Excitation Wavefronts Research Articles

Responsive fungal insoles for pressure detection

Mycelium bound composites are promising materials for a diverse range of applications including wearables and building elements. Their functionality surpasses some of the capabilities of traditionally passive materials, such as synthetic fibres, reconstituted cellulose fibres and natural fibres. Thereby, creating novel propositions including augmented functionality (sensory) and aesthetic (personal fashion). Biomaterials can offer multiple modal sensing capability such as mechanical loading (compressive and tensile) and moisture content. To assess the sensing potential of fungal insoles we undertook laboratory experiments on electrical response of bespoke insoles made from capillary matting colonised with oyster fungi Pleurotus ostreatus to compressive stress which mimics human loading when standing and walking. We have shown changes in electrical activity with compressive loading. The results advance the development of intelligent sensing insoles which are a building block towards more generic reactive fungal wearables. Using FitzHugh-Nagumo model we numerically illustrated how excitation wave-fronts behave in a mycelium network colonising an insole and shown that it may be possible to discern pressure points from the mycelium electrical activity.

On interplay between excitability and geometry

Excitability is an intrinsic feature of a living matter. A commonly accepted feature of an excitable medium is that a local excitation leads to a propagation of circular or spiral excitation wave-fronts. This is indeed the case in fully excitable medium. However, with a decrease of an excitability localised wave-fragments emerge and propagate ballistically. Using FitzhHugh–Nagumo model we numerically study how excitation wave-fronts behave in a geometrically constrained medium and how the wave-fronts explore a random planar graph. We uncover how excitability controls propagation of excitation in angled branches, influences arrest of excitation entering a sudden expansion, and determines patterns of traversing of a random planar graph by an excitation waves.

A brief history of liquid computers.

A substrate does not have to be solid to compute. It is possible to make a computer purely from a liquid. I demonstrate this using a variety of experimental prototypes where a liquid carries signals, actuates mechanical computing devices and hosts chemical reactions. We show hydraulic mathematical machines that compute functions based on mass transfer analogies. I discuss several prototypes of computing devices that employ fluid flows and jets. They are fluid mappers, where the fluid flow explores a geometrically constrained space to find an optimal way around, e.g. the shortest path in a maze, and fluid logic devices where fluid jet streams interact at the junctions of inlets and results of the computation are represented by fluid jets at selected outlets. Fluid mappers and fluidic logic devices compute continuously valued functions albeit discretized. There is also an opportunity to do discrete operation directly by representing information by droplets and liquid marbles (droplets coated by hydrophobic powder). There, computation is implemented at the sites, in time and space, where droplets collide one with another. The liquid computers mentioned above use liquid as signal carrier or actuator: the exact nature of the liquid is not that important. What is inside the liquid becomes crucial when reaction-diffusion liquid-phase computing devices come into play: there, the liquid hosts families of chemical species that interact with each other in a massive-parallel fashion. I shall illustrate a range of computational tasks, including computational geometry, implementable by excitation wave fronts in nonlinear active chemical medium. The overview will enable scientists and engineers to understand how vast is the variety of liquid computers and will inspire them to design their own experimental laboratory prototypes. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Street map analysis with excitable chemical medium.

Belousov-Zhabotinsky (BZ) thin layer solution is a fruitful substrate for designing unconventional computing devices. A range of logical circuits, wet electronic devices, and neuromorphic prototypes have been constructed. Information processing in BZ computing devices is based on interaction of oxidation (excitation) wave fronts. Dynamics of the wave fronts propagation is programed by geometrical constraints and interaction of colliding wave fronts is tuned by illumination. We apply the principles of BZ computing to explore a geometry of street networks. We use two-variable Oregonator equations, the most widely accepted and verified in laboratory experiments BZ models, to study propagation of excitation wave fronts for a range of excitability parameters, with gradual transition from excitable to subexcitable to nonexcitable. We demonstrate a pruning strategy adopted by the medium with decreasing excitability when wider and ballistically appropriate streets are selected. We explain mechanics of streets selection and pruning. The results of the paper will be used in future studies of studying dynamics of cities and characterizing geometry of street networks.

Pro-arrhythmic atrial phenotypes in incrementally paced murine Pgc1β-/- hearts: effects of age.

New Findings What is the central question of this study? Can we experimentally replicate atrial pro‐arrhythmic phenotypes associated with important chronic clinical conditions, including physical inactivity, obesity, diabetes mellitus and metabolic syndrome, compromising mitochondrial function, and clarify their electrophysiological basis? What is the main finding and its importance? Electrocardiographic and intracellular cardiomyocyte recording at progressively incremented pacing rates demonstrated age‐dependent atrial arrhythmic phenotypes in Langendorff‐perfused murine Pgc1β −/− hearts for the first time. We attributed these to compromised action potential conduction and excitation wavefronts, whilst excluding alterations in recovery properties or temporal electrophysiological instabilities, clarifying these pro‐arrhythmic changes in chronic metabolic disease. Atrial arrhythmias, most commonly manifesting as atrial fibrillation, represent a major clinical problem. The incidence of atrial fibrillation increases with both age and conditions associated with energetic dysfunction. Atrial arrhythmic phenotypes were compared in young (12–16 week) and aged (>52 week) wild‐type (WT) and peroxisome proliferative activated receptor, gamma, coactivator 1 beta (Ppargc1b)‐deficient (Pgc1β −/−) Langendorff‐perfused hearts, previously used to model mitochondrial energetic disorder. Electrophysiological explorations were performed using simultaneous whole‐heart ECG and intracellular atrial action potential (AP) recordings. Two stimulation protocols were used: an S1S2 protocol, which imposed extrasystolic stimuli at successively decremented intervals following regular pulse trains; and a regular pacing protocol at successively incremented frequencies. Aged Pgc1β −/− hearts showed greater atrial arrhythmogenicity, presenting as atrial tachycardia and ectopic activity. Maximal rates of AP depolarization (dV/dt max) were reduced in Pgc1β −/− hearts. Action potential latencies were increased by the Pgc1β −/− genotype, with an added interactive effect of age. In contrast, AP durations to 90% recovery (APD90) were shorter in Pgc1β −/− hearts despite similar atrial effective recovery periods amongst the different groups. These findings accompanied paradoxical decreases in the incidence and duration of alternans in the aged and Pgc1β −/− hearts. Limiting slopes of restitution curves of APD90 against diastolic interval were correspondingly reduced interactively by Pgc1β −/− genotype and age. In contrast, reduced AP wavelengths were associated with Pgc1β −/− genotype, both independently and interacting with age, through the basic cycle lengths explored, with the aged Pgc1β −/− hearts showing the shortest wavelengths. These findings thus implicate AP wavelength in possible mechanisms for the atrial arrhythmic changes reported here.

Cellular Automaton Belousov–Zhabotinsky Model for Binary Full Adder

The continuous increment in the performance of classical computers has been driven to its limit. New ways are studied to avoid this oncoming bottleneck and many answers can be found. An example is the Belousov–Zhabotinsky (BZ) reaction which includes some fundamental and essential characteristics that attract chemists, biologists, and computer scientists. Interaction of excitation wave-fronts in BZ system, can be interpreted in terms of logical gates and applied in the design of unconventional hardware components. Logic gates and other more complicated components have been already proposed using different topologies and particular characteristics. In this study, the inherent parallelism and simplicity of Cellular Automata (CAs) modeling is combined with an Oregonator model of light-sensitive version of BZ reaction. The resulting parallel and computationally-inexpensive model has the ability to simulate a topology that can be considered as a one-bit full adder digital component towards the design of an Arithmetic Logic Unit (ALU).

On Emulation of Flueric Devices in Excitable Chemical Medium.

Flueric devices are fluidic devices without moving parts. Fluidic devices use fluid as a medium for information transfer and computation. A Belousov-Zhabotinsky (BZ) medium is a thin-layer spatially extended excitable chemical medium which exhibits travelling excitation wave-fronts. The excitation wave-fronts transfer information. Flueric devices compute via jets interaction. BZ devices compute via excitation wave-fronts interaction. In numerical model of BZ medium we show that functions of key flueric devices are implemented in the excitable chemical system: signal generator, and, xor, not and nor Boolean gates, delay elements, diodes and sensors. Flueric devices have been widely used in industry since late 1960s and are still employed in automotive and aircraft technologies. Implementation of analog of the flueric devices in the excitable chemical systems opens doors to further applications of excitation wave-based unconventional computing in soft robotics, embedded organic electronics and living technologies.

Boundary control of bidomain equations with state-dependent switching source functions in the ionic model

Optimal control for cardiac electrophysiology based on the bidomain equations in conjunction with the Fenton–Karma ionic model is considered. This generic ventricular model approximates well the restitution properties and spiral wave behavior of more complex ionic models of cardiac action potentials. However, it is challenging due to the appearance of state-dependent discontinuities in the source terms. A computational framework for the numerical realization of optimal control problems is presented. Essential ingredients are a shape calculus based treatment of the sensitivities of the discontinuous source terms and a marching cubes algorithm to track iso-surface of excitation wavefronts. Numerical results exhibit successful defibrillation by applying an optimally controlled extracellular stimulus.

Heterogeneous and anisotropic integrative model of pulmonary veins: computational study of arrhythmogenic substrate for atrial fibrillation

Mechanisms underlying the genesis of re-entrant substrate for the most common cardiac arrhythmia, atrial fibrillation (AF), are not well understood. In this study, we develop a multi-scale three-dimensional computational model that integrates cellular electrophysiology of the left atrium (LA) and pulmonary veins (PVs) with the respective tissue geometry and fibre orientation. The latter is reconstructed in unique detail from high-resolution (approx. 70 μm) contrast micro-computed tomography data. The model is used to explore the mechanisms of re-entry initiation and sustenance in the PV region, regarded as the primary source of high-frequency electrical activity in AF. Simulations of the three-dimensional model demonstrate that an initial break-down of normal electrical excitation wave-fronts can be caused by the electrical heterogeneity between the PVs and LA. High tissue anisotropy is then responsible for the slow conduction and generation of a re-entrant circuit near the PVs. Evidence of such circuits has been seen clinically in AF patients. Our computational study suggests that primarily the combination of electrical heterogeneity and conduction anisotropy between the PVs and LA tissues leads to the generation of a high-frequency (approx. 10 Hz) re-entrant source near the PV sleeves, thus providing new insights into the arrhythmogenic mechanisms of excitation waves underlying AF.

The role of fine‐scale anatomical structure in the dynamics of reentry in computational models of the rabbit ventricles

Fine-scale anatomical structures in the heart may play an important role in sustaining cardiac arrhythmias. However, the extent of this role and how it may differ between species are not fully understood. In this study we used computational modelling to assess the impact of anatomy upon arrhythmia maintenance in the rabbit ventricles. Specifically, we quantified the dynamics of excitation wavefronts during episodes of simulated tachyarrhythmias and fibrillatory arrhythmias, defined as being respectively characterised by relatively low and high spatio-temporal disorganisation. Two computational models were used: a highly anatomically detailed MR-derived rabbit ventricular model (representing vasculature, endocardial structures) and a simplified equivalent model, constructed from the same MR-data but lacking such fine-scale anatomical features. During tachyarrhythmias, anatomically complex and simplified models showed very similar dynamics; however, during fibrillatory arrhythmias, as activation wavelength decreased, the presence of fine-scale anatomical details appeared to marginally increase disorganisation of wavefronts during arrhythmias in the complex model. Although a small amount of clustering of reentrant rotor centres (filaments) around endocardial structures was witnessed in follow-up analysis (which slightly increased during fibrillation as rotor size decreased), this was significantly less than previously reported in large animals. Importantly, no anchoring of reentrant rotors was visibly identifiable in arrhythmia movies. These differences between tachy- and fibrillatory arrhythmias suggest that the relative size of reentrant rotors with respect to anatomical obstacles governs the influence of fine-scale anatomy in the maintenance of ventricular arrhythmias in the rabbit. In conclusion, our simulations suggest that fine-scale anatomical features play little apparent role in the maintenance of tachyarrhythmias in the rabbit ventricles and, contrary to experimental reports in larger animals, appear to play only a minor role in the maintenance of fibrillatory arrhythmias. These findings also have important implications in optimising the level of detail required in anatomical computational meshes frequently used in arrhythmia investigations.

Curvature-Dependent Excitation Propagation in Cultured Cardiac Tissue.

The geometry of excitation wave front may play an important role on the propagation block and spiral wave formation. The wave front which is bent over the critical value due to interaction with the obstacles may partially cease to propagate and appearing wave breaks evolve into rotating waves or reentry. This scenario may explain how reentry spontaneously originates in a heart. We studied highly curved excitation wave fronts in the cardiac tissue culture and found that in the conditions of normal, non-inhibited excitability the curvature effects do not play essential role in the propagation. Neither narrow isthmuses nor sharp corners of the obstacles, being classical objects for production of extremely curved wave front, affect non-inhibited wave propagation. The curvature-related phenomena of the propagation block and wave detachment from the obstacle boundary were observed only after partial suppression of the sodium channels with Lidocaine. Computer simulations confirmed the experimental observations. The explanation of the observed phenomena refers to the fact that the heart tissue is made of finite size cells so that curvature radii smaller than the cardiomyocyte size loses sense, and in non-inhibited tissue the single cell is capable to transmit excitation to its neighbors.

The Effects of Control Domain Position on Optimal Control of Cardiac Arrhythmia

We study the effects of control domain position on optimal control problem of cardiac arrhythmia. The well‐established mathematical model, namely, the monodomain model, is used to represent the electrical behavior of the cardiac tissue. Two test cases are considered in this paper: the control domain for Test Case 1 is close to the excitation domain, while the control domain for Test Case 2 is a little bit far away from the excitation domain. The modified Dai‐Yuan nonlinear conjugate gradient method is employed for computing the optimal applied extracellular current. Our experiment results show that the excitation wavefronts are successfully dampened out for both test cases. Also, experiment results show that the position of the control domain for Test Case 1 is preferable than that of Test Case 2 during the defibrillation process.

Solving Optimal Control Problem of Monodomain Model Using Hybrid Conjugate Gradient Methods

We present the numerical solutions for the PDE‐constrained optimization problem arising in cardiac electrophysiology, that is, the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model. The monodomain model consists of a parabolic partial differential equation coupled to a system of nonlinear ordinary differential equations, which has been widely used for simulating cardiac electrical activity. Our control objective is to dampen the excitation wavefront using optimal applied extracellular current. Two hybrid conjugate gradient methods are employed for computing the optimal applied extracellular current, namely, the Hestenes‐Stiefel‐Dai‐Yuan (HS‐DY) method and the Liu‐Storey‐Conjugate‐Descent (LS‐CD) method. Our experiment results show that the excitation wavefronts are successfully dampened out when these methods are used. Our experiment results also show that the hybrid conjugate gradient methods are superior to the classical conjugate gradient methods when Armijo line search is used.

Development of an anatomically detailed MRI-derived rabbit ventricular model and assessment of its impact on simulations of electrophysiological function

Recent advances in magnetic resonance (MR) imaging technology have unveiled a wealth of information regarding cardiac histoanatomical complexity. However, methods to faithfully translate this level of fine-scale structural detail into computational whole ventricular models are still in their infancy, and, thus, the relevance of this additional complexity for simulations of cardiac function has yet to be elucidated. Here, we describe the development of a highly detailed finite-element computational model (resolution: ∼125 μm) of rabbit ventricles constructed from high-resolution MR data (raw data resolution: 43 × 43 × 36 μm), including the processes of segmentation (using a combination of level-set approaches), identification of relevant anatomical features, mesh generation, and myocyte orientation representation (using a rule-based approach). Full access is provided to the completed model and MR data. Simulation results were compared with those from a simplified model built from the same images but excluding finer anatomical features (vessels/endocardial structures). Initial simulations showed that the presence of trabeculations can provide shortcut paths for excitation, causing regional differences in activation after pacing between models. Endocardial structures gave rise to small-scale virtual electrodes upon the application of external field stimulation, which appeared to protect parts of the endocardium in the complex model from strong polarizations, whereas intramural virtual electrodes caused by blood vessels and extracellular cleft spaces appeared to reduce polarization of the epicardium. Postshock, these differences resulted in the genesis of new excitation wavefronts that were not observed in more simplified models. Furthermore, global differences in the stimulus recovery rates of apex/base regions were observed, causing differences in the ensuing arrhythmogenic episodes. In conclusion, structurally simplified models are well suited for a large range of cardiac modeling applications. However, important differences are seen when behavior at microscales is relevant, particularly when examining the effects of external electrical stimulation on tissue electrophysiology and arrhythmia induction. This highlights the utility of histoanatomically detailed models for investigations of cardiac function, in particular for future patient-specific modeling.

Transitional QRS Morphology during CRT Timing Optimization Is Associated with the Largest Improvement in Myocardial Performance Index

Background: Optimization of CRT timing may result in an improvement in cardiac function and long-term clinical outcome. Previous studies have suggested that the maximal improvement in left-ventricular contractility is achieved when fusion between electrical excitation wavefronts originating from the left- (LV) and right-ventricular (RV) pacing sites is observed. We investigated the relationship between QRS morphology in surface ECG and echocardiographic indices of cardiac function upon changes in CRT timing.

Physarum machines: encapsulating reaction–diffusion to compute spanning tree

The Physarum machine is a biological computing device, which employs plasmodium of Physarum polycephalum as an unconventional computing substrate. A reaction-diffusion computer is a chemical computing device that computes by propagating diffusive or excitation wave fronts. Reaction-diffusion computers, despite being computationally universal machines, are unable to construct certain classes of proximity graphs without the assistance of an external computing device. I demonstrate that the problem can be solved if the reaction-diffusion system is enclosed in a membrane with few 'growth points', sites guiding the pattern propagation. Experimental approximation of spanning trees by P. polycephalum slime mold demonstrates the feasibility of the approach. Findings provided advance theory of reaction-diffusion computation by enriching it with ideas of slime mold computation.

Method for quantifiying conduction velocity during ventricular fibrillation

Velocity of propagation of electrical excitation in the heart is important for the understanding of complex arrhythmias such as ventricular fibrillation (VF). In this paper, we present a method to estimate the conduction velocity of electrical activation wavefronts that are defined to be a particular isovalue of any scalar field, such as electrical activation times, electrical phase, or indeed any other quantity that can be used to determine excitation wavefronts. This general method is based on tracking trajectories of material points that are assumed to be embedded within the wavefronts, whilst the direction of propagation is assumed to be perpendicular to the wavefront. We have derived an explicit expression for the conduction velocity in terms of the spatiotemporal gradients of the scalar field used to define wavefronts. Moreover, although it is often difficult to use activation times to compute conduction velocities during complex VF, we show that other scalar fields such as detrended voltage or electrical phase, which can faithfully represent the electrical activity during fibrillatory conduction, can be used to determine conduction velocities. We demonstrate the application of our method to determine conduction velocities from contact mapping recordings over the entire epicardial surface of the fibrillating pig heart.

Ionic mechanisms of wavebreak in fibrillation

out an intermediate band of resting tissue. This causes extinction of the segment of wavefront that hits this functional obstacle and the formation of two singularity points (white dots, 33 ms). The two resulting wavefronts pivot around the points of the wavebreaks (53‐73 ms) and make a complete rotation in approximately 83 ms. The results clearly demonstrate that at the high frequencies of VF, excitation wavefronts frequently encounter and interact with functional and/or anatomic obstacles, giving way to intermittent propagation block patterns, with consequent fragmentation of the wavefront into new daughter wavelets. Therefore, irrespective of the underlying mechanisms, wavebreak and fibrillatory conduction account for the complex patterns of propagation, wavelet formation, and apparent aperiodic activity that typify fibrillation. 11 The question that arises, however, is: What mechanisms underlie wavebreak formation at the ionic/molecular level?

Cardiac vulnerability to electric shocks during phase 1A of acute global ischemia

The purpose of this study is to characterize the changes in vulnerability to electric shocks during phase 1A of global ischemia in the rabbit ventricles and to determine the mechanisms responsible for these changes. Mechanisms responsible for the changes in cardiac vulnerability over the course of ischemia phase 1A remain poorly understood. The lack of understanding results from the rapid ischemic change in cardiac electrophysiologic properties, which renders experimental evaluation of vulnerability difficult. To examine dynamic changes in vulnerability to electric shocks over the course of acute global ischemia phase 1A, this study used a three-dimensional anatomically accurate bidomain model of ischemic rabbit ventricles. Monophasic shocks are applied at various coupling intervals to construct vulnerability grids in normoxia and at various stages of ischemia phase 1A. Our simulations demonstrate that 2 to 3 minutes after the onset of ischemia, the upper limit of vulnerability remains at its normoxic value (12.75 V/cm); however, arrhythmias are induced at shorter coupling intervals. As ischemia progresses, the upper limit of vulnerability decreases, reaching 6.4 V/cm in the advanced stage of ischemia phase 1A, and the vulnerable window shifts towards longer coupling intervals. Changes in the upper limit of vulnerability result from an increase in the spatial extent of the shock-end excitation wavefronts and the slower recovery from shock-induced positive polarization. Shifts in the vulnerable window stem from decreases in local repolarization times and the occurrence of postshock conduction failure caused by prolonged postrepolarization refractoriness.

Mechanisms of myocardial capture and temporal excitable gap during spiral wave reentry in a bidomain model.

Recent studies have demonstrated that regional capture during cardiac fibrillation is associated with an elevated capture threshold. It is typically assumed that the temporal excitable gap (capture window) during fibrillation reflects the size of the spatial excitable gap (excitable tissue between fibrillation waves). Because capture threshold is high, virtual electrode polarization is expected to be involved in the process. However, little is known about the underlying mechanisms of myocardial capture during fibrillation. To clarify these issues, we conducted altogether 3168 simulations of single spiral wave capture in a bidomain sheet. Unipolar stimuli of strengths 4, 8, 16, and 24 mA and 2-ms duration were delivered at 99 locations in the sheet. We found that cathode-break rather than cathode-make excitation was the dominant mechanism of myocardial capture. When the stimulation site was located diagonally with respect to the core (upper left or lower right if the spiral wave rotates counterclockwise), the cathode-break excitation easily invaded the spatial excitable gap and resulted in a successful capture as a result of the formation of virtual anodes in the direction of the myocardial fibers. Thus, the spatial distribution of the temporal excitable gap did not reflect the spatial excitable gap. The areas exhibiting wide temporal excitable gaps were areas in which the cathode-break excitation wave fronts easily invaded the spatial excitable gap via the virtual anodes. This study provides mechanistic insight into myocardial capture.