Finite-element method in electrical impedance tomography

A new current injection and voltage measurement strategy of 3D electrical impedance tomography based on scanning electrode

Electrical impedance tomography (EIT) technology is an important imaging approach to show the conductivity distribution of the area noninvasively. Recently, 3D EIT has been extensively studied for its more comprehensive display of electrical properties. Nonetheless, most 3D EIT electrode models are based on multilayer ring electrodes and only suitable for specific scenarios. In order to overcome its limitations and alleviate the ill-condition of 3D EIT, we propose a new current injection and voltage measurement strategy based on scanning row electrodes (SRE) called the back electrode excitation (BEEM) strategy and select the optimal number of excitation electrodes according to different imaging effects. A 3D electrical impedance imaging system based on SRE is designed. Then, the traditional excitation measurement strategy is introduced, and the two strategies are compared through simulation and actual experiments. The results show that the BEEM strategy with SRE can not only obtain rich potential information in the finite field but also significantly improve the imaging detection depth, accuracy, and noise immunity compared with the flat electrode array.

Wearable Electrical Impedance Tomography Belt With Dry Electrodes

Electrical impedance tomography (EIT) is a noninvasive imaging technology used to reconstruct the conductivity distribution in objects and the human body. In recent years, numerous EIT systems and image reconstruction algorithms have been developed. However, most of these EIT systems require conventional electrodes with conductive gels (wet electrodes) and cannot be adapted to different body types, resulting in limited applicability. In this study, a wearable wireless EIT belt with dry electrodes was designed to enable EIT imaging of the human body without using wet electrodes. The specific design of the belt mechanism and dry electrodes provide the advantages of easy wear and adaptation to different body sizes. Additionally, the GaussNewton method was used to optimize the EIT image. Finally, experiments were performed on the phantom and human body to validate the performance of the proposed EIT belt. The results demonstrate that the proposed system can provide accurate location information of the objects in the EIT image and the system can be successfully applied for noninvasive measurement of the human body.

An efficient Point-Matching Method-of-Moments for 2D and 3D Electrical Impedance Tomography Using Radial Basis functions

AbstractObjective: The inverse problem of computing conductivity distributions in 2D and 3D objects interrogated by low frequency electrical signals, which is called Electrical Impedance Tomography (EIT), is treated using a Method-of-Moment technique.

METHODS

A Point-Matching-Method-of-Moment technique is used to formulate a global integral equation solver. Radial Basis Functions are adopted to express the conductivity distribution. Single-step quadratic-norm (L2) and iterative total variation (L1) regularization techniques are exploited to solve the inverse problem.

RESULTS

Simulation and experimental tests on a circular reconstruction domain show satisfactory performance in deriving conductivity distribution, achieving a Correlation Coefficient (CC) up to 0:863 for 70 dB voltage SNR and 0:842 for 40 dB voltage SNR. The proposed methodology with L2-norm regularization provided better results than traditional iterative Gauss-Newtons approach, whereas with L1-norm regularization it showed promising performance. Moreover, 3D reconstructions on a cylindrical cavity demonstrated superior results near the electrodes planes compared to those of the conventional linearized approach. Finally, application to EIT medical data for dynamic lung imaging successfully revealed the breath-cycle conductivity changes.

CONCLUSION

The results show that the proposed method can be effective for both 2D and 3D EIT and applicable to many applications.

SIGNIFICANCE

Strong conductivity variations are successfully tackled with a very good Correlation Coefficient. In contrast to conventional EIT solutions based on weak-form and linearization on small conductivity changes, the proposed method requires only one step to converge with L2-norm regularization. The proposed method with L1-norm regularization also achieves good reconstruction quality with a low number of iterations.

Focusing Sensor Design for Open Electrical Impedance Tomography Based on Shape Conformal Transformation

Electrical Impedance Tomography (EIT) is a non-invasive detection method to image the conductivity changes inside an observation region by using the electrical measurements at the boundary of this region. In some applications of EIT, the observation domain is infinite and is only accessible from one side, which leads to the so-called open EIT (OEIT) problem. Compared with conventional EIT problems, the observation region in OEIT can only be measured from limited projection directions, which makes high resolution imaging much more challenging. To improve the imaging quality of OEIT, a focusing sensor design strategy is proposed based on shape conformal theory. The conformal bijection is used to map a standard EIT sensor defined at a unit circle to a focusing OEIT sensor defined at an upper half plane. A series of numerical and experimental testes are conducted. Compared with the traditional sensor structure, the proposed focusing sensor has higher spatial resolution at the near-electrode region and is good at distinguishing multi-inclusions which are close to each other.

Effects of individualized electrical impedance tomography and image reconstruction settings upon the assessment of regional ventilation distribution: Comparison to 4-dimensional computed tomography in a porcine model

Electrical impedance tomography (EIT) is a promising imaging technique for bedside monitoring of lung function. It is easily applicable, cheap and requires no ionizing radiation, but clinical interpretation of EIT-images is still not standardized. One of the reasons for this is the ill-posed nature of EIT, allowing a range of possible images to be produced–rather than a single explicit solution. Thus, to further advance the EIT technology for clinical application, thorough examinations of EIT-image reconstruction settings–i.e., mathematical parameters and addition of a priori (e.g., anatomical) information–is essential. In the present work, regional ventilation distribution profiles derived from different EIT finite-element reconstruction models and settings (for GREIT and Gauss Newton) were compared to regional aeration profiles assessed by the gold-standard of 4-dimensional computed tomography (4DCT) by calculating the root mean squared error (RMSE). Specifically, non-individualized reconstruction models (based on circular and averaged thoracic contours) and individualized reconstruction models (based on true thoracic contours) were compared. Our results suggest that GREIT with noise figure of 0.15 and non-uniform background works best for the assessment of regional ventilation distribution by EIT, as verified versus 4DCT. Furthermore, the RMSE of anteroposterior ventilation profiles decreased from 2.53±0.62% to 1.67±0.49% while correlation increased from 0.77 to 0.89 after embedding anatomical information into the reconstruction models. In conclusion, the present work reveals that anatomically enhanced EIT-image reconstruction is superior to non-individualized reconstruction models, but further investigations in humans, so as to standardize reconstruction settings, is warranted.

Combining the finite element method with structural connectome-based analysis for modeling neurotrauma: connectome neurotrauma mechanics

This article presents the integration of brain injury biomechanics and graph theoretical analysis of neuronal connections, or connectomics, to form a neurocomputational model that captures spatiotemporal characteristics of trauma. We relate localized mechanical brain damage predicted from biofidelic finite element simulations of the human head subjected to impact with degradation in the structural connectome for a single individual. The finite element model incorporates various length scales into the full head simulations by including anisotropic constitutive laws informed by diffusion tensor imaging. Coupling between the finite element analysis and network-based tools is established through experimentally-based cellular injury thresholds for white matter regions. Once edges are degraded, graph theoretical measures are computed on the “damaged” network. For a frontal impact, the simulations predict that the temporal and occipital regions undergo the most axonal strain and strain rate at short times (less than 24 hrs), which leads to cellular death initiation, which results in damage that shows dependence on angle of impact and underlying microstructure of brain tissue. The monotonic cellular death relationships predict a spatiotemporal change of structural damage. Interestingly, at 96 hrs post-impact, computations predict no network nodes were completely disconnected from the network, despite significant damage to network edges. At early times () network measures of global and local efficiency were degraded little; however, as time increased to 96 hrs the network properties were significantly reduced. In the future, this computational framework could help inform functional networks from physics-based structural brain biomechanics to obtain not only a biomechanics-based understanding of injury, but also neurophysiological insight.

According to the Centers for Disease Control and Prevention in the United States, approximately 1.7 million people, on average, sustain a traumatic brain injury annually. During the last few decades, brain neurotrauma biomechanics has been an active area of research involving medical clinicians and a broad range of scientists and engineers. In addition, advances and fast growth of human connectomics continues to reveal new insights into the damaged brain. With recent advances in computational methods and high performance computing, we see the need and the exciting possibility to merge brain neurotrauma biomechanics and human connectomics science to form a new area of investigation - connectome neurotrauma mechanics. For neurotrauma, the idea is simple - inform human structural connectome analysis using physics-based predictions of biomechanical brain injury. If successful, this technique may be further used to inform human functional connectome analysis, thus providing a new tool to help understand the pathophysiology of mild traumatic brain injury.

Modelling of an oesophageal electrode for cardiac function tomography

There is a need in critical care units for continuous cardiopulmonary monitoring techniques. ECG gated electrical impedance tomography is able to localize the impedance variations occurring during the cardiac cycle. This method is a safe, inexpensive and potentially fast technique for cardiac output imaging but the spatial resolution is presently low, particularly for central locations such as the heart. Many parameters including noise deteriorate the reconstruction result. One of the main obstacles in cardiac imaging at the heart location is the high impedance of lungs and muscles on the dorsal and posterior side of body. In this study we are investigating improvements of the measurement and initial conductivity estimation of the internal electrode by modelling an internal electrode inside the esophagus. We consider 16 electrodes connected around a cylindrical mesh. With the random noise level set near 0.05% of the signal we evaluated the Graz consensus reconstruction algorithm for electrical impedance tomography. The modelling and simulation results showed that the quality of the target in reconstructed images was improved by up to 5 times for amplitude response, position error, resolution, shape deformation and ringing effects with perturbations located in cardiac related positions when using an internal electrode.

Fast intersections on nested tetrahedrons (FINT): An algorithm for adaptive finite element based distributed parameter estimation

A variety of biomedical imaging techniques such as optical and fluorescence tomography, electrical impedance tomography, and ultrasound imaging can be cast as inverse problems, wherein image reconstruction involves the estimation of spatially distributed parameter(s) of the PDE system describing the physics of the imaging process. Finite element discretization of imaged domain with tetrahedral elements is a popular way of solving the forward and inverse imaging problems on complicated geometries. A dual-adaptive mesh-based approach wherein, one mesh is used for solving the forward imaging problem and the other mesh used for iteratively estimating the unknown distributed parameter, can result in high resolution image reconstruction at minimum computation effort, if both the meshes are allowed to adapt independently. Till date, no efficient method has been reported to identify and resolve intersection between tetrahedrons in independently refined or coarsened dual meshes. Herein, we report a fast and robust algorithm to identify and resolve intersection of tetrahedrons within nested dual meshes generated by 8-similar subtetrahedron subdivision scheme. The algorithm exploits finite element weight functions and gives rise to a set of weight functions on each vertex of disjoint tetrahedron pieces that completely cover up the intersection region of two tetrahedrons. The procedure enables fully adaptive tetrahedral finite elements by supporting independent refinement and coarsening of each individual mesh while preserving fast identification and resolution of intersection. The computational efficiency of the algorithm is demonstrated by diffuse photon density wave solutions obtained from a single- and a dual-mesh, and by reconstructing a fluorescent inclusion in simulated phantom from boundary frequency domain fluorescence measurements.

Optimum design of electrode structure and parameters in electrical impedance tomography

In electrical impedance tomography (EIT) the electrode structure and parameters significantly influence measurement sensitivity and image quality, so how to optimize the electrode structure and parameters is one of the key problems in research today. This paper presents a method to optimize the EIT electrode structure and parameters based on coercive equipotential node models. The coercive equipotential mode of the compound electrode has been established based on that of the line electrode. A simulation study for the line electrode and the compound electrode of EIT has been made on a simulation software platform. The influences of different electrode structures and parameters on measurement sensitivity and the image reconstruction quality are studied. For line electrode simulation studies, two important conclusions are drawn. First, a narrower electrode is helpful in improving the imaging quality. Second, although it is known that a wider electrode is beneficial in decreasing the contact impedance, using a too wide electrode causes the measurement sensitivity to decrease. Furthermore the electrode width that leads to the best measurement sensitivity is different for different measurement depths. The compound electrode has four parameters: the excitation electrode width, the measurement electrode width, the space between the excitation electrode and the measurement electrode, and the distance between two adjacent compound electrodes. These parameters have mutual restrictions and complex influences on each other. It is unwise to optimize the design of a compound electrode by only using the overlay rate of electrodes. A simulation study of EIT electrode structure and parameter influences can be carried out according to this paper to determine the optimum design of the electrode structure and its parameters.

Three-dimensional electrical impedance tomography based on the complete electrode model

In electrical impedance tomography an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. It is often assumed that the injected currents are confined to the two-dimensional (2-D) electrode plane and the reconstruction is based on 2-D assumptions. However, the currents spread out in three dimensions and, therefore, off-plane structures have significant effect on the reconstructed images. In this paper we propose a finite element-based method for the reconstruction of three-dimensional resistivity distributions. The proposed method is based on the so-called complete electrode model that takes into account the presence of the electrodes and the contact impedances. Both the forward and the inverse problems are discussed and results from static and dynamic (difference) reconstructions with real measurement data are given. It is shown that in phantom experiments with accurate finite element computations it is possible to obtain static images that are comparable with difference images that are reconstructed from the same object with the empty (saline filled) tank as a reference.

Tikhonov regularization and prior information in electrical impedance tomography

The solution of impedance distribution in electrical impedance tomography is a nonlinear inverse problem that requires the use of a regularization method. The generalized Tikhonov regularization methods have been popular in the solution of many inverse problems. The regularization matrices that are usually used with the Tikhonov method are more or less ad hoc and the implicit prior assumptions are, thus, in many cases inappropriate. In this paper, we propose an approach to the construction of the regularization matrix that conforms to the prior assumptions on the impedance distribution. The approach is based on the construction of an approximating subspace for the expected impedance distributions. It is shown by simulations that the reconstructions obtained with the proposed method are better than with two other schemes of the same type when the prior is compatible with the true object. On the other hand, when the prior is incompatible with the true object, the method will still give reasonable estimates.

A dual mesh scheme for finite element based reconstruction algorithms

The finite element (FE) method has found several applications in emerging imaging modalities, especially microwave imaging which has been shown to be potentially useful in a number of areas including thermal estimation. In monitoring temperature distributions, the biological phenomena of temperature variations of tissue dielectric properties is exploited. By imaging these properties and their changes during such therapies as hyperthermia, temperature distributions can be deduced using difference imaging techniques. The authors focus on a microwave imaging problem where the hybrid element (HE) method is used in conjunction with a dual mesh scheme in an effort to image complex wavenumbers, k(2). The dual mesh scheme is introduced to improve the reconstructed images of tissue properties and is ideally suited for systems using FE methods as their computational base. Since the electric fields typically vary rapidly over a given body when irradiated by high-frequency electromagnetic sources, a dense mesh is needed for these fields to be accurately represented. Conversely, k(2) may be fairly constant over subregions of the body which would allow for a less dense sampling of this parameter in those regions. In the dual mesh system employed, the first mesh, which is uniformly dense, is used for calculating the electric fields over the body whereas the second mesh, which is nonuniform and less dense, is used for representing the k(2) distribution within the region of interest. The authors examine the 2-D TM polarization case for a pair of dielectric distributions on both a large and small problem to demonstrate the flexibility of the dual mesh method along with some of the difficulties associated with larger imaging problems. Results demonstrate the capabilities of the dual mesh concept in comparison to a single mesh approach for a variety of test cases, suggesting that the dual mesh method is critical for FE based image reconstruction where rapidly varying physical quantities are used to recover smoother property profiles, as can occur in microwave imaging of biological bodies.