A Statistical Shape-Constrained Reconstruction Framework for Electrical Impedance Tomography

Comparing machine learning algorithms for non-invasive detection and classification of failure in piezoresistive bone cement via electrical impedance tomography

At an estimated cost of $8 billion annually in the United States, revision surgeries to total joint replacements represent a substantial financial burden to the health care system and a tremendous mental and physical burden on patients and their caretakers. Fixation failures, such as implant loosening, wear, and mechanical instability of the poly(methyl methacrylate) (PMMA) cement, which bonds the implant to the bone, are the main causes of long-term implant failure. Early and accurate diagnosis of cement failure is critical for developing novel therapeutic strategies and reducing the high risk of a misjudged revision. Unfortunately, prevailing imaging modalities, notably plain radiographs, struggle to detect the precursors of implant failure and are often interpreted incorrectly. Our prior work has shown that the modification of PMMA bone cement with low concentrations of conductive fillers makes it piezoresistive and therefore self-sensing. When combined with a conductivity imaging modality such as electrical impedance tomography (EIT), it is possible to monitor load transfer across the PMMA using cost-effective, physiologically benign, non-contact, and real-time electrical measurements. Despite the ability of EIT for monitoring load transfer across self-sensing PMMA bone cement, it is unable to accurately characterize failure mechanisms. Overcoming this challenge is critical to the success of this technology in practice. Therefore, we herein expand upon our previous results by integrating machine learning techniques with EIT for cement condition characterization with the goal of establishing the feasibility of even off-the-shelf machine learning algorithms to address this important problem. We survey a wide variety of different machine learning algorithms for application to this problem, including neural networks on voltage readings of an EIT phantom for tracking the spatial position of a sample, specifying defect orientation within a sample, and classifying defect types, including cracks and delaminations. In addition, we explore the utilization of principal component analysis (PCA) for pre-treating impedance signals in each of these problems. Within the tested algorithms, our results show clear advantages of neural networks, support vector machines, and K-nearest neighbor algorithms for interpreting EIT signals. We also show that PCA is an effective addition to machine learning. These preliminary results demonstrate that the combination of smart materials, EIT, and machine learning may be a powerful instrumentation tool for diagnosing the origin and evolution of mechanical failure in joint replacements.

MMV-Net: A Multiple Measurement Vector Network for Multifrequency Electrical Impedance Tomography

Multifrequency electrical impedance tomography (mfEIT) is an emerging biomedical imaging modality to reveal frequency-dependent conductivity distributions in biomedical applications. Conventional model-based image reconstruction methods suffer from low spatial resolution, unconstrained frequency correlation, and high computational cost. Deep learning has been extensively applied in solving the EIT inverse problem in biomedical and industrial process imaging. However, most existing learning-based approaches deal with the single-frequency setup, which is inefficient and ineffective when extended to the multifrequency setup. This article presents a multiple measurement vector (MMV) model-based learning algorithm named MMV-Net to solve the mfEIT image reconstruction problem. MMV-Net considers the correlations between mfEIT images and unfolds the update steps of the Alternating Direction Method of Multipliers for the MMV problem (MMV-ADMM). The nonlinear shrinkage operator associated with the weighted l2,1 regularization term of MMV-ADMM is generalized in MMV-Net with a cascade of a Spatial Self-Attention module and a Convolutional Long Short-Term Memory (ConvLSTM) module to better capture intrafrequency and interfrequency dependencies. The proposed MMV-Net was validated on our Edinburgh mfEIT Dataset and a series of comprehensive experiments. The results show superior image quality, convergence performance, noise robustness, and computational efficiency against the conventional MMV-ADMM and the state-of-the-art deep learning methods.

Improved Electrical Impedance Tomography Reconstruction via a Bayesian Approach With an Anatomical Statistical Shape Model

OBJECTIVE

electrical impedance tomography (EIT) is a promising technique for rapid and continuous bedside monitoring of lung function. Accurate and reliable EIT reconstruction of ventilation requires patient-specific shape information. However, this shape information is often not available and current EIT reconstruction methods typically have limited spatial fidelity. This study sought to develop a statistical shape model (SSM) of the torso and lungs and evaluate whether patient-specific predictions of torso and lung shape could enhance EIT reconstructions in a Bayesian framework.

METHODS

torso and lung finite element surface meshes were fitted to computed tomography data from 81 participants, and a SSM was generated using principal component analysis and regression analyses. Predicted shapes were implemented in a Bayesian EIT framework and were quantitatively compared to generic reconstruction methods.

RESULTS

Five principal shape modes explained 38% of the cohort variance in lung and torso geometry, and regression analysis yielded nine total anthropometrics and pulmonary function metrics that significantly predicted these shape modes. Incorporation of SSM-derived structural information enhanced the accuracy and reliability of the EIT reconstruction as compared to generic reconstructions, demonstrated by reduced relative error, total variation, and Mahalanobis distance.

CONCLUSION

As compared to deterministic approaches, Bayesian EIT afforded more reliable quantitative and visual interpretation of the reconstructed ventilation distribution. However, no conclusive improvement of reconstruction performance using patient specific structural information was observed as compared to the mean shape of the SSM.

SIGNIFICANCE

The presented Bayesian framework builds towards a more accurate and reliable method for ventilation monitoring via EIT.

Regularization Solver Guided FISTA for Electrical Impedance Tomography

Electrical impedance tomography (EIT) is non-destructive monitoring technology that can visualize the conductivity distribution in the observed area. The inverse problem for imaging is characterized by a serious nonlinear and ill-posed nature, which leads to the low spatial resolution of the reconstructions. The iterative algorithm is an effective method to deal with the imaging inverse problem. However, the existing iterative imaging methods have some drawbacks, such as random and subjective initial parameter setting, very time consuming in vast iterations and shape blurring with less high-order information, etc. To solve these problems, this paper proposes a novel fast convergent iteration method for solving the inverse problem and designs an initial guess method based on an adaptive regularization parameter adjustment. This method is named the Regularization Solver Guided Fast Iterative Shrinkage Threshold Algorithm (RS-FISTA). The iterative solution process under the L1-norm regular constraint is derived in the LASSO problem. Meanwhile, the Nesterov accelerator is introduced to accelerate the gradient optimization race in the ISTA method. In order to make the initial guess contain more prior information and be independent of subjective factors such as human experience, a new adaptive regularization weight coefficient selection method is introduced into the initial conjecture of the FISTA iteration as it contains more accurate prior information of the conductivity distribution. The RS-FISTA method is compared with the methods of Landweber, CG, NOSER, Newton-Raphson, ISTA and FISTA, six different distributions with their optimal parameters. The SSIM, RMSE and PSNR of RS-FISTA methods are 0.7253, 3.44 and 37.55, respectively. In the performance test of convergence, the evaluation metrics of this method are relatively stable at 30 iterations. This shows that the proposed method not only has better visualization, but also has fast convergence. It is verified that the RS-FISTA algorithm is the better algorithm for EIT reconstruction from both simulation and physical experiments.

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.

Artificial Intelligence Segmented Dynamic Video Images for Continuity Analysis in the Detection of Severe Cardiovascular Disease

In this paper, an artificial intelligence segmented dynamic video image based on the process of intensive cardiovascular and cerebrovascular disease monitoring is deeply investigated, and a sparse automatic coding deep neural network with a four layers stack structure is designed to automatically extract the deep features of the segmented dynamic video image shot, and six categories of normal, atrial premature, ventricular premature, right bundle branch block, left bundle branch block, and pacing are achieved through hierarchical training and optimization. Accurate recognition of heartbeats with an average accuracy of 99.5%. It provides technical assistance for the intelligent prediction of high-risk cardiovascular diseases like ventricular fibrillation. An intelligent prediction algorithm for sudden cardiac death based on the echolocation network was proposed. By designing an echolocation network with a multilayer serial structure, an intelligent distinction between sudden cardiac death signal and non-sudden death signal was realized, and the signal was predicted 5 min before sudden death occurred, with an average prediction accuracy of 94.32%. Using the self-learning capability of stack sparse auto-coding network, a large amount of label-free data is designed to train the stack sparse auto-coding deep neural network to automatically extract deep representations of plaque features. A small amount of labeled data then introduced to micro-train the entire network. Through the automatic analysis of the fiber cap thickness in the plaques, the automatic identification of thin fiber cap-like vulnerable plaques was achieved, and the average overlap of vulnerable regions reached 87%. The overall time for the automatic plaque and vulnerable plaque recognition algorithm was 0.54 s. It provides theoretical support for accurate diagnosis and endogenous analysis of high-risk cardiovascular diseases.

A Shape-Based Statistical Inversion Method for EIT/URT Dual-Modality Imaging

A shape-based statistical inversion method is proposed for Electrical Impedance Tomography (EIT) and Ultrasound Reflection Tomography (URT) dual-modality imaging. It is promising to improve the imaging accuracy in inclusion detection problems. The proposed image reconstruction method is based on the statistical shape inversion framework. The likelihood function is derived from EIT and URT forward models. The prior distribution is constructed using the Markov random field (MRF) prior. The measurement uncertainty is modeled by conditional error model method. The statistical shape inversion problem is solved by the Maximum a posterior (MAP) method with conventional error model. A set of numerical and experimental tests are carried out to evaluate the performance of the proposed method. The results show that the proposed EIT/URT dual-modality imaging method has obvious improvement in imaging accuracy compared to the traditional single-modality EIT and URT methods.

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

This paper presents a new computational framework in electrical impedance tomography (EIT) for shape reconstruction based on the concept of moving morphable components (MMC). In the proposed framework, the shape reconstruction problem is solved in an explicit and geometrical way. Compared with the traditional pixel or shape-based solution framework, the proposed framework can incorporate more geometry and prior information into shape and topology optimization directly and therefore render the solution process more flexibility. It also has the afford potential to substantially reduce the computational burden associated with shape and topology optimization. The effectiveness of the proposed approach is tested with noisy synthetic data and experimental data, which demonstrates the most popular biomedical application of EIT: lung imaging. In addition, robustness studies of the proposed approach considering modeling errors caused by non-homogeneous background, varying initial guesses, differing numbers of candidate shape components, and differing exponent in the shape and topology description function are performed. The simulation and experimental results show that the proposed approach is tolerant to modeling errors and is fairly robust to these parameter choices, offering significant improvements in image quality in comparison to the conventional absolute reconstructions using smoothness prior regularization and total variation regularization.

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%.

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.

A Lagrange-Newton Method for EIT/UT Dual-Modality Image Reconstruction

An image reconstruction method is proposed based on Lagrange-Newton method for electrical impedance tomography (EIT) and ultrasound tomography (UT) dual-modality imaging. Since the change in conductivity distribution is usually accompanied with the change in acoustic impedance distribution, the reconstruction targets of EIT and UT are unified to the conductivity difference using the same mesh model. Some background medium distribution information obtained from ultrasound transmission and reflection measurements can be used to construct a hard constraint about the conductivity difference distribution. Then, the EIT/UT dual-modality inverse problem is constructed by an equality constraint equation, and the Lagrange multiplier method combining Newton-Raphson iteration is used to solve the EIT/UT dual-modality inverse problem. The numerical and experimental results show that the proposed dual-modality image reconstruction method has a better performance than the single-modality EIT method and is more robust to the measurement noise.