A Post-Processing Method for Three-Dimensional 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.

Advances of deep learning in electrical impedance tomography image reconstruction

Electrical impedance tomography (EIT) has been widely used in biomedical research because of its advantages of real-time imaging and nature of being non-invasive and radiation-free. Additionally, it can reconstruct the distribution or changes in electrical properties in the sensing area. Recently, with the significant advancements in the use of deep learning in intelligent medical imaging, EIT image reconstruction based on deep learning has received considerable attention. This study introduces the basic principles of EIT and summarizes the application progress of deep learning in EIT image reconstruction with regards to three aspects: a single network reconstruction, deep learning combined with traditional algorithm reconstruction, and multiple network hybrid reconstruction. In future, optimizing the datasets may be the main challenge in applying deep learning for EIT image reconstruction. Adopting a better network structure, focusing on the joint reconstruction of EIT and traditional algorithms, and using multimodal deep learning-based EIT may be the solution to existing problems. In general, deep learning offers a fresh approach for improving the performance of EIT image reconstruction and could be the foundation for building an intelligent integrated EIT diagnostic system in the future.

Study and comparison of different Machine Learning-based approaches to solve the inverse problem in Electrical Impedance Tomographies

Electrical Impedance Tomography (EIT) is a non-invasive technique used to obtain the electrical internal conductivity distribution from the interior of bodies. This is a promising method from the manufacturing viewpoint, since it could be used to estimate different physical inner body properties during the production of goods. Nevertheless, this technique requires dealing with an inverse problem that makes its usage in real-time processes challenging. Recently, Machine Learning techniques have been proposed to solve the inverse problem accurately. However, the majority of prior research is focused on qualitative results, and they typically lack a systematic methodology to determine the optimal hyperparameters appropriately. This work presents a systematic comparison of six popular Machine Learning algorithms: Artificial Neural Network, Random Forest, K-Nearest Neighbors, Elastic Net, Ada Boost, and Gradient Boosting. Particularly, the last two algorithms were based on decision tree learners. Furthermore, we studied the relationship between model performance and different EIT configurations. Specifically, we analyzed whether the measurement pattern and the number of used electrodes could increase the model performance. Experiments revealed that tree-based models present high performance, even better than Neural Networks, the most widely-used Machine Learning model to deal with EIT. Experiments also showed a model performance improvement when the EIT configuration was optimized. Most favorable metrics were attained using the tree-based Gradient Boosting model with a combination of both adjacent and mono measurement patterns as well as with 32 electrodes deployed during the tomographic process. With this particular setting, we achieved an accuracy of 99.14% detecting internal artifacts and a Root Mean Square Error of 4.75 predicting internal conductivity distributions.

A Deep Neural Network Method for Arterial Blood Flow Profile Reconstruction

Arterial stenosis will reduce the blood flow to various organs or tissues, causing cardiovascular diseases. Although there are mature diagnostic techniques in clinical practice, they are not suitable for early cardiovascular disease prediction and monitoring due to their high cost and complex operation. In this paper, we studied the electromagnetic effect of arterial blood flow and proposed a method based on the deep neural network for arterial blood flow profile reconstruction. The potential difference and weight matrix are used as inputs to the method, and its output is an estimate of the internal blood flow velocity distribution for arterial blood flow profile reconstruction. Firstly, the weight matrix is input into the convolutional auto-encode (CAE) network to extract its features. Then, the weight matrix features and potential difference are combined to obtain the features of the blood velocity distribution. Finally, the velocity features are reconstructed into blood flow velocity distribution by a convolution neural network (CNN). All data sets are obtained from a model of the carotid artery with different rates of stenosis in a uniform magnetic field by COMSOL. The results show that the average root mean square error of the reconstruction results obtained by the proposed method is 0.0333, and the average correlation coefficient is 0.9721, which is better than the corresponding indicators of the Tikhonov, back propagation (BP) and CNN methods. The simulation results show that the proposed method can achieve high accuracy in blood flow profile reconstruction and is of great significance for the early diagnosis of arterial stenosis and other vessel diseases.

Evaluation of Thoracic Equivalent Multiport Circuits Using an Electrical Impedance Tomography Hardware Simulation Interface

Electrical impedance tomography is a low-cost, safe, and high temporal resolution medical imaging modality which finds extensive application in real-time thoracic impedance imaging. Thoracic impedance changes can reveal important information about the physiological condition of patients’ lungs. In this way, electrical impedance tomography can be a valuable tool for monitoring patients. However, this technique is very sensitive to measurement noise or possible minor signal errors, coming from either the hardware, the electrodes, or even particular biological signals. Thus, the design of a good performance electrical impedance tomography hardware setup which properly interacts with the tissue examined is both an essential and a challenging concept. In this paper, we adopt an extensive simulation approach, which combines the system’s analogue and digital hardware, along with equivalent circuits of 3D finite element models that represent thoracic cavities. Each thoracic finite element model is created in MATLAB based on existing CT images, while the tissues’ conductivity and permittivity values for a selected frequency are acquired from a database using Python. The model is transferred to a multiport RLC network, embedded in the system’s hardware which is simulated at LT SPICE. The voltage output data are transferred to MATLAB where the electrical impedance tomography signal sampling and digital processing is also simulated. Finally, image reconstructions are performed in MATLAB, using the EIDORS library tool and considering the signal noise levels and different electrode and signal sampling configurations (ADC bits, sampling frequency, number of taps).

Magnetic-resonance-based measurement of electromagnetic fields and conductivity in vivo using single current administration-A machine learning approach

Diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) is a newly developed technique that combines MR-based measurements of magnetic flux density with diffusion tensor MRI (DT-MRI) data to reconstruct electrical conductivity tensor distributions. DT-MREIT techniques normally require injection of two independent current patterns for unique reconstruction of conductivity characteristics. In this paper, we demonstrate an algorithm that can be used to reconstruct the position dependent scale factor relating conductivity and diffusion tensors, using flux density data measured from only one current injection. We demonstrate how these images can also be used to reconstruct electric field and current density distributions. Reconstructions were performed using a mimetic algorithm and simulations of magnetic flux density from complementary electrode montages, combined with a small-scale machine learning approach. In a biological tissue phantom, we found that the method reduced relative errors between single-current and two-current DT-MREIT results to around 10%. For in vivo human experimental data the error was about 15%. These results suggest that incorporation of machine learning may make it easier to recover electrical conductivity tensors and electric field images during neuromodulation therapy without the need for multiple current administrations.

Signal conditioning using logarithmic amplifier for biomedical applications of electrical impedance tomography

OBJECTIVE

The aim of this study was to explore the use of a logarithmic amplifier to improve the spatial resolution (RES) of a low-cost electrical impedance tomography (EIT) system. In an EIT system, the measured signal has a large dynamic range from µV to mV, which requires high-RES (analog to digital conversion) cards. The logarithmic amplifier reduces the dynamic range by expanding lower values and compressing higher values, thereby improving the sensitivity and at the same time preventing the signal from saturation. In addition, a low-RES analog to digital conversion (ADC) cards can be used, making the system cost effective. This work evaluates the performance of a logarithmic amplifier and a linear amplifier used for signal conditioning in a low-cost EIT system.

APPROACH

Two EIT systems based on a linear amplifier and logarithmic amplifier were designed. Phantom experiments were carried out with very small amounts of current injection. The signal-to-noise ratio (SNR), image quality, minimum detectable size and minimum detectable conductivity change were obtained.

MAIN RESULTS

The logarithmic amplifier-based EIT system increased the average SNR by 4 dB. It also showed improvement in the RES and contrast-to-noise ratio of the images. The minimum size detectable by the logarithmic amplifier-based system was of radius 0.25 cm in a tank of radius 11 cm and the minimum change in conductivity detectable was 11%.

SIGNIFICANCE

Logarithmic amplifier-based signal conditioning is a promising technique for improving the spatial RES of a low-cost EIT system that has a low-RES ADC.

Supervised Descent Learning for Thoracic Electrical Impedance Tomography

OBJECTIVE

The absolute image reconstruction problem of electrical impedance tomography (EIT) is ill-posed. Traditional methods usually solve a nonlinear least squares problem with some kind of regularization. These methods suffer from low accuracy, poor anti-noise performance, and long computation time. Besides, the integration of a priori information is not very flexible. This work tries to solve EIT inverse problem using a machine learning algorithm for the application of thorax imaging.

METHODS

We developed the supervised descent learning EIT (SDL-EIT) inversion algorithm based on the idea of supervised descent method (SDM). The algorithm approximates the mapping from measured data to the conductivity image by a series of descent directions learned from training samples. We designed a training data set in which the thorax contour, and some general structure of lungs, and heart are embedded. The algorithm is implemented in both two-, and three-dimensional cases, and is evaluated using synthetic, and measured thoracic data. Results, and conclusion: For synthetic data, SDL-EIT shows better accuracy, and anti-noise performance compared with traditional Gauss-Newton inversion (GNI) method. For measured data, the result of SDL-EIT is reasonable compared with computed tomography (CT) scan image.

SIGNIFICANCE

Using SDL-EIT, prior information can be easily integrated through the specifically designed training data set, and the image reconstruction process can be accelerated. The algorithm is effective in inverting measured thoracic data. It is a potential algorithm for human thorax imaging.

Neural network-based supervised descent method for 2D electrical impedance tomography

OBJECTIVE

In this work, we study the application of the neural network-based supervised descent method (NN-SDM) for 2D electrical impedance tomography.

APPROACH

The NN-SDM contains two stages: offline training and online prediction. In the offline stage, neural networks are iteratively applied to learn a sequence of descent directions for minimizing the objective function, where the training data set is generated in advance according to prior information or historical data. In the online stage, the trained neural networks are directly used to predict the descent directions.

MAIN RESULTS

Numerical and experimental results are reported to assess the efficiency and accuracy of the NN-SDM for both model-based and pixel-based inversions. In addition, the performance of the NN-SDM is compared with the linear SDM (LSDM), an end-to-end neural network (E2E-NN) and the Gauss-Newton (GN) method. The results demonstrate that the NN-SDM achieves faster convergence than the LSDM and GN method, and achieves a stronger generalization ability than the E2E-NN.

SIGNIFICANCE

The NN-SDM combines the strong non-linear fitting ability of the neural network and good generalization capability of the supervised descent method (SDM), which also provides good flexibility to incorporate prior information and accelerates the convergence of iteration.

Improved Imaging Resolution of Electrical Impedance Tomography Using Artificial Neural Networks for Image Reconstruction

Electrical impedance tomography (EIT) is a noninvasive and non-radiative medical imaging technique based on detecting the inhomogeneous electrical properties of the tissue. The inverse problem of EIT is a highly nonlinear ill-posed problem, which is the main reason that affects image quality. Our goal is to solve the EIT inverse problem using the nonlinear mapping properties of artificial neural networks (ANNs) and convolutional neural networks (CNNs). In this paper, the adaptive moment estimation (ADAM) optimization method and mean-square-error (MSE) function are used to train an ANN to solve the inverse problem and a CNN to process the ANN image. The networks are trained on datasets of simulated data, and tested on datasets of simulated data and experimental data. Results for time-difference EIT (td-EIT) images are presented using simulated EIT data from EIDORS and experimental EIT data from our EIT systems. The results are used to compare the proposed method with the one-step Gauss-Newton linear method and RBFNN method. The proposed method offers improved resolution (RES), low position error (PE) and excellent artefact removal compared to the existing methods. The experimental results show that our method can improve the RES by 50 to 70 percent and reduce the PE by 60 to 70 percent. The improvements in RES and processing speed are essential for clinical EIT measurement of dynamic physiological processes.

Real-Time Radiofrequency Ablation Lesion Depth Estimation Using Multi-frequency Impedance With a Deep Neural Network and Tree-Based Ensembles

OBJECTIVE

Design and optimization of statistical models for use in methods for estimating radiofrequency ablation (RFA) lesion depths in soft real-time performance.

METHODS

Using tissue multi-frequency complex electrical impedance data collected from a low-cost embedded system, a deep neural network (NN) and tree-based ensembles (TEs) were trained for estimating the RFA lesion depth via regression.

RESULTS

Addition of frequency sweep data, previous depth data, and previous RF power state data boosted accuracy of the statistical models. The root mean square errors were 2 mm for NN and 0.5 mm for TEs for previous statistical models and the root mean square errors were 0.4 mm for NN and 0.04 mm for TEs for the statistical models presented in this paper. Simulation ablation performance showed a mean difference against physical measurements of 0.5 ±0.2 mm for the NN-based depth estimation method and 0.7 ±0.4 mm for the TE-based depth estimation method.

CONCLUSION

The results show that multi-frequency data significantly improves the depth estimation performance of the statistical models.

SIGNIFICANCE

The RFA lesion depth estimation methods presented in this work achieve millimeter-resolution accuracy with soft real-time performance on an ARMv7-based embedded system for potential translation to clinical RFA technologies.

Beltrami-net: domain-independent deep D-bar learning for absolute imaging with electrical impedance tomography (a-EIT)

OBJECTIVE

To develop, and demonstrate the feasibility of, a novel image reconstruction method for absolute electrical impedance tomography (a-EIT) that pairs deep learning techniques with real-time robust D-bar methods and examine the influence of prior information on the reconstruction.

APPROACH

A D-bar method is paired with a trained convolutional neural network (CNN) as a post-processing step. Training data is simulated for the network using no knowledge of the boundary shape by using an associated nonphysical Beltrami equation rather than simulating the traditional current and voltage data specific to a given domain. This allows the training data to be boundary shape independent. The method is tested on experimental data from two EIT systems (ACT4 and KIT4) with separate training sets of varying prior information.

MAIN RESULTS

Post-processing the D-bar images with a CNN produces significant improvements in image quality measured by structural SIMilarity indices (SSIMs) as well as relative [Formula: see text] and [Formula: see text] image errors.

SIGNIFICANCE

This work demonstrates that more general networks can be trained without being specific about boundary shape, a key challenge in EIT image reconstruction. The work is promising for future studies involving databases of anatomical atlases.

Real-time monitoring radiofrequency ablation using tree-based ensemble learning models

BACKGROUND

Radiofrequency ablation is a minimally-invasive treatment method that aims to destroy undesired tissue by exposing it to alternating current in the 100 kHz-800 kHz frequency range and heating it until it is destroyed via coagulative necrosis. Ablation treatment is gaining momentum especially in cancer research, where the undesired tissue is a malignant tumor. While ablating the tumor with an electrode or catheter is an easy task, real-time monitoring the ablation process is a must in order to maintain the reliability of the treatment. Common methods for this monitoring task have proven to be accurate, however, they are all time-consuming or require expensive equipment, which makes the clinical ablation process more cumbersome and expensive due to the time-dependent nature of the clinical procedure.

METHODS

A machine learning (ML) approach is presented that aims to reduce the monitoring time while keeping the accuracy of the conventional methods. Two different hardware setups are used to perform the ablation and collect impedance data at the same time and different ML algorithms are tested to predict the ablation depth in 3 dimensions, based on the collected data.

RESULTS

Both the random forest and adaptive boosting (adaboost) models had over 98% R² on the data collected with the embedded system-based hardware instrumentation setup, outperforming Neural Network-based models.

CONCLUSIONS

It is shown that an optimal pair of hardware setup and ML algorithm (Adaboost) is able to control the ablation by estimating the lesion depth within a test average of 0.3mm while keeping the estimation time within 10ms on a ×86-64 workstation.

Towards a Fast and Accurate EIT Inverse Problem Solver: A Machine Learning Approach

Different industrial and medical situations require the non-invasive extraction of information from the inside of bodies. This is usually done through tomographic methods that generate images based on internal body properties. However, the image reconstruction involves a mathematical inverse problem, for which accurate resolution demands large computation time and capacity. In this paper we explore the use of Machine Learning to develop an accurate solver for reconstructing Electrical Impedance Tomography images in real-time. We compare the results with the Iterative Gauss-Newton and the Primal Dual Interior Point Method, which are both largely used and well-validated solvers. The approaches were compared from the qualitative as well as the quantitative viewpoints. The former was focused on correctly detecting the internal body features. The latter was based on accurately predicting internal property distributions. Experiments revealed that our approach achieved better accuracy and Cohen’s kappa coefficient (97.57% and 94.60% respectively) from the qualitative viewpoint. Moreover, it also obtained better quantitative metrics with a Mean Absolute Percentage Error of 18.28%. Experiments confirmed that Neural Networks algorithms can reconstruct internal body properties with high accuracy, so they would be able to replace more complex and slower alternatives.

Deep D-Bar: Real-Time Electrical Impedance Tomography Imaging With Deep Neural Networks

The mathematical problem for electrical impedance tomography (EIT) is a highly nonlinear ill-posed inverse problem requiring carefully designed reconstruction procedures to ensure reliable image generation. D-bar methods are based on a rigorous mathematical analysis and provide robust direct reconstructions by using a low-pass filtering of the associated nonlinear Fourier data. Similarly to low-pass filtering of linear Fourier data, only using low frequencies in the image recovery process results in blurred images lacking sharp features, such as clear organ boundaries. Convolutional neural networks provide a powerful framework for post-processing such convolved direct reconstructions. In this paper, we demonstrate that these CNN techniques lead to sharp and reliable reconstructions even for the highly nonlinear inverse problem of EIT. The network is trained on data sets of simulated examples and then applied to experimental data without the need to perform an additional transfer training. Results for absolute EIT images are presented using experimental EIT data from the ACT4 and KIT4 EIT systems.

Real-time estimation of lesion depth and control of radiofrequency ablation within ex vivo animal tissues using a neural network

BACKGROUND

Radiofrequency ablation (RFA), a method of inducing thermal ablation (cell death), is often used to destroy tumours or potentially cancerous tissue. Current techniques for RFA estimation (electrical impedance tomography, Nakagami ultrasound, etc.) require long compute times (≥ 2 s) and measurement devices other than the RFA device. This study aims to determine if a neural network (NN) can estimate ablation lesion depth for control of bipolar RFA using complex electrical impedance - since tissue electrical conductivity varies as a function of tissue temperature - in real time using only the RFA therapy device's electrodes.

METHODS

Three-dimensional, cubic models comprised of beef liver, pork loin or pork belly represented target tissue. Temperature and complex electrical impedance from 72 data generation ablations in pork loin and belly were used for training the NN (403 s on Xeon processor). NN inputs were inquiry depth, starting complex impedance and current complex impedance. Training-validation-test splits were 70%-0%-30% and 80%-10%-10% (overfit test). Once the NN-estimated lesion depth for a margin reached the target lesion depth, RFA was stopped for that margin of tissue.

RESULTS

The NN trained to 93% accuracy and an NN-integrated control ablated tissue to within 1.0 mm of the target lesion depth on average. Full 15-mm depth maps were calculated in 0.2 s on a single-core ARMv7 processor.

CONCLUSIONS

The results show that a NN could make lesion depth estimations in real-time using less in situ devices than current techniques. With the NN-based technique, physicians could deliver quicker and more precise ablation therapy.

Three-dimensional Pulmonary Monitoring Using Focused Electrical Impedance Measurements

Lung pathologies such as edema, atelectasis or pneumonia are potentially life threatening conditions. Especially in critically ill and mechanically ventilated patients, an early diagnosis and treatment is crucial to prevent an Acute Respiratory Distress Syndrome [1]. Thus, continuous monitoring tool for the lung condition available at the bedside would be highly appreciated. One concept for this is Electrical Impedance Tomography (EIT). In EIT, an electrode belt of typically 16 or 32 electrodes is attached at the body surface and multiple impedance measurements are performed. From this, the conductivity change inside the body is reconstructed in a two-dimensional image. In various studies, EIT proved to be a useful tool for quantifying recruitment maneuvers, the assessment of the ventilation homogeneity, the detection of lung edema or perfusion monitoring [2, 3, 4, 5]. Nevertheless, the main problem of EIT is the low spatial resolution (compared to CT) and the limitation to two dimensional images. In this paper, we try to address the latter issue: Instead of projecting conductivity changes onto a two-dimensional image, we adjust electrode positions to focus single tetrapolar measurements to specific, three-dimensional regions of interest. In earlier work, we defined guidelines to achieve this focusing [6, 7]. In this paper, we demonstrate in simulations and in a water tank experiment that applying these guidelines can help to detect pathologies in specific lung regions.

A novel post-processing scheme for two-dimensional electrical impedance tomography based on artificial neural networks

OBJECTIVE

Electrical Impedance Tomography (EIT) is a powerful non-invasive technique for imaging applications. The goal is to estimate the electrical properties of living tissues by measuring the potential at the boundary of the domain. Being safe with respect to patient health, non-invasive, and having no known hazards, EIT is an attractive and promising technology. However, it suffers from a particular technical difficulty, which consists of solving a nonlinear inverse problem in real time. Several nonlinear approaches have been proposed as a replacement for the linear solver, but in practice very few are capable of stable, high-quality, and real-time EIT imaging because of their very low robustness to errors and inaccurate modeling, or because they require considerable computational effort.

METHODS

In this paper, a post-processing technique based on an artificial neural network (ANN) is proposed to obtain a nonlinear solution to the inverse problem, starting from a linear solution. While common reconstruction methods based on ANNs estimate the solution directly from the measured data, the method proposed here enhances the solution obtained from a linear solver.

CONCLUSION

Applying a linear reconstruction algorithm before applying an ANN reduces the effects of noise and modeling errors. Hence, this approach significantly reduces the error associated with solving 2D inverse problems using machine-learning-based algorithms.

SIGNIFICANCE

This work presents radical enhancements in the stability of nonlinear methods for biomedical EIT applications.