Electrical Wave Propagation Research Articles

The influence of microwave irradiation on rocks for microwave-assisted underground excavation

Demand is growing for explosive-free rock breakage systems for civil and mining engineering, and space industry applications. This paper highlights the work being undertaken in the Geomechanics Laboratory of McGill University to make a real application of microwave-assisted mechanical rock breakage to full-face tunneling machines and drilling. Comprehensive laboratory tests investigated the effect of microwave radiation on temperature profiles and strength reduction in hard rocks (norite, granite, and basalt) for a range of exposure times and microwave power levels. The heating rate on the surface of the rock specimens linearly decreased with distance between the sample and the microwave antenna, regardless of microwave power level and exposure time. Tensile and uniaxial compressive strengths were reduced with increasing exposure time and power level. Scanning electron micrographs (SEMs) highlighted fracture development in treated basalt. It was concluded that the microwave power level has a strong positive influence on the amount of heat damage induced to the rock surface. Numerical simulations of electric field intensity and wave propagation conducted with COMSOL Multiphysics® software generated temperature profiles that were in close agreement with experimental results.

High-density mapping of atrial fibrillation in a chronic substrate: Evidence for distinct modes of repetitive wavefront propagation

BackgroundTemporal dynamics of electrical wave propagation during AF is unknown. There are reports of transient linking of atrial activation. We aim to characterize temporal dynamics of wave propagation patterns during AF in an established chronically remodeled substrate. MethodsBi-atrial epicardial mapping of AF (mean duration 62±61s) was performed in 13 sheep with induced hypertension using custom-designed plaques. Wave propagation patterns were classified into periods of repetitive activity termed modes. ResultsIn total, we identified 9241 distinct depolarization events which were classified as: passing wave (69% occurrence, 68.6% of total time), point source (20.4%, 13.1%), wave collision (4%, 2.8%), re-entrant wave (0.7%, 6.3%), half-rotation (2.9%, 4.4%), wave splitting (2.7%, 4.3%), conduction block (0.05%, 0.03%) and figure of eight reentry (0.05%, 0.05%). Episodes of re-entrant activity had mean length 701±1012ms. A total of 435 modes of distinct periods of repetitive activity were detected (121 in LA and 314 in RA). Looking at temporal changes between modes, we found a preferential transition: change between train of waves propagating from direction of coronary sinus and reentrant activity. High density mapping of the hypertensive fibrillating atria observed 20% point sources and 0.7% of reentrant activation which may have served as drivers of AF. Remaining activations were peripheral waves. Majority of the activation was organized into events of transient linking with existence of preferential types of transitions. ConclusionsThese findings support the importance of substrate based regions of anatomically or functionally determined preferential conduction in the maintenance of AF.

Control of cardiac alternans in an electromechanical model of cardiac tissue

Electrical alternations in cardiac action potential duration have been shown to be a precursor to arrhythmias and sudden cardiac death. Through the mechanism of excitation–contraction coupling, the presence of electrical alternans induces alternations in the heart muscle contractile activity. Also, contraction of cardiac tissue affects the process of cardiac electric wave propagation through the mechanism of the so-called mechanoelectrical feedback. Electrical excitation and contraction of cardiac tissue can be linked by an electromechanical model such as the Nash–Panfilov model. In this work, we explore the feasibility of suppressing cardiac alternans in the Nash-Panfilov model which is employed for small and large deformations. Several electrical pacing and mechanical perturbation feedback strategies are considered to demonstrate successful suppression of alternans on a one-dimensional cable. This is the first attempt to combine electrophysiologically relevant cardiac models of electrical wave propagation and contractility of cardiac tissue in a synergistic effort to suppress cardiac alternans. Numerical examples are provided to illustrate the feasibility and the effects of the proposed algorithms to suppress cardiac alternans.

Regulation of gastric electrical and mechanical activity by cholinesterases in mice.

Background/AimsGastric peristalsis begins in the orad corpus and propagates to the pylorus. Directionality of peristalsis depends upon orderly generation and propagation of electrical slow waves and a frequency gradient between proximal and distal pacemakers. We sought to understand how chronotropic agonists affect coupling between corpus and antrum.MethodsElectrophysiological and imaging techniques were used to investigate regulation of gastric slow wave frequency by muscarinic agonists in mice. We also investigated the expression and role of cholinesterases in regulating slow wave frequency and motor patterns in the stomach.ResultsBoth acetycholinesterase (Ache) and butyrylcholine esterase (Bche) are expressed in gastric muscles and AChE is localized to varicose processes of motor neurons. Inhibition of AChE in the absence of stimulation increased slow wave frequency in corpus and throughout muscle strips containing corpus and antrum. CCh caused depolarization and increased slow wave frequency. Stimulation of cholinergic neurons increased slow wave frequency but did not cause depolarization. Neostigmine (1 μM) increased slow wave frequency, but uncoupling between corpus and antrum was not detected. Motility mapping of contractile activity in gastric muscles showed similar effects of enteric nerve stimulation on the frequency and propagation of slow waves, but neostigmine (> 1 μM) caused aberrant contractile frequency and propagation and ectopic pacemaking.ConclusionsOur data show that slow wave uncoupling is difficult to assess with electrical recording from a single or double sites and suggest that efficient metabolism of ACh released from motor neurons is an extremely important regulator of slow wave frequency and propagation and gastric motility patterns.

Concise review: growing hearts in the right place: on the design of biomimetic materials for cardiac stem cell differentiation.

Tissue engineering aims at recapitulating permissive conditions that enable cells to collaborate and form functional tissues. Applications range from human tissue modeling for diagnostic purposes to therapeutic solutions in regenerative medicine and surgery. Across this spectrum, human stem cells are the active ingredient, expandable virtually indefinitely and with the propensity to generate new tissue. Engaging lineage-specific differentiation requires a precise concerto of key spatial and temporal factors, such as soluble molecules and growth factors, but also physical and mechanical stimuli. These stimuli compete to modulate distinct developmental signaling pathways and ultimately affect the differentiation efficiency. The heart is a chemo-mechano-electrical biological system that behaves as both a sensor and an actuator. It can transduce electrical inputs to generate mechanical contraction and electrical wave propagation. Such a complex organ arises from multipart developmental events that interact with one another to self-regulate. Here, we overview the main events of heart development and the role of mechanical forces in modifying the microenvironment of the progenitor cells. We analyze the cascades regulating cardiac gene activation to illustrate how mechanotransduction is already involved in the most popular protocols for stem cell differentiation (SCD) into cardiomyocytes. We then review how forces are transmitted to embryonic stem cells by cell-substrate or cell-cell communications, and how biomaterials can be designed to mimic these interactions and help reproduce key features of the developmental milieu. Putting this back in a clinical perspective, many challenges need to be overcome before biomaterials-based SCD protocols can be scaled up and marketed.

Achromatic wave plate in THz frequency region based on parallel metal plate waveguides with a pillar array.

We demonstrated an achromatic wave plate based on parallel metal plate waveguides in the high THz frequency region. The metal plates have periodic rough structures on the surface, which allow slow transverse magnetic wave propagation and fast transverse electric wave propagation. A numerical simulation showed that the height of the periodic roughness is important for optimizing the birefringence. We fabricated stacked metal plates containing two types of structures by chemical etching. An array of small pillars on the metal plates allows higher frequency optimization. We experimentally demonstrated an achromatic quarter-wave plate in the frequency region from 2.0 to 3.1 THz.

Adaptive Mesh Refinement and Adaptive Time Integration for Electrical Wave Propagation on the Purkinje System.

A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones. The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method. The adaptive algorithm can automatically recognize when and where the electrical wave starts to leave or enter the computational domain due to external current/voltage stimulation, self-excitation, or local change of membrane properties. Numerical examples demonstrating efficiency and accuracy of the adaptive algorithm are presented.

Correction: Electrical Wave Propagation in an Anisotropic Model of the Left Ventricle Based on Analytical Description of Cardiac Architecture

Correction: Electrical Wave Propagation in an Anisotropic Model of the Left Ventricle Based on Analytical Description of Cardiac Architecture

Electrical wave propagation in an anisotropic model of the left ventricle based on analytical description of cardiac architecture.

We develop a numerical approach based on our recent analytical model of fiber structure in the left ventricle of the human heart. A special curvilinear coordinate system is proposed to analytically include realistic ventricular shape and myofiber directions. With this anatomical model, electrophysiological simulations can be performed on a rectangular coordinate grid. We apply our method to study the effect of fiber rotation and electrical anisotropy of cardiac tissue (i.e., the ratio of the conductivity coefficients along and across the myocardial fibers) on wave propagation using the ten Tusscher–Panfilov (2006) ionic model for human ventricular cells. We show that fiber rotation increases the speed of cardiac activation and attenuates the effects of anisotropy. Our results show that the fiber rotation in the heart is an important factor underlying cardiac excitation. We also study scroll wave dynamics in our model and show the drift of a scroll wave filament whose velocity depends non-monotonically on the fiber rotation angle; the period of scroll wave rotation decreases with an increase of the fiber rotation angle; an increase in anisotropy may cause the breakup of a scroll wave, similar to the mother rotor mechanism of ventricular fibrillation.

Stabilized wave segments in an excitable medium with a phase wave at the wave back

The propagation velocity and the shape of a stationary propagating wave segment are determined analytically for excitable media supporting excitation waves with trigger fronts and phase backs. The general relationships between the mediumʼs excitability and the wave segment parameters are obtained in the framework of the free boundary approach under quite usual assumptions. Two universal limits restricting the region of existence of stabilized wave segments are found. The comparison of the analytical results with numerical simulations of the well-known Kessler–Levine model demonstrates their good quantitative agreement. The findings should be applicable to a wide class of systems, such as the propagation of electrical waves in the cardiac muscle or wave propagation in autocatalytic chemical reactions, due to the generality of the free-boundary approach used.

Stability of Impulsively Forced Excitable Fibers to Perturbations of the Forcing Period

Fibers of electrically coupled nerve or cardiac cells are among the best-known examples of excitable media. Such fibers are often forced periodically at one end by an impulsive electrical stimulus current, eliciting sequences of traveling pulses. If the excitable medium happens to be cardiac tissue, it is natural to ask whether a sudden change in the period of the forcing (e.g., the heart rate) might induce an abnormal pattern of electrical wave propagation. In this manuscript, we analyze the transient response of an excitable medium following a change in the period of impulsive forcing. There are two specific questions that we shall address: First, under what conditions is a periodic train of identical traveling pulses stable to small perturbations in the period of forcing? Second, in the stable regime, what can be said analytically regarding the transient behavior in response to a perturbation in the period of forcing? Instead of using the traditional reaction-diffusion model for wave propagation in excitable fibers, we analyze a kinematic model which describes the progress of each propagating wave front and wave back. The linearization of the kinematic model, presented as a recursive sequence of ordinary differential equations, can be solved exactly in terms of generalized Laguerre polynomials integrated against an exponential kernel. The solution gives the desired approximation to the transient behavior following a change in the forcing period and, with the aid of some basic functional analytic formalism, a criterion for linear stability of a periodic pulse train. In the appendix, we illustrate how this framework applies to a specific model of an excitable cardiac fiber.

Approximate analysis of spatial fading correlation for multiple antenna system

Spatial fading correlation (SFC) mainly depends on power azimuth spectrum (PAS) of arrival signals and the transceiver mode of multi-antenna arrays. This paper investigates in depth the approximate algorithm and its complexity in SFC of multi-antenna arrays in a mobile communication system. First, we derive the closed-form formulas for SFCs under three typical PAS: i. e. a uniform distribution, a Gaussian distribution and a Laplace distribution. Based on these theoretical formulas, we study the approximate algorithm when the angle spread in PAS for arrival signals is small. From this, we develop a multi-antenna reception channel model and analyze in detail the impact of the antenna array and electric wave propagation parameters we choose on the capacity of multiple-input multiple-output (MIMO) channel. By using theoretical calculations and simulation experiments, we find that in a particular situation the approximate algorithm provides a good approximation for SFC. Furthermore, a method is used to quantify the applicability and calculation efficiency while analyzing the MIMO multi-antenna array. Finally, it can be concluded that the approximate method has a good approximation in particular situations, and it will greatly reduce the theoretical computational complexity. The method we suggest will improve the efficiency of analyzing and simulating a complex MIMO multi-antenna system.

Induced nonlocal electric wave propagation of boron nitride nanotubes

Axial displacement and electric wave propagation of single-walled Boron-Nitride nanotubes (SWBNNTs) induced by alternating current (AC) are investigated in this study. A single-walled zigzag structure BNNT is modeled based on nonlocal piezoelasticity theory and Euler-Bernoulli beam (EBB). Equations correspond to lateral displacement have been obtained. Using Hamilton’s principle and considering charge equation for coupling of electrical and mechanical fields, the higher order of governing equations are derived. Analytical solution is applied to solve governing equations. Also the axial and lateral displacement of a SWBNNT and electric potential induced by AC through it are presented. The detailed parametric study is conducted, focusing on the remarkable effects of the half wave number on the behavior of the SWBNNT. The results indicate applying alternating field, leads to propagation of axial displacement along the SWBNNT. Also the result of this study can be useful to design and manufacture of smart micro/nano-electro-mechanical systems in advanced biomechanics applications by controlling axial and lateral displacements.

Abstract 332: Mitochondrial Inner-Membrane Potential Instability Promotes Sarcolemmal Electrical Instability after Ischemia-Reperfusion in Monolayers of Cardiac Myocytes

Mitochondrial uncoupling due to oxidative stress can, through opening of sarcolemmal KATP channels, alter cellular electrical excitability, and it has been proposed that mitochondrial function is a major factor in arrhythmogenesis during ischemia-reperfusion. Here, we examine the effects of ischemia-reperfusion on mitochondrial inner membrane potential (ΔΨm) and corresponding changes in electrical excitability and wave propagation in monolayer cultures of neonatal rat ventricular myocytes. Changes in ΔΨm were observed using TMRM and changes in the sarcolemmal voltage were recorded with a 464-element photodiode array using di-4-ANEPPS. Ischemia was induced by covering the center part of the monolayer (D = 22 mm) with a coverslip (D = 15 mm). Cell contractions ceased after approximately 6 min of ischemia; however, electrical activity continued for 11.3 ± 4.2 min (N = 5). Amplitude and conduction velocity of the action potentials in the ischemic region decreased over the same time period. ΔΨm was lost in two phases: a reversible phase of partial depolarization, after 11.2 ± 1.3 min of ischemia, and a nonreversible phase, which happened after 30 ± 6 min of ischemia, during which the whole mitochondrial network of the myocyte became depolarized and the cells underwent contracture (N = 4). Reperfusion after the long ischemia resulted in only partial recovery and the observance of oscillations of ΔΨm in the mitochondrial network or rapid flickering of individual mitochondrial clusters and was associated with heterogeneous electrical recovery, and formation of wavelets and reentry (4/5 monolayers). In contrast, mitochondria fully recovered and reentry was rare (1/5 monolayers) for reperfusion after the short ischemia (10-12 min). 4’-chlorodiazepam, an inhibitor of inner membrane anion channels, stabilized mitochondrial function after the long ischemia, and prevented wavelets (5/5 monolayers) and reentry (4/5 monolayers). In conclusion, incomplete or unstable recovery of mitochondrial function after ischemia correlates with reentrant arrhythmias in monolayers of cardiac myocytes. Our findings suggest that stabilization of mitochondrial network dynamics is an important strategy for preventing ischemia/reperfusion-related arrhythmias.

Reentry near the percolation threshold in a heterogeneous discrete model for cardiac tissue.

Arrhythmias in cardiac tissue are related to irregular electrical wave propagation in the heart. Cardiac tissue is formed by a discrete cell network, which is often heterogeneous. A localized region with a fraction of nonconducting links surrounded by homogeneous conducting tissue can become a source of reentry and ectopic beats. Extensive simulations in a discrete model of cardiac tissue show that a wave crossing a heterogeneous region of cardiac tissue can disintegrate into irregular patterns, provided the fraction of nonconducting links is close to the percolation threshold of the cell network. The dependence of the reentry probability on this fraction, the system size, and the degree of excitability can be inferred from the size distribution of nonconducting clusters near the percolation threshold.

Introduction to the Series on Computational Approaches to Cardiac Arrhythmias

Of all the cardiac arrhythmias seen in clinical practice, atrial fibrillation (AF) and ventricular tachycardia/fibrillation (VT/VF) are among the leading causes of morbidity and mortality in the developed world. AF is the most common sustained arrhythmia and is associated with an increased risk of stroke, heart failure, dementia, and death.1–3 In developed nations overall prevalence of AF is 0.9% and the number of people affected is projected to more than double over the next 2 decades.3,4 VT/VF is the most important immediate cause of sudden cardiac death (SCD). Incidence of SCD is estimated to be 4 to 5 million cases per year worldwide.5,6 Thus arrhythmias and SCD are among the most significant manifestations of cardiovascular diseases worldwide, but their underlying mechanisms remain elusive. Arrhythmogenic substrates may be established by ischemia, infarction, heart failure and genetic mutations, all of which may cause inflammation, extracellular matrix remodeling, interstitial fibrosis, fatty infiltration, and changes in the 3-dimensional cellular architecture of the working myocardium.7,8 Over the last 17 years, the study of the molecular genetic basis of monogenic cardiac rhythm disorders, together with characterization of functional expression and biophysical properties of mutant channels from patients with inheritable ion channel diseases, has significantly advanced our understanding of the molecular basis of cardiac arrhythmias.9 Yet, this clearly has not been sufficient. Despite such advances, predictable prevention of AF or VF is currently not possible and the development of effective antiarrhythmic pharmacological agents has been extremely difficult. Not all questions related to arrhythmia mechanisms are directly answerable by reductionist experiments such as DNA sequencing or patch clamping. There is a hierarchy of questions whose levels are determined by the generality of the answers sought. Thus the question of what a mutation in an ion …

Dynamical modelling of cardiac electrical activity using bidomain approach: The effects of variation of ionic model parameters

This work presents the dynamical modelling of cardiac electrical activity using bidomain approach. It focuses on the effects of variation of the ionic model parameters on cardiac wave propagation. Cardiac electrical activity is governed by partial differential equations coupled to a system of ordinary differential equations. Numerical simulation of these equations is computationally expensive due to their non-linearity and stiffness. Nevertheless, we adopted the bidomain model due to its ability to reflect the actual cardiac wave propagation. The derived bidomain equations coupled with FitzHugh-Nagumo’s ionic equations were time-discretized using explicit forward Euler method and space-discretized using 2-D network modelling to obtain linearized equations for transmembrane potential Vm, extracellular potential φe and gating variable w. We implemented the discretized model and performed simulation experiments to study the effects of variation of ionic model parameters on the propagation of electrical wave across the cardiac tissue. Time characteristic of transmembrane potential, Vm, in the normal cardiac tissue was obtained by setting the values of ionic model parameters to 0.2, 0.2, 0.7 and 0.8 for excitation rate constant ε1, recovery rate constant ε2, recovery decay constant γ and excitation decay constant β respectively. Changing the values of ε1, ε2 to 0.04 and 0.28 respectively, the obtained Vm showed a time dilation at 0.04 indicating cardiac arrhythmia but no significant change to Vm was observed at 0.28. Also, changing β to 0.3 and 1.1 and γ to 0.4 and 1.2 sequentially, there was no significant change to the time characteristic of Vm. The obtained results revealed that only decrease in ε1, ε2 impacted significantly on the cardiac wave propagation.

Propagation and Confinement of Electric Field Waves along One-Dimensional Porous Silicon Hybrid Periodic/Quasiperiodic Structure

Selective spatial confinement of the electric field intensity is theoretically obtained for the light propagation along hybrid structures conformed by periodic and Fibonacci quasiperiodic dielectric multilayers. Sandwich-like configurations featuring periodic-quasiperiodic-periodic as well as quasiperiodic-periodic-quasiperiodic designs exhibit spatial localization of a large percent of the optical signal within specific zones of the hybrid system. Such a feature might be of interest in the pursuing of lasing devices based on porous silicon. It is found that the electric field confinement does not only depend on the quality of the defect or a particular transmission mode observed in the reflectivity spectra. We show that it is possible to enhance the electric field confinement solely varying the angle of incidence. The possibility of realizing finite photonic crystals with reduced size and very well defined band gap by means of a quasiperiodic-periodic-quasiperiodic hybrid multilayer is also revealed.

Mathematical model of the anatomy and fibre orientation field of the left ventricle of the heart

BackgroundOne of the main factors affecting propagation of electrical waves and contraction in ventricles of the heart is anisotropy of cardiac tissue. Anisotropy is determined by orientation of myocardial fibres. Determining fibre orientation field and shape of the heart is important for anatomically accurate modelling of electrical and mechanical function of the heart. The aim of this paper is to introduce a theoretical rule-based model for anatomy and fibre orientation of the left ventricle (LV) of the heart and to compare it with experimental data. We suggest explicit analytical formulae that allow us to obtain the left ventricle form and its fibre direction field. The ventricle band concept of cardiac architecture given by Torrent-Guasp is chosen as the model postulate.MethodsIn our approach, anisotropy of the heart is derived from some general principles. The LV is considered as a set of identical spiral surfaces, each of which can be produced from the other by rotation around one vertical axis. Each spiral surface is filled with non-intersecting curves which represent myocardial fibres.For model verification, we use experimental data on fibre orientation in human and canine hearts.ResultsLV shape and anisotropy are represented by explicit analytical expressions in a curvilinear 3-D coordinate system. The derived fibre orientation field shows good qualitative agreement with experimental data. The model reveals the most thorough quantitative simulation of fibre angles at the LV middle zone.ConclusionsOur analysis shows that the band concept can generate realistic anisotropy of the LV. Our model shows good qualitative agreement between the simulated fibre orientation field and the experimental data on LV anisotropy, and the model can be used for various numerical simulations to study the effects of anisotropy on cardiac excitation and mechanical function.

A Novel Rule-Based Algorithm for Assigning Myocardial Fiber Orientation to Computational Heart Models

Electrical waves traveling throughout the myocardium elicit muscle contractions responsible for pumping blood throughout the body. The shape and direction of these waves depend on the spatial arrangement of ventricular myocytes, termed fiber orientation. In computational studies simulating electrical wave propagation or mechanical contraction in the heart, accurately representing fiber orientation is critical so that model predictions corroborate with experimental data. Typically, fiber orientation is assigned to heart models based on Diffusion Tensor Imaging (DTI) data, yet few alternative methodologies exist if DTI data is noisy or absent. Here we present a novel Laplace-Dirichlet Rule-Based (LDRB) algorithm to perform this task with speed, precision, and high usability. We demonstrate the application of the LDRB algorithm in an image-based computational model of the canine ventricles. Simulations of electrical activation in this model are compared to those in the same geometrical model but with DTI-derived fiber orientation. The results demonstrate that activation patterns from simulations with LDRB and DTI-derived fiber orientations are nearly indistinguishable, with relative differences ≤6%, absolute mean differences in activation times ≤3.15 ms, and positive correlations ≥0.99. These results convincingly show that the LDRB algorithm is a robust alternative to DTI for assigning fiber orientation to computational heart models.