Electrical Propagation Research Articles

Electro-hyperelasticity with phase field for electric breakdown modeling

In this paper, we systematically derive the phase field model for electric breakdown channel propagation. The model includes electric charge, mass, momentum and energy conservation equations as well as Allen–Cahn type equation which governs the phase field evolution. The medium motion is described by the Godunov–Romenski type hyperelastic model. Electromagnetic part of the model consists of Maxwell’s equations in quasi(electro)stationary approximation including electric charge conservation law. Derivation of the model is based on the Coleman–Noll procedure and Gurtin’s microforces and microstress framework.

Multiphysics simulations reveal haemodynamic impacts of patient-derived fibrosis-related changes in left atrial tissue mechanics.

Stroke is a leading cause of death and disability worldwide. Atrial myopathy, including fibrosis, is associated with an increased risk of ischaemic stroke, but the mechanisms underlying this association are poorly understood. Fibrosis modifies myocardial structure, impairing electrical propagation and tissue biomechanics, and creating stagnant flow regions where clots could form. Fibrosis can be mapped non-invasively using late gadolinium enhancement magnetic resonance imaging (LGE-MRI). However, fibrosis maps are not currently incorporated into stroke risk calculations or computational electro-mechano-fluidic models. We present multiphysics simulations of left atrial (LA) myocardial motion and haemodynamics using patient-specific anatomies and fibrotic maps from LGE-MRI. We modify tissue stiffness and active tension generation in fibrotic regions and investigate how these changes affect LA flow for different fibrotic burdens. We find that fibrotic regions and, to a lesser extent, non-fibrotic regions experience reduced myocardial strain, resulting in decreased LA emptying fraction consistent with clinical observations. Both fibrotic tissue stiffening and hypocontractility independently reduce LA function, but, together, these two alterations cause more pronounced effects than either one alone. Fibrosis significantly alters flow patterns throughout the atrial chamber, and particularly, the filling and emptying jets of the left atrial appendage (LAA). The effects of fibrosis in LA flow are largely captured by the concomitant changes in LA emptying fraction except inside the LAA, where a multifactorial behaviour is observed. This work illustrates how high-fidelity, multiphysics models can be used to study thrombogenesis mechanisms in patient-specific anatomies, shedding light onto the links between atrial fibrosis and ischaemic stroke. KEY POINTS: Left atrial (LA) fibrosis is associated with arrhythmogenesis and increased risk of ischaemic stroke; its extent and pattern can be quantified on a patient-specific basis using late gadolinium enhancement magnetic resonance imaging. Current stroke risk prediction tools have limited personalization, and their accuracy could be improved by incorporating patient-specific information such as fibrotic maps and haemodynamic patterns. We present the first electro-mechano-fluidic multiphysics computational simulations of LA flow, including fibrosis and anatomies from medical imaging. Mechanical changes in fibrotic tissue impair global LA motion, decreasing LA and left atrial appendage (LAA) emptying fractions, especially in subjects with higher fibrosis burdens. Fibrotic-mediated LA motion impairment alters LA and LAA flow near the endocardium and the whole cavity, ultimately leading to more stagnant blood regions in the LAA.

ModulatioAn of Hybrid Plasmon Phonon Polaritons Mode in Circular Cylindrical Three-Layer Graphene Waveguide

In this present research article, we have investigated analytically the characteristics of the fundamental mode of hybrid surface plasmon phonon polariton (HSPPhPs) mode in a circular cylindrical three-layer graphene (CTLG) waveguide structure. The dispersion equation of HSPPhPs is derived by using Maxwell’s equations and continuity conditions of tangential components of electric and magnetic fields in cylindrical geometry. The dispersion curve has been illustrated and thoroughly examined in relation to the effects of temperature and chemical potential (μc) of graphene, as well as variations in the thickness of silicon dioxide (SiO2) and hexagonal boron nitride (hBN) layers, and found that in the presence of hBN, the effective mode index exhibits hyperbolic behavior with wave number. Up to the first Reststrahlen band (∼830.57cm⁻¹), it varies slightly with graphene temperature; increasing graphene's (μc) lowers the index, while a thicker hBN layer reduces it, whereas the index increases with SiO₂ layer thickness. Also, we looked at how the CTLG waveguide structure is affected by the electric field distribution, phase speed, and propagation length.

Vector Field Heterogeneity as a Novel Omnipolar Mapping Metric for Functional Substrate Characterisation in Scar-related Ventricular Tachycardias

BackgroundVector Field Heterogeneity (VFH) is a novel omnipolar metric to quantify local propagation heterogeneities that may identify functionally critical sites for ablation in scar-related VT. ObjectiveAssess the diagnostic value of VFH to identify abnormal propagation patterns during ventricular substrate mapping and compare VFH in VT isthmus sites (IS), low-voltage bystander (LVA) and normal voltage areas (NVA). MethodsSubstrate maps acquired with a 16-pole grid catheter in patients with scar-related VT were segmented into sites corresponding to IS, LVA and NVA (defined as omnipolar voltages >&<1.5mV) based on corresponding VT activation maps. For each 4×4 electrode-array acquisition, omnipolar-derived vector maps of the directions of electrical propagation were computed offline and a VFH value per clique ranging from 0 (perfect planar wave) to 1 (maximal disorganisation) derived. Results16 patients were studied (56.3% ischemic) evaluating 9 endocardial/7 epicardial substrate maps. VFH metric at IS was 0.57±0.26, LVA 0.52±0.34, NVA 0.16±0.24. VFH at IS was higher (more disorganised) than at LVA (p<0.001). VFH in NVA was significantly lower (i.e. more homogenous) compared to IS and LVA (p<0.001, respectively). Within the isthmus, highest heterogeneity was recorded at entry (0.61±0.24), lowest at exit sites (0.44±0.27). ConclusionVFH mapping identified a significant increase in electrical heterogeneity at IS compared to bystanders with highest heterogeneity at the entrance. Absolute differences were small and substantial overlap between sites were recorded precluding its use as a stand-alone mapping approach. VFH may be integrated in existing mapping strategies as complementary information to support identification of ablation targets.

Nonlinear generalized piezothermoelasticity of spherical vessels made of functionally graded piezoelectric materials

The present study investigates the thermoelastic response of a heterogeneous piezoelectric sphere under thermal shock loading. Boundary conditions as well as loading are considered as symmetric; thus, the response of the sphere is expected to be symmetric. All of the properties of the thick-walled sphere, including mechanical, electrical and thermal properties, are considered dependent on the radial position, except for the relaxation time, which is considered a constant value along the radius. The governing equations of the sphere have been derived under heterogeneous anisotropic assumptions. The general form of the second law of thermodynamics, which is nonlinear in nature, and is called nonlinear energy equation is used. The number of the established equations is three, which includes the motion equation, energy equation and Maxwell electrostatic equation of Maxwell. These equations are obtained in terms of radial displacement, temperature difference and electric potential. The energy equation is derived based on Lord and Shulman theory with a single relaxation time. In the next step, by introducing dimensionless variables, the governing equations are provided in dimensionless presentation. Then these equations have been discretized using generalized differential quadrature method. Also, in order to follow the solution of the equations in time domain, Newmark method has been used. Since the system of equations is nonlinear, Picard algorithm is applied as a predictor-corrector mechanism to solve the nonlinear system of equations. Then numerical results are presented to investigate the propagation of mechanical, thermal and electric waves inside the heterogeneous sphere and also their reflection from the outer surface of the sphere. By examining the results, it can be seen that mechanical and thermal waves propagate with a limited speed, while the speed of electric wave propagation is infinite.

Vector Field Heterogeneity (VFH) as a novel quantitative marker of electrical disarray in Arrhythmogenic CardioMyopathy (ACM) with ventricular tachycardia

Abstract Background ACM is a hereditary condition characterized by fibrofatty infiltration and replacement of cardiac myocytes predominantly presenting with ventricular arrhythmias (VA). Cardiac imaging allows for detailed structural phenotyping of scar patterns in ACM. Yet, there is a lack of tools to objectively quantify the electrical substrate alterations that may enable a more precise identification of critical sites that predispose to VA. Purpose To quantify locally disorganized cardiac electrical propagation wavefronts using the Vector Field Heterogeneity (VFH) metric from high-density multi-electrodes in patients with ACM with VT and compare to healthy controls. Methods High density epicardial substrate maps acquired with a 16-pole grid catheter during SR or RV pacing in patients with ACM with VA, who underwent clinically indicated catheter ablation, were retrospectively reviewed. Patients with structurally normal heart and idiopathic VA with epicardial ablation were analysed as a control group. Unipolar contact mapping data was exported &amp; processed offline. From the 4×4 electrode array EGMs, vector maps of the directions of electrical propagation for recorded sites were computed. The VFH was then computed as a quantitative measure of local heterogeneity of propagation, with higher VFH expected to correlate with sites of (micro)structural tissue alterations. VFH was compared between ACM and control patients as well as at sites of normal, border zone &amp; scar based on omnipolar voltage in ACM patients (&amp;gt;1.5mV, 0.5mV–1.5mV, &amp;lt;0.5mV, respectively). Results 10 patients with ACM (70% male, aged 52 ±18 years, ARVC 70%, biventricular 30%, RVEF 40.7±4.7%, LVEF 66±12%) and 2 patients with structurally normal heart (female, 38 &amp; 61 years) were included. Epicardial maps had an average of 9258 ±5412 EGM points. Median VFH was statistically significantly higher in the ACM cohort compared to control for global maps (0.33±0.33 vs 0.13±0.22, p&amp;lt;0.001) and at sites with voltage &amp;gt;1.5mV (i.e. greater disorganization in ACM, p&amp;lt;0.001). In ACM, assessment of VFH according to omnipolar voltage sites (as a surrogate of scar) showed a quantifiable statistically significant increase in electrical disorganized propagation at sites of lower voltage (&amp;lt;0.5mV, median VFH 0.53±0.36) compared to borderzone (0.5-1.5mV, VFH 0.29±0.41) and normal voltage (&amp;gt;1.5mV, VFH 0.15±0.26), p &amp;lt;0.001 respectively. Conclusion Heterogenous electrical propagation as quantified by VFH is significantly increased in patients with ACM at sites of scar, but importantly also in areas of normal voltages when compared to non-ACM controls, possibly indicating microstructural alterations that are missed in traditional assessments of the arrhythmogenic substrate. Identifying and quantifying disorganized conduction patterns by VFH is a promising new mapping approach that could allow improved substrate characterization. Its diagnostic value to guide ablation therapy is currently being validated.VFH Metric ACM and ControlVFH Map Examples

Quantifying cardiac tissue heterogeneity using high-density grid catheter: validation in porcine model

Abstract Background and Objectives Characterizing cardiac substrate is crucial for diagnosing and treating cardiac arrhythmias due to its association with the presence of fibrotic tissue. Omnipolar Electrogram (EGM) technology provides orientation-independent signal generation and instantaneous propagation direction determination. Although traditionally, the amplitude of the bipolar signal has been the most used metric, it alone does not suffice for comprehensive tissue characterization. Recently, a novel metric has been developed to quantify the degree of directional propagation disorganization within cardiac tissue, defined as Vector Field Heterogenity (VFH)[1] that can provide additional insights to the tissue characterization. Due to the presence of tissues with varying impedance, changes in the direction of propagation of cardiac electrical signals can occur. Therefore, the objective of this study is to characterize how the presence of fibrotic or necrotic tissue can influence the disorganization of electrical activity propagation, and thus assess the effectiveness of the heterogeneity metric in characterizing these tissues. Method We worked with a database of a female swine records of the left atrium. These records include data pre and post-ablation by electroporation. From the unipolar signals available in the database, we have calculated the Omnipolar EGMs in cross configuration. From the omnipolar signals, we calculated the propagation direction. On this propagation direction, we applied the heterogeneity metric for each catheter position along all the left atrium. This metric has a normalized range between 0 and 1, 0 describing the minimum disorganization and 1 the maximum. These calculations have been applied in the same way in the registers pre and post-ablation to evaluate the differences. Results Pre-procedure bipolar peak-to-peak voltages averaged 2.7591mV (SD = 3.4257), decreasing post-procedure to 0.754mV (SD = 1.1666), (p&amp;lt; 0.0001) indicating a significant decrease in bipolar amplitude following ablation. Heterogeneity scores increased post-ablation (mean = 0.3753, SD = 0.21218; post: mean = 0.53526, SD = 0.1320, p&amp;lt;0.0001. This indicates that after ablation, not only does the signal amplitude decrease, but also the level of disorganization of electrical propagation increases. These findings are visually depicted in Figure 1. Conclusion The ablation procedure led to reduced tissue electrical activity, manifested by decreased amplitude and increased propagation heterogeneity, indicative of tissue disorganization. Transitioning from homogeneous to heterogeneous conduction post-ablation suggests the presence of necrotic tissue, hindering uniform wave propagation. This highlights the significance of heterogeneity scoring in evaluating tissue health and ablative intervention outcomes.Figure 1.Catheter HD Grid

Vector field heterogeneity as a novel omnipolar mapping metric for functional substrate characterization in scar-related ventricular tachycardias

Abstract Background Identification of functionally critical sites to target for ablation in scar-related VT during substrate mapping remains challenging. Vector Field Heterogeneity (VFH) is a novel omnipolar metric to quantify locally heterogeneous propagation patterns. Objective Assess the diagnostic value of VFH for characterizing abnormal propagation patterns during ventricular substrate mapping and compare between sites of VT isthmus, low voltage bystander areas (LVA) and normal voltage areas (NVA). Methods High-density substrate maps and VT activation maps acquired with a 16-pole grid catheter in patients with scar-related VT were retrospectively reviewed. Based on the VT activation maps with either entrainment and/or VT termination with RF ablation to confirm critical sites, the correlating substrate maps were segmented into sites corresponding to isthmus-site, LVA (omnipolar voltage &amp;lt;1.5mV) and NVA (&amp;gt;1.5mV). To compute the VFH, contact mapping data including all EGMs of each grid-catheter acquisition (16 unipols) was exported and processed offline. From each of the 4×4 electrode array acquisitions, omnipolar-derived vector maps of the directions of electrical propagation for recorded sites were estimated using an orientation-independent cross-clique configuration of 4 adjacent unipols, respectively, resulting in 9 vectors with a spatial resolution of 1.4mm2 each. The angle between each vector and horizontal bipole was assessed and compared between neighbouring vectors using finite differences to derive a VFH value per 2x2 EGM clique as a quantitative metric of local heterogeneity ranging from 0 (perfect planar wave) to 1 (maximal disorganisation - "chaos"). The VFH metric was estimated for each segment of the substrate map and compared against each other. Results Nine patients with scar related VT were included (100% male, age 62±20y, ischemic 66.7%, LVEF 36±16%). On average 3.5 VTs (1-8) were induced per case. Avg. substrate map point count was 3825±3190. Computed median VFH metric at sites corresponding to VT isthmus was 0.58±0.30, LVA bystander 0.47±0.39, NVA sites 0.20±0.34. VFH at isthmus-sites was statistically significant higher (i.e. more disorganised) than at LVA bystander sites (p&amp;lt;0.01). VFH in NVA was significantly lower (i.e. more organised) compared to isthmus and LVA sites (p&amp;lt;0.01, respectively). Median omnipolar voltage at isthmus sites was 0.16±0.27mV compared to LVA bystander 0.22±0.36mV (p=0.0816) and NVA 2.97±3.38mV (p&amp;lt;0.01). Conclusion VFH is a promising novel omnipolar mapping metric for electrical substrate characterisation in scar related VTs. VFH mapping identified a quantifiable and significant increase in electrical heterogeneity at sites corresponding to the critical isthmus compared to LVA bystander and normal voltage sites. VFH may provide new insights in the arrhythmogenicity of scar tissue and support more specific functional mapping strategies to identify targets for ablation without the need to induce VT.

Simulation study on parameter optimization of transcranial direct current stimulation based on rat brain slices

Transcranial direct current stimulation (tDCS) is an important method for treating mental illnesses and neurodegenerative diseases. This paper reconstructed two ex vivo brain slice models based on rat brain slice staining images and magnetic resonance imaging (MRI) data respectively, and the current densities of hippocampus after cortical tDCS were obtained through finite element calculation. Subsequently, a neuron model was used to calculate the response of rat hippocampal pyramidal neuron under these current densities, and the neuronal responses of the two models under different stimulation parameters were compared. The results show that a minimum stimulation voltage of 17 V can excite hippocampal pyramidal neuron in the model based on brain slice staining images, while 24 V is required in the MRI-based model. The results indicate that the model based on brain slice staining images has advantages in precision and electric field propagation simulation, and its results are closer to real measurements, which can provide guidance for the selection of tDCS parameters and scientific basis for precise stimulation.

Enhancing non-invasive pre-surgical evaluation through functional connectivity and graph theory in drug-resistant focal epilepsy

BackgroundEpilepsy, characterized as a network disorder, involves widely distributed areas following seizure propagation from a limited onset zone. Accurate delineation of the epileptogenic zone (EZ) is crucial for successful surgery in drug-resistant focal epilepsy. While visual analysis of scalp electroencephalogram (EEG) primarily elucidates seizure spreading patterns, we employed brain connectivity techniques and graph theory principles during the pre-ictal to ictal transition to define the epileptogenic network. MethodCortical sources were reconstructed from 40-channel scalp EEG in five patients during pre-surgical evaluation for focal drug-resistant epilepsy. Temporal Granger connectivity was estimated ten seconds before seizure and at seizure onset. Results have been analyzed using some centrality indices taken from Graph theory (Outdegree, Hubness). A new lateralization index is proposed by taking into account the sum of the most relevant hubness values across left and right regions of interest. ResultsIn three patients with positive surgical outcomes, analysis of the most relevant Hubness regions closely aligned with clinical hypotheses, demonstrating consistency in EZ lateralization and location. In one patient, the method provides unreliable results due to the abundant movement artifacts preceding the seizure. In a fifth patient with poor surgical outcome, the proposed method suggests a wider epileptic network compared with the clinically suspected EZ, providing intriguing new indications beyond those obtained with traditional electro-clinical analysis. ConclusionsThe proposed method could serve as an additional tool during pre-surgical non-invasive evaluation, complementing data obtained from EEG visual inspection. It represents a first step toward a more sophisticated analysis of seizure onset based on connectivity imbalances, electrical propagation, and graph theory principles.

Simulation study on electrical tree propagation under electrical and mechanical stresses

Simulation study on electrical tree propagation under electrical and mechanical stresses

Magneto-thermoelastic surface waves phenomenon with voids, gravity, initial stress, and rotation under four theories

This paper addresses a significant research gap in the study of surface waves propagation in a nonhomogeneous, within a magneto-thermoviscoelastic material of higher order, initial stress, rotation, gravity effects and voids. This study provides analytical solutions for surface waves propagating through a medium consisting of a magneto-thermoelastic material with voids under the rotation, electro-magnetic field, gravity field and initial stress. The analytical solutions are derived for the displacement components, volume fraction, temperature to Stoneley and Rayleigh waves are computed numerically and presented graphically considering the external parameters impact. Furthermore, this investigates how magnetic field, voids, gravity, initial stress and fiber-reinforced parameters influence these wave phenomena. This investigation provides valuable insights into the synergistic dynamics among electric constituents, voids, Stoneley and Rayleigh waves propagation, enabling advancements in sensor technology, augmented energy harvesting methodologies, and pioneering seismic monitoring approaches. For certain materials, numerical simulations are provided and graphically displayed. The results of this study reveal several unique cases that significantly contribute to the understanding of Rayleigh and Stoneley waves propagation within this intricate material system, particularly in the presence of voids.

Abstract We015: Modeling Cardiac Arrhythmogenicity of hiPSC-CMs and Cardiac Fibroblasts Nanopatterned Coculture and Machine Learning

Background: Sudden cardiac death is one of the most threatening heart conditions in the U.S. Most individuals have an underlying structural cardiac disease associated with cardiac fibrosis and ventricular arrhythmia. The relationship between fibrosis and arrhythmias is found to be related to cardiovascular cell couplings, especially cardiomyocytes (CMs) and cardiac fibroblasts (CFs). While animal models have been applied to model cardiac arrhythmias, the disparities between animal models and humans limit the accuracy of pro-arrhythmic predictions. The use of human induced pluripotent stem cells (hiPSCs)-derived CMs has permitted highly modular testing conditions, specifically the ratio of CFs to CMs in an engineered coculture system. Moreover, machine learning (ML) has become an emerging tool in cardiology, such as cardiac toxicity and function evaluation and classification, with its unique advantages of high accuracy and efficiency with less human bias and intuition. Hypothesis: We hypothesize that cardiac fibrosis-associated arrhythmia will be modeled by nanopatterned coculture of hiPSC-CMs and CFs at varied ratios, and the arrhythmic samples will be accurately and efficiently classified by ML algorithms. Approach: The hiPSC-CMs were cocultured and nanopatterned with CFs at ratios of 0 to 30% for 7 days. Upon the electrical pacing at 1Hz, the action potential was recorded by live-cell optical mapping with FluoVolt. The recorded membrane potential and electrical propagation were analyzed by Matlab-based Electomap software. Results: The cocultured hiPSC-CMs and CFs were aligned with aligned sarcomeres and uni-directional contraction ( Fig. 1a ). The cardiac arrhythmia was observed in 15% CFs with spiral wave ( Fig. 1b ) in comparison to the hiPSC-CMs with 0% CF. Beat-to-beat and depolarization durations were found significant with top ranks in Feature Importance to facilitate the distinction between arrhythmic and non-arrhythmic samples by the unsupervised K-means Clustering ( Figs. 1c and d ). Conclusions: We have successfully established a nanopatterned coculturing system of hiPSC-CMs and CFs for modeling cardiac fibrosis-induced arrhythmia, which was further analyzed and classified by ML algorithms. This system reveals great potential for better understanding the relationship between cardiac fibrosis-associated arrhythmia and sudden cardiac death and also drug evaluation for anti-cardiac arrhythmia.

Transcriptional regulation of the postnatal cardiac conduction system heterogeneity

The cardiac conduction system (CCS) is a network of specialized cardiomyocytes that coordinates electrical impulse generation and propagation for synchronized heart contractions. Although the components of the CCS, including the sinoatrial node, atrioventricular node, His bundle, bundle branches, and Purkinje fibers, were anatomically discovered more than 100 years ago, their molecular constituents and regulatory mechanisms remain incompletely understood. Here, we demonstrate the transcriptomic landscape of the postnatal mouse CCS at a single-cell resolution with spatial information. Integration of single-cell and spatial transcriptomics uncover region-specific markers and zonation patterns of expression. Network inference shows heterogeneous gene regulatory networks across the CCS. Notably, region-specific gene regulation is recapitulated in vitro using neonatal mouse atrial and ventricular myocytes overexpressing CCS-specific transcription factors, Tbx3 and/or Irx3. This finding is supported by ATAC-seq of different CCS regions, Tbx3 ChIP-seq, and Irx motifs. Overall, this study provides comprehensive molecular profiles of the postnatal CCS and elucidates gene regulatory mechanisms contributing to its heterogeneity.

Abstract Mo061: The major voltage-gated sodium channel accessory subunit in working ventricular myocytes may be β1B, not β1

Voltage-gated sodium channels, crucial for the action potential upstroke in cardiomyocytes, consist primarily of a single pore-forming α-subunit and 1 or 2 accessory β-subunits. SCN1B encodes two variants: β1, a transmembrane cell adhesion molecule, and β1B, typically described as a soluble secreted protein. While β1 and β1B share identical sequences in the amino-terminal (NT) extracellular Ig domain, they differ in their carboxy-terminal (CT) sequence. The Ig domain of β1/β1B has been deemed critical in maintaining normal cardiac conduction by various groups. Traditionally, effects on cardiac conduction have been attributed to β1, despite difficulties in detecting it at the protein level in the heart. We hypothesized that β1B, rather than β1, plays a significant role in electrical activity propagation in the heart. Utilizing an NT antibody (detects both variants), a β1-specific CT antibody, and a custom β1B-specific CT antibody, we examined SCN1B gene product profiles in various cardiac cell types, including neonatal rat ventricular myocytes and fibroblasts (NRVMs and NFs), isolated adult mouse cardiomyocytes (MCMs), and tissue slices from isolated adult rat hearts. The β1-specific CT antibody failed to label any bands in Western Blots (WB) of these cells and tissues, whereas the NT antibody detected a 37 kD band in all cell types and showed high levels of localization at cell-cell contacts using immunofluorescence (IF) with NRVMs. Conversely, the CT antibody showed minimal immunolabeling evidence. Moreover, an inhibitor of β1 Regulated Intramembrane Proteolysis failed to generate the expected 19 kD fragment if β1 were present in NRVMs. In adult rat hearts, the NT antibody labeled intercalated discs, while the CT showed minimal signal. Conversely, in WBs of NRVMs using our custom β1B antibody, we observed a 37 kD band consistent with the presence of β1B, and in heart sections, we found labeling of intercalated discs. These findings suggest that the major β subunit in working ventricular myocytes may be β1B, not β1. Further investigation is warranted, as these results could significantly impact our understanding of the roles and functional effects of β1 and β1B on cardiac conduction.

Polynomial Solutions of Electric Field Equations in Anisotropic Media

The time-dependent system of partial differential equations of the second order describing the electric wave propagation in electrically and magnetically anisotropic homogeneous media is considered in the paper. A method for the computation of the polynomial solutions of the initial value problem for the considered system is proposed. Symbolic computations are used and these symbolic computations are implemented in Maple. It is proved also that these polynomial solutions are approximate solutions of the considered initial value problem with smooth initial data and the inhomogeneous term. The computational experiments confirm the robustness of the suggested method for the computation of electric fields in general electrically and magnetically anisotropic media.

Perlin noise generation of physiologically realistic cardiac fibrosis

Fibrosis, a pathological increase in extracellular matrix proteins, is a significant health issue that hinders the function of many organs in the body, in some cases fatally. In the heart, fibrosis impacts on electrical propagation in a complex and poorly predictable fashion, potentially serving as a substrate for dangerous arrhythmias. Individual risk depends on the spatial manifestation of fibrotic tissue, and learning the spatial arrangement on the fine scale in order to predict these impacts still relies upon invasive ex vivo procedures. As a result, the effects of spatial variability on the symptomatic impact of cardiac fibrosis remain poorly understood. In this work, we address the issue of availability of such imaging data via a computational methodology for generating new realisations of cardiac fibrosis microstructure. Using the Perlin noise technique from computer graphics, together with an automated calibration process that requires only a single training image, we demonstrate successful capture of collagen texturing in four types of fibrosis microstructure observed in histological sections. We then use this generator to quantitatively analyse the conductive properties of these different types of cardiac fibrosis, as well as produce three-dimensional realisations of histologically-observed patterning. Owing to the generator’s flexibility and automated calibration process, we also anticipate that it might be useful in producing additional realisations of other physiological structures.

Nonlinear dynamic wave characteristics of optical soliton solutions in ion-acoustic wave

Traveling wave solutions are utilized to depict reaction-diffusion and analyze electrical signal transmission and propagation in space-time nonlinear fractional order partial differential equations like the space-time fractional Telegraph and Kolmogorov-Petrovsky Piskunov equations, and that are used in physical science to model combustion, biological research to model nerve impulse propagation, chemical dynamics to model concentration in order wave propagation, and plasma to model the progression of a set of duffing oscillators. In this study, the new generalized (G′/G)−expansion technique was employed to construct some novel and more universal closed-form traveling wave solutions in the sense of conformable derivatives which explain the above-stated phenomena properly. By utilizing complex fractional transformation, the ordinary differential equations are generated from fractional order differential equations. The recommended technique allowed us to produce some dynamical wave patterns of kink, single soliton, compacton, periodic shape, multiple periodic waves, anti-kink, and other structures are developed, which are shown using 3D plots and contour plots to illustrate the physical layout clearly. The traveling waveform responses can be defined in terms of functions based on trigonometry, hyperbolic operations, and rational functions and that are quick, flexible, and simple to reproduce. Furthermore, the obtained closed-form solutions for nonlinear fractional evolution equations make stability analysis and accuracy comparison amongst numerical solvers easier, which asserts that the new generalized (G′/G)−expansion technique is one of the most proficient and effective approaches.

The smooth-walled human RVOT contains trabeculations that cause conduction delay

Abstract Funding Acknowledgements None. Background The right ventricular outflow tract (RVOT) is the outlet from the right ventricle and is the initiating substrate of life-threatening arrhythmias. While the luminal wall of the RVOT is often assumed to be without the complex trabecular meshwork that characterizes the right ventricular free wall, the anatomy of the RVOT is an understudied subject. Aim to investigate whether trabeculations occur in the RVOT and to assess whether this impacts electrical propagation. Methods Human hearts were investigated using high-resolution MRI, histology, RNA-sequencing, and optical and electrical mapping. Results We used high-resolution MRI and serial sectioning to reconstruct the macroscopic details of the human RVOT and identified cases exhibiting much trabeculation. The smooth lumen of the RVOT varied between 9% and 23% of the total RV anterior surface (N=11). Histological analysis on additional six hearts indicated that the RVOT compact layer is thinner when trabeculations are present. RNA sequencing of four human donor hearts revealed enrichment in the subendocardial region of 88 genes associated with cardiac conduction and trabeculations (P adjusted&amp;lt;0.05). Finally, we selected two human donor hearts showing trabeculations in the RVOT from which we generated wedge preparation and performed optical and electrical mapping. The trabecular regions demonstrated high degree of fractionation when compared to non-trabeculated regions, which coincided with delayed activation. Conclusion Trabeculations are found in the RVOT, and their extent varies among individuals. This impacts on the thickness of the compact wall in the RVOT, restricting the depth of tissue at which clinical interventions can be performed, as well as influencing electrical propagation and possible arrhythmogenicity.

Matching of Water Breakthroughs in a Low-Resistivity Oil Reservoir Using Permeability Anisotropy

In a mature middle and lower Gharif field in Oman, uncertainties surrounding initial water saturation and early water breakthroughs of unknown sources and paths suggest the presence of significant bypassed oil. In order to determine the areas with remaining oil, petrophysical and logging data of seven wells were processed using Techlog software and imported into Petrel software for modelling and simulation. Porosity was calculated using the Electric Propagation Time log and was utilized to evaluate the presence of oil, particularly in the upper tight zone of the formation. Despite the low resistivity readings in the highly porous layers, caused by good network connectivity and high formation water salinity, the resistivity contrast was sufficient to differentiate them from the oil zone. However, the calculated water saturation (Sw) in the tight top oil zone was high, consistent with the observed water production in the field. To improve the match between production data and simulation results, sensitivity analyses were conducted on various permeability anisotropy and relative permeability values within the model. The analyses showed that core-derived permeability anisotropy (vertical to horizontal ratio of 1:1) yielded a better history match for water production compared to the conventionally used value of 1:10. Water saturation maps were generated at the start and the end of production to highlight saturation distribution within the reservoirs. The maps revealed that in the lower porous part, the oil was fully depleted around the wells but remained trapped in the undrilled areas.