Lp-norm regularization in volumetric imaging of cardiac current sources

GAN-based generation of realistic 3D volumetric data: A systematic review and taxonomy

With the massive proliferation of data-driven algorithms, such as deep learning-based approaches, the availability of high-quality data is of great interest. Volumetric data is very important in medicine, as it ranges from disease diagnoses to therapy monitoring. When the dataset is sufficient, models can be trained to help doctors with these tasks. Unfortunately, there are scenarios where large amounts of data is unavailable. For example, rare diseases and privacy issues can lead to restricted data availability. In non-medical fields, the high cost of obtaining enough high-quality data can also be a concern. A solution to these problems can be the generation of realistic synthetic data using Generative Adversarial Networks (GANs). The existence of these mechanisms is a good asset, especially in healthcare, as the data must be of good quality, realistic, and without privacy issues. Therefore, most of the publications on volumetric GANs are within the medical domain. In this review, we provide a summary of works that generate realistic volumetric synthetic data using GANs. We therefore outline GAN-based methods in these areas with common architectures, loss functions and evaluation metrics, including their advantages and disadvantages. We present a novel taxonomy, evaluations, challenges, and research opportunities to provide a holistic overview of the current state of volumetric GANs.

Comparison of dipole-based and potential-based ECGI methods for premature ventricular contraction beat localization with clinical data

Introduction: Localization of premature ventricular contraction (PVC) origin to guide the radiofrequency ablation (RFA) procedure is one of the prominent clinical goals of non-invasive electrocardiographic imaging. However, the results reported in the literature vary significantly depending on the source model and the level of complexity in the forward model. This study aims to compare the paced and spontaneous PVC localization performances of dipole-based and potential-based source models and corresponding inverse methods using the same clinical data and to evaluate the effects of torso inhomogeneities on these performances. Methods: The publicly available EP solution data from the EDGAR data repository (BSPs from a maximum of 240 electrodes) with known pacing locations and the Bratislava data (BSPs in 128 leads) with spontaneous PVCs from patients who underwent successful RFA procedures were used. Homogeneous and inhomogeneous torso models and corresponding forward problem solutions were used to relate sources on the closed epicardial and epicardial-endocardial surfaces. The localization error (LE) between the true and estimated pacing site/PVC origin was evaluated. Results: For paced data, the median LE values were 25.2 and 13.9 mm for the dipole-based and potential-based models, respectively. These median LE values were higher for the spontaneous PVC data: 30.2-33.0 mm for the dipole-based model and 28.9-39.2 mm for the potential-based model. The assumption of inhomogeneities in the torso model did not change the dipole-based solutions much, but using an inhomogeneous model improved the potential-based solutions on the epicardial-endocardial ventricular surface. Conclusion: For the specific task of localization of pacing site/PVC origin, the dipole-based source model is more stable and robust than the potential-based source model. The torso inhomogeneities affect the performances of PVC origin localization in each source model differently. Hence, care must be taken in generating patient-specific geometric and forward models depending on the source model representation used in electrocardiographic imaging (ECGI).

Evaluation of In Vitro Wound-Healing Potential, Antioxidant Capacity, and Antimicrobial Activity of Stellaria media (L.) Vill

The healing of skin wounds remains an important concern in medicine, especially in chronic wounds caused by various diseases such as diabetes. Using herbs or herbal products to heal skin wounds is a therapeutic challenge for traditional medicine. In this context, the main aim of our work was to highlight the in vitro healing potential of Stellaria media (L.) Vill. (SM) extract using the scratch assay on normal human dermal fibroblasts (NHDF). The ability to stimulate cell migration and proliferation under the influence of different concentrations of SM extract (range between 12.5 and 200 µg/mL) was determined compared to the control (untreated in vitro-simulated wound) and positive control (allantoin 50 µg/mL). Our results showed that the concentration of 100 µg/mL SM extract applied on the simulated wound recorded the strongest and fastest (24 h) migration (with wound closure) and proliferation of NHDF compared with the control. In addition, the SM extract was characterized in terms of bioactive compounds (total phenols and flavonoids content), antioxidant capacity (FRAP (The Ferric-Reducing Antioxidant Power) assay and electrochemical method), and antimicrobial activity. The results show that the SM extract contains a considerable amount of polyphenols (17.19 ± 1.32 mg GAE/g dw and 7.28 ± 1.18 mg QE/g dw for total phenol and flavonoid content, respectively) with antioxidant capacity. Antimicrobial activity against Gram-positive bacteria (S. aureus) is higher than E. coli at a dose of 15 µg/mL. This study showed that Stellaria media is a source of polyphenols compounds with antioxidant capacity, and for the first time, its wound healing potential was emphasized.

A Novel Data-Adaptive Regression Framework Based on Multivariate Adaptive Regression Splines for Electrocardiographic Imaging

OBJECTIVE

Noninvasive electrocardiographic imaging (ECGI) is a promising tool for revealing crucial cardiac electrical events with diagnostic potential. We propose a novel nonparametric regression framework based on multivariate adaptive regression splines (MARS) for ECGI.

METHODS

The inverse problem was solved by using the regression model trained with body surface potentials (BSP) and corresponding electrograms (EGM). Simulated data as well as experimental data from torso-tank experiments were used as to assess the performance of the proposed method. The robustness of the method to measurement noise and geometric errors were assessed in terms of electrogram reconstruction quality, activation time accuracy, and localization error metrics. The methods were compared with Tikhonov regularization and neural network (NN)-based methods. The resulting mapping functions between the BSPs and EGMs were also used to evaluate the most influential measurement leads.

RESULTS

MARS-based method outperformed Tikhonov regularization in terms of reconstruction accuracy and robustness to measurement noise. The effects of geometric errors were remedied to some extent by enriching the training set composition including model errors. The MARS-based method had a comparable performance with NN-based methods, which require the adjustment of many parameters.

CONCLUSION

MARS-based method successfully discovers the inverse mapping functions between the BSPs and EGMs yielding accurate reconstructions, and quantifies the contribution of each BSP lead.

SIGNIFICANCE

MARS-based method is adaptive, requires fewer parameter adjustments than NN-based methods, and robust to errors. Thus, it can be a feasible data-driven approach for accurately solving inverse imaging problems.

ML and MAP estimation of parameters for the Kalman filter and smoother applied to electrocardiographic imaging

In electrocardiographic imaging (ECGI), one solves the inverse problem of electrocardiography (ECG) to reconstruct equivalent cardiac sources based on the body surface potential measurements and a mathematical model of the torso. Due to attenuation and spatial smoothing within the torso, this inverse problem is ill-posed. Among many regularization approaches used in the ECG literature to overcome this ill-posedness, statistical techniques have received great attention because of their flexibility to represent the data, and ability to provide performance evaluation tools for quantification of uncertainties and errors in the model. However, despite their potential to accurately reconstruct the equivalent cardiac sources, one major challenge in these methods is how to best utilize the prior information available in terms of training data. In this paper, we address the question of how to define the prior probability distributions (pdf) of the sources and the error terms so that we can obtain more accurate and robust inverse solutions. We employ two methods, maximum likelihood (ML) and maximum a posteriori (MAP), for estimating the model parameters such as the prior pdfs, error pdfs, and the state-transition matrix, based on the same training data. These model parameters are then used for the state-space representation and estimation of the epicardial potentials, which constitute the equivalent cardiac sources in this study. The performances of ML- and MAP-based model parameter estimation methods are evaluated qualitatively and quantitatively at various noise levels and geometric disturbances using two different simulated datasets. Bayesian MAP estimation, which is also a well-known statistical inversion technique, and Tikhonov regularization, which can be formulated as a special and simplified version of Bayesian MAP estimation, have been included here for comparison with the Kalman filtering method. Our results show that the state-space approach outperforms Bayesian MAP estimation in all cases; ML yields accurate results when the test and training beats come from the same physiological model, but MAP is superior to ML, especially if the test and training beats are from different physiological models. Graphical Abstract ML and MAP estimation of parameters for the Kalman filter and smoother applied to electrocardiographic imaging.

Paired cycle-GAN-based image correction for quantitative cone-beam computed tomography

PURPOSE

The incorporation of cone-beam computed tomography (CBCT) has allowed for enhanced image-guided radiation therapy. While CBCT allows for daily 3D imaging, images suffer from severe artifacts, limiting the clinical potential of CBCT. In this work, a deep learning-based method for generating high quality corrected CBCT (CCBCT) images is proposed.

METHODS

The proposed method integrates a residual block concept into a cycle-consistent adversarial network (cycle-GAN) framework, called res-cycle GAN, to learn a mapping between CBCT images and paired planning CT images. Compared with a GAN, a cycle-GAN includes an inverse transformation from CBCT to CT images, which constrains the model by forcing calculation of both a CCBCT and a synthetic CBCT. A fully convolution neural network with residual blocks is used in the generator to enable end-to-end CBCT-to-CT transformations. The proposed algorithm was evaluated using 24 sets of patient data in the brain and 20 sets of patient data in the pelvis. The mean absolute error (MAE), peak signal-to-noise ratio (PSNR), normalized cross-correlation (NCC) indices, and spatial non-uniformity (SNU) were used to quantify the correction accuracy of the proposed algorithm. The proposed method is compared to both a conventional scatter correction and another machine learning-based CBCT correction method.

RESULTS

Overall, the MAE, PSNR, NCC, and SNU were 13.0 HU, 37.5 dB, 0.99, and 0.05 in the brain, 16.1 HU, 30.7 dB, 0.98, and 0.09 in the pelvis for the proposed method, improvements of 45%, 16%, 1%, and 93% in the brain, and 71%, 38%, 2%, and 65% in the pelvis, over the CBCT image. The proposed method showed superior image quality as compared to the scatter correction method, reducing noise and artifact severity. The proposed method produced images with less noise and artifacts than the comparison machine learning-based method.

CONCLUSIONS

The authors have developed a novel deep learning-based method to generate high-quality corrected CBCT images. The proposed method increases onboard CBCT image quality, making it comparable to that of the planning CT. With further evaluation and clinical implementation, this method could lead to quantitative adaptive radiation therapy.

Noninvasive Activation Imaging of Ventricular Arrhythmias by Spatial Gradient Sparse in Frequency Domain-Application to Mapping Reentrant Ventricular Tachycardia

The aim of this paper is to develop and evaluate a novel imaging method [spatial gradient sparse in frequency domain (SSF)] for the reconstruction of activation sequences of ventricular arrhythmia from noninvasive body surface potential map (BSPM) measurements. We formulated and solved the electrocardiographic inverse problem in the frequency domain, and the activation time was encoded in the phase information of the imaging solution. A cellular automaton heart model was used to generate focal ventricular tachycardia (VT). Different levels of Gaussian white noise were added to simulate noise-contaminated BSPM. The performance of SSF was compared with that of weighted minimum norm inverse solution. We also evaluated the method in a swine model with simultaneous intracardiac and body surface recordings. Four reentrant VTs were observed in pigs with myocardial infarction generated by left anterior descending artery occlusion. The imaged activation sequences of reentrant VTs were compared with those obtained from intracardiac electrograms. In focal VT simulation, SSF has increased the correlation coefficient (CC) by 5% and decreased localization errors (LEs) by 2.7 mm on average under different noise levels. In the animal validation with reentrant VT, SSF has achieved an average CC of 88% and an average LE of 6.3 mm in localizing the earliest and latest activation site in the reentry circuit. Our promising results suggest that the SSF provides noninvasive imaging capability of detecting and mapping macro-reentrant circuits in 3-D ventricular space. The SSF may become a useful imaging tool of identifying and localizing the potential targets for ablation of focal and reentrant VT.

Evaluation of multivariate adaptive non-parametric reduced-order model for solving the inverse electrocardiography problem: a simulation study

In the inverse electrocardiography (ECG) problem, the goal is to reconstruct the heart's electrical activity from multichannel body surface potentials and a mathematical model of the torso. Over the years, researchers have employed various approaches to solve this ill-posed problem including regularization, optimization, and statistical estimation. It is still a topic of interest especially for researchers and clinicians whose goal is to adopt this technique in clinical applications. Among the wide range of mathematical tools available in the fields of operational research, inverse problems, optimization, and parameter estimation, spline-based techniques have been applied to inverse problems in several areas. If proper spline bases are chosen, the complexity of the problem can be significantly reduced while increasing estimation accuracy. However, there are few studies within the context of the inverse ECG problem that take advantage of this property of the spline-based approaches. In this paper, we evaluate the performance of Multivariate Adaptive Regression Splines (MARS)-based method for the solution of the inverse ECG problem using two different collections of simulated data. The results show that the MARS-based method improves the inverse ECG solutions and is "robust" to modeling errors, especially in terms of localizing the arrhythmia sources. Graphical Abstract Multivariate adaptive non-parametric model for inverse ECG problem.

Wavelet-promoted sparsity for non-invasive reconstruction of electrical activity of the heart

We investigated a novel sparsity-based regularization method in the wavelet domain of the inverse problem of electrocardiography that aims at preserving the spatiotemporal characteristics of heart-surface potentials. In three normal, anesthetized dogs, electrodes were implanted around the epicardium and body-surface electrodes were attached to the torso. Potential recordings were obtained simultaneously on the body surface and on the epicardium. A CT scan was used to digitize a homogeneous geometry which consisted of the body-surface electrodes and the epicardial surface. A novel multitask elastic-net-based method was introduced to regularize the ill-posed inverse problem. The method simultaneously pursues a sparse wavelet representation in time-frequency and exploits correlations in space. Performance was assessed in terms of quality of reconstructed epicardial potentials, estimated activation and recovery time, and estimated locations of pacing, and compared with performance of Tikhonov zeroth-order regularization. Results in the wavelet domain obtained higher sparsity than those in the time domain. Epicardial potentials were non-invasively reconstructed with higher accuracy than with Tikhonov zeroth-order regularization (p < 0.05), and recovery times were improved (p < 0.05). No significant improvement was found in terms of activation times and localization of origin of pacing. Next to improved estimation of recovery isochrones, which is important when assessing substrate for cardiac arrhythmias, this novel technique opens potentially powerful opportunities for clinical application, by allowing to choose wavelet bases that are optimized for specific clinical questions. Graphical Abstract The inverse problem of electrocardiography is to reconstruct heart-surface potentials from recorded bodysurface electrocardiograms (ECGs) and a torso-heart geometry. However, it is ill-posed and solving it requires additional constraints for regularization. We introduce a regularization method that simultaneously pursues a sparse wavelet representation in time-frequency and exploits correlations in space. Our approach reconstructs epicardial (heart-surface) potentials with higher accuracy than common methods. It also improves the reconstruction of recovery isochrones, which is important when assessing substrate for cardiac arrhythmias. This novel technique opens potentially powerful opportunities for clinical application, by allowing to choose wavelet bases that are optimized for specific clinical questions.

ECG imaging of ventricular tachycardia: evaluation against simultaneous non-contact mapping and CMR-derived grey zone

ECG imaging is an emerging technology for the reconstruction of cardiac electric activity from non-invasively measured body surface potential maps. In this case report, we present the first evaluation of transmurally imaged activation times against endocardially reconstructed isochrones for a case of sustained monomorphic ventricular tachycardia (VT). Computer models of the thorax and whole heart were produced from MR images. A recently published approach was applied to facilitate electrode localization in the catheter laboratory, which allows for the acquisition of body surface potential maps while performing non-contact mapping for the reconstruction of local activation times. ECG imaging was then realized using Tikhonov regularization with spatio-temporal smoothing as proposed by Huiskamp and Greensite and further with the spline-based approach by Erem et al. Activation times were computed from transmurally reconstructed transmembrane voltages. The results showed good qualitative agreement between the non-invasively and invasively reconstructed activation times. Also, low amplitudes in the imaged transmembrane voltages were found to correlate with volumes of scar and grey zone in delayed gadolinium enhancement cardiac MR. The study underlines the ability of ECG imaging to produce activation times of ventricular electric activity-and to represent effects of scar tissue in the imaged transmembrane voltages.

Examining the Impact of Prior Models in Transmural Electrophysiological Imaging: A Hierarchical Multiple-Model Bayesian Approach

Noninvasive cardiac electrophysiological (EP) imaging aims to mathematically reconstruct the spatiotemporal dynamics of cardiac sources from body-surface electrocardiographic (ECG) data. This ill-posed problem is often regularized by a fixed constraining model. However, a fixed-model approach enforces the source distribution to follow a pre-assumed structure that does not always match the varying spatiotemporal distribution of actual sources. To understand the model-data relation and examine the impact of prior models, we present a multiple-model approach for volumetric cardiac EP imaging where multiple prior models are included and automatically picked by the available ECG data. Multiple models are incorporated as an Lp-norm prior for sources, where p is an unknown hyperparameter with a prior uniform distribution. To examine how different combinations of models may be favored by different measurement data, the posterior distribution of cardiac sources and hyperparameter p is calculated using a Markov Chain Monte Carlo (MCMC) technique. The importance of multiple-model prior was assessed in two sets of synthetic and real-data experiments, compared to fixed-model priors (using Laplace and Gaussian priors). The results showed that the posterior combination of models (the posterior distribution of p) as determined by the ECG data differed substantially when reconstructing sources with different sizes and structures. While the use of fixed models is best suited in situations where the prior assumption fits the actual source structures, the use of an automatically adaptive set of models may have the ability to better address model-data mismatch and to provide consistent performance in reconstructing sources with different properties.

Mixed-norm regularization for brain decoding

This work investigates the use of mixed-norm regularization for sensor selection in event-related potential (ERP) based brain-computer interfaces (BCI). The classification problem is cast as a discriminative optimization framework where sensor selection is induced through the use of mixed-norms. This framework is extended to the multitask learning situation where several similar classification tasks related to different subjects are learned simultaneously. In this case, multitask learning helps in leveraging data scarcity issue yielding to more robust classifiers. For this purpose, we have introduced a regularizer that induces both sensor selection and classifier similarities. The different regularization approaches are compared on three ERP datasets showing the interest of mixed-norm regularization in terms of sensor selection. The multitask approaches are evaluated when a small number of learning examples are available yielding to significant performance improvements especially for subjects performing poorly.

Hierarchical multiple-model Bayesian approach to transmural electrophysiological imaging

Noninvasive electrophysiological (EP) imaging of the heart aims to mathematically reconstruct the spatiotemporal dynamics of cardiac current sources from body-surface electrocardiographic (ECG) data. This ill-posed problem is often regularized by a fixed constraining model. However, this approach enforces the source distribution to follow a preassumed spatial structure that does not always match the varying spatiotemporal distribution of current sources. We propose a hierarchical Bayesian approach to transmural EP imaging that employs a continuous combination of multiple models, each reflecting a specific spatial property for current sources. Multiple models are incorporated as an Lp-norm prior for current sources, where p is an unknown hyperparameter with a prior probabilistic distribution. The current source estimation is obtained as an optimally weighted combination of solutions across all models, the weight being determined from the posterior distribution of p inferred from ECG data. The accuracy of our approach is assessed in a set of synthetic and real-data experiments on human heart-torso models. While the use of fixed models (L1- and L2-norm) only properly recovers sources with specific structures, our method delivers consistent performance in reconstructing sources with various extents and structures.