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The heart consists of a complex network of billions of cells. Under physiological conditions, cardiac cells propagate electrical signals in space, generating the heartbeat in a synchronous and coordinated manner. When such a synchronization fails, life-threatening events can arise. The inherent complexity of the underlying nonlinear dynamics and th...
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... Another helpful version of these systems, where the cells follow a combination of rules, is called a hybrid cellular automaton. The rule set of this type of CA, applied as a linear variant, can be analyzed through matrix algebra [18]. ...
The theory and application of cellular automata (CA) for a stream cipher-based encryption principle are presented in this study. Certain fundamental transformations are developed based on CA theory regarding decentralized computation for modeling different system’s behavior. The changes governing state transitions rely on simple evolution rules, which can easily be translated into functions using logic operators. A class of linear hybrid cellular automata (LHCA) based on rules 90 and 150 is used to implement these functions. Symmetric key systems theory is the foundation of the suggested algorithm. The algorithm functions use the proprieties provided by the LHCA evolution in order to convert plain text into cipher text and vice versa, in each case starting from the same initial state of the system and performing the same number of steps for each operation. Cellular automata’s parallel information processing property, in addition to their regular and dynamical structure, makes hardware implementation of such schemes best suited for VLSI implementation. Testing of the proposed algorithm was performed by developing both software and hardware solutions. Hardware implementation of the presented cryptosystem was developed using VHDL hardware description language and a FPGA device (XILINX Spartan3E XC3S500E). Design and software simulations have been carried out using the C# programming language.
... Ultimately, to enable the clinical translation of the proposed methodology to a real-case scenario, computational aspects should be addressed. A reduction of complexity in the model [42], an inverse estimation of cardiac conductivities [38,74,75], along with graphical process units (GPU) acceleration [76,77] could enable real-time prediction of HBP outcome which can guide clinicians during the implantation procedure. ...
His bundle pacing (HBP) has emerged as a feasible alternative to right (RVP) and biventricular pacing (BVP) for Cardiac Resynchronization Therapy (CRT). This study sought to assess, in ex-vivo experimental models, the optimal setup for HBP in terms of electrode placement and pacing protocol to achieve superior electrical synchrony in the case of complete His-Purkinje block and left bundle branch block (LBBB). We developed a 3D model of His bundle and bundle branches, embedded in a patient-specific biventricular heart model reconstructed from CT images. A monodomain reaction-diffusion model was adopted to describe the propagation of cardiac action potential, and a custom procedure was developed to compute pseudo-ECGs. Experimental measurements of tip electrode potential waveforms have been performed on ex-vivo swine myocardium to determine the appropriate boundary condition for delivering the electrical stimulus in the numerical model. An extended parametric analysis, investigating the effect of the electrode orientation and helix length, pacing protocol, and atrioventricular delay, allowed us to determine the optimal setup for HBP therapy. Both selective (S-HBP) and non-selective (NS-HBP) His bundle pacing were tested, as the variable anatomical location of the His bundle can result in the activation of the surrounding myocardium. Our study indicates a perpendicular placement of the electrode as the most advantageous for restoring the physiological function of the His-Purkinje system. We found that higher-energy protocols can compensate for the effects of an angled placement though concurring to potential tip fibrosis. Promisingly, we also revealed that an increased electrode helix length can provide optimal resynchronization even with low-energy pacing protocols. Our results provide informative guidance for implant procedure and therapy optimization, which will hopefully have clinical implications further improving the procedural success rates and patients’ quality of life, due to reduced incidence of lead revision and onset of complications.
... Firstly, the inclusion of the anisotropic ratio and the myocardial layer for each ventricle in the optimization pipeline could give more degrees of freedom to match EAM data. Additionally, the parameter optimization schemes used by all participants of the CRT-Epiggy19 challenge were not taking advantage of recent technological advances such as the use of deep learning algorithms [55,56], variational approaches [57], reduced-order models [58,59] or GPUbased architectures [60], which allows for the exploration of a larger space of parameter solutions at reduced computational times. Moreover, cardiac multi-physical models should provide more realistic simulations, allowing for the inclusion of hemodynamic factors and improving the adjustment of CRT configuration through flow ratios [61], perfusion models [17], lumped models of the whole cardiovascular circulation [18] or with a complete torso [20]. ...
Computational models of cardiac electrophysiology are promising tools for reducing the rates of non-response patients suitable for cardiac resynchronization therapy (CRT) by optimizing electrode placement. The majority of computational models in the literature are mesh-based, primarily using the finite element method (FEM). The generation of patient-specific cardiac meshes has traditionally been a tedious task requiring manual intervention and hindering the modeling of a large number of cases. Meshless models can be a valid alternative due to their mesh quality independence. The organization of challenges such as the CRT-EPiggy19, providing unique experimental data as open access, enables benchmarking analysis of different cardiac computational modeling solutions with quantitative metrics. We present a benchmark analysis of a meshless-based method with finite-element methods for the prediction of cardiac electrical patterns in CRT, based on a subset of the CRT-EPiggy19 dataset. A data assimilation strategy was designed to personalize the most relevant parameters of the electrophysiological simulations and identify the optimal CRT lead configuration. The simulation results obtained with the meshless model were equivalent to FEM, with the most relevant aspect for accurate CRT predictions being the parameter personalization strategy (e.g., regional conduction velocity distribution, including the Purkinje system and CRT lead distribution).
... New simulation techniques may be needed to help alleviate the computational load. 42,43 Physiologists have postulated that gap junction nonlinear dynamics might contribute to conduction slowing and to the maintenance of reentrant arrhythmia. 33,44 Testing this hypothesis in silico necessitates an organ-scale model in two or three dimensions and, therefore, some form of homogenization to limit computational requirements (e.g., 100 µm instead of 5 µm discretization). ...
Gap junctions exhibit nonlinear electrical properties that have been hypothesized to be relevant to arrhythmogenicity in a structurally remodeled tissue. Large-scale implementation of gap junction dynamics in 3D propagation models remains challenging. We aim to quantify the impact of nonlinear diffusion during episodes of arrhythmias simulated in a left atrial model. Homogenization of conduction properties in the presence of nonlinear gap junctions was performed by generalizing a previously developed mathematical framework. A monodomain model was solved in which conductivities were time-varying and depended on transjunctional potentials. Gap junction conductances were derived from a simplified Vogel–Weingart model with first-order gating and adjustable time constant. A bilayer interconnected cable model of the left atrium with 100 [Formula: see text]m resolution was used. The diffusion matrix was recomputed at each time step according to the state of the gap junctions. Sinus rhythm and atrial fibrillation episodes were simulated in remodeled tissue substrates. Slow conduction was induced by reduced coupling and by diffuse or stringy fibrosis. Simulations starting from the same initial conditions were repeated with linear and nonlinear gap junctions. The discrepancy in activation times between the linear and nonlinear diffusion models was quantified. The results largely validated the linear approximation for conduction velocities >20 cm/s. In very slow conduction substrates, the discrepancy accumulated over time during atrial fibrillation, eventually leading to qualitative differences in propagation patterns, while keeping the descriptive statistics, such as cycle lengths, unchanged. The discrepancy growth rate was increased by impaired conduction, fibrosis, conduction heterogeneity, lateral uncoupling, fast gap junction time constant, and steeper action potential duration restitution.
... Innovative multiscale and multiphysics formulations of cell-cell couplings aim at filling this gap. Nonlinear, stress-assisted, and fractional diffusion (Lin and Keener, 2010;Hurtado et al., 2016;Cherubini et al., 2017;Cusimano et al., 2020;Cusimano et al., 2021), ephaptic and gap junction-mediated couplings (Lenarda et al., 2018;Weinberg, 2017), cellular automata, and coarse-grained homogenized gap junction approaches (Treml et al., 2021;Irakoze and Jacquemet, 2021) represent the state-of-the-art in this direction. Furthermore, within the specific context of cardiac electrophysiology, recent studies are proposing novel methods of data estimation, data assimilation, and uncertainty quantification (Barone et al., 2020a;Barone et al., 2020b;Pathmanathan et al., 2020;Marcotte et al., 2021) to reproduce complex cardiac dynamics with a reduced computational cost. ...
Understanding and predicting the mechanisms promoting the onset and sustainability of cardiac arrhythmias represent a primary concern in the scientific and medical communities still today. Despite the long-lasting effort in clinical and physico-mathematical research, a critical aspect to be fully characterized and unveiled is represented by spatiotemporal alternans patterns of cardiac excitation. The identification of discordant alternans and higher-order alternating rhythms by advanced data analyses as well as their prediction by reliable mathematical models represents a major avenue of research for a broad and multidisciplinary scientific community. Current limitations concern two primary aspects: 1) robust and general-purpose feature extraction techniques and 2) in silico data assimilation within reliable and predictive mathematical models. Here, we address both aspects. At first, we extend our previous works on Fourier transformation imaging (FFI), applying the technique to whole-ventricle fluorescence optical mapping. Overall, we identify complex spatial patterns of voltage alternans and characterize higher-order rhythms by a frequency-series analysis. Then, we integrate the optical ultrastructure obtained by FFI analysis within a fine-tuned electrophysiological mathematical model of the cardiac action potential. We build up a novel data assimilation procedure demonstrating its reliability in reproducing complex alternans patterns in two-dimensional computational domains. Finally, we prove that the FFI approach applied to both experimental and simulated signals recovers the same information, thus closing the loop between the experiment, data analysis, and numerical simulations.
... Considering the integration of cellular automata with other techniques, in [22] is designed an automaton that could be part of a more complex system to make bio-computers that can be used for teachers in multidisciplinary education. Meanwhile, in [23] is considered a Hybrid Cellular Automata (HCA) architecture for modeling the cardiac cell-cell membrane resistance. This work shows that the modeling proposal reproduces important and complex spatio-temporal properties that can be used in future models. ...
Given the grid features of digital images, a direct relation with cellular automata can be established with transition rules based on information of the cells in the grid. This document presents the modeling of an algorithm based on cellular automata for digital images processing. Using an adaptation mechanism, the algorithm allows the elimination of impulsive noise in digital images. Additionally, the comparison of the cellular automata algorithm and median and mean filters is carried out to observe that the adaptive process obtains suitable results for eliminating salt and pepper type-noise. Finally, by means of examples, the result of the algorithm are shown graphically.
... In this manuscript, we consider the space-fractional approach and build on the motivations proposed in the original work by Bueno-Orovio et al. 38 to formulate a two-domain generalization of the fractional models previously studied in these settings: the fractional bidomain (FBD). While the assumption of fractional diffusion in the extracellular domain could be attributed to the composite microstructure of cardiac tissue (i.e., the presence of blood vessels and cardiac interstitial cells, including endothelial, smooth muscle cells, pericytes, peripheral nerves, and fibroblasts, in addition to cardiac myocytes), the assumption of fractional diffusion in the intercellular domain could be associated with the role played by gap junctions in modulating intercellular signal propagation 46,47 as well as to the complexity of the intracellular space through which chemical species (and calcium ions in particular) diffuse. 48,49 We introduce the novel model and make a preliminary study of the complex spatiotemporal dynamics resulting from the use of nonlocal fractional diffusive operators in one or both cellular domains of the bidomain formulation. ...
Cardiac electrophysiology modeling deals with a complex network of excitable cells forming an intricate syncytium: the heart. The electrical activity of the heart shows recurrent spatial patterns of activation, known as cardiac alternans, featuring multiscale emerging behavior. On these grounds, we propose a novel mathematical formulation for cardiac electrophysiology modeling and simulation incorporating spatially non-local couplings within a physiological reaction–diffusion scenario. In particular, we formulate, a space-fractional electrophysiological framework, extending and generalizing similar works conducted for the monodomain model. We characterize one-dimensional excitation patterns by performing an extended numerical analysis encompassing a broad spectrum of space-fractional derivative powers and various intra- and extracellular conductivity combinations. Our numerical study demonstrates that (i) symmetric properties occur in the conductivity parameters’ space following the proposed theoretical framework, (ii) the degree of non-local coupling affects the onset and evolution of discordant alternans dynamics, and (iii) the theoretical framework fully recovers classical formulations and is amenable for parametric tuning relying on experimental conduction velocity and action potential morphology.
... Understanding the nonlinear nature of electrical activity and the drivers of cardiac arrhythmias [18] in terms of variations of physical parameters (e.g., local heterogeneity and thermal state) in simplified systems [19,20] plays a key role in the development of medical devices for the monitoring and treatment of heart diseases [21][22][23][24]. Novel bioelectronic patches, for example, able to perform spatiotemporal mapping of the cardiac conduction system, can provide therapeutic capabilities, such as electrical pacing, thermal ablation, and cardiac monitoring [25][26][27]. ...
Alternans of cardiac action potential duration represent critical precursors for the development of life-threatening arrhythmias and sudden cardiac death. The system's thermal state affects these electrical disorders requiring additional theoretical and experimental efforts to improve a patient-specific clinical understanding. In such a scenario, we generalize a recent work from Loppini et al. [Phys. Rev. E 100, 020201(R) (2019)] by performing an extended spatiotemporal correlation study. We consider high-resolution optical mapping recordings of canine ventricular wedges' electrical activity at different temperatures and pacing frequencies. We aim to recommend the extracted characteristic length as a potential predictive index of cardiac alternans onset and evolution within a wide range of system states. In particular, we show that a reduction of temperature results in a drop of the characteristic length, confirming the impact of thermal instabilities on cardiac dynamics. Moreover, we theoretically investigate the use of such an index to identify and predict different alternans regimes. Finally, we propose a constitutive phenomenological law linking conduction velocity, characteristic length, and temperature in view of future numerical investigations.
The effects of fibroblast on the excitable media are investigated using a proposed myocyte–fibroblast Fitzhugh–Nagumo bioheat model. At the cellular level, the model of human excitable cell and fibroblast is modified to incorporate the Penne bioheat equation with the addition of the Joule effect. The spatial discretization is based on the fourth-order finite difference approximation and the implicit forward Euler method for the time stepping for the study the one-dimensional (1D) model. We introduce a fine adaptive algorithm of the Comsol Multiphysics software to solve the two-dimensional (2D) model and initiate spiral waves. The effects of fibroblast are analyzed in 1D and 2D models under normal and fibrillation conditions. We establish that the fibroblast slows down wave propagation, induces conduction block, is responsible for the rapid thermal block and dissipates temperature in the medium. Our research exhibits the role played by the fibroblast in modulating the electrothermal activities of cardiac or excitable cells.
