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Current exercise recommendations make it difficult for long QT syndrome (LQTS) patients to adopt a physically active and/or athletic lifestyle. The purpose of this review is to summarize the current evidence, identify knowledge gaps, and discuss research perspectives in the field of exercise and LQTS. The first aim is to document the influence of exercise training, exercise stress, and postural change interventions on ventricular repolarization in LQTS patients, while the second aim is to describe electrophysiological measurements used to study the above. Studies examining the effects of exercise on congenital or acquired LQTS in human subjects of all ages were included. Systematic searches were performed on 1 October 2021, through PubMed (NLM), Ovid Medline, Ovid All EBM Reviews, Ovid Embase, and ISI Web of Science, and limited to articles written in English or French. A total of 1986 LQTS patients and 2560 controls were included in the 49 studies. Studies were mainly case–control studies (n = 41) and examined exercise stress and/or postural change interventions (n = 48). One study used a 3-month exercise training program. Results suggest that LQTS patients have subtype-specific repolarization responses to sympathetic stress. Measurement methods and quality were found to be very heterogeneous, which makes inter-study comparisons difficult. In the absence of randomized controlled trials, the current recommendations may have long-term risks for LQTS patients who are discouraged from performing physical activity, rendering its associated health benefits out of range. Future research should focus on discovering the most appropriate levels of exercise training that promote ventricular repolarization normalization in LQTS.

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.

Heat therapy has been shown to improve markers of cardiometabolic health in preclinical and clinical studies. However, the effects of heat therapy in individuals with type 2 diabetes mellitus (T2DM) remain understudied. We examined the acute effect of hot water immersion on glucose tolerance, flow-mediated dilation, reactive hyperemia, inflammatory markers, and heat shock proteins in adults with T2DM. Hot water immersion did not acutely improve the markers studied.

The aim of this study was to investigate the effects of exercise training on ventricular repolarization dynamicity and heart rate variability in chronic heart failure patients. A total of 22 chronic heart failure patients with reduced ejection fraction in sinus rhythm were included in the study. The patients were in NYHA classes II–III with an ejection fraction of 29.7 ± 7.7%. Before and after 4 weeks of aerobic exercise training, all patients performed a cardiopulmonary exercise test, a standard twelve-lead electrocardiogram and a 24 h Holter recording from which heart rate variability and ventricular repolarization dynamicity were assessed. We observed a significant decrease of QTpeak (p p Four weeks of exercise training induced significant changes in ventricular repolarization dynamicity in chronic heart failure patients. In addition, short-term exercise training was enough to improve patients’ heart rate variability.

Aims The aim of this study is to design a computer model of the left atrium for investigating fibre-orientation-dependent microstructure such as stringy fibrosis. Methods and results We developed an approach for automatic construction of bilayer interconnected cable models from left atrial geometry and epi- and endocardial fibre orientation. The model consisted of two layers (epi- and endocardium) of longitudinal and transverse cables intertwined-like fabric threads, with a spatial discretization of 100 µm. Model validation was performed by comparison with cubic volumetric models in normal conditions. Then, diffuse (n = 2904), stringy (n = 3600), and mixed fibrosis patterns (n = 6840) were randomly generated by uncoupling longitudinal and transverse connections in the interconnected cable model. Fibrosis density was varied from 0% to 40% and mean stringy obstacle length from 0.1 to 2 mm. Total activation time, apparent anisotropy ratio, and local activation time jitter were computed during normal rhythm in each pattern. Non-linear regression formulas were identified for expressing measured propagation parameters as a function of fibrosis density and obstacle length (stringy and mixed patterns). Longer obstacles (even below tissue space constant) were independently associated with prolonged activation times, increased anisotropy, and local fluctuations in activation times. This effect was increased by endo-epicardial dissociation and mitigated when fibrosis was limited to the epicardium. Conclusion Interconnected cable models enable the study of microstructure in organ-size models despite limitations in the description of transmural structures.

The dynamics of cardiac fibrillation can be described by the number, the trajectory, the stability, and the lifespan of phase singularities (PSs). Accurate PS tracking is straightforward in simple uniform tissues but becomes more challenging as fibrosis, structural heterogeneity, and strong anisotropy are combined. In this paper, we derive a mathematical formulation for PS tracking in two-dimensional reaction–diffusion models. The method simultaneously tracks wavefronts and PS based on activation maps at full spatiotemporal resolution. PS tracking is formulated as a linear assignment problem solved by the Hungarian algorithm. The cost matrix incorporates information about distances between PS, chirality, and wavefronts. A graph of PS trajectories is generated to represent the creations and annihilations of PS pairs. Structure-preserving graph transformations are applied to provide a simplified description at longer observation time scales. The approach is validated in 180 simulations of fibrillation in four different types of substrates featuring, respectively, wavebreaks, ionic heterogeneities, fibrosis, and breakthrough patterns. The time step of PS tracking is studied in the range from 0.1 to 10 ms. The results show the benefits of improving time resolution from 1 to 0.1 ms. The tracking error rate decreases by an order of magnitude because the occurrence of simultaneous events becomes less likely. As observed on PS survival curves, the graph-based analysis facilitates the identification of macroscopically stable rotors despite wavefront fragmentation by fibrosis.

D-amphetamine maintenance therapy shows promise as a treatment for people with cocaine addiction. Preclinical studies using Long Access (LgA) cocaine self-administration procedures suggest D-amphetamine may act by preventing tolerance to cocaine’s effects at the dopamine transporter (DAT). However, Intermittent Access (IntA) cocaine self-administration better reflects human patterns of use, is especially effective in promoting addiction-relevant behaviors, and instead of tolerance, produces psychomotor, incentive, and neural sensitization. We asked, therefore, how D-amphetamine maintenance during IntA influences cocaine use and cocaine’s potency at the DAT. Male rats self-administered cocaine intermittently (5 min ON, 25 min OFF x10; 5-h/session) for 14 sessions, with or without concomitant D-amphetamine maintenance therapy during these 14 sessions (5 mg/kg/day via s.c. osmotic minipump). We then assessed responding for cocaine under a progressive ratio schedule, responding under extinction and cocaine-primed reinstatement of drug seeking. We also assessed the ability of cocaine to inhibit dopamine uptake in the nucleus accumbens core using fast scan cyclic voltammetry ex vivo. IntA cocaine self-administration produced psychomotor (locomotor) sensitization, strong motivation to take and seek cocaine, and it increased cocaine’s potency at the DAT. D-amphetamine co-administration suppressed the psychomotor sensitization produced by IntA cocaine experience. After cessation of D-amphetamine treatment, the motivation to take and seek cocaine was also reduced, and sensitization of cocaine’s actions at the DAT was reversed. Thus, treatment with D-amphetamine might reduce cocaine use by preventing sensitization-related changes in cocaine potency at the DAT, consistent with an incentive-sensitization view of addiction.

BackgroundD-amphetamine maintenance therapy shows promise as a treatment for people with cocaine addiction. Preclinical studies using Long Access (LgA) cocaine self-administration procedures suggest D-amphetamine may act by preventing tolerance to cocaine’s effects at the dopamine transporter (DAT). However, Intermittent Access (IntA) cocaine self-administration better reflects human patterns of use, is especially effective in promoting addiction-relevant behaviors, and instead of tolerance, produces psychomotor, incentive, and neural sensitization. We asked, therefore, how D-amphetamine maintenance during IntA influences cocaine use and cocaine’s potency at the DAT.MethodsMale rats self-administered cocaine intermittently (5 minutes ON, 25 minutes OFF x 10) for 14 sessions, with or without concomitant D-amphetamine (5 mg/kg/day via s.c. osmotic minipump). In Experiment 1, psychomotor sensitization, responding for cocaine under a progressive ratio schedule, responding under extinction and cocaine-primed relapse were assessed. In Experiment 2, rats self-administered cocaine or saline intermittently, with or without D-amphetamine, and the ability of cocaine to inhibit dopamine uptake in the nucleus accumbens core was assessed using fast scan cyclic voltammetry ex vivo.ResultsIntA cocaine self-administration produced psychomotor sensitization, strong motivation to take and seek cocaine, and it increased cocaine’s potency at the DAT. The co-administration of D-amphetamine suppressed both the psychomotor sensitization and high motivation for cocaine produced by IntA experience, and also reversed sensitization of cocaine’s actions at the DAT, leaving baseline DAT function unchanged.ConclusionsTreatment with D-amphetamine might reduce cocaine use by preventing sensitization-related changes in cocaine potency at the DAT, consistent with an incentive-sensitization view of addiction.

The arrhythmogenic role of discrete cardiac propagation may be assessed by comparing discrete (fine-grained) and equivalent continuous (coarse-grained) models. We aim to develop an optimization algorithm for estimating the smooth conductivity field that best reproduces the diffusion properties of a given discrete model. Our algorithm iteratively adjusts local conductivity of the coarse-grained continuous model by simulating passive diffusion from white noise initial conditions during 3-10 ms and computing the root mean square error with respect to the discrete model. The coarse-grained conductivity field was interpolated from up to 300 evenly spaced control points. We derived an approximate formula for the gradient of the cost function that required (in two dimensions) only two additional simulations per iteration regardless of the number of estimated parameters. Conjugate gradient solver facilitated simultaneous optimization of multiple conductivity parameters. The method was tested in rectangular anisotropic tissues with uniform and nonuniform conductivity (slow regions with sinusoidal profile) and random diffuse fibrosis, as well as in a monolayer interconnected cable model of the left atrium with spatially-varying fibrosis density. Comparison of activation maps served as validation. The results showed that after convergence the errors in activation time were1 ms for rectangular geometries and 1-3 ms in the atrial model. Our approach based on the comparison of passive properties (10 ms simulation) avoids performing active propagation simulations (100 ms) at each iteration while reproducing activation maps, with possible applications to investigating the impact of microstructure on arrhythmias.

Objective: In the electrocardiogram, adaptation of the QT interval to variations in heart rate is not instantaneous. Quantification of this hysteresis phenomenon relies on mathematical models describing the relation between the RR and QT time series. These models reproduce hysteresis through an effective RR interval computed as a linear combination of the history of past RR intervals. This filter depends on a time constant parameter that may be used as a biomarker. Approach: The most common hysteresis model is based on an autoregressive filter with an impulse response that decreases exponentially with the beat number (lag-based model). Recognizing that the QT time series is unevenly spaced, we propose two exponential moving average filters (time-based models) to define the effective RR interval: one with an impulse response that decreases exponentially with time in seconds, and one with a step response that relaxes exponentially with time in seconds. These two filters are neither linear nor time-invariant. Recurrence formulas are derived to enable efficient implementation. Main results: Application to clinical signals recorded during tilt table test, exercise and 24 h Holter demonstrates that the three models perform similarly in terms of goodness-of-fit. When comparing the hysteresis time constant in two conditions with different heart rates, however, the time-based models are shown to reduce the bias on the hysteresis time constant caused by heart rate acceleration and deceleration. Significance: Time-based models should be considered when intergroup differences in both heart rate and QT hysteresis are expected.

The extracellular domain of the heart is anisotropic, which affects volume conduction and therefore body surface potentials. This paper tests the hypothesis that when wall thickness is sufficiently small (such as in the atria), the effect of extracellular anisotropy can be estimated by modifying local dipole current sources. A formula based on the Gabor-Nelson equivalent dipole and on the reciprocity theorem is derived to compute a linear transformation of the dipole sources that approximates in an isotropic volume conductor the far-field of the actual sources in an anisotropic volume conductor. It involves solving three Poisson equation (once for all). The results obtained in an atrial model embedded in a boundary-element torso model suggest that when wall thickness is3 mm, simulated P waves are weakly altered by extracellular anisotropy during sinus rhythm: an anisotropy ratio of 4:1 typically reduced the longitudinal component of the dipole sources by3%, increased the transverse component by5%, and increased the transmural component by ≈ 25% (which may be relevant in case of epicardial-endocardial dissociation). Due to uncertainty on experimental conductivity values, it is proposed that atrial extracellular anisotropy may be neglected when computing P waves.

Correction of the QT interval in the ECG for changes in heart rate (RR interval) is needed to compare groups of patients and assess the risk of sudden cardiac death. The QTc represents the QT interval at 60 bpm, although most patients typically have a faster heart rate, thus requiring extrapolation of the QT-RR relationship. Objective This paper investigates the ability of QT-RR models with increasing number of parameters to fit beat-to-beat variations in the QT interval and provide a reliable estimate of the QTc. Approach One-, two- and three-parameter functions generalising the Bazett and Fridericia formulas were used in combination with hysteresis reduction (memory) obtained by time-averaging the history of RR intervals with exponentially-decaying weights. In normal men and women datasets of Holter recordings in normal subjects (24 h monitoring), two measures were computed for each model: the root mean square error (RMSE) of fitting and the difference between the estimated QTc and a reference QTc obtained by collecting data points around RR = 1000 ms. Main results The two- and three-parameter functions all gave similar low RMSE with uncorrelated residues. An optimal memory parameter was found that still minimized the RMSE and could be used for all functions and subjects. This reduction in RMSE resulted from changes in the parameters linked to the increased steepness of the QT-RR relation after hysteresis reduction. At optimal memory, the two and three-parameter models provided poorer prediction of the QTc as compared to the Fridericia's model in subjects with fast heart rates, since accurate representation of the steeper QT-RR relation worsened the extrapolation that was then needed to determine the QTc. Significance As a result, among all models investigated, the Fridericia formulation offered the best trade-off for QTc prediction robust to memory and fast heart rates.

The autonomic nervous system modulates atrial activity, notably through acetylcholine (ACh)release. This time-dependent action may alter the dynamics of atrial arrhythmia, and in particular its wavelength. Wavelength is a critical factor that determines the vulnerability to reentry. It represents the spatial extent of refractory periods and may be estimated as the product of action potential duration and conduction velocity. When electrophysiological properties vary in space and/or time, and when conduction is anisotropic, that estimate may be inaccurate. We assessed an instantaneous geometric measure of wavelength applicable to monitoring the effect of externally-driven variations in ACh concentration at a shorter time scale than action potential duration. The method was applied to quantify the hysteresis in wavelength caused by release and degradation of ACh.

This paper reviews the simulations of catheter ablation in computer models of the atria, from the first attempts to the most recent anatomical models. It describes how postulated substrates of atrial fibrillation can be incorporated into mathematical models, how modelling studies can be designed to test ablation strategies, what their current trade-offs and limitations are, and what clinically relevant lessons can be learnt from these simulations. Drawing a parallel between clinical and modelling studies, six ablation targets are considered: pulmonary vein isolation, linear ablation, ectopic foci, complex fractionated atrial electrogram, rotors and ganglionated plexi. The examples presented for each ablation target illustrate a major advantage of computer models, the ability to identify why a therapy is successful or not in a given atrial fibrillation substrate. The integration of pathophysiological data to create detailed models of arrhythmogenic substrates is expected to solidify the understanding of ablation mechanisms and to provide theoretical arguments supporting substrate-specific ablation strategies.

Electrotonic interactions between cardiac cells modulate the dispersion of action potential duration (APD). This paper provides a complete mathematical analysis of a simple model of exponential-shaped repolarization in a network of electrotonically-coupled cells with different intrinsic APDs. The forward problem consists in computing the APD map in the coupled system from the intrinsic APD map. A closed-form algebraic formula is derived for the forward problem. The inverse problem, inferring the intrinsic APDs from an APD map, is proved to have a unique solution (if any). Perturbation analysis leads to an efficient and accurate Newton-based solver for this specific inverse problem. Finally, an analytical expression is obtained for the convolution filter that solves the forward problem in one dimension. This mathematical framework forms a solid theoretical basis for future development and validation of repolarization parameter estimation techniques in detailed models of cardiac tissue.

Aims Evidences of asynchrony between epicardial and endocardial activation in the atrial wall have been reported. We used a computer model of the atria and torso to investigate the consequences of such activation delay on P wave morphology, while controlling for P wave duration. Methods and results We created 390 models of the atria based on the same geometry. These models differed by atrial wall thickness (from 2 to 3 mm), transmural coupling, and tissue conductivity in the endocardial and epicardial layers. Among them, 18 were in baseline, 186 had slower conduction in the epicardium layer and 186 in the endocardial layer. Conduction properties were adjusted in such a way that total activation time was the same in all models. P waves on a 16-lead system were simulated during sinus rhythm. Activation maps were similar in all cases. Endo-epicardial delay varied between -5.5 and 5.5 ms vs. 0 ± 0.5 ms in baseline. All P waves had the same duration but variability in their morphology was observed. With slower epicardial conduction, P wave amplitude was reduced by an average of 20% on leads V3-V5 and P wave area decreased by 50% on leads V1-V2 and by 40% on lead V3. Reversed, lower magnitude effects were observed with slower endocardial conduction. Conclusion An endo-epicardial delay of a few milliseconds is sufficient to significantly alter P wave morphology, even if the activation map remains the same.

Due to their transient nature, spontaneous terminations of atrial fibrillation (AF) are difficult to investigate. Apparently, confounding experimental findings about the time scale of this phenomenon have been reported, with values ranging from 1 s to 1 min. We propose a biophysical modeling approach to study the mechanisms of spontaneous termination in two models of AF with different levels of dynamical complexity. 8 s preceding spontaneous terminations were studied and the evolution of cycle length and wavefront propagation were documented to assess the time scale and anatomical location of the phenomenon. Results suggest that termination mechanisms are dependent on the underlying complexity of AF. During simulated AF of low complexity, the total process of spontaneous termination lasted 3,200 ms and was triggered in the left atrium 800 ms earlier than in the right atrium. The last fibrillatory activity was observed more often in the right atrium. These asymmetric termination mechanisms in both time and space were not observed during spontaneous terminations of complex AF simulations, which showed less predictable termination patterns lasting only 1,600 ms. This study contributes to the interpretation of previous clinical observations, and illustrates how computer modeling provides a complementary approach to study the mechanisms of cardiac arrhythmias.

The complexity of cardiac fibrillation dynamics can be assessed by analyzing the distribution of phase singularities (PSs) observed using mapping systems. Interelectrode distance, however, limits the accuracy of PS detection. To investigate in a theoretical framework the PS false negative and false positive rates in relation to the characteristics of the mapping system and fibrillation dynamics, we propose a statistical model of phase maps with controllable number and locations of PSs. In this model, phase maps are generated from randomly distributed PSs with physiologically-plausible directions of rotation. Noise and distortion of the phase are added. PSs are detected using topological charge contour integrals on regular grids of varying resolutions. Over 100 × 106 realizations of the random field process are used to estimate average false negative and false positive rates using a Monte-Carlo approach. The false detection rates are shown to depend on the average distance between neighboring PSs expressed in units of interelectrode distance, following approximately a power law with exponents in the range of 1.14 to 2 for false negatives and around 2.8 for false positives. In the presence of noise or distortion of phase, false detection rates at high resolution tend to a non-zero noise-dependent lower bound. This model provides an easy-to-implement tool for benchmarking PS detection algorithms over a broad range of configurations with multiple PSs.

Aim The autonomic nervous system modulates atrial activity, notably through acetylcholine (ACh) release. This time-dependent action may alter the dynamics of atrial arrhythmia. Our aim is to investigate in a computer model the changes induced by ACh release and degradation on the dynamical regime of a reentry. Methods and results A functional reentry was simulated in a 10 × 5 cm2 two-dimensional tissue with canine atrial membrane kinetics including an ACh-dependent K+ current. The local ACh concentration was altered over time in a circular region following a predefined spatiotemporal profile (ACh release and degradation) characterized by its maximum ACh level, time constant of release/degradation, and diameter of the region. Phase singularities were tracked to monitor the complexity of the dynamics. Four scenarios were identified: (i) the original reentry remained stable; (ii) repolarization gradients induced by ACh release caused wavebreaks, resulting in a transient complex dynamics that spontaneously converted to a single stable reentry; (iii) the reentry self-terminated through wavebreaks and wavefront interactions; (4) wavebreaks led to a complex dynamics that converted to two or three reentries that remained stable after ACh degradation. Higher ACh level, short ACh release time constant, larger heterogeneous region, and short distance between the heterogeneous region and the spiral tip were associated with higher occurrence of ACh-induced wavebreaks. Conclusion Variation of ACh concentration over time may modulate the complexity of atrial arrhythmias.

Experimental evidences suggest the occurrence of epicardial-endocardial activation delays in structurally remodeled atrial tissue. Our aim was to investigate the consequences of this delay on electrogram morphology. We created a 50×50×2 mm monodomain model of atrial tissue composed of an epicardial and an endocardial layer (1 mm thickness each) with different conductivities. Plane waves with epicardial-endocardial delays were simulated. Unipolar electrograms were computed. Simulated electrogram asymmetry was compared to a theoretical formula that expresses asymmetry in terms of the angle between the equivalent dipole and the tissue surface. The results showed that electrogram asymmetry is strongly related to the sine of the angle of the equivalent dipole. Further analysis suggests that epicardial-endocardial delay and transmural coupling are important determinants of asymmetry. These findings contribute to the interpretation of unipolar electrogram morphology.