A sensitivity method for electrical impedance tomography

A Fidelity-Embedded Regularization Method for Robust Electrical Impedance Tomography

Electrical impedance tomography (EIT) provides functional images of an electrical conductivity distribution inside the human body. Since the 1980s, many potential clinical applications have arisen using inexpensive portable EIT devices. EIT acquires multiple trans-impedance measurements across the body from an array of surface electrodes around a chosen imaging slice. The conductivity image reconstruction from the measured data is a fundamentally ill-posed inverse problem notoriously vulnerable to measurement noise and artifacts. Most available methods invert the ill-conditioned sensitivity or the Jacobian matrix using a regularized least-squares data-fitting technique. Their performances rely on the regularization parameter, which controls the trade-off between fidelity and robustness. For clinical applications of EIT, it would be desirable to develop a method achieving consistent performance over various uncertain data, regardless of the choice of the regularization parameter. Based on the analysis of the structure of the Jacobian matrix, we propose a fidelity-embedded regularization (FER) method and a motion artifact reduction filter. Incorporating the Jacobian matrix in the regularization process, the new FER method with the motion artifact reduction filter offers stable reconstructions of high-fidelity images from noisy data by taking a very large regularization parameter value. The proposed method showed practical merits in experimental studies of chest EIT imaging.

Accelerated reconstruction of electrical impedance tomography images via patch based sparse representation

Electrical impedance tomography (EIT) reconstruction is a nonlinear and ill-posed problem. Exact reconstruction of an EIT image inverts a high dimensional mathematical model to calculate the conductivity field, which causes significant problems regarding that the computational complexity will reduce the achievable frame rate, which is considered as a major advantage of EIT imaging. The single-step method, state estimation method, and projection method were always used to accelerate reconstruction process. The basic principle of these methods is to reduce computational complexity. However, maintaining high resolution in space together with not much cost is still challenging, especially for complex conductivity distribution. This study proposes an idea to accelerate image reconstruction of EIT based on compressive sensing (CS) theory, namely, CSEIT method. The novel CSEIT method reduces the sampling rate through minimizing redundancy in measurements, so that detailed information of reconstruction is not lost. In order to obtain sparse solution, which is the prior condition of signal recovery required by CS theory, a novel image reconstruction algorithm based on patch-based sparse representation is proposed. By applying the new framework of CSEIT, the data acquisition time, or the sampling rate, is reduced by more than two times, while the accuracy of reconstruction is significantly improved.

Distribution of tidal ventilation during volume-targeted ventilation is variable and influenced by age in the preterm lung

PURPOSE

Synchronised volume-targeted ventilation (SIPPV + VTV) attempts to reduce lung injury by standardising volume delivery to the preterm lung. The aim of this study is to describe the regional distribution and variability of ventilation within the preterm lung during SIPPV + VTV.

METHODS

Twenty-seven stable, supine, preterm infants with <32 weeks gestation receiving SIPPV + VTV were studied. From each infant, the anterior-to-posterior impedance change due to tidal ventilation (∆Z (VT); countless units) was determined during every breath from three, 30-s, electrical impedance tomography recordings. ∆Z (VT) within the anterior, middle and posterior thirds of the chest were compared using area under the curve analysis. The coefficient of variation (CV) of ∆Z (VT) in the anterior and posterior hemithoraces, inflation pressure and, where available, V (T) at airway opening were compared. Infants were sub-grouped by age (≤7 and >7 days), supplemental oxygen requirement and set tidal volume.

RESULTS

In all sub-groups, the middle third of the chest accounted for the greatest ∆Z (VT) [p < 0.0001, repeated-measures analysis of variance (ANOVA)]. The middle third of the chest constituted a greater relative ∆Z (VT) in infants aged >7 days compared with ≤7 days (p < 0.0001, repeated-measures ANOVA). Set tidal volume and oxygen requirement did not significantly influence the regional distribution of ∆Z (VT). The mean (standard deviation, SD) CV of ∆Z (VTANT) and ∆Z (VTPOST) were 30.6% (14.0%) and 31.9% (12.7%). ∆Z (VTANT) and ∆Z (VTPOST) expressed greater breath-to-breath variability than the variation in inflation pressure and V (T) at airway opening (p = 0.012 and p < 0.0001, respectively, paired t-tests).

CONCLUSION

During SIPPV + VTV the preterm infant exhibits marked breath-to-breath variability in regional ventilation which is influenced by age.

Estimation of electrical conductivity distribution within the human head from magnetic flux density measurement

We have developed a new algorithm for magnetic resonance electrical impedance tomography (MREIT), which uses only one component of the magnetic flux density to reconstruct the electrical conductivity distribution within the body. The radial basis function (RBF) network and simplex method are used in the present approach to estimate the conductivity distribution by minimizing the errors between the 'measured' and model-predicted magnetic flux densities. Computer simulations were conducted in a realistic-geometry head model to test the feasibility of the proposed approach. Single-variable and three-variable simulations were performed to estimate the brain-skull conductivity ratio and the conductivity values of the brain, skull and scalp layers. When SNR = 15 for magnetic flux density measurements with the target skull-to-brain conductivity ratio being 1/15, the relative error (RE) between the target and estimated conductivity was 0.0737 +/- 0.0746 in the single-variable simulations. In the three-variable simulations, the RE was 0.1676 +/- 0.0317. Effects of electrode position uncertainty were also assessed by computer simulations. The present promising results suggest the feasibility of estimating important conductivity values within the head from noninvasive magnetic flux density measurements.

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.

Three-dimensional electrical impedance tomography

The electrical resistivity of mammalian tissues varies widely and is correlated with physiological function. Electrical impedance tomography (EIT) can be used to probe such variations in vivo, and offers a non-invasive means of imaging the internal conductivity distribution of the human body. But the computational complexity of EIT has severe practical limitations, and previous work has been restricted to considering image reconstruction as an essentially two-dimensional problem. This simplification can limit significantly the imaging capabilities of EIT, as the electric currents used to determine the conductivity variations will not in general be confined to a two-dimensional plane. A few studies have attempted three-dimensional EIT image reconstruction, but have not yet succeeded in generating images of a quality suitable for clinical applications. Here we report the development of a three-dimensional EIT system with greatly improved imaging capabilities, which combines our 64-electrode data-collection apparatus with customized matrix inversion techniques. Our results demonstrate the practical potential of EIT for clinical applications, such as lung or brain imaging and diagnostic screening.

3D reconstruction in electrical impedance imaging using a direct sensitivity matrix approach

This paper represents a reconstruction algorithm using a direct sensitivity matrix (DSM) approach for fast 3D image reconstruction in electrical impedance imaging. The boundary element method (BEM) is used in the construction of this matrix. The first images of a conductivity perturbation inside a sphere are reconstructed, using theoretical data.

A direct sensitivity matrix approach for fast reconstruction in electrical impedance tomography

In electrical impedance imaging, several proposed reconstruction algorithms have employed the concept of a sensitivity matrix, which can be used to relate the magnitude of a boundary voltage change of a 2D object to the change in conductivity inside the object that has given rise to it. The search for an appropriate inversion of the sensitivity matrix is the key to these algorithms. In this work, a method called the direct sensitivity matrix (DSM) approach for fast image reconstruction is proposed. Both theoretical and experimental results showing the efficiency of this proposed method are also presented.