Andrea Borsic

GREIT: A unified approach to 2D linear EIT reconstruction of lung images

Electrical impedance tomography (EIT) is an attractive method for clinically monitoring patients during mechanical ventilation, because it can provide a non-invasive continuous image of pulmonary impedance which indicates the distribution of ventilation. However, most clinical and physiological research in lung EIT is done using older and proprietary algorithms; this is an obstacle to interpretation of EIT images because the reconstructed images are not well characterized. To address this issue, we develop a consensus linear reconstruction algorithm for lung EIT, called GREIT (Graz consensus Reconstruction algorithm for EIT). This paper describes the unified approach to linear image reconstruction developed for GREIT. The framework for the linear reconstruction algorithm consists of (1) detailed finite element models of a representative adult and neonatal thorax, (2) consensus on the performance figures of merit for EIT image reconstruction and (3) a systematic approach to optimize a linear reconstruction matrix to desired performance measures. Consensus figures of merit, in order of importance, are (a) uniform amplitude response, (b) small and uniform position error, (c) small ringing artefacts, (d) uniform resolution, (e) limited shape deformation and (f) high resolution. Such figures of merit must be attained while maintaining small noise amplification and small sensitivity to electrode and boundary movement. This approach represents the consensus of a large and representative group of experts in EIT algorithm design and clinical applications for pulmonary monitoring. All software and data to implement and test the algorithm have been made available under an open source license which allows free research and commercial use.

In Vivo Impedance Imaging With Total Variation Regularization

We show that electrical impedance tomography (EIT) image reconstruction algorithms with regularization based on the total variation (TV) functional are suitable for in vivo imaging of physiological data. This reconstruction approach helps to preserve discontinuities in reconstructed profiles, such as step changes in electrical properties at interorgan boundaries, which are typically smoothed by traditional reconstruction algorithms. The use of the TV functional for regularization leads to the minimization of a nondifferentiable objective function in the inverse formulation. This cannot be efficiently solved with traditional optimization techniques such as the Newton method. We explore two implementations methods for regularization with the TV functional: the lagged diffusivity method and the primal dual-interior point method (PD-IPM). First we clarify the implementation details of these algorithms for EIT reconstruction. Next, we analyze the performance of these algorithms on noisy simulated data. Finally, we show reconstructed EIT images of in vivo data for ventilation and gastric emptying studies. In comparison to traditional quadratic regularization, TV regulariza tion shows improved ability to reconstruct sharp contrasts.

The correlation of in vivo and ex vivo tissue dielectric properties to validate electromagnetic breast imaging: initial clinical experience

Electromagnetic (EM) breast imaging provides low-cost, safe and potentially a more specific modality for cancer detection than conventional imaging systems. A primary difficulty in validating these EM imaging modalities is that the true dielectric property values of the particular breast being imaged are not readily available on an individual subject basis. Here, we describe our initial experience in seeking to correlate tomographic EM imaging studies with discrete point spectroscopy measurements of the dielectric properties of breast tissue. The protocol we have developed involves measurement of in vivo tissue properties during partial and full mastectomy procedures in the operating room (OR) followed by ex vivo tissue property recordings in the same locations in the excised tissue specimens in the pathology laboratory immediately after resection. We have successfully applied all of the elements of this validation protocol in a series of six women with cancer diagnoses. Conductivity and permittivity gauged from ex vivo samples over the frequency range 100 Hz-8.5 GHz are found to be similar to those reported in the literature. A decrease in both conductivity and permittivity is observed when these properties are gauged from ex vivo samples instead of in vivo. We present these results in addition to a case study demonstrating how discrete point spectroscopy measurements of the tissue can be correlated and used to validate EM imaging studies.

Generation of anisotropic-smoothness regularization filters for EIT

In the inverse conductivity problem, as in any ill-posed inverse problem, regularization techniques are necessary in order to stabilize inversion. A common way to implement regularization in electrical impedance tomography is to use Tikhonov regularization. The inverse problem is formulated as a minimization of two terms: the mismatch of the measurements against the model, and the regularization functional. Most commonly, differential operators are used as regularization functionals, leading to smooth solutions. Whenever the imaged region presents discontinuities in the conductivity distribution, such as interorgan boundaries, the smoothness prior is not consistent with the actual situation. In these cases, the reconstruction is enhanced by relaxing the smoothness constraints in the direction normal to the discontinuity. In this paper, we derive a method for generating Gaussian anisotropic regularization filters. The filters are generated on the basis of the prior structural information, allowing a better reconstruction of conductivity profiles matching these priors. When incorporating prior information into a reconstruction algorithm, the risk is of biasing the inverse solutions toward the assumed distributions. Simulations show that, with a careful selection of the regularization parameters, the reconstruction algorithm is still able to detect conductivities patterns that violate the prior information. A generalized singular-value decomposition analysis of the effects of the anisotropic filters on regularization is presented in the last sections of the paper.

A primal?dual interior-point framework for using the L1 or L2 norm on the data and regularization terms of inverse problems

Maximum a posteriori estimates in inverse problems are often based on quadratic formulations, corresponding to a least-squares fitting of the data and to the use of the L2 norm on the regularization term. While the implementation of this estimation is straightforward and usually based on the Gauss–Newton method, resulting estimates are sensitive to outliers and result in spatial distributions of the estimates that are smooth. As an alternative, the use of the L1 norm on the data term renders the estimation robust to outliers, and the use of the L1 norm on the regularization term allows the reconstruction of sharp spatial profiles. The ability therefore to use the L1 norm either on the data term, on the regularization term, or on both is desirable, though the use of this norm results in non-smooth objective functions which require more sophisticated implementations compared to quadratic algorithms. Methods for L1-norm minimization have been studied in a number of contexts, including in the recently popular total variation regularization. Different approaches have been used and methods based on primal–dual interior-point methods (PD-IPMs) have been shown to be particularly efficient. In this paper we derive a PD-IPM framework for using the L1 norm indifferently on the two terms of an inverse problem. We use electrical impedance tomography as an example inverse problem to demonstrate the implementation of the algorithms we derive, and the effect of choosing the L2 or the L1 norm on the two terms of the inverse problem. Pseudo-codes for the algorithms and a public domain implementation are provided.

Electrical impedance tomography reconstruction for three-dimensional imaging of the prostate

Transrectal electrical impedance tomography (TREIT) has been proposed as an adjunct modality for enhancing standard clinical ultrasound (US) imaging of the prostate. The proposed TREIT probe has an array of electrodes adhered to the surface of a cylindrical US probe that is introduced inside of the imaging volume. Reconstructing TREIT images in the open-domain geometry established with this technique poses additional challenges to those encountered with closed-domain geometries, present in more conventional EIT systems, because of the rapidly decaying current densities at increasing distances from the probe surface. We developed a finite element method (FEM)-based dual-mesh reconstruction algorithm which employs an interpolation scheme for linking a fine forward mesh with a coarse grid of pixels, used for conductivity estimation. Simulation studies using the developed algorithm demonstrate the feasibility of imaging moderately contrasting inclusions at distances of three times the probe radius from the probe surface and at multiple angles about the probes axis. The large, dense FEM meshes used here require significant computational effort. We have optimized our reconstruction algorithm with multi-core processing hardware and efficient parallelized computational software packages to achieve a speedup of 9.3 times when compared to a more traditional Matlab-based, single CPU solution. The simulation findings and computational optimization provide a state-of-the-art reconstruction platform for use in further evaluating transrectal electrical impedance tomography.

FPGA-Based Voltage and Current Dual Drive System for High Frame Rate Electrical Impedance Tomography

Electrical impedance tomography (EIT) is used to image the electrical property distribution of a tissue under test. An EIT system comprises complex hardware and software modules, which are typically designed for a specific application. Upgrading these modules is a time-consuming process, and requires rigorous testing to ensure proper functioning of new modules with the existing ones. To this end, we developed a modular and reconfigurable data acquisition (DAQ) system using National Instruments (NI) hardware and software modules, which offer inherent compatibility over generations of hardware and software revisions. The system can be configured to use up to 32-channels. This EIT system can be used to interchangeably apply current or voltage signal, and measure the tissue response in a semi-parallel fashion. A novel signal averaging algorithm, and 512-point fast Fourier transform (FFT) computation block was implemented on the FPGA. FFT output bins were classified as signal or noise. Signal bins constitute a tissues response to a pure or mixed tone signal. Signal bins data can be used for traditional applications, as well as synchronous frequency-difference imaging. Noise bins were used to compute noise power on the FPGA. Noise power represents a metric of signal quality, and can be used to ensure proper tissue-electrode contact. Allocation of these computationally expensive tasks to the FPGA reduced the required bandwidth between PC, and the FPGA for high frame rate EIT. In 16-channel configuration, with a signal-averaging factor of 8, the DAQ frame rate at 100 kHz exceeded 110 frames s -1, and signal-to-noise ratio exceeded 90 dB across the spectrum. Reciprocity error was found to be for frequencies up to 1 MHz. Static imaging experiments were performed on a high-conductivity inclusion placed in a saline filled tank; the inclusion was clearly localized in the reconstructions obtained for both absolute current and voltage mode data.

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 systems 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 technologys ability to detect low contrast inclusions suggests that it has the potential to successfully detect prostate cancer.

An experimental clinical evaluation of EIT imaging with ℓ1 data and image norms

Electrical impedance tomography (EIT) produces an image of internal conductivity distributions in a body from current injection and electrical measurements at surface electrodes. Typically, image reconstruction is formulated using regularized schemes in which ℓ2-norms are used for both data misfit and image prior terms. Such a formulation is computationally convenient, but favours smooth conductivity solutions and is sensitive to outliers. Recent studies highlighted the potential of ℓ1-norm and provided the mathematical basis to improve image quality and robustness of the images to data outliers. In this paper, we (i) extended a primal-dual interior point method (PDIPM) algorithm to 2.5D EIT image reconstruction to solve ℓ1 and mixed ℓ1/ℓ2 formulations efficiently, (ii) evaluated the formulation on clinical and experimental data, and (iii) developed a practical strategy to select hyperparameters using the L-curve which requires minimum user-dependence. The PDIPM algorithm was evaluated using clinical and experimental scenarios on human lung and dog breathing with known electrode errors, which requires a rigorous regularization and causes the failure of reconstruction with an ℓ2-norm solution. The results showed that an ℓ1 solution is not only more robust to unavoidable measurement errors in a clinical setting, but it also provides high contrast resolution on organ boundaries.

Sensitivity study and optimization of a 3D electric impedance tomography prostate probe

In current clinical practice, the primary diagnostic method for testing for prostate cancer is ultrasound-guided biopsy. In this paper, we consider using a sonolucent array of electrodes, printed on a thin Kapton layer and positioned on the imaging window of a transrectal ultrasound probe, as a method for providing coregistered electrical and ultrasound imaging of the prostate. As the electrical properties of malignant tissues have been shown to differ significantly from benign tissues, the estimation of the electrical properties is expected to be helpful in distinguishing certain beginning pathologies from cancer and in improving the detection rate that current biopsy methods provide. One of the main difficulties in estimating electrical properties of tissues with this electrode configuration is the rapid decay of the sensitivity with distance from the sensing array. In order to partially overcome this difficulty, we propose to use prior information from the ultrasound (US). Specifically we intend to delineate the boundaries of the prostate from the US, to subdivide the organ into a small number of voxels and to estimate the conductivity as constant on each of these subvolumes. We use a 3D forward model based on the finite element method for studying the sensitivity of a simulated segmented prostate for three different electrode array designs. The three designs present different electrode areas and inter-electrode gaps. Larger electrodes are desirable as they present a better contact, but we show that as they result in smaller inter-electrode gaps, shunting currents can be significant and the sensitivity is reduced. Because our clinical measurement system employs a single current source, we consider tetrapolar measurement patterns for evaluating these electrode configurations. Optimal measurement patterns are well defined for adaptive systems, where multiple currents are injected at the same time. For the electrode array designs we consider, which are three dimensional, there are no established systematic methods for forming sets of linearly independent tetrapolar measurement patterns. We develop a novel method for automatically computing a full set of independent tetrapolar measurement patterns that maximizes the sensitivity in a region of interest (ROI). We use these patterns in the forward modeling and sensitivity studies. In addition to the electrode arrays on the probe, we study the use of a further configuration, where a distal electrode is positioned on the exterior of the body and used for current injection.