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.

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.

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.

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.

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.

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.

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.

OBJECTIVE: 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.

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.

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.