测病变区域。结论 本法是一种简单、鲁棒性强的进化类全局优化算法,用于电阻抗成像技术中,进化总能得到很好收敛,成像质量较高,可靠性较强。