Finite element implementation of Maxwell's equations for image reconstruction in electrical impedance tomography

Mapping the conductivity of graphene with Electrical Resistance Tomography

Electronic applications of large-area graphene films require rapid and accurate methods to map their electrical properties. Here we present the first electrical resistance tomography (ERT) measurements on large-area graphene samples, obtained with a dedicated measurement setup and reconstruction software. The outcome of an ERT measurement is a map of the graphene electrical conductivity. The same setup allows to perform van der Pauw (vdP) measurements of the average conductivity. We characterised the electrical conductivity of chemical-vapour deposited graphene samples by performing ERT, vdP and scanning terahertz time-domain spectroscopy (TDS), the last one by means of a commercial instrument. The measurement results are compared and discussed, showing the potential of ERT as an accurate and reliable technique for the electrical characterization of graphene samples.

An instrumental electrode model for solving EIT forward problems

An instrumental electrode model (IEM) capable of describing the performance of electrical impedance tomography (EIT) systems in the MHz frequency range has been proposed. Compared with the commonly used Complete Electrode Model (CEM), which assumes ideal front-end interfaces, the proposed model considers the effects of non-ideal components in the front-end circuits. This introduces an extra boundary condition in the forward model and offers a more accurate modelling for EIT systems. We have demonstrated its performance using simple geometry structures and compared the results with the CEM and full Maxwell methods. The IEM can provide a significantly more accurate approximation than the CEM in the MHz frequency range, where the full Maxwell methods are favoured over the quasi-static approximation. The improved electrode model will facilitate the future characterization and front-end design of real-world EIT systems.

Intracranial electrical impedance tomography: a method of continuous monitoring in an animal model of head trauma

BACKGROUND

Electrical impedance tomography (EIT) is a method that can render continuous graphical cross-sectional images of the brain's electrical properties. Because these properties can be altered by variations in water content, shifts in sodium concentration, bleeding, and mass deformation, EIT has promise as a sensitive instrument for head injury monitoring to improve early recognition of deterioration and to observe the benefits of therapeutic intervention. This study presents a swine model of head injury used to determine the detection capabilities of an inexpensive bedside EIT monitoring system with a novel intracranial pressure (ICP)/EIT electrode combination sensor on induced intraparenchymal mass effect, intraparenchymal hemorrhage, and cessation of brain blood flow. Conductivity difference images are shown in conjunction with ICP data, confirming the effects.

METHODS

Eight domestic piglets (3-4 weeks of age, mean 10 kg), under general anesthesia, were subjected to 4 injuries: induced intraparenchymal mass effect using an inflated, and later, deflated 0.15-mL Fogarty catheter; hemorrhage by intraparenchymal injection of 1-mL arterial blood; and ischemia/infarction by euthanasia. EIT and ICP data were recorded 10 minutes before inducing the injury until 10 minutes after injury. Continuous EIT and ICP monitoring were facilitated by a ring of circumferentially disposed cranial Ag/AgCl electrodes and 1 intraparenchymal ICP/EIT sensor electrode combination. Data were recorded at 100 Hz. Two-dimensional tomographic conductivity difference (Δσ) images, rendered using data before and after an injury, were displayed in real time on an axial circular mesh. Regions of interest (ROI) within the images were automatically selected as the upper or lower 5% of conductivity data depending on the nature of the injury. Mean Δσ within the ROIs and background were statistically analyzed. ROI Δσ was compared with the background Δσ after an injury event using an unpaired, unequal variance t test. Conductivity change within an ROI after injury was likewise compared with the same ROI before the injury making use of unpaired t tests with unequal variance.

RESULTS

Eight animal subjects were studied, each undergoing 4 injury events including euthanasia. Changes in conductivity due to injury showed expected pathophysiologic effects in an ROI identified within the middle of the left hemisphere; this localization is reasonable given the actual site of injury (left hemisphere) and spatial warping associated with estimating a 3-dimensional conductivity distribution in 2-dimensional space. Results are shown as mean ± 1 SD. When averaged across all 8 animals, balloon inflation caused the mean Δσ within the ROI to shift by -11.4 ± 10.9 mS/m; balloon deflation by +9.4 ± 8.8 mS/m; blood injection by +19.5 ± 11.5 mS/m; death by -12.6 ± 13.2 mS/m. All induced injuries were detectable to statistical significance (P < 0.0001).

CONCLUSION

This study confirms that the bedside EIT system with ICP/EIT combination sensor can detect induced trauma. Such a technique may hold promise for further research in the monitoring and management of traumatically brain-injured individuals.

Reconstruction convergence and speed enhancement in electrical impedance tomography for domains with known internal boundaries

An improved approach for electrical impedance tomography (EIT) image reconstruction, based on modifying the forward and inverse solutions, is proposed. In this approach, the EIT forward problem is solved via the finite element method (FEM) using two types of elements. The inverse problem is solved by the modified Newton-Raphson method, whereas the condition number of the Hessian matrix is being monitored. At the early stage of the reconstruction, first-order elements are used, and if the condition number exceeds the allowable limit, the algorithm restarts. Otherwise, if the reconstruction error becomes lower than a predefined threshold, second-order elements are employed in the forward solution in order to preserve the precision of the final results. The latter stage converges in very few iterations. Since the solution speed with the first-order FEM is considerably higher than the second-order FEM, the reconstruction speed improves considerably by this approach, whereas the accuracy of the results is guaranteed by the well-conditioned Hessian matrix. Numerical simulations and experiments are followed by comparisons with other reconstruction methods which demonstrate the reliability and high solution speed of this approach. According to the results, the convergence of the proposed method is significantly improved, and its speed is 2-200 times higher than the previously developed methods with the same level of precision.

Absolute electrical impedance tomography (aEIT) guided ventilation therapy in critical care patients: simulations and future trends

Thoracic electrical impedance tomography (EIT) is a noninvasive, radiation-free monitoring technique whose aim is to reconstruct a cross-sectional image of the internal spatial distribution of conductivity from electrical measurements made by injecting small alternating currents via an electrode array placed on the surface of the thorax. The purpose of this paper is to discuss the fundamentals of EIT and demonstrate the principles of mechanical ventilation, lung recruitment, and EIT imaging on a comprehensive physiological model, which combines a model of respiratory mechanics, a model of the human lung absolute resistivity as a function of air content, and a 2-D finite-element mesh of the thorax to simulate EIT image reconstruction during mechanical ventilation. The overall model gives a good understanding of respiratory physiology and EIT monitoring techniques in mechanically ventilated patients. The model proposed here was able to reproduce consistent images of ventilation distribution in simulated acutely injured and collapsed lung conditions. A new advisory system architecture integrating a previously developed data-driven physiological model for continuous and noninvasive predictions of blood gas parameters with the regional lung function data/information generated from absolute EIT (aEIT) is proposed for monitoring and ventilator therapy management of critical care patients.

Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography

Diffuse optical tomography (DOT) involves estimation of tissue optical properties using noninvasive boundary measurements. The image reconstruction procedure is a nonlinear, ill-posed, and ill-determined problem, so overcoming these difficulties requires regularization of the solution. While the methods developed for solving the DOT image reconstruction procedure have a long history, there is less direct evidence on the optimal regularization methods, or exploring a common theoretical framework for techniques which uses least-squares (LS) minimization. A generalized least-squares (GLS) method is discussed here, which takes into account the variances and covariances among the individual data points and optical properties in the image into a structured weight matrix. It is shown that most of the least-squares techniques applied in DOT can be considered as special cases of this more generalized LS approach. The performance of three minimization techniques using the same implementation scheme is compared using test problems with increasing noise level and increasing complexity within the imaging field. Techniques that use spatial-prior information as constraints can be also incorporated into the GLS formalism. It is also illustrated that inclusion of spatial priors reduces the image error by at least a factor of 2. The improvement of GLS minimization is even more apparent when the noise level in the data is high (as high as 10%), indicating that the benefits of this approach are important for reconstruction of data in a routine setting where the data variance can be known based upon the signal to noise properties of the instruments.

Methods and evaluations of MRI content-adaptive finite element mesh generation for bioelectromagnetic problems

In studying bioelectromagnetic problems, finite element analysis (FEA) offers several advantages over conventional methods such as the boundary element method. It allows truly volumetric analysis and incorporation of material properties such as anisotropic conductivity. For FEA, mesh generation is the first critical requirement and there exist many different approaches. However, conventional approaches offered by commercial packages and various algorithms do not generate content-adaptive meshes (cMeshes), resulting in numerous nodes and elements in modelling the conducting domain, and thereby increasing computational load and demand. In this work, we present efficient content-adaptive mesh generation schemes for complex biological volumes of MR images. The presented methodology is fully automatic and generates FE meshes that are adaptive to the geometrical contents of MR images, allowing optimal representation of conducting domain for FEA. We have also evaluated the effect of cMeshes on FEA in three dimensions by comparing the forward solutions from various cMesh head models to the solutions from the reference FE head model in which fine and equidistant FEs constitute the model. The results show that there is a significant gain in computation time with minor loss in numerical accuracy. We believe that cMeshes should be useful in the FEA of bioelectromagnetic problems.