A computational study on the influence of antegrade accessory pathway location on the 12-lead electrocardiogram in Wolff-Parkinson-White syndrome.

Wolff-Parkinson-White syndrome is a cardiovascular disease characterized by abnormal atrio-ventricular conduction facilitated by accessory pathways (APs). Invasive catheter ablation of the AP represents the primary treatment modality. Accurate localization of APs is crucial for successful ablation outcomes, but current diagnostic algorithms based on the 12 lead electrocardiogram (ECG) often struggle with precise determination of AP locations. In order to gain insight into the mechanisms underlying localization failures observed in current diagnostic algorithms, we employ a virtual cardiac model to elucidate the relationship between AP location and ECG morphology. We first introduce a cardiac model of electrophysiology that was specifically tailored to represent antegrade APs in the form of a short atrio-ventricular bypass tract. Locations of antegrade APs were then automatically swept across both ventricles in the virtual model to generate a synthetic ECG database consisting of 9271 signals. Regional grouping of antegrade APs revealed overarching morphological patterns originating from diverse cardiac regions. We then applied variance-based sensitivity analysis relying on polynomial chaos expansion on the ECG database to mathematically quantify how variation in AP location and timing relates to morphological variation in the 12 lead ECG. We utilized our mechanistic virtual model to showcase limitations of AP localization using standard ECG-based algorithms and provide mechanistic explanations through exemplary simulations. Our findings highlight the potential of virtual models of cardiac electrophysiology not only to deepen our understanding of the underlying mechanisms of Wolff-Parkinson-White syndrome but also to potentially enhance the diagnostic accuracy of ECG-based algorithms and facilitate personalized treatment planning.

Ising-like Critical Behavior of Vortex Lattices in an Active Fluid.

Turbulent vortex structures emerging in bacterial active fluids can be organized into regular vortex lattices by weak geometrical constraints such as obstacles. Here we show, using a continuum-theoretical approach, that the formation and destruction of these patterns exhibit features of a continuous second-order equilibrium phase transition, including long-range correlations, divergent susceptibility, and critical slowing down. The emerging vorticity field can be mapped onto a two-dimensional (2D) Ising model with antiferromagnetic nearest-neighbor interactions by coarse graining. The resulting effective temperature is found to be proportional to the strength of the nonlinear advection in the continuum model.

Turbulence-induced clustering in compressible active fluids.

We study a novel phase of active polar fluids, which is characterized by the continuous creation and destruction of dense clusters due to self-sustained turbulence. This state arises due to the interplay between self-advection of the aligned swimmers and their defect topology. The typical cluster size is determined by the characteristic vortex size. Our results are obtained by investigating a continuum model of compressible polar active fluids, which incorporates typical experimental observations in bacterial suspensions, in particular a non-monotone dependence of speed on density.

Extinction spectra of suspensions of microspheres: determination of the spectral refractive index and particle size distribution with nanometer accuracy.

A method is presented to infer simultaneously the wavelength-dependent real refractive index (RI) of the material of microspheres and their size distribution from extinction measurements of particle suspensions. To derive the averaged spectral optical extinction cross section of the microspheres from such ensemble measurements, we determined the particle concentration by flow cytometry to an accuracy of typically 2% and adjusted the particle concentration to ensure that perturbations due to multiple scattering are negligible. For analysis of the extinction spectra, we employ Mie theory, a series-expansion representation of the refractive index and nonlinear numerical optimization. In contrast to other approaches, our method offers the advantage to simultaneously determine size, size distribution, and spectral refractive index of ensembles of microparticles including uncertainty estimation.

Local control of globally competing patterns in coupled Swift-Hohenberg equations.

We present analytical and numerical investigations of two anti-symmetrically coupled 1D Swift-Hohenberg equations (SHEs) with cubic nonlinearities. The SHE provides a generic formulation for pattern formation at a characteristic length scale. A linear stability analysis of the homogeneous state reveals a wave instability in addition to the usual Turing instability of uncoupled SHEs. We performed weakly nonlinear analysis in the vicinity of the codimension-two point of the Turing-wave instability, resulting in a set of coupled amplitude equations for the Turing pattern as well as left- and right-traveling waves. In particular, these complex Ginzburg-Landau-type equations predict two major things: there exists a parameter regime where multiple different patterns are stable with respect to each other and that the amplitudes of different patterns interact by local mutual suppression. In consequence, different patterns can coexist in distinct spatial regions, separated by localized interfaces. We identified specific mechanisms for controlling the position of these interfaces, which distinguish what kinds of patterns the interface connects and thus allow for global pattern selection. Extensive simulations of the original SHEs confirm our results.

Control of electrical turbulence by periodic excitation of cardiac tissue.

Electrical turbulence in cardiac tissue is associated with arrhythmias such as life-threatening ventricular fibrillation. Recent experimental studies have shown that a sequence of low-energy electrical far-field pulses is able to terminate fibrillation more gently than a single high-energy pulse which causes severe side effects. During this low-energy antifibrillation pacing (LEAP), only tissue near sufficiently large conduction heterogeneities, such as large coronary arteries, is activated. In order to optimize LEAP, we performed extensive simulations of cardiac tissue perforated by blood vessels, employing two alternative cellular models that exhibit electrical turbulence at a similar length scale. Moreover, the scale of blood vessels in our two-dimensional simulations was chosen such that the threshold for single pulse defibrillation matches experimental values. For each of the 100 initial conditions, we tested different electrical field strengths, pulse shapes, numbers of pulses, and periods between the pulses. LEAP is successful for both models, albeit with substantial differences. One model exhibits a spectrum of chaotic activity featuring a narrow peak around a dominant frequency. In this case, the optimal period between low-energy pulses matches this frequency and LEAP greatly reduces the required energy for successful defibrillation. For pulses with larger energies, the system is perturbed such that underdrive pacing becomes advantageous. The spectrum of the second model features a broader peak, resulting in a less pronounced optimal pacing period and a decreased energy reduction. In both cases, pacing with five or six pulses which are separated by the dominant period maximizes the energy reduction.

Nonlinear physics of electrical wave propagation in the heart: a review.

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.

Determining the refractive index of human hemoglobin solutions by Kramers-Kronig relations with an improved absorption model.

The real part of the refractive index of aqueous solutions of human hemoglobin is computed from their absorption spectra in the wavelength range 250-1100 nm using the Kramers-Kronig (KK) relations, and the corresponding uncertainty analysis is provided. The strong ultraviolet (UV) and infrared absorbance of the water outside this spectral range were taken into account in a previous study employing KK relations. We improve these results by including the concentration dependence of the water absorbance as well as by modeling the deep UV absorbance of hemoglobin's peptide backbone. The two free parameters of the model for the deep UV absorbance are fixed by a global fit.

Vortex arrays and mesoscale turbulence of self-propelled particles.

Inspired by the Turing mechanism for pattern formation, we propose a simple self-propelled particle model with short-range alignment and antialignment at larger distances. It is able to produce orientationally ordered states, periodic vortex patterns, and mesoscale turbulence, which resembles observations in dense suspensions of swimming bacteria. The model allows a systematic derivation and analysis of a kinetic theory as well as hydrodynamic equations for density and momentum fields. A phase diagram with regions of pattern formation as well as orientational order is obtained from a linear stability analysis of these continuum equations. Microscopic Langevin simulations of self-propelled particles are in agreement with these findings.

Hydrodynamic synchronization of elastic cilia: How surface effects determine the characteristics of metachronal waves.

Cilia are hairlike microactuators whose cyclic motion is specialized to propel extracellular fluids at low Reynolds numbers. Clusters of these organelles can form synchronized beating patterns, called metachronal waves, which presumably arise from hydrodynamic interactions. We model hydrodynamically interacting cilia by microspheres elastically bound to circular orbits, whose inclinations with respect to a no-slip wall model the ciliary power and recovery stroke, resulting in an anisotropy of the viscous flow. We derive a coupled phase-oscillator description by reducing the microsphere dynamics to the slow timescale of synchronization and determine analytical metachronal wave solutions and their stability in a periodic chain setting. In this framework, a simple intuition for the hydrodynamic coupling between phase oscillators is established by relating the geometry of flow near the surface of a cell or tissue to the directionality of the hydrodynamic coupling functions. This intuition naturally explains the properties of the linear stability of metachronal waves. The flow near the surface stabilizes metachronal waves with long wavelengths propagating in the direction of the power stroke and, moreover, metachronal waves with short wavelengths propagating perpendicularly to the power stroke. Performing simulations of phase-oscillator chains with periodic boundary conditions, we indeed find that both wave types emerge with a variety of linearly stable wave numbers. In open chains of phase oscillators, the dynamics of metachronal waves is fundamentally different. Here the elasticity of the model cilia controls the wave direction and selects a particular wave number: At large elasticity, waves traveling in the direction of the power stroke are stable, whereas at smaller elasticity waves in the opposite direction are stable. For intermediate elasticity both wave directions coexist. In this regime, waves propagating towards both ends of the chain form, but only one wave direction prevails, depending on the elasticity and initial conditions.

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.

Intracellular mechanochemical waves in an active poroelastic model.

Many processes in living cells are controlled by biochemical substances regulating active stresses. The cytoplasm is an active material with both viscoelastic and liquid properties. We incorporate the active stress into a two-phase model of the cytoplasm which accounts for the spatiotemporal dynamics of the cytoskeleton and the cytosol. The cytoskeleton is described as a solid matrix that together with the cytosol as an interstitial fluid constitutes a poroelastic material. We find different forms of mechanochemical waves including traveling, standing, and rotating waves by employing linear stability analysis and numerical simulations in one and two spatial dimensions.

Twists of opposite handedness on a scroll wave.

The dynamic interaction of scroll waves in the Belousov-Zhabotinsky reaction with a vertically orientated gradient of excitability is studied by optical tomography. This study focuses on scroll waves, whose filaments were oriented almost perpendicular to the gradient. Whereas scroll waves with filaments exactly perpendicular to the gradient remain unaffected, filaments with a component parallel to the gradient develop a twist. Scroll waves with U-shaped filaments exhibit twists starting from both of its ends, resulting in scroll waves whose filaments display a pair of twists of opposite handedness. These twists are separated by a nodal plane where the filament remains straight and untwisted. The experimental findings were reproduced by numerical simulations using the Oregonator model and a linear gradient of excitability almost perpendicular to the orientation of the filament.

Fluid dynamics of bacterial turbulence.

Self-sustained turbulent structures have been observed in a wide range of living fluids, yet no quantitative theory exists to explain their properties. We report experiments on active turbulence in highly concentrated 3D suspensions of Bacillus subtilis and compare them with a minimal fourth-order vector-field theory for incompressible bacterial dynamics. Velocimetry of bacteria and surrounding fluid, determined by imaging cells and tracking colloidal tracers, yields consistent results for velocity statistics and correlations over 2 orders of magnitude in kinetic energy, revealing a decrease of fluid memory with increasing swimming activity and linear scaling between kinetic energy and enstrophy. The best-fit model allows for quantitative agreement with experimental data.

Negative tension of scroll wave filaments and turbulence in three-dimensional excitable media and application in cardiac dynamics.

Scroll waves are vortices that occur in three-dimensional excitable media. Scroll waves have been observed in a variety of systems including cardiac tissue, where they are associated with cardiac arrhythmias. The disorganization of scroll waves into chaotic behavior is thought to be the mechanism of ventricular fibrillation, whose lethality is widely known. One possible mechanism for this process of scroll wave instability is negative filament tension. It was discovered in 1987 in a simple two variables model of an excitable medium. Since that time, negative filament tension of scroll waves and the resulting complex, often turbulent dynamics was studied in many generic models of excitable media as well as in physiologically realistic models of cardiac tissue. In this article, we review the work in this area from the first simulations in FitzHugh-Nagumo type models to recent studies involving detailed ionic models of cardiac tissue. We discuss the relation of negative filament tension and tissue excitability and the effects of discreteness in the tissue on the filament tension. Finally, we consider the application of the negative tension mechanism to computational cardiology, where it may be regarded as a fundamental mechanism that explains differences in the onset of arrhythmias in thin and thick tissue.

MedalCare-XL: 16,900 healthy and pathological synthetic 12 lead ECGs from electrophysiological simulations.

Mechanistic cardiac electrophysiology models allow for personalized simulations of the electrical activity in the heart and the ensuing electrocardiogram (ECG) on the body surface. As such, synthetic signals possess known ground truth labels of the underlying disease and can be employed for validation of machine learning ECG analysis tools in addition to clinical signals. Recently, synthetic ECGs were used to enrich sparse clinical data or even replace them completely during training leading to improved performance on real-world clinical test data. We thus generated a novel synthetic database comprising a total of 16,900 12 lead ECGs based on electrophysiological simulations equally distributed into healthy control and 7 pathology classes. The pathological case of myocardial infraction had 6 sub-classes. A comparison of extracted features between the virtual cohort and a publicly available clinical ECG database demonstrated that the synthetic signals represent clinical ECGs for healthy and pathological subpopulations with high fidelity. The ECG database is split into training, validation, and test folds for development and objective assessment of novel machine learning algorithms.

PTB-XL+, a comprehensive electrocardiographic feature dataset.

Machine learning (ML) methods for the analysis of electrocardiography (ECG) data are gaining importance, substantially supported by the release of large public datasets. However, these current datasets miss important derived descriptors such as ECG features that have been devised in the past hundred years and still form the basis of most automatic ECG analysis algorithms and are critical for cardiologists' decision processes. ECG features are available from sophisticated commercial software but are not accessible to the general public. To alleviate this issue, we add ECG features from two leading commercial algorithms and an open-source implementation supplemented by a set of automatic diagnostic statements from a commercial ECG analysis software in preprocessed format. This allows the comparison of ML models trained on clinically versus automatically generated label sets. We provide an extensive technical validation of features and diagnostic statements for ML applications. We believe this release crucially enhances the usability of the PTB-XL dataset as a reference dataset for ML methods in the context of ECG data.

A maximum likelihood approach to the inverse problem of scatterometry.

Scatterometry is frequently used as a non-imaging indirect optical method to reconstruct the critical dimensions (CD) of periodic nanostructures. A particular promising direction is EUV scatterometry with wavelengths in the range of 13 - 14 nm. The conventional approach to determine CDs is the minimization of a least squares function (LSQ). In this paper, we introduce an alternative method based on the maximum likelihood estimation (MLE) that determines the statistical error model parameters directly from measurement data. By using simulation data, we show that the MLE method is able to correct the systematic errors present in LSQ results and improves the accuracy of scatterometry. In a second step, the MLE approach is applied to measurement data from both extreme ultraviolet (EUV) and deep ultraviolet (DUV) scatterometry. Using MLE removes the systematic disagreement of EUV with other methods such as scanning electron microscopy and gives consistent results for DUV.

Improved grating reconstruction by determination of line roughness in extreme ultraviolet scatterometry.

The accurate determination of critical dimensions and roughness is necessary to ensure the quality of photoresist masks that are crucial for the operational reliability of electronic components. Scatterometry provides a fast indirect optical nondestructive method for the determination of profile parameters that are obtained from scattered light intensities using inverse methods. We illustrate the effect of line roughness on the reconstruction of grating parameters employing a maximum likelihood scheme. Neglecting line roughness introduces a strong bias in the parameter estimations. Therefore, such roughness has to be included in the mathematical model of the measurement in order to obtain accurate reconstruction results. In addition, the method allows to determine line roughness from scatterometry. The approach is demonstrated for simulated scattering intensities as well as for experimental data of extreme ultraviolet light scatterometry measurements. The results obtained from the experimental data are in agreement with independent atomic force microscopy measurements.

Collective motion and nonequilibrium cluster formation in colonies of gliding bacteria.

We characterize cell motion in experiments and show that the transition to collective motion in colonies of gliding bacterial cells confined to a monolayer appears through the organization of cells into larger moving clusters. Collective motion by nonequilibrium cluster formation is detected for a critical cell packing fraction around 17%. This transition is characterized by a scale-free power-law cluster-size distribution, with an exponent 0.88±0.07, and the appearance of giant number fluctuations. Our findings are in quantitative agreement with simulations of self-propelled rods. This suggests that the interplay of self-propulsion and the rod shape of bacteria is sufficient to induce collective motion.