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.

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.

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.

A DIRECT RECONSTRUCTION ALGORITHM FOR THE ANISOTROPIC INVERSE CONDUCTIVITY PROBLEM BASED ON CALDERÓN'S METHOD IN THE PLANE.

A direct reconstruction algorithm based on Calderón's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic inverse conductivity problem, the entries of the unperturbed anisotropic tensors are assumed known a priori, and it remains to reconstruct the multiplicative scalar field. The quasi-conformal map in the plane facilitates the Calderón-based approach for anisotropic conductivities. The method is demonstrated on discontinuous radially symmetric conductivities of high and low contrast.

The ACE1 Electrical Impedance Tomography System for Thoracic Imaging.

The design and performance of the ACE1 (Active Complex Electrode) electrical impedance tomography system for single-ended phasic voltage measurements is presented. The design of the hardware and calibration procedures allow for reconstruction of conductivity and permittivity images. Phase measurement is achieved with the ACE1 active electrode circuit which measures the amplitude and phase of the voltage and the applied current at the location at which current is injected into the body. An evaluation of the system performance under typical operating conditions includes details of demodulation and calibration and an in-depth look at insightful metrics, such as signal-to-noise ratio variations during a single current pattern. Static and dynamic images of conductivity and permittivity are presented from ACE1 data collected on tank phantoms and human subjects to illustrate the system's utility.

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 Review of Electrical Impedance Tomography in Lung Applications: Theory and Algorithms for Absolute Images.

Electrical Impedance Tomography (EIT) is under fast development, the present paper is a review of some procedures that are contributing to improve spatial resolution and material properties accuracy, admitivitty or impeditivity accuracy. A review of EIT medical applications is presented and they were classified into three broad categories: ARDS patients, obstructive lung diseases and perioperative patients. The use of absolute EIT image may enable the assessment of absolute lung volume, which may significantly improve the clinical acceptance of EIT. The Control Theory, the State Observers more specifically, have a developed theory that can be used for the design and operation of EIT devices. Electrode placement, current injection strategy and electrode electric potential measurements strategy should maximize the number of observable and controllable directions of the state vector space. A non-linear stochastic state observer, the Unscented Kalman Filter, is used directly for the reconstruction of absolute EIT images. Historically, difference images were explored first since they are more stable in the presence of modelling errors. Absolute images require more detailed models of contact impedance, stray capacitance and properly refined finite element mesh where the electric potential gradient is high. Parallelization of the forward program computation is necessary since the solution of the inverse problem often requires frequent solutions of the forward problem. Several reconstruction algorithms benefit by the Bayesian inverse problem approach and the concept of prior information. Anatomic and physiologic information are used to form the prior information. An already tested methodology is presented to build the prior probability density function using an ensemble of CT scans and in vivo impedance measurements. Eight absolute EIT image algorithms are presented.

Imaging of ventilation and lung injury with low-frequency tomographic ultrasound.

BACKGROUND: Mechanical ventilation in the intensive care unit (ICU) is a life-saving technique for patients with acute respiratory failure, but is also associated with a high incidence of complications in the injured lung. Currently, there is no widely used monitoring technique to guide the ventilator setting to facilitate a precision medicine approach or to provide a real-time alert for developing adverse pulmonary conditions. Conventional ultrasound has been used as a thoracic bedside technology, but the lack of signal penetration into lung tissue results in images that often contain more information in their artifacts than in the images themselves. Perhaps the greatest obstacle to using traditional ultrasound in the ICU is the need for highly skilled technicians to perform the data collection. In contrast, low-frequency ultrasound (50-500 kHz) has been shown to penetrate the lung, and can detect air trapping in patients with chronic obstructive pulmonary disease (COPD). PURPOSE: Here, we present a method of collecting low-frequency ultrasound computed tomographic (USCT) data in vivo on a mechanically ventilated porcine model and computing tomographic reconstructions of airflow during tidal breathing and induced lung injuries. We evaluate the ability of the novel low-frequency USCT system to image regional changes in sound speed in the thorax due to changes in airflow during tidal breathing and induced lung injuries. This represents the first study of low-frequency tomographic ultrasound imaging in vivo and the first to produce tomographic images of ventilatory changes in vivo. METHODS: USCT and computed tomography (CT) scan data were collected alternately on a mechanically ventilated Landrace pig weighing approximately 75 kg during tidal breathing, induced pneumothorax, atelectasis, and pleural effusion. The pneumothorax was induced by injecting air through a 5 mm thick intrathoracic tube inserted in the 8th posterior intercostal space. After removing the air, atelectasis was induced by ventilating the animal with a high concentration of oxygen and low tidal volumes. The pleural effusion was induced by injecting a saline solution through the tube. The USCT data were collected at 125 kHz using the USCT low-frequency ultrasound tomography (LUFT) system on a transducer belt placed around the animal's thorax. Tomographic reconstructions were computed from the USCT data using a regularized refraction-corrected Gauss-Newton-based time-of-flight reconstruction algorithm. RESULTS: Cyclic changes in computed lung area during tidal breathing were demonstrated to agree with the respiratory rate on the mechanical ventilator. Reconstructed images computed at time steps during the procedure demonstrate regional changes consistent with what would be expected during the induced lung injury. No ground truth was available for images during the procedures since CT scans could only be taken before and after each established lung injury. CONCLUSIONS: In this work, we have demonstrated in the first in vivo study using a mechanically ventilated porcine animal model that low-frequency ultrasound tomography has the ability to image regional changes in sound speed in the thorax corresponding to changes in airflow during tidal breathing and induced lung injury. The results show promise for using low-frequency USCT as a bedside imaging technique in the future for patients with acute respiratory distress syndrome.

ACT5 Electrical Impedance Tomography System.

OBJECTIVE: This article introduces the Adaptive Current Tomograph 5 (ACT5) Electrical Impedance Tomography (EIT) system. ACT5 is a 32 electrode applied-current multiple-source EIT system that can display real-time images of conductivity and susceptivity at 27 frames per second. The adaptive current sources in ACT5 can apply fully programmable current patterns with frequencies varying from 5 kHz to 500 kHz. The system also displays real-time ECG readings during the EIT imaging process. METHODS: The hardware and software design and specifications are presented, including the current source design, FPGA hardware, safety features, calibration, and shunt impedance measurement. RESULTS: Images of conductivity and susceptivity are presented from ACT5 data collected on tank phantoms and a human subject illustrating the system's ability to provide real-time images of pulsatile perfusion and ECG traces. SIGNIFICANCE: The portability, high signal-to-noise ratio, and flexibility of applied currents over a wide range of frequencies enable this instrument to be used to obtain useful human subject data with relative clinical ease.

Evaluation of Pulmonary Structure and Function in Patients with Cystic Fibrosis from Electrical Impedance Tomography Data.

Electrical impedance tomography (EIT) is a medical imaging technique in which low frequency, low amplitude electromagnetic fields applied through electrodes on the skin are used to compute the conductivity and/or permittivity inside the body and form functional images from the reconstructed values. This work describes methods of computing EIT-derived surrogate measures of pulmonary function and identifying regions of air trapping and consolidation from functional EIT images. These methods were developed for pediatric patients with cystic fibrosis, for whom a real-time non-ionizing imaging modality can be of great benefit for monitoring disease progression or a pulmonary exacerbation.

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.

Reconstruction of Organ Boundaries With Deep Learning in the D-Bar Method for Electrical Impedance Tomography.

OBJECTIVE: Medical electrical impedance tomography is a non-ionizing imaging modality in which low-amplitude, low-frequency currents are applied on electrodes on the body, the resulting voltages are measured, and an inverse problem is solved to determine the conductivity distribution in the region of interest. Due the ill-posedness of the inverse problem, the boundaries of internal organs are typically blurred in the reconstructed image. METHODS: A deep learning approach is introduced in the D-bar method for reconstructing a 2-D slice of the thorax to recover the boundaries of organs. This is accomplished by training a deep neural network on labeled pairs of scattering transforms and the boundaries of the organs in the data from which the transforms were computed. This allows the network to "learn" the nonlinear mapping between them by minimizing the error between the output of the network and known actual boundaries. Further, a "sparse" reconstruction is computed by fusing the results of the standard D-bar reconstruction with reconstructed organ boundaries from the neural network. RESULTS: Results are shown on simulated and experimental data collected on a saline-filled tank with agar targets simulating the conductivity of the heart and lungs. CONCLUSIONS AND SIGNIFICANCE: The results demonstrate that deep neural networks can successfully learn the mapping between scattering transforms and the internal boundaries of structures.

A Three Dimensional Calderon-Based Method for EIT on the Cylindrical Geometry.

OBJECTIVE: Electrical impedance tomography (EIT) is an imaging modality in which voltage data arising from currents applied on the boundary are used to reconstruct the conductivity distribution in the interior. This paper provides a novel direct (noniterative) 3-D reconstruction algorithm for EIT in the cylindrical geometry. METHODS: The algorithm is based on Calderón's method [Calderón, 1980], and is implemented for data collected on two or four rows of electrodes on the boundary of a cylinder. RESULTS: The effectiveness of the method to localize inhomogeneities in the plane of the electrodes and in the z-direction is demonstrated on simulated and experimental data. CONCLUSIONS AND SIGNIFICANCE: The results from simulated and experimental data show that the method is effective for distinguishing in-plane and nearby out-of-plane inhomogeneities with good spatial resolution in the vertical z direction with computational efficiency.

Electrical impedance tomography detects changes in ventilation after airway clearance in spinal muscular atrophy type I.

The effect of mechanical insufflation-exsufflation (MIE) for airway clearance in patients with spinal muscular atrophy type I (SMA-I) on the distribution of ventilation in the lung is unknown, as is the duration of its beneficial effects. A pilot study to investigate the feasibility of using three dimensional (3-D) electrical impedance tomography (EIT) images to estimate lung volumes pre- and post-MIE for assessing the effectiveness of mechanical insufflation-exsufflation (MIE) was conducted in 6 pediatric patients with SMA-I in the neuromuscular clinic at Children's Hospital Colorado. EIT data were collected before, during, and after the MIE procedure on two rows of 16 electrodes placed around the chest. Lung volumes were computed from the images and compared before, during, and after the MIE procedure to assess the ability of EIT to estimate changes in lung volume during insufflation and exsufflation. Images of pulsatile pulmonary perfusion were computed in subjects able to perform breath-holding. In four of the six subjects, lung volumes during tidal breathing increased after MIE (average change from pre to post MIE was 58.8±55.1 mL). The time-dependent plots of lung volume computed from the EIT data clearly show when the MIE device insufflates and exsufflates air and the rest periods between mechanical coughs. Images of pulmonary pulsatile perfusion were computed from data collected during breathing pauses. The results suggest that EIT holds promise for estimating lung volumes and ventilation/perfusion mismatch, both of which are useful for assessing the effectiveness of MIE in clearing mucus plugs.

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.

The health-related impacts and costs of violence against women and girls on survivors, households and communities in Ghana.

Past research on violence in Ghana primarily discusses domestic violence and some types of sexual violence, but lacks a comprehensive analysis of violence against women and girls (VAWG) and its wider costs and impacts. Our study on the social costs of VAWG is a unique contribution, which aims to fill that gap. Through indepth interviews (IDIs) and focus group discussions (FGDs) with adult women and men, we explored the health impact of VAWG and the resulting social and economic consequences on survivors, their families and their communities. The research, which took place in the Eastern, Central, and Greater Accra regions of Ghana, points to several physical and mental health outcomes among survivors including physical injuries and disability, as well as impacts on mental health such as anxiety and suicidal ideation. Many VAWG survivors also experience stigma and social isolation. Our findings also reveal that survivors' families can bear various social and economic costs. Lack of public and private service provision and shelters for survivors heighten these impacts. Without institutional support for survivors, families and communities absorb these costs of VAWG.

Evaluation of surrogate measures of pulmonary function derived from electrical impedance tomography data in children with cystic fibrosis.

OBJECTIVE: Lung function monitoring by spirometry plays a critical role in the clinical care of pediatric cystic fibrosis (CF) patients, but many young children are unable to perform spirometry, and the outputs are often normal even in the presence of lung disease. Measures derived from electrical impedance tomography (EIT) images were studied for their utility as potential surrogates for spirometry in CF patients and to assess response to intravenous antibiotic treatment for acute pulmonary exacerbations (PEx) in a subset of patients. APPROACH: EIT data were collected on 35 subjects (21 with CF, 14 healthy controls, 8 CF patients pre- and post-treatment for an acute PEx) ages 2 to 20 years during tidal breathing and also concurrently with spirometry on subjects over age 8. EIT-derived measures of FEV1, FVC, and FEV1/FVC were computed globally and regionally from dynamic EIT images. MAIN RESULTS: Global EIT-derived FEV1/FVC showed good correlation with spirometry FEV1/FVC values (r = 0.54, p = 0.01), and were able to distinguish between the groups (p = 0.01). Lung heterogeneity was assessed through the spatial coefficient of variation (CV) of EIT difference images between key time points, and the CVs for EIT-derived FEV1 and FVC showed significant correlation with the CV for tidal breathing (r = 0.47, p = 0.01 and r = 0.50, p = 0.01, respectively). Global EIT-derived FEV1/FVC was better able to distinguish between groups than spirometry FEV1 (F-values 776.5 and 146.3, respectively, p < 0.01.) The same held true for the CVs for EIT-derived FEV1, FVC, and tidal breathing (F-values 215.93, 193.89, 204.57, respectively, p < 0.01). SIGNIFICANCE: The strong correlation between the CVs for tidal breathing, FEV1, and FVC, and the statistically significant ability of CV for tidal breathing to distinguish between healthy subjects and CF patients, and between the studied CF disease states suggests that the CV may be useful for measuring the extent and severity of structural lung disease.

Estimating regions of air trapping from electrical impedance tomography data.

OBJECTIVE: Electrical impedance tomography (EIT) has been shown to be a viable non-invasive, bedside imaging modality to monitor lung function. This paper introduces a method for identifying regions of air trapping from EIT data collected during tidal breathing and breath-holding maneuvers. APPROACH: Ventilation-perfusion index maps are computed from dynamic EIT images. These maps are then used to identify regions of air trapping in the area of the lung as regions that are poorly ventilated but well perfused throughout the breathing and cardiac cycles. These EIT-identified regions are then compared with independently identified regions of low attenuation, or air trapping, on chest CT. Results of this method are demonstrated in two children with cystic fibrosis and on a healthy control subject. MAIN RESULTS: In both CF children, the EIT-identified regions of air trapping matched the regions indicated from the chest CT. The EIT-based method is only validated with CT scans within 4 cm of the chest cross-section defined by the electrode plane. SIGNIFICANCE: The results indicate the potential use of EIT-derived ventilation-perfusion index maps as a non-invasive method for identifying regions of air trapping.