Table of contents

This focus section of Physiological Measurement follows the successful 13th International Conference on Biomedical Applications of Electrical Impedance Tomography (EIT 2012). The conference was held in China and hosted at Tianjin University. It was co-organized by Professor Xuemin Wang from Tianjin University, Professor Jie Zhang from the University of Kentucky, and Professor Eung Je Woo of Kyung Hee University.

This was the first time in the history of the conference that it was held in China. It provided a platform for investigators in all aspects of biomedical application of EIT to engage in common areas of interest, whilst also allowing an opportunity for the community to broaden its outlook in the areas of clinical applications and new technologies associated with this area of research. It focused on a wide range of medical applications of EIT, magnetic induction tomography, and magnetic resonance EIT.

This upholds the tradition of successful conferences on biomedical applications of EIT. The 12th International Conference on Electrical Impedance Tomography (EIT 2011) took place at the University of Bath, on 4–6 May 2011. Recently, the XV International Conference on Electrical Bio-Impedance (ICEBI) and the XIV Conference on Electrical Impedance Tomography 2013 (EIT) was held in Heilbad Heiligenstadt, Germany and will be followed by a focus issue of Physiological Measurement. The next conference planned is the 14th International Conference on Biomedical Applications of Electrical Impedance Tomography (EIT) and it will be held in Canada in 2014.

This focus section contains papers stemming from discussion and feedback during the conference in these research areas. It was also an opportunity for new researchers to join the community and propose recent innovations. There were over 54 oral papers presented at the conference, and all authors were invited to prepare new peer-reviewed papers for inclusion in this focus section of Physiological Measurement. The manuscripts went through a process of careful review before selection. A total of eight papers were accepted covering an important range of topics.

The field of EIT imaging continues to provide researchers with new challenges and attract more researchers into this field, as evident by the number of attendees to this conference. A total of 120 delegates attended the conference. This wide participation shows a step change in interest in medical EIT imaging.

The high quality of the research papers in this focus section is clear evidence of the significant advances in the field.

Richard Bayford, Xuemin Wang and Jie ZhangGuest Editors

Measurement of regional lung volume changes during a quasi-static pressure–volume (PV) manoeuvre using electrical impedance tomography (EIT) could be used to assess regional respiratory system mechanics and to determine optimal ventilator settings in individual patients. Using this approach, we studied regional respiratory system mechanics in healthy and lung-injured animals, before and after surfactant administration during inflation and deflation PV manoeuvres. The comparison of the EIT-derived regional PV curves in ventral, middle and dorsal regions of the right and left lungs showed not only different amounts of hysteresis in these regions but also marked differences among different landmark pressures calculated on the inflation and deflation limbs of the curves. Regional pressures at maximum compliance as well as the lower and upper pressures of maximum compliance change differed between the inflation and deflation and increased from ventral to dorsal regions in all lung conditions. All these pressure values increased in the injured and decreased in the surfactant treated lungs. Examination of regional respiratory system mechanics using EIT enables the assessment of spatial and temporal heterogeneities in the ventilation distribution. Characteristic landmarks on the inflation and especially on the deflation limb of regional PV curves may become useful measures for guiding mechanical ventilation.

Electrical impedance tomography (EIT) estimates an image of conductivity change within a body from stimulation and measurement at body surface electrodes. There is significant interest in EIT for imaging the thorax, as a monitoring tool for lung ventilation. To be useful in this application, we require an understanding of if and when EIT images can produce inaccurate images. In this paper, we study the consequences of the homogeneous background assumption, frequently made in linear image reconstruction, which introduces a mismatch between the reference measurement and the linearization point. We show in simulation and experimental data that the resulting images may contain large and clinically significant errors. A 3D finite element model of thorax conductivity is used to simulate EIT measurements for different heart and lung conductivity, size and position, as well as different amounts of gravitational collapse and ventilation-associated conductivity change. Three common linear EIT reconstruction algorithms are studied. We find that the asymmetric position of the heart can cause EIT images of ventilation to show up to 60% undue bias towards the left lung and that the effect is particularly strong for a ventilation distribution typical of mechanically ventilated patients. The conductivity gradient associated with gravitational lung collapse causes conductivity changes in non-dependent lung to be overestimated by up to 100% with respect to the dependent lung. Eliminating the mismatch by using a realistic conductivity distribution in the forward model of the reconstruction algorithm strongly reduces these undesirable effects. We conclude that subject-specific anatomically accurate forward models should be used in lung EIT and extra care is required when analysing EIT images of subjects whose background conductivity distribution in the lungs is known to be heterogeneous or exhibiting large changes.

We present an adaptive Kaczmarz method for solving the inverse problem in electrical impedance tomography and determining the conductivity distribution inside an object from electrical measurements made on the surface. To best characterize an unknown conductivity distribution and avoid inverting the Jacobian-related term J^TJ which could be expensive in terms of computation cost and memory in large-scale problems, we propose solving the inverse problem by applying the optimal current patterns for distinguishing the actual conductivity from the conductivity estimate between each iteration of the block Kaczmarz algorithm. With a novel subset scheme, the memory-efficient reconstruction algorithm which appropriately combines the optimal current pattern generation with the Kaczmarz method can produce more accurate and stable solutions adaptively as compared to traditional Kaczmarz- and Gauss–Newton-type methods. Choices of initial current pattern estimates are discussed in this paper. Several reconstruction image metrics are used to quantitatively evaluate the performance of the simulation results.

One possible application for electrical impedance tomography is in medical imaging where lung and heart function may be monitored. One drawback of current algorithms is that they are implemented for use in a circular domain, but a human thorax is more elliptical than circular. In this paper, a reconstruction algorithm based on the work of Calderón (1980 Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro) pp 65–75) on the inverse conductivity problem is derived for an elliptical domain. It is explained how this reconstruction algorithm uses a transformed Dirichlet-to-Neumann map. Experimental results from an elliptical tank are given to show how correct domain modelling reduces the artefacts produced by this version of Calderón's reconstruction algorithm.

Imaging the electrical properties of human tissue may aid in cancer diagnoses or monitoring organ function. Traditionally, the electrical properties are revealed with electrical impedance tomography, where currents are injected into human tissue and voltages are measured on the surface. This paper focuses on a method of measuring the electrical properties using a magnetic resonance (MR) scanner without current injection. In magnetic resonance driven electrical impedance tomography (MRDEIT), the MR phenomenon is used to induce currents in the body and the complex permittivity map is inversely computed from the difference between the modeled electric field and the actual surface electrode measurements. Computer simulations indicate that with noise level under 20%, the contrast is visually discernible in the reconstruction image. A phantom experiment is demonstrated and this supports results from computer simulation studies. The noise level in electrode measurements is evaluated to be approximately 7.8% from repeated experiments, confirming the potential to reconstruct conductivity contrast using MRDEIT. With further improvements in hardware and image reconstruction, MRDEIT may provide an additional contrast mechanism reflecting the electrical properties of human tissue, which may ultimately be used to diagnose a cancer or assist in electroencephalography.

Electrical impedance tomography (EIT) is a fast and cost-effective technique to provide a tomographic conductivity image of a subject from boundary current–voltage data. This paper proposes a time and memory efficient method for solving a large scale 3D EIT inverse problem using a parallel conjugate gradient (CG) algorithm. The 3D EIT system with a large number of measurement data can produce a large size of Jacobian matrix; this could cause difficulties in computer storage and the inversion process. One of challenges in 3D EIT is to decrease the reconstruction time and memory usage, at the same time retaining the image quality. Firstly, a sparse matrix reduction technique is proposed using thresholding to set very small values of the Jacobian matrix to zero. By adjusting the Jacobian matrix into a sparse format, the element with zeros would be eliminated, which results in a saving of memory requirement. Secondly, a block-wise CG method for parallel reconstruction has been developed. The proposed method has been tested using simulated data as well as experimental test samples. Sparse Jacobian with a block-wise CG enables the large scale EIT problem to be solved efficiently. Image quality measures are presented to quantify the effect of sparse matrix reduction in reconstruction results.

There has been a surge of interest in using electrical impedance tomography (EIT) for monitoring regional lung ventilation, however, EIT is an ill-conditioned problem, and errors/noise in the boundary voltages can have an undesirable effect on the quality of the final image. Most EIT systems in clinical usage use serial data collection hence data used to create a single image will have been collected at different times. This paper presents a study of the resulting image distortion, and proposes a method for correcting this lag in situations where the frame rate is insufficient to prevent significant image degradation. Significant correlation between the standard deviation of the time dependent reciprocity error and time delay dL_e between the reciprocal electrode combinations was found for both adult and neonate data. This was reduced when the data was corrected for dL_e. Original and corrected data was reconstructed with the GREIT algorithm and visible differences were found for the neonate data. Ideally EIT systems should be run at a frame rate of at least 50 times the frequency of the dominant and interesting physiological signals. Where this is not practical, the intra-frame system timings should be determined and lag corrected for.

In this paper, we present a new pipeline for the fast and accurate segmentation of impedance images of the lungs using electrical impedance tomography (EIT). EIT is an emerging, promising, non-invasive imaging modality that produces real-time, low spatial but high temporal resolution images of impedance inside a body. Recovering impedance itself constitutes a nonlinear ill-posed inverse problem, therefore the problem is usually linearized, which produces impedance-change images, rather than static impedance ones. Such images are highly blurry and fuzzy along object boundaries. We provide a mathematical reasoning behind the high suitability of the Kalman filter when it comes to segmenting and tracking conductivity changes in EIT lung images. Next, we use a two-fold approach to tackle the segmentation problem. First, we construct a global lung shape to restrict the search region of the Kalman filter. Next, we proceed with augmenting the Kalman filter by incorporating an adaptive foreground detection system to provide the boundary contours for the Kalman filter to carry out the tracking of the conductivity changes as the lungs undergo deformation in a respiratory cycle. The proposed method has been validated by using performance statistics such as misclassified area, and false positive rate, and compared to previous approaches. The results show that the proposed automated method can be a fast and reliable segmentation tool for EIT imaging.

Generating synthetic physiological signals using information extracted from real world physiological signals plays an important role in the field of medical device development and education. Most of the existing approaches are limited in the sense that they either focus on a particular physiological signal or lack flexibility in generating signals that mimic real world scenarios. In this paper, we present a cubic B-Spline interpolator-based flexible signal generator intended for simulating a variety of physiological signals. A simulated artifact generator (SAG) is also included in the proposed scheme to add artifacts to the physiological signals mimicking signal deviations associated with real world scenarios. In addition, the proposed method offers the ability to easily present a parametric representation to model a case-specific physiological signal. To demonstrate the ability of the proposed method, case studies on electromyogram (EMG), electro-oculogram (EOG), and electrocardiogram (ECG) during ventricular fibrillation are presented. Using a database of 20 ECG signals, the proposed approach was compared with an existing-model-based method and the results confirm the flexibility of our proposed approach as well as higher signal reproduction accuracy (a mean root mean square error improvement of 47.9% for waveform-based modeling and 4.3% for parametric-based modeling).

Muscle stiffness is known to vary as a result of a variety of disease states, yet current clinical methods for quantifying muscle stiffness have limitations including cost and availability. We investigated the capability of shear wave elastography (SWE) to measure variations in gastrocnemius shear wave speed induced via active contraction and passive stretch. Ten healthy young adults were tested. Shear wave speeds were measured using a SWE transducer positioned over the medial gastrocnemius at ankle angles ranging from maximum dorsiflexion to maximum plantarflexion. Shear wave speeds were also measured during voluntary plantarflexor contractions at a fixed ankle angle. Average shear wave speed increased significantly from 2.6 to 5.6 m s^–1 with passive dorsiflexion and the knee in an extended posture, but did not vary with dorsiflexion when the gastrocnemius was shortened in a flexed knee posture. During active contractions, shear wave speed monotonically varied with the net ankle moment generated, reaching 8.3 m s^–1 in the maximally contracted condition. There was a linear correlation between shear wave speed and net ankle moment in both the active and passive conditions; however, the slope of this linear relationship was significantly steeper for the data collected during passive loading conditions. The results show that SWE is a promising approach for quantitatively assessing changes in mechanical muscle loading. However, the differential effect of active and passive loading on shear wave speed makes it important to carefully consider the relevant loading conditions in which to use SWE to characterize in vivo muscle properties.

A methodology to determine dielectrical properties of human skin is presented and analyzed. In short, it is based on a mathematical model that considers the local transport of charge in the various layers of the skin, which is coupled with impedance measurements of both stripped and intact skin, an automated code generator, and an optimization algorithm. New resistivity and permittivity values for the stratum corneum soaked with physiological saline solution for 1 min and the viable skin beneath are obtained and expressed as easily accessible functions. The methodology can be extended to account for different electrode designs as well as more physical phenomena that are relevant to electrical impedance measurements of skin and their interpretation.

This paper analyzes the accuracy of metabolic rate calculations performed in the whole room indirect calorimeter using the molar balance equations. The equations are treated from the point of view of cause–effect relationship where the gaseous exchange rates representing the unknown causes need to be inferred from a known, noisy effect—gaseous concentrations. Two methods of such inference are analyzed. The first method is based on the previously published regularized deconvolution of the molar balance equation and the second one, proposed in this paper, relies on regularized differentiation of gaseous concentrations. It is found that both methods produce similar results for the absolute values of metabolic variables and their accuracy. The uncertainty for O₂ consumption rate is found to be 7% and for CO₂ production-–3.2%. The uncertainties in gaseous exchange rates do not depend on the absolute values of O₂ consumption and CO₂ production. In contrast, the absolute uncertainty in respiratory quotient is a function of the gaseous exchange rates and varies from 9.4% during the night to 2.3% during moderate exercise. The uncertainty in energy expenditure was found to be 5.9% and independent of the level of gaseous exchange. For both methods, closed form analytical formulas for confidence intervals are provided allowing quantification of uncertainty for four major metabolic variables in real world studies.