Fast and Accurate EEG/MEG BEM-Based Forward Problem Solution for High-Resolution Head Models.

A BEM (boundary element method) based approach is developed to accurately solve an EEG/MEG forward problem for a modern high-resolution head model in approximately 60 seconds using a common workstation. The method utilizes a charge-based BEM with fast multipole acceleration (BEM-FMM) and a "smart" mesh pre-refinement (called b-refinement) close to the singular source(s). No costly matrix-filling or direct solution steps typical for the standard BEM are required; the method generates on-skin voltages as well as MEG magnetic fields for high-resolution head models in approximately 60 seconds after initial model assembly. The method is verified both theoretically and experimentally.

A hybrid boundary element-finite element approach for solving the EEG forward problem in brain modeling.

This article introduces a hybrid BE-FE method for solving the EEG forward problem, leveraging the strengths of both the Boundary Element Method (BEM) and Finite Element Method (FEM). FEM accurately models complex and anisotropic tissue properties for realistic head geometries, while BEM excels in handling isotropic tissue regions and dipolar sources efficiently. The proposed hybrid method divides regions into homogeneous boundary element (BE) regions that include sources and heterogeneous anisotropic finite element (FE) regions. So, BEM models the brain, including dipole sources, and FEM models other head layers. Validation includes inhomogeneous isotropic/anisotropic three- and four-layer spherical head models, and a four-layer MRI-based realistic head model. Results for six dipole eccentricities and two orientations are computed using BEM, FEM, and hybrid BE-FE method. Statistical analysis, comparing error criteria of RDM and MAG, reveals notable improvements using the hybrid FE-BE method. In the spherical head model, the hybrid BE-FE method compared with FEM demonstrates enhancements of at least 1.05 and 38.31% in RDM and MAG criteria, respectively. Notably, in the anisotropic four-layer head model, improvements reach a maximum of 88.3% for RDM and 93.27% for MAG over FEM. Moreover, in the anisotropic four-layer realistic head model, the proposed hybrid method exhibits 55.4% improvement in RDM and 89.3% improvement in MAG compared to FEM. These findings underscore the proposed method is a promising approach for solving the realistic EEG forward problems, advancing neuroimaging techniques and enhancing understanding of brain function.

Forward problem of electrocardiography based on cardiac source vector orientations.

To localize the unusual cardiac activities non-invasively, one has to build a prior forward model that relates the heart, torso, and detectors. This model has to be constructed to mathematically relate the geometrical and functional activities of the heart. Several methods are available to model the prior sources in the forward problem, which results in the lead field matrix generation. In the conventional technique, the lead field assumed the fixed prior sources, and the source vector orientations were presumed to be parallel to the detector plane with the unit strength in all directions. However, the anomalies cannot always be expected to occur in the same location and orientation, leading to misinterpretation and misdiagnosis. To overcome this, the work proposes a new forward model constructed using the VCG signals of the same subject. Furthermore, three transformation methods were used to extract VCG in constructing the time-varying lead fields to steer to the orientation of the source rather than just reconstructing its activities in the inverse problem. In addition, the unit VCG loop of the acute ischemia patient was extracted to observe the changes compared to the normal subject. The abnormality condition was achieved by delaying the depolarization time by 15ms. The results involving the unit vectors of VCG demonstrated the anisotropic nature of cardiac source orientations, providing information about the heart's electrical activity.

[Developments of ex vivo cardiac electrical mapping and intelligent labeling of atrial fibrillation substrates].

Cardiac three-dimensional electrophysiological labeling technology is the prerequisite and foundation of atrial fibrillation (AF) ablation surgery, and invasive labeling is the current clinical method, but there are many shortcomings such as large trauma, long procedure duration, and low success rate. In recent years, because of its non-invasive and convenient characteristics, ex vivo labeling has become a new direction for the development of electrophysiological labeling technology. With the rapid development of computer hardware and software as well as the accumulation of clinical database, the application of deep learning technology in electrocardiogram (ECG) data is becoming more extensive and has made great progress, which provides new ideas for the research of ex vivo cardiac mapping and intelligent labeling of AF substrates. This paper reviewed the research progress in the fields of ECG forward problem, ECG inverse problem, and the application of deep learning in AF labeling, discussed the problems of ex vivo intelligent labeling of AF substrates and the possible approaches to solve them, prospected the challenges and future directions for ex vivo cardiac electrophysiology labeling.

CutFEM forward modeling for EEG source analysis.

Introduction: Source analysis of Electroencephalography (EEG) data requires the computation of the scalp potential induced by current sources in the brain. This so-called EEG forward problem is based on an accurate estimation of the volume conduction effects in the human head, represented by a partial differential equation which can be solved using the finite element method (FEM). FEM offers flexibility when modeling anisotropic tissue conductivities but requires a volumetric discretization, a mesh, of the head domain. Structured hexahedral meshes are easy to create in an automatic fashion, while tetrahedral meshes are better suited to model curved geometries. Tetrahedral meshes, thus, offer better accuracy but are more difficult to create. Methods: We introduce CutFEM for EEG forward simulations to integrate the strengths of hexahedra and tetrahedra. It belongs to the family of unfitted finite element methods, decoupling mesh and geometry representation. Following a description of the method, we will employ CutFEM in both controlled spherical scenarios and the reconstruction of somatosensory-evoked potentials. Results: CutFEM outperforms competing FEM approaches with regard to numerical accuracy, memory consumption, and computational speed while being able to mesh arbitrarily touching compartments. Discussion: CutFEM balances numerical accuracy, computational efficiency, and a smooth approximation of complex geometries that has previously not been available in FEM-based EEG forward modeling.

EEG-based source localization with enhanced virtual aperture using second order statistics.

For the past few decades source localization, based on EEG modality, has been a very active area of research. EEG signal provides temporal resolution in millisecond range that can capture rapidly changing patterns of brain activity but it has a low spatial resolution as compared to techniques like fMRI, PET, CT scan, etc. So, one of the motives of this research is to improve the spatial resolution of the EEG signal. Many successful attempts have been made to localise the active neural sources using EEG signals with the introduction of techniques like MNE, LORETA, sLORETA, FOCUSS, etc. But these techniques require a large number of electrodes for correct localization of a few sources. This paper aims at providing a new method for the localization of EEG sources with a fewer electrode. This is achieved by exploiting the second-order statistics to enhance the aperture and solve the EEG localization problem. The comparison of the proposed method with the state-of-the-art methods is done by observing the localization error with variation in SNR, number of snapshots (time samples), number of active sources, and number of electrodes. The results show that the proposed method can detect a greater number of sources with fewer electrodes and with higher accuracy as compared to methods available in the literature. Real -time EEG signal during an arithmetic task is considered and the proposed algorithm clearly shows a sparse activity in the frontal region.

Non-Contact Monitoring of ECG in the Home Environment-Selecting Optimal Electrode Configuration.

Capacitive electrocardiography (cECG) is most often used in wearable or embedded measurement systems. The latter is considered in the paper. An optimal electrocardiographic lead, as an individual feature, was determined based on model studies. It was defined as the possibly highest value of the R-wave amplitude measured on the back of the examined person. The lead configuration was also analyzed in terms of minimizing its susceptibility to creating motion artifacts. It was found that the direction of the optimal lead coincides with the electrical axis of the heart. Moreover, the electrodes should be placed in the areas preserving the greatest voltage and at the same time characterized by the lowest gradient of the potential. Experimental studies were conducted using the developed measurement system on a group of 14 people. The ratio of the R-wave amplitude (as measured on the back and chest, using optimal leads) was less than 1 while the SNR reached at least 20 dB. These parameters allowed for high-quality QRS complex detection with a PPV of 97%. For the "worst" configurations of the leads, the signals measured were practically uninterpretable.

Improvement of performance and sensitivity of 2D and 3D image reconstruction in EIT using EFG forward model.

This paper presents a pure element-free Galerkin method (EFGM) forward model for image reconstruction in 2D and 3D electrical impedance tomography (EIT) using an adaptive current injection method. In EIT systems with the adapting current injection method, both static and dynamic images can be reconstructed; however, determination of electrode contact impedances in the complete electrode model is difficult and the Gap model is used. In this paper, in the EIT forward problem a weak form functional based on the Gap model and a pure EFGM approach are developed, and in the EIT inverse problem, Jacobian matrix is computed by the EFGM, and a fast integration technique is introduced to calculate the entries of the Jacobian matrix within an adequate computation time. The influence of increasing the density of nodes at and near the electrodes with steep electric potential gradients on the accuracy of FEM and EFGM forward solutions is investigated, and the performance of the image reconstruction algorithm with the proposed fast integration technique is examined. The numerical results reveal that the proposed EFGM forward model with the fast integration technique has an efficient performance both in terms of mean relative imaging errors and computational time.

Impact of skull sutures, spongiform bone distribution, and aging skull conductivities on the EEG forward and inverse problems.

Objective. Source imaging is a principal objective for electroencephalography (EEG), the solutions of which require forward problem (FP) computations characterising the electric potential distribution on the scalp due to known sources. Additionally, the EEG-FP is dependent upon realistic, anatomically correct volume conductors and accurate tissue conductivities, where the skull is particularly important. Skull conductivity, however, deviates according to bone composition and the presence of adult sutures. The presented study therefore analyses the effect the presence of adult sutures and differing bone composition have on the EEG-FP and inverse problem (IP) solutions.Approach. Utilising a well-established head atlas, detailed head models were generated including compact and spongiform bone and adult sutures. The true skull conductivity was considered as inhomogeneous according to spongiform bone proportion and sutures. The EEG-FP and EEG-IP were solved and compared to results employing homogeneous skull models, with varying conductivities and omitting sutures, as well as using a hypothesised aging skull conductivity model.Main results. Significant localised FP errors, with relative error up to 85%, were revealed, particularly evident along suture lines and directly related to the proportion of spongiform bone. This remained evident at various ages. Similar EEG-IP inaccuracies were found, with the largest (maximum 4.14 cm) across suture lines.Significance. It is concluded that modelling the skull as an inhomogeneous layer that varies according to spongiform bone proportion and includes differing suture conductivity is imperative for accurate EEG-FP and source localisation calculations. Their omission can result in significant errors, relevant for EEG research and clinical diagnosis.

The electrocardiographic forward problem: A benchmark study.

BACKGROUND: Electrocardiographic forward problems are crucial components for noninvasive electrocardiographic imaging (ECGI) that compute torso potentials from cardiac source measurements. Forward problems have few sources of error as they are physically well posed and supported by mature numerical and computational techniques. However, the residual errors reported from experimental validation studies between forward computed and measured torso signals remain surprisingly high. OBJECTIVE: To test the hypothesis that incomplete cardiac source sampling, especially above the atrioventricular (AV) plane is a major contributor to forward solution errors. METHODS: We used a modified Langendorff preparation suspended in a human-shaped electrolytic torso-tank and a novel pericardiac-cage recording array to thoroughly sample the cardiac potentials. With this carefully controlled experimental preparation, we minimized possible sources of error, including geometric error and torso inhomogeneities. We progressively removed recorded signals from above the atrioventricular plane to determine how the forward-computed torso-tank potentials were affected by incomplete source sampling. RESULTS: We studied 240 beats total recorded from three different activation sequence types (sinus, and posterior and anterior left-ventricular free-wall pacing) in each of two experiments. With complete sampling by the cage electrodes, all correlation metrics between computed and measured torso-tank potentials were above 0.93 (maximum 0.99). The mean root-mean-squared error across all beat types was also low, less than or equal to 0.10 mV. A precipitous drop in forward solution accuracy was observed when we included only cage measurements below the AV plane. CONCLUSION: First, our forward computed potentials using complete cardiac source measurements set a benchmark for similar studies. Second, this study validates the importance of complete cardiac source sampling above the AV plane to produce accurate forward computed torso potentials. Testing ECGI systems and techniques with these more complete and highly accurate datasets will improve inverse techniques and noninvasive detection of cardiac electrical abnormalities.

A New Method of Haemorrhagic Stroke Detection Via Deep Magnetic Induction Tomography.

Hemorrhage imaging is one of the most common applications of magnetic induction tomography (MIT). Depth and the mass of stroke stimulated (MSS) are the most important issues that need to be solved for this application. Transcranial magnetic stimulation (TMS) is a technique belonging to the deep brain stimulation (DBS) field, which aims at overcoming human diseases such as depression. TMS coils, namely, circular, figure-8, and H-coils, play an important role in TMS. Among these, H-coils individually focus on the issues of achieving effective stimulation of deep region. MIT and TMS mechanisms are similar. Herein, for the first time, improved TMS coils, including figure-8 and H-coils, are applied as MIT excitation coils to study the possibility of achieving the mass of stroke stimulated and deep detection through MIT. In addition, the configurations of the detection coils are varied to analyze their influence and determine the optimal coils array. Finally, MIT is used to detect haemorrhagic stroke occurring in humans, and the application of deep MIT to the haemorrhagic stroke problem is computationally explored. Results show that among the various coils, the improved H-coils have MSS and depth characteristics that enable the detection of deep strokes through MIT. Although the detecting depth of the figure-8 coil is weaker, its surface signal is good. The deep MIT technique can be applied to haemorrhagic detection, providing a critical base for deeper research.

Computational imaging of the cardiac activities using magnetocardiography.

The electrical impulses of the heart will generate a tiny magnetic field outside the thorax that is measured as Magnetocardiographic signals. The challenging study is to estimate the cardiac activities in terms of depolarisation and repolarization maps from the measured signals called as inverse problem. This is computed only if one has solved generic or subject- specific prior models using the anatomical structures of the myocardium, the torso and the detectors called as forward problem. In this study, the Discretised heart is priorily assumed as the dipolar sources forming a double layer. The thorax structure modelled with finite element meshes is considered in the forward study. The magnetocardiographic data are simulated using uniform double layer model representing transmembrane distribution on the epicardium and endocardium. Using this data, the activation maps are non-invasively imaged on the heart surface using Tikhonov's regularisation technique. The inverse study is extended to reconstruct the depolarisation sequences of the abnormal cases.

EEG source localization.

Since the discovery of electroencephalography (EEG), when it was hoped that EEG would offer "a window into the brain," researchers and clinicians have attempted to localize the neuronal activity in the brain that generates the scalp potentials measured noninvasively with EEG. Early explorations in the 1950s using electric field theory to infer the location and orientation of the current dipole in the brain from the scalp potential distribution triggered considerable efforts to quantitatively deduce these sources. Initially, dipole fitting, or dipole localization, was the method of choice and many studies used this approach in experimental and clinical studies with remarkable success. Later on, new methods were proposed that attempted to overcome the problem of having to fix the number of sources a priori; these methods are known as distributed source imaging techniques. The introduction and increasing availability of magnetic resonance imaging, allowing detailed realistic anatomy of the brain and head to be incorporated in source localization methods, has drastically increased the precision of such approaches. Today, source localization of EEG (and magnetoencephalography, or MEG) has reached a level of consistency and precision that allows these methods to be placed in the family of brain imaging techniques. The particular advantage that they have over other imaging methods is their high temporal resolution, which allows the origin of activity to be distinguished from its propagation and information flow in large-scale brain networks to be examined. This chapter gives an overview of these methods and illustrates them with several examples, thereby focusing on EEG source imaging in epilepsy and presurgical planning, as clinical applications with remarkable maturation.

Machine-readable Yin-Yang imbalance: traditional Chinese medicine syndrome computer modeling based on three-dimensional noninvasive cardiac electrophysiology imaging.

OBJECTIVES: The principal diagnostic methods of traditional Chinese medicine (TCM) are inspection, auscultation and olfaction, inquiry, and pulse-taking. Treatment by syndrome differentiation is likely to be subjective. This study was designed to provide a basic theory for TCM diagnosis and establish an objective means of evaluating the correctness of syndrome differentiation. METHODS: We herein provide the basic theory of TCM syndrome computer modeling based on a noninvasive cardiac electrophysiology imaging technique. Noninvasive cardiac electrophysiology imaging records the heart's electrical activity from hundreds of electrodes on the patient's torso surface and therefore provides much more information than 12-lead electrocardiography. Through mathematical reconstruction algorithm calculations, the reconstructed heart model is a machine-readable description of the underlying mathematical physics model that reveals the detailed three-dimensional (3D) electrophysiological activity of the heart. RESULTS: From part of the simulation results, the imaged 3D cardiac electrical source provides dynamic information regarding the heart's electrical activity at any given location within the 3D myocardium. CONCLUSIONS: This noninvasive cardiac electrophysiology imaging method is suitable for translating TCM syndromes into a computable format of the underlying mathematical physics model to offer TCM diagnosis evidence-based standards for ensuring correct evaluation and rigorous, scientific data for demonstrating its efficacy.

A Finite-Difference Solution for the EEG Forward Problem in Inhomogeneous Anisotropic Media.

Accurate source localization of electroencephalographic (EEG) signals requires detailed information about the geometry and physical properties of head tissues. Indeed, these strongly influence the propagation of neural activity from the brain to the sensors. Finite difference methods (FDMs) are head modelling approaches relying on volumetric data information, which can be directly obtained using magnetic resonance (MR) imaging. The specific goal of this study is to develop a computationally efficient FDM solution that can flexibly integrate voxel-wise conductivity and anisotropy information. Given the high computational complexity of FDMs, we pay particular attention to attain a very low numerical error, as evaluated using exact analytical solutions for spherical volume conductor models. We then demonstrate the computational efficiency of our FDM numerical solver, by comparing it with alternative solutions. Finally, we apply the developed head modelling tool to high-resolution MR images from a real experimental subject, to demonstrate the potential added value of incorporating detailed voxel-wise conductivity and anisotropy information. Our results clearly show that the developed FDM can contribute to a more precise head modelling, and therefore to a more reliable use of EEG as a brain imaging tool.

New Strategy for Finite Element Mesh Generation for Accurate Solutions of Electroencephalography Forward Problems.

The finite element method (FEM) is a numerical method that is often used for solving electroencephalography (EEG) forward problems involving realistic head models. In this study, FEM solutions obtained using three different mesh structures, namely coarse, densely refined, and adaptively refined meshes, are compared. The simulation results showed that the accuracy of FEM solutions could be significantly enhanced by adding a small number of elements around regions with large estimated errors. Moreover, it was demonstrated that the adaptively refined regions were always near the current dipole sources, suggesting that selectively generating additional elements around the cortical surface might be a new promising strategy for more efficient FEM-based EEG forward analysis.

Tracking the Position of the Heart From Body Surface Potential Maps and Electrograms.

The accurate generation of forward models is an important element in general research in electrocardiography, and in particular for the techniques for ElectroCardioGraphic Imaging (ECGI). Recent research efforts have been devoted to the reliable and fast generation of forward models. However, these model can suffer from several sources of inaccuracy, which in turn can lead to considerable error in both the forward simulation of body surface potentials and even more so for ECGI solutions. In particular, the accurate localization of the heart within the torso is sensitive to movements due to respiration and changes in position of the subject, a problem that cannot be resolved with better imaging and segmentation alone. Here, we propose an algorithm to localize the position of the heart using electrocardiographic recordings on both the heart and torso surface over a sequence of cardiac cycles. We leverage the dependency of electrocardiographic forward models on the underlying geometry to parameterize the forward model with respect to the position (translation) and orientation of the heart, and then estimate these parameters from heart and body surface potentials in a numerical inverse problem. We show that this approach is capable of localizing the position of the heart in synthetic experiments and that it reduces the modeling error in the forward models and resulting inverse solutions in canine experiments. Our results show a consistent decrease in error of both simulated body surface potentials and inverse reconstructed heart surface potentials after re-localizing the heart based on our estimated geometric correction. These results suggest that this method is capable of improving electrocardiographic models used in research settings and suggest the basis for the extension of the model presented here to its application in a purely inverse setting, where the heart potentials are unknown.

Finite-element analysis of microwave scattering from a three-dimensional human head model for brain stroke detection.

In this paper, a detailed analysis of microwave (MW) scattering from a three-dimensional (3D) anthropomorphic human head model is presented. It is the first time that the finite-element method (FEM) has been deployed to study the MW scattering phenomenon of a 3D realistic head model for brain stroke detection. A major contribution of this paper is to add anatomically more realistic details to the human head model compared with the literature available to date. Using the MRI database, a 3D numerical head model was developed and segmented into 21 different types through a novel tissue-mapping scheme and a mixed-model approach. The heterogeneous and frequency-dispersive dielectric properties were assigned to brain tissues using the same mapping technique. To mimic the simulation set-up, an eight-elements antenna array around the head model was designed using dipole antennae. Two types of brain stroke (haemorrhagic and ischaemic) at various locations inside the head model were then analysed for possible detection and classification. The transmitted and backscattered signals were calculated by finding out the solution of the Helmholtz wave equation in the frequency domain using the FEM. FE mesh convergence analysis for electric field values and comparison between different types of iterative solver were also performed to obtain error-free results in minimal computational time. At the end, specific absorption rate analysis was conducted to examine the ionization effects of MW signals to a 3D human head model. Through computer simulations, it is foreseen that MW imaging may efficiently be exploited to locate and differentiate two types of brain stroke by detecting abnormal tissues' dielectric properties. A significant contrast between electric field values of the normal and stroke-affected brain tissues was observed at the stroke location. This is a step towards generating MW scattering information for the development of an efficient image reconstruction algorithm.

A Framework for Image-Based Modeling of Acute Myocardial Ischemia Using Intramurally Recorded Extracellular Potentials.

The biophysical basis for electrocardiographic evaluation of myocardial ischemia stems from the notion that ischemic tissues develop, with relative uniformity, along the endocardial aspects of the heart. These injured regions of subendocardial tissue give rise to intramural currents that lead to ST segment deflections within electrocardiogram (ECG) recordings. The concept of subendocardial ischemic regions is often used in clinical practice, providing a simple and intuitive description of ischemic injury; however, such a model grossly oversimplifies the presentation of ischemic disease-inadvertently leading to errors in ECG-based diagnoses. Furthermore, recent experimental studies have brought into question the subendocardial ischemia paradigm suggesting instead a more distributed pattern of tissue injury. These findings come from experiments and so have both the impact and the limitations of measurements from living organisms. Computer models have often been employed to overcome the constraints of experimental approaches and have a robust history in cardiac simulation. To this end, we have developed a computational simulation framework aimed at elucidating the effects of ischemia on measurable cardiac potentials. To validate our framework, we simulated, visualized, and analyzed 226 experimentally derived acute myocardial ischemic events. Simulation outcomes agreed both qualitatively (feature comparison) and quantitatively (correlation, average error, and significance) with experimentally obtained epicardial measurements, particularly under conditions of elevated ischemic stress. Our simulation framework introduces a novel approach to incorporating subject-specific, geometric models and experimental results that are highly resolved in space and time into computational models. We propose this framework as a means to advance the understanding of the underlying mechanisms of ischemic disease while simultaneously putting in place the computational infrastructure necessary to study and improve ischemia models aimed at reducing diagnostic errors in the clinic.

Recent methodology advances in fluorescence molecular tomography.

Molecular imaging (MI) is a novel imaging discipline that has been continuously developed in recent years. It combines biochemistry, multimodal imaging, biomathematics, bioinformatics, cell & molecular physiology, biophysics, and pharmacology, and it provides a new technology platform for the early diagnosis and quantitative analysis of diseases, treatment monitoring and evaluation, and the development of comprehensive physiology. Fluorescence Molecular Tomography (FMT) is a type of optical imaging modality in MI that captures the three-dimensional distribution of fluorescence within a biological tissue generated by a specific molecule of fluorescent material within a biological tissue. Compared with other optical molecular imaging methods, FMT has the characteristics of high sensitivity, low cost, and safety and reliability. It has become the research frontier and research hotspot of optical molecular imaging technology. This paper took an overview of the recent methodology advances in FMT, mainly focused on the photon propagation model of FMT based on the radiative transfer equation (RTE), and the reconstruction problem solution consist of forward problem and inverse problem. We introduce the detailed technologies utilized in reconstruction of FMT. Finally, the challenges in FMT were discussed. This survey aims at summarizing current research hotspots in methodology of FMT, from which future research may benefit.