Electric and magnetic fields from two-dimensional anisotropic bisyncytia.

Cardiac tissue can be considered macroscopically as a bidomain, anisotropic conductor in which simple depolarization wavefronts produce complex current distributions. Since such distributions may be difficult to measure using electrical techniques, we have developed a mathematical model to determine the feasibility of magnetic localization of these currents. By applying the finite element method to an idealized two-dimensional bisyncytium with anisotropic conductivities, we have calculated the intracellular and extracellular potentials, the current distributions, and the magnetic fields for a circular depolarization wavefront. The calculated magnetic field 1 mm from the tissue is well within the sensitivity of a SQUID magnetometer. Our results show that complex bisyncytial current patterns can be studied magnetically, and these studies should provide valuable insight regarding the electrical anisotropy of cardiac tissue.     

基于模拟退火法由脑磁图推测电流偶极子参数

利用模拟退火（Ｓｉｍｕｌａｔｅｄ Ａｎｎｅａｌｉｎｇ） 算法,由脑磁图（ ＭＥＧ） 数据反演脑内作为磁源的单电流偶极子参数,可以得到理想的结果。在上述工作的基础上,对脑内多电流偶极子参数的反演,则呈现如下状况：即以少于实际源数目的偶极子为源假设反演,目标函数得不到极小优化。反之,目标函数可以得到极小优化, 但出现多余的伪偶极子, 且这些伪偶极子在多次不同条件的反演结果中,处于不稳定状态。若将多次反演结果中处于不稳定状态的偶极子作为伪偶极子的判据而将其排除,则可以得到一种判断磁源偶极子数目的方法     

Simultaneous suppression of disturbing fields and localization of magnetic markers by means of multipole expansion

BACKGROUND: Magnetically marked capsules serve for the analysis of peristalsis and throughput times within the intestinal tract. Moreover, they can be used for the targeted disposal of drugs. The capsules get localized in time by field measurements with a superconducting quantum interference device (SQUID) magnetometer array. Here it is important to ensure an online localization with high speed and high suppression of disturbing fields. In this article we use multipole expansions for the simultaneous localization and suppression of disturbing fields. METHODS: We expand the measurement data in terms of inner and outer multipoles. Thereby we obtain directly a separation of marker field and outer disturbing fields. From the inner dipoles and quadrupoles we compute the magnetization and position of the capsule. The outer multipoles get eliminated. RESULTS: The localization goodness has been analyzed depending on the order of the multipoles used and depending on the systems noise level. We found upper limits of the noise level for the usage of certain multipole moments. Given a signal to noise ratio of 40 and utilizing inner dipoles and quadrupoles and outer dipoles, the method enables an accuracy of 5 mm with a speed of 10 localizations per second. CONCLUSION: The multipole localization is an effective method and is capable of online-tracking magnetic markers.     

Investigation of the temporal and spatial dynamics of muscular action potentials through optically pumped magnetometers

AimThis study aims to simultaneously record the magnetic and electric components of the propagating muscular action potential.MethodA single-subject study of the monosynaptic stretch reflex of the musculus rectus femoris was performed; the magnetic field generated by the muscular activity was recorded in all three spatial directions by five optically pumped magnetometers. In addition, the electric field was recorded by four invasive fine-wire needle electrodes. The magnetic and electric fields were compared by modelling the muscular anatomy of the rectus femoris muscle and by simulating the corresponding magnetic field vectors.ResultsThe magnetomyography (MMG) signal can reliably be recorded following the stimulation of the monosynaptic stretch reflex. The MMG signal shows several phases of activity inside the muscle, the first of which is the propagating muscular action potential. As predicted by the finite wire model, the magnetic field vectors of the propagating muscular action potential are generated by the current flowing along the muscle fiber. Based on the magnetic field vectors, it was possible to reconstruct the pinnation angle of the muscle fibers. The later magnetic field components are linked to the activation of the contractile apparatus.InterpretationMMG allows to analyze the muscle physiology from the propagating muscular action potential to the initiation of the contractile apparatus. At the same time, this methods reveals information about muscle fiber direction and extend. With the development of high-resolution magnetic cameras, that are based on OPM technology, it will be possible to image the function and structure of the biomagnetic field of any skeletal muscle with high precision. This method could be used both, in clinical medicine and also in sports science.     

Magneto-electric nano-particles for non-invasive brain stimulation

This paper for the first time discusses a computational study of using magneto-electric (ME) nanoparticles to artificially stimulate the neural activity deep in the brain. The new technology provides a unique way to couple electric signals in the neural network to the magnetic dipoles in the nanoparticles with the purpose to enable a non-invasive approach. Simulations of the effect of ME nanoparticles for non-invasively stimulating the brain of a patient with Parkinson's Disease to bring the pulsed sequences of the electric field to the levels comparable to those of healthy people show that the optimized values for the concentration of the 20-nm nanoparticles (with the magneto-electric (ME) coefficient of 100 V cm(-1) Oe(-1) in the aqueous solution) is 3×10(6) particles/cc, and the frequency of the externally applied 300-Oe magnetic field is 80 Hz.     

Optically pumped magnetometers disclose magnetic field components of the muscular action potential

AimAiming at analysing the signal conduction in muscular fibres, the spatio-temporal dynamics of the magnetic field generated by the propagating muscle action potential (MAP) is studied.MethodIn this prospective, proof of principle study, the magnetic activity of the intrinsic foot muscle after electric stimulation of the tibial nerve was measured using optically pumped magnetometers (OPMs). A classical biophysical electric dipole model of the propagating MAP was implemented to model the source of the data. In order to account for radial currents of the muscular tubules system, a magnetic dipole oriented along the direction of the muscle was added.ResultsThe signal profile generated by the activity of the intrinsic foot muscles was measured by four OPM devices. Three OPM sensors captured the spatio-temporal magnetic field pattern of the longitudinal intrinsic foot muscles. Changes of the activation pattern reflected the propagating muscular action potential along the muscle. A combined electric and magnetic dipole model could explain the recorded magnetic activity.InterpretationOPM devices allow for a new, non-invasive way to study MAP patterns. Since magnetic fields are less altered by the tissue surrounding the dipole source compared to electric activity, a precise analysis of the spatial characteristics and temporal dynamics of the MAP is possible. The classic electric dipole model explains major but not all aspects of the magnetic field. The field has longitudinal components generated by intrinsic structures of the muscle fibre. By understanding these magnetic components, new methods could be developed to analyse the muscular signal transduction pathway in greater detail. The approach has the potential to become a promising diagnostic tool in peripheral neurological motor impairments.     

Whole-head mapping of middle-latency auditory evoked magnetic fields

We recorded middle-latency auditory evoked magnetic fields from 9 healthy subjects with a 122-channel whole-head SQUID gradiometer. The stimuli were click triplets, 2.5 msec in total duration, delivered alternately to the two ears once every 333 msec. Contralateral clicks elicited P30m responses in 16 and P50m responses in 12 out of 18 hemispheres studied; ipsilateral clicks did so in 7 and 13 hemispheres, respectively. The field patterns were satisfactorily explained by current dipoles in 16 and 4 hemispheres for contra- and ipsilateral P30m, and in 4 and 10 hemispheres for contra- and ipsilateral P50m. The peak latencies of P30m and P50m were not affected by stimulation side. The results show that middle-latency auditory evoked responses receive a strong contribution from auditory cortical structures, and that differences of input latency to cortical auditory areas, evaluated from MLAEF latencies, do not explain the latency differences seen in late auditory evoked fields to contralateral vs. ipsilateral stimulation.     

Modelling gastrointestinal bioelectric activity

The development of an anatomically realistic biophysically based model of the human gastrointestinal (GI) tract is presented. A major objective of this work is to develop a modelling framework that can be used to integrate the physiological, anatomical and medical knowledge of the GI system. The anatomical model was developed by fitting derivative continuous meshes to digitised data taken from images of the visible man. Structural information, including fibre distributions of the smooth muscle layers and the arrangement of the networks of interstitial cells of Cajal, were incorporated using published information. A continuum modelling framework was used to simulate electrical activity from the single cell to the whole organ and body. Also computed was the external magnetic field generated from the GI electrical activity.

The set of governing equations were solved using a combination of numerical techniques. Activity at the (continuum) cell level was solved using a high-resolution trilinear finite element procedure that had been defined from the previously fitted C¹ continuous anatomical mesh. Multiple dipolar sources were created from the excitation waves which were embedded within a coupled C¹ continuous torso model to produce both the cutaneous electrical field and the external magnetic field.

Initial simulations were performed using a simplified geometry to test the implementation of the numerical solution procedure. The numerical procedures were shown to rapidly converge with mesh refinement. In the process of this testing, errors in a long standing analytic solution were identified and are corrected in Appendix B.

Results of single cell activity were compared to published results illustrating that the key features of the slow wave activity were successfully replicated. Simulations using a two-dimensional slice through the gastric wall produced slow wave activity that agreed with the known frequency and propagation characteristics. Three-dimensional simulations were also performed using the full stomach mesh and results illustrated the slow wave propagation throughout the stomach musculature.     

High-resolution magnetoencephalography--studies with a small-volume phantom]

To investigate the spatiotemporal organisation of neuronal processes in an animal model using magnetoencephalography (MEG), a high temporal resolution (ms) and an appropriate spatial resolution of about 1 mm is necessary. With the aim of determining the localization error and the resolution power of high-resolution MEG systems, we developed a phantom capable of simulating the characteristics of animal models. The phantom enables us to variably position at least two magnetic field sources to within 0.1 mm. For source localization on the basis of the magnetic field data, a spatial filtering algorithm was used. The investigation of a 16-channel micro SQUID-MEG system with a current dipole orientated tangentially to the phantom surface produced the following localization data (min ... max, x, y--horizontal plane, z--depth); systematic localization error e(x) = 1.16 ... 1.67 mm, e(y) = -1.01 ... -1.28 mm, e(z) = -5.22 ... -7.64 mm, standard deviation of the individual measurements perpendicular to the dipole axis s(perp) = 0.05 ... 0.22 mm, along this axis s(long) = 0.20 ... 1.73 mm, in the depths sz = 0.17 ... 3.17 mm. The "goodness of fit" was > 95%. Separation of two dipoles was still possible for parallel dipoles at a distance apart of d(parallel) = 0.03 mm and for those oriented perpendicularly to each other at a distance apart of d(perp) = 0.10 mm. On the basis of these results we conclude that the MEG system can achieve a resolution sufficient to permit the investigation of neuronal microstructures. The spatial errors detected were related to sensor position in the cryostatic vessel as well as to external low-frequency noise.     

Electro-Acoustic Behavior of the Mitotic Spindle: A Semi-Classical Coarse-Grained Model

The regulation of chromosome separation during mitosis is not fully understood yet. Microtubules forming mitotic spindles are targets of treatment strategies which are aimed at (i) the triggering of the apoptosis or (ii) the interruption of uncontrolled cell division. Despite these facts, only few physical models relating to the dynamics of mitotic spindles exist up to now. In this paper, we present the first electromechanical model which enables calculation of the electromagnetic field coupled to acoustic vibrations of the mitotic spindle. This electromagnetic field originates from the electrical polarity of microtubules which form the mitotic spindle. The model is based on the approximation of resonantly vibrating microtubules by a network of oscillating electric dipoles. Our computational results predict the existence of a rapidly changing electric field which is generated by either driven or endogenous vibrations of the mitotic spindle. For certain values of parameters, the intensity of the electric field and its gradient reach values which may exert a not-inconsiderable force on chromosomes which are aligned in the spindle midzone. Our model may describe possible mechanisms of the effects of ultra-short electrical and mechanical pulses on dividing cells—a strategy used in novel methods for cancer treatment.     

Field-induced reorganization of the neural membrane lipid bilayer: a proposed role in the regulation of ion-channel dynamics

We present a computational model demonstrating that an electric field propagating in the plane of the neural membrane during transmembrane ion movement creates lateral concentration gradients of the lipids. Due to this field-induced reorganization, ethenes of the lipid chains become aligned and polarized. This finding is interpreted within the context of molecular studies of protein folding in biological membranes. We propose that electrostatic interactions between membrane dipoles and charged amino acid residues of the unfolded ion-channel protein regulate protein-folding kinetics (channel closing). These electrostatic interactions thus regulate electrical signaling in neurons.     

Magnetic detection of injury-induced ionic currents in bean plants

A superconducting quantum interference device (SQUID) multichannel magnetometer was used to measure the temporal and spatial evolution of the magnetic field accompanying stimulation by burning and/or cutting of Vicia faba plants. These magnetic fields are caused by ionic currents that appear after injury in different parts of the plant. All measured V. faba plants responded to the burning stimulation with detectable quasi-d.c. magnetic signals. In order to measure these signals, a suitable modulation had to be used. The covariance method was applied to analyse the measured data. The results demonstrate a dipolar-like magnetic signal, exponentially decreasing in time, above the cutting type of injury. After the burning stimulation, the magnetically detected activity was concentrated predominantly above the leaves/petioles and less above the stem. Possible mechanisms for this behaviour are suggested. A comparison with previously known electrical measurements of plant injury is given.     

Magnetic and electric fields induce directional responses in Steinernema carpocapsae

Entomopathogenic nematode species respond directionally to various cues including electrical stimuli. For example, in prior research Steinernema carpocapsae was shown to be attracted to an electrical current that was applied to an agar dish. Thus, we hypothesised that these nematodes may use electromagnetic reception to assist in navigating through the soil and finding a host. In this study we discovered that S. carpocapsae also responds to electrical fields (without current) and to magnetic fields; to our knowledge this is the first report of nematode directional movement in response to a magnetic field. Our research expands on the range of known stimuli that entomopathogenic nematodes respond to. The findings may have implications for foraging behavior.     

Spatio-temporal multiple source localization by wavelet-type decomposition of evoked potentials

Scalp recording of electrical events allows evaluation of human cerebral function, but contributions of the specific brain structures generating the recorded activity are ambiguous. This problem is ill-posed and cannot be solved without auxiliary physiological knowledge about the spatio-temporal characteristics of the generators' activity. In our source localization by model-based wavelet-type decomposition, scalp recorded signals are decomposed into a combination of wavelets, each of which may describe the coherent activity of a population of neurons. We chose the Hermite functions (derived from the Gaussian function to form mono-, bi- and triphasic wave forms) as the mathematical model to describe the temporal pattern of mass neural activity.For each wavelet we solve the inverse problem for two symmetrically positioned and oriented dipoles, one of which attains zero magnitude when a single source is more suitable. We use the wavelet to model the temporal activity pattern of the symmetrical dipoles. By this we reduce the dimension of inverse problem and find a plausible solution. Once the number and the initial parameters of the sources are given, we can apply multiple source localization to correct the solution for generators with overlapping activities.Application of the procedure to subcortical and cortical components of somatosensory evoked potentials demonstrates its feasibility.     

A new study of bacterial motion: superconducting quantum interference device microscopy of magnetotactic bacteria.

The recently developed "microscope" based on a high-Tc dc SQUID (superconducting quantum interference device) is used to detect the magnetic fields produced by the motion of magnetotactic bacteria, which have permanent dipole moments. The bacteria, in growth medium at room temperature, can be brought to within 15 micron of a SQUID at liquid nitrogen temperature. Measurements are performed on both motile and nonmotile bacteria. In the nonmotile case, we obtain the power spectrum of the magnetic field noise produced by the rotational Brownian motion of the ensemble of bacteria. Furthermore, we measure the time-dependent field produced by the ensemble in response to an applied uniform magnetic field. In the motile case, we obtain the magnetic field power spectra produced by the swimming bacteria. Combined, these measurements determine the average rotational drag coefficient, magnetic moment, and the frequency and amplitude of the vibrational and rotational modes of the bacteria in a unified set of measurements. In addition, the microscope can easily resolve the motion of a single bacterium. This technique can be extended to any cell to which a magnetic tag can be attached.     

Models of Electrical Activity: Calibration and Prediction Testing on?the?Same Cell

Mathematical models are increasingly important in biology, and testability is becoming a critical issue. One limitation is that one model simulation tests a parameter set representing one instance of the biological counterpart, whereas biological systems are heterogeneous in their properties and behavior, and a model often is fitted to represent an ideal average. This is also true for models of a cell’s electrical activity; even within a narrowly defined population there can be considerable variation in electrophysiological phenotype. Here, we describe a computational experimental approach for parameterizing a model of the electrical activity of a cell in real time. We combine the inexpensive parallel computational power of a programmable graphics processing unit with the flexibility of the dynamic clamp method. The approach involves 1), recording a cell’s electrical activity, 2), parameterizing a model to the recording, 3), generating predictions, and 4), testing the predictions on the same cell used for the calibration. We demonstrate the experimental feasibility of our approach using a cell line (GH4C1). These cells are electrically active, and they display tonic spiking or bursting. We use our approach to predict parameter changes that can convert one pattern to the other.     

Models of cardiac electromechanics based on individual hearts imaging data Image-based electromechanical models of the heart

Current multi-scale computational models of ventricular electromechanics describe the full process of cardiac contraction on both the micro- and macro- scales including: the depolarization of cardiac cells, the release of calcium from intracellular stores, tension generation by cardiac myofilaments, and mechanical contraction of the whole heart. Such models are used to reveal basic mechanisms of cardiac contraction as well as the mechanisms of cardiac dysfunction in disease conditions. In this paper, we present a methodology to construct finite element electromechanical models of ventricular contraction with anatomically accurate ventricular geometry based on magnetic resonance and diffusion tensor magnetic resonance imaging of the heart. The electromechanical model couples detailed representations of the cardiac cell membrane, cardiac myofilament dynamics, electrical impulse propagation, ventricular contraction, and circulation to simulate the electrical and mechanical activity of the ventricles. The utility of the model is demonstrated in an example simulation of contraction during sinus rhythm using a model of the normal canine ventricles.     

Identification of genes related to proliferative diabetic retinopathy through RWR algorithm based on protein–protein interaction network

Proliferative diabetic retinopathy (PDR) is one of the most common complications of diabetes and can lead to blindness. Proteomic studies have provided insight into the pathogenesis of PDR and a series of PDR-related genes has been identified but are far from fully characterized because the experimental methods are expensive and time consuming. In our previous study, we successfully identified 35 candidate PDR-related genes through the shortest-path algorithm. In the current study, we developed a computational method using the random walk with restart (RWR) algorithm and the protein–protein interaction (PPI) network to identify potential PDR-related genes. After some possible genes were obtained by the RWR algorithm, a three-stage filtration strategy, which includes the permutation test, interaction test and enrichment test, was applied to exclude potential false positives caused by the structure of PPI network, the poor interaction strength, and the limited similarity on gene ontology (GO) terms and biological pathways. As a result, 36 candidate genes were discovered by the method which was different from the 35 genes reported in our previous study. A literature review showed that 21 of these 36 genes are supported by previous experiments. These findings suggest the robustness and complementary effects of both our efforts using different computational methods, thus providing an alternative method to study PDR pathogenesis.     

Magnetoencephalography and its Achilles' heel

Magnetoencephalography (MEG) has practically unlimited temporal resolution. Fundamental physical reasons, however, restrict the capability of MEG to separate simultaneously active sources. After a brief tutorial introduction into MEG, various aspects of spatial resolution are reviewed with the help of examples. First the estimation of a single current dipole is examined. A consideration of the resolution field shows that the spatial selectivity of the estimated dipole moment is highly dependent on methodological issues. A subsequent consideration of various two-dipole configurations illustrates how the topography of the magnetic field depends on the distance between the two dipoles and their relative orientations. The resolution fields associated with the estimation of the dipole moments reveal a strong interference for closely spaced dipoles. A simple model suggests that the standard deviations of the estimated moments are inversely proportional to the distance of the dipoles. Spatial information provided by techniques like functional magnetic resonance imaging (fMRI) could help to overcome problems resulting from the limited spatial resolution of MEG (multimodal integration). But a straightforward synthesis, according to the principle that fMRI provides the spatial structure of the sources and MEG adds the temporal information, is probably doomed to failure in many situations. A serious dilemma, among other problems, is that the fMRI signal generally represents a temporal integral over several seconds: The knowledge that a certain brain region was active sometime or other is not necessarily helpful for disentangling the MEG activity within a specified short time window. An intriguing fact is that the spatio-temporal pattern of the MEG signals can be considered as a signature of the brain which is suitable for hypothesis testing with high temporal and spatial resolution.     

A phenomenological computational model of the evoked action potential fitted to human cochlear implant responses

There is a growing interest in biomedical engineering in developing procedures that provide accurate simulations of the neural response to electrical stimulus produced by implants. Moreover, recent research focuses on models that take into account individual patient characteristics.We present a phenomenological computational model that is customized with the patient’s data provided by the electrically evoked compound action potential (ECAP) for simulating the neural response to electrical stimulus produced by the electrodes of cochlear implants (CIs). The model links the input currents of the electrodes to the simulated ECAP.Potentials and currents are calculated by solving the quasi-static approximation of the Maxwell equations with the finite element method (FEM). In ECAPs recording, an active electrode generates a current that elicits action potentials in the surrounding auditory nerve fibers (ANFs). The sum of these action potentials is registered by other nearby electrode. Our computational model emulates this phenomenon introducing a set of line current sources replacing the ANFs by a set of virtual neurons (VNs). To fit the ECAP amplitudes we assign a suitable weight to each VN related with the probability of an ANF to be excited. This probability is expressed by a cumulative beta distribution parameterized by two shape parameters that are calculated by means of a differential evolution algorithm (DE). Being the weights function of the current density, any change in the design of the CI affecting the current density produces changes in the weights and, therefore, in the simulated ECAP, which confers to our model a predictive capacity.The results of the validation with ECAP data from two patients are presented, achieving a satisfactory fit of the experimental data with those provided by the proposed computational model.