A Moving Morphable Components Based Shape Reconstruction Framework for Electrical Impedance Tomography

Moving morphable component (MMC) topology optimization with different void structure scaling factors

The explicit topology optimization method based on moving morphable component (MMC) has attracted more and more attention, and components are the basic building blocks of the implementation of MMC method. In the present work, a MMC topology optimization method based on component with void structure is followed with interest. On the basis of analyzing the characteristics of components used by MMC method, the topology description function for component with void structure is presented, where a quantitative scaling factor is introduced without increasing the number of design variables. Taking the minimum flexibility as the optimization objective, an example of short beam is analyzed with different void structure scaling factors. The results show that different scaling factors have a greater impact on the final topology optimization structure, and an ideal topology structure can be obtained with an appropriate scaling factor. Finally, some problems in the optimization process are analyzed and indicate that appropriate mesh density should be chose for component with void structure in order to achieve good optimization results.

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.

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.

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.

Fusing electrical and elasticity imaging

Electrical and elasticity imaging are promising modalities for a suite of different applications, including medical tomography, non-destructive testing and structural health monitoring. These emerging modalities are capable of providing remote, non-invasive and low-cost opportunities. Unfortunately, both modalities are severely ill-posed nonlinear inverse problems, susceptive to noise and modelling errors. Nevertheless, the ability to incorporate complimentary datasets obtained simultaneously offers mutually beneficial information. By fusing electrical and elastic modalities as a joint problem, we are afforded the possibility to stabilize the inversion process via the utilization of auxiliary information from both modalities as well as joint structural operators. In this study, we will discuss a possible approach to combine electrical and elasticity imaging in a joint reconstruction problem giving rise to novel multi-modality applications for use in both medical and structural engineering. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

Shape-Driven EIT Reconstruction Using Fourier Representations

Shape-driven approaches have been proposed as an effective strategy for the electrical impedance tomography (EIT) reconstruction problem in recent years. In order to augment the shape-driven approaches, we propose a new method that transforms the shape to be reconstructed as basic primitives directly modeled by using Fourier representations. To allow automatic topological changes between the basic primitives and surrounding objects simultaneously, Boolean operations are employed. The Boolean operations with direct representation of primitives can be utilized for dimensionality and ill-posedness reduction, enabling feasible shape and topology optimization with shape-driven approaches. As a proof of principle, we leverage the proposed method for two dimensional shape reconstruction in EIT with various conductivity distributions. We demonstrate that our method is able to improve EIT reconstructions by enabling accurate shape and topology optimization.

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.

Shape-Driven Difference Electrical Impedance Tomography

This work proposes a novel shape-driven reconstruction approach for difference electrical impedance tomography (EIT). In the proposed approach, the reconstruction problem is formulated as a shape reconstruction problem and solved via an explicit and geometrical methodology, where the geometry of the embedded inclusions is represented by a shape and topology description function (STDF). To incorporate more geometry and prior information directly into the reconstruction and to provide better flexibility in the solution process, the concept of a moving morphable component (MMC) is applied here implying that MMC is treated as the basic building block of the embedded inclusions. Simulations, phantom studies, and in vivo pig data are used to test the proposed approach for the most popular biomedical application of EIT - lung imaging - and the performance is compared with the conventional linear approach. In addition, the modality's robustness is studied in cases where (i) modeling errors are caused by inhomogeneity in the background conductivity, and (ii) uncertainties in the contact impedances and reference state are present. The results of this work indicate that the proposed approach is tolerant to modeling errors and is fairly robust to typical EIT uncertainties, producing greatly improved image quality compared to the conventional linear approach.

Shape Reconstruction Using Boolean Operations in Electrical Impedance Tomography

In this work, we propose a new shape reconstruction framework rooted in the concept of Boolean operations for electrical impedance tomography (EIT). Within the framework, the evolution of inclusion shapes and topologies are simultaneously estimated through an explicit boundary description. For this, we use B-spline curves as basic shape primitives for shape reconstruction and topology optimization. The effectiveness of the proposed approach is demonstrated using simulated and experimentally-obtained data (testing EIT lung imaging). In the study, improved preservation of sharp features is observed when employing the proposed approach relative to the recently developed moving morphable components-based approach. In addition, robustness studies of the proposed approach considering background inhomogeneity and differing numbers of B-spline curve control points are performed. It is found that the proposed approach is tolerant to modeling errors caused by background inhomogeneity and is also quite robust to the selection of control points.

B-Spline Level Set Method for Shape Reconstruction in Electrical Impedance Tomography

A B-spline level set (BLS) based method is proposed for shape reconstruction in electrical impedance tomography (EIT). We assume that the conductivity distribution to be reconstructed is piecewise constant, transforming the image reconstruction problem into a shape reconstruction problem. The shape/interface of inclusions is implicitly represented by a level set function (LSF), which is modeled as a continuous parametric function expressed using B-spline functions. Starting from modeling the conductivity distribution with the B-spline based LSF, we show that the shape modeling allows us to compute the solution by restricting the minimization problem to the space spanned by the B-splines. As a consequence, the solution to the minimization problem is obtained in terms of the B-spline coefficients. We illustrate the behavior of this method using simulated as well as water tank data. In addition, robustness studies considering varying initial guesses, differing numbers of control points, and modeling errors caused by inhomogeneity are performed. Both simulation and experimental results show that the BLS-based approach offers clear improvements in preserving the sharp features of the inclusions in comparison to the recently published parametric level set method.

Development of a Wearable Electrical Impedance Tomographic Sensor for Gesture Recognition With Machine Learning

A wearable electrical impedance tomographic (wEIT) sensor with 8 electrodes is developed to realize gesture recognition with machine learning algorithms. To optimize the wEIT sensor, gesture recognition rates are compared by using a series of electrodes with different materials and shapes. To improve the gesture recognition rates, several Machine Learning algorithms are used to recognize three different gestures with the obtained voltage data. To clarify the gesture recognition mechanism, an electrical model of the electrode-skin contact impedance is established. Experimental results show that: rectangular copper electrodes realize the highest recognition rate; the existence of the electrode-skin contact impedance could improve the gesture recognition rate; Medium Gaussian SVM (Support Vector Machine) algorithm is the optimal algorithm with an average recognition rate of 95%.