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In native conditions, cardiac cells must continuously comply with diverse stimuli necessitating a perpetual adaptation. Polydimethylsiloxane (PDMS) is commonly used in cell culture to study cellular response to changes in the mechanical environment. The aim of this study was to evaluate the impact of using PDMS substrates on the properties of spontaneous activity of cardiomyocyte monolayer cultures. We compared PDMS to the gold standard normally used in culture: a glass substrate. Although mean frequency of spontaneous activity remained unaltered, incidence of reentrant activity was significantly higher in samples cultured on glass compared to PDMS substrates. Higher spatial and temporal instability of the spontaneous rate activation was found when cardiomyocytes were cultured on PDMS, and correlated with decreased connexin-43 and increased CaV3.1 and HCN2 mRNA levels. Compared to cultures on glass, cultures on PDMS were associated with the strongest response to isoproterenol and acetylcholine. These results reveal the importance of carefully selecting the culture substrate for studies involving mechanical stimulation, especially for tissue engineering or pharmacological high-throughput screening of cardiac tissue analog.

The dynamics of reentry in a model of a two-dimensional annulus of homogeneous cardiac tissue, with a Beeler-Reuter type formulation of the membrane ionic currents, is examined. The bifurcation structure of the sustained propagated solutions is described as a function of Rin and Rout, the inner and outer radii of the annulus. The transition from periodic to quasiperiodic reentry occurs at a critical Rin, which first diminishes and then saturates as Rout is increased. The reduction of the critical Rin is a consequence of the increase of the wave-front curvature. There is a range of Rin below the critical radius in which two distinct quasiperiodic solutions coexist. Each of these solutions disappears at its own specific value of Rin, and their annihilation is preceded by a new type of bifurcation leading to a regime of propagation with transient successive detachments of the wave front from the inner border of the annulus.

Spiral wave formation and disorganized activity in excitable media require the existence of broken waves and are related to partial wave block. The determinants of wave block in excitable systems are incompletely understood, especially for cardiac excitable tissue. Previous work in one-dimensional cardiac models has suggested that wave break of a premature excitation (PE) requires critical timing and that the conditions for broken waves are improbable. We analyzed the mechanism of unidirectional wave block that occurs when two consecutive PEs interact with a normal plane wave in a generic one-dimensional spatial excitable medium. A nondimensional coupled-map model built from mesoscopic characteristics of the substrate (the velocity and action potential duration restitution functions) shows that block can occur over a large interval of timing between the two PEs and leads to wave break in two-dimensional media. This mechanism may be an important determinant of spiral wave formation by the response to premature excitations.

The “leading circle model” was the first detailed attempt at understanding the mechanisms of functional reentry, and remains a widely-used notion in cardiac electrophysiology. The “spiral wave” concept was developed more recently as a result of modern theoretical analysis and is the basis for consideration of reentry mechanisms in present biophysical theory. The goal of this paper is to present these models in a way that is comprehensible to both the biophysical and electrophysiology communities, with the idea of helping clinical and experimental electrophysiologists to understand better the spiral wave concept and of helping biophysicists to understand why the leading circle concept is so attractive and widely used by electrophysiologists. To this end, the main properties of the leading circle and spiral wave models of reentry are presented. Their basic assumptions and determinants are discussed and the predictions of the two concepts with respect to pharmacological responses of arrhythmias are reviewed. A major difference between them lies in the predicted responses to Na+-channel blockade, for which the spiral wave paradigm appears more closely to correspond to the results of clinical and experimental observations. The basis of this difference is explored in the context of the fundamental properties of the models.

We present the bifurcation analysis of a revised version of the integral-delay model [Courtemanche et al., Siam J. Appl. Math. 56, 119 (1996)] of reentry in a one-dimensional ring that includes a spatial coupling in the calculation of the action potential duration. This coupling is meant to reproduce the modulation of repolarization by the diffusive current flowing through the intercellular resistance. We show that coupling modifies the criterion for the stability of the period-1 solution, which is no longer uniquely related to the action potential restitution curve, but depends also on the degree of coupling between cells and on the dispersion relation of the velocity. Coupling also changes the scenario from an infinite-dimension Hopf bifurcation to a finite sequence of Hopf bifurcations that take place at different ring lengths.

Resetting and annihilation of reentrant activity by a single stimulus pulse (S1) or a pair (S1-S2) of coupled pulses are studied in a model of one-dimensional loop of cardiac tissue using a Beeler-Reuter-type ionic model. Different modes of reentry termination are described. The classical mode of termination by unidirectional block, in which a stimulus produces only a retrograde front that collides with the activation front of the reentry, can be obtained for both S1 and S1-S2 applied over a small vulnerable window. We demonstrate that another scenario of termination-that we term collision block-can also be induced by the S1-S2 protocol. This scenario is obtained over a much wider range of S1-S2 coupling intervals than the one leading to a unidirectional block. In the collision block, S1 produces a retrograde front, colliding with the activation front of the pre-existing reentry, and an antegrade front propagating in the same direction as the initial reentry. Then, S2 also produces an antegrade and a retrograde front. However, the propagation of these fronts in the spatial profile of repolarization left by S1 leads to a termination of the reentrant activity. More complex behaviors also occur in which the antegrade fronts produced by S1 and S2 both persist for several turns, displaying a growing alternation in action potential duration ("alternans amplification") that may lead to the termination of the reentrant activity. The hypothesis that both collision block and alternans amplification depend on the interaction between the action potential duration restitution curve and the recovery curve of conduction velocity is supported by the fact that the dynamical behaviors were reproduced using an integro-delay equation based on these two properties. We thus describe two new mechanisms (collision block and alternans amplification) whereby electrical stimulation can terminate reentrant activity. (c) 2002 American Institute of Physics.

Self-organization of pacemaker (PM) activity of interconnected elements is important to the general theory of reaction–diffusion systems as well as for applications such as PM activity in cardiac tissue to initiate beating of the heart. Monolayer cultures of neonatal rat ventricular myocytes (NRVMs) are often used as experimental models in studies on cardiac electrophysiology. These monolayers exhibit automaticity (spontaneous activation) of their electrical activity. At low plated density, cells usually show a heterogeneous population consisting of PM and quiescent excitable cells (QECs). It is therefore highly probable that monolayers of NRVMs consist of a heterogeneous network of the two cell types. However, the effects of density and spatial distribution of the PM cells on spontaneous activity of monolayers remain unknown. Thus, a simple stochastic pattern formation algorithm was implemented to distribute PM and QECs in a binary-like 2D network. A FitzHugh–Nagumo excitable medium was used to simulate electrical spontaneous and propagating activity. Simulations showed a clear nonlinear dependency of spontaneous activity (occurrence and amplitude of spontaneous period) on the spatial patterns of PM cells. In most simulations, the first initiation

Reentry is a major mechanism underlying the initiation and perpetuation of many cardiac arrhythmias [1][2][3][4][5]. Stimulated ventricular myocytes give action potential characterized by a fast upstroke, a long-lasting plateau, and a late repolarization phase. The plateau phase determines the action potential duration (APD) during which the system remains refractory, a property essential to the synchronization of the heart cycle. The APD varies much with prematurity and this change has been shown to be the main determinant of the dynamics in models of paced cells and cable, and during reentry in the one-dimensional loop. Curvature has also been shown to be an important factor for propagation in experimental and theoretical cardiac extended tissue. The objective of this paper is to combine both curvature and prematurity effects in a kinematical model of propagation in cardiac tissue. First, an approximation of the ionic model is used to obtain the effects of curvature and prematurity on the speed of propagation, the APD, and the absolute refractory period. Two versions of the ionic model are studied that differ in their rate of excitability recovery. The functions are used in a kinematical model describing the propagation of period-1 solutions around an annulus.

Cardiomyocytes are electrically-active heart cells whose electrical properties vary with the local electrical and mechanical environment. Variations in myocytes electrical properties are known to play a role on abnormal rhythms.The purpose of the project is to design a fluorescence-based photodetection system for measurement of transmembrane potential variations by combined electrical and mechanical stimulations in post-culture cardiomyocytes.The isolated cardiomyocytes are seeded on a 10mm x 10mm x 0.127mm silicon sheet held by a pair of pliers, coupled to a stretcher apparatus made of two linear guide systems and two computer controlled linear stepper motors. The cells are kept in bubbled Tyrode solution and are electrically stimulated during the 10 minutes staining by the voltage-sensitive dye di-8-Anepps (Invitrogen) at 5 μmol/L concentration. Field electrical stimulation is done by a pair of parallel carbon electrodes with grounded anode. The cathode voltage is supplied by a bipolar isolation amplifier circuit whose input is a set of pulses from the digital-to-analog converter of a National Instruments card (NI USB-6221). The light source is a green LED array (wavelength = 523nm, NTE Electronics Inc.), with intensity controlled by a Darlington array receiving TTL signals. The emitted fluorescence is filtered (λ > 610nm), converted to voltage with a fast photodiode (S1226-5BK, Hamamatsu), and amplified by an instrumentation amplifier (AD524ADZ, Analog Digital Inc). The voltage is then digitized with a National Instruments card, filtered and saved for post-experiment analysis.Each sub-system has been successfully validated. Testing the whole system with cardiac-derived HL1 cells allowed final improvement on the signal-to-noise ratio and optimization of excitation intensity. This ready to use bioinstrument will play a key role in further studies on cultured cardiomyocytes.

Background: Connexin alterations occur in various atrial fibrillation (AF) paradigms, but their functional significance remains unclear. No data are available regarding the effects of CHF on atrial connexin expression and phosphorylation. We therefore analyzed connexin changes and their contribution to the AF substrate during the development and reversal ofCHF. Methods and Results: Dogs were allocated to three groups: CHF induced by 2-week ventricular tachypacing (CHF, n=15); CHF dogs allowed to recover for 4 weeks after 2-week tachypacing (REC, n=15) and non-paced shams (CTL, n=11). Left ventricular end-diastolic pressure increased with CHF (14.5±1.0*** vs.3.7±0.7, ***P < 0.001 vs. CTL) and normalized upon CHF recovery (5.1±1.0^†††, ^††† P < 0.001 vs. CHF). Real-time PCR and Western-blot analyses revealed connexin43 (Cx43) and connexin40 (Cx40) mRNA and protein expression to be unchanged by CHF and REC. However, CHF caused Cx43 dephosphorylation(by ~73%***) and increased Cx40/Cx43 protein ratio (by ~35%***), with both alterations completely reversing in REC. Immunofluorescent confocal microscopy confirmed connexin protein trends, with a reduction in phosphorylated Cx43 (by ~68%*** in CHF) that returned to control in REC. CHF caused conduction abnormalities (phasedelay-range and heterogeneity index, both P < 0.01) and burst pacing-induced AF prolongation (CTL 22±7s, CHF 1100±171s***, REC 884±220s***) which persisted in the recovery period, along with residual fibrosis (CTL 3.6±0.7%, CHF 14.7±1.5%***, REC13.3±2.3%***). Fibrosis physically interrupted muscle bundle continuity and anionically-based action potential model of canine atrium showed that fibrosiswas able to account for the observed conduction abnormalities. Conclusions: CHF causes connexin-dephosphorylation and Cx40/Cx43ratio increases. With CHF reversal, atrial connexin alterations recover completely, but tissue fibrosis, conduction abnormalities and a substrate forAF remain with fibrosis accounting for conduction abnormalities. Thus, althougha trial connexin changes occur with CHF, they are not essential for conduction disturbances and AF promotion, which appear rather to be related primarily tofibrotic interruption of muscle-bundle continuity.

Electrical pacing is a common procedure in both experimental and clinical settings to study and/or annihilate anatomical reentry. A previous study [Comtois and Vinet, Chaos 12, 903 (2002)] has described new ways to terminate reentry in a one-dimensional loop model by a protocol consisting of only two stimulations. Annihilation of the reentrant activity was much more likely with these new scenarios than through a unidirectional block. This paper investigates the sensitivity of these scenarios of annihilation to the length of the pathway. It shows that double-pulse stimulation can stop the reentry if the circuit is shorter than a limiting length. Beyond this upper limit, stimulation rather yields sustained double-wave reentry. The same dynamical mechanism, labeled alternans amplification, is found to be responsible for these two types of post-stimulus dynamics.

Atrial fibrillation (AF), arising in the cardiac atria, is a common cardiac rhythm disorder that is incompletely understood. Numerous characteristics of the atrial tissue are thought to play a role in the maintenance of AF. Most traditional theoretical models of AF have considered the atrium to be a flat two-dimensional sheet. Here, we analyzed the relationship between atrial geometry, substrate size, and AF persistence, in a mathematical model involving heterogeneity. Spatially periodic properties were created by variations in times required for reactivation due to periodic acetylcholine concentration [ACh] distribution. The differences in AF maintenance between the sheet and the cylinder geometry are found for intermediate gradients of inexcitable time (intermediate [ACh]). The maximum difference in AF maintenance between geometry decreases with increasing tissue size, down to zero for a substrate of dimensions 20 × 10 cm. Generators have the tendency to be anchored to the regions of longer inexcitable period (low [ACh]). The differences in AF maintenance between geometries correlate with situations of moderate anchoring for which rotor-core drifts between low-[ACh] regions occur, favoring generator disappearance. The drift of generators increases their probability of disappearance at the tissue borders, resulting in a decreased maintenance rate in the sheet due to the higher number of no-flux boundaries. These interactions between biological variables and the role of geometry must be considered when selecting an appropriate model for AF in intact hearts.

Mechanical stretch of cardiomyocytes modulates the action potential (AP) via stretch-activated channels. The electrical activity is also modulated by the parasympathetic nervous system via the acetylcholine (ACh)-dependent potassium current. The ACh effect is however heterogeneous throughout the atria thus facilitating arrhythmic events. Simultaneous activation of both systems could occur and may facilitate atrial arrhythmias. Simulations of a canine atrial ionic model in an isolated cell and linear tissue strand were computed with varying stretch and ACh levels. Pacing at 1Hz, AP duration (APD) is increased (see APs in panel A) by ∼47 ms with 20% stretch compared to control (CTL). However, stretch did not increase APD in presence of 25 nmol/L of ACh (ACh vs. ACh+stretch in panel A). Restitution curves calculated with the S1-S2 protocol (S1=1 Hz) are plotted in panel B. Stretch (20%) results in an upshift of ∼47 ms of the restitution curve compared to CTL. ACh almost eliminate atrial restitution compared to CTL with no important changes with stretch (ACh vs. ACh+stretch curves). Preliminary results obtained in a cable with heterogeneous ACh distribution showed an increased interval for block of electrical propagation with tissue stretch.View Large Image | View Hi-Res Image | Download PowerPoint Slide

Problematic. The biological pacemaker is a new therapeutic approach that could lead to optimized treatment of bradycardia. A possibility is the development of a thin sheet of cardiomyocytes, cultured to obtain a target activation rate. Fundamental research, often conducted with neonatal rat ventricular myocytes (NRVMs), partially revealed two basic coupled mechanisms of automaticity termed Voltage Clock (synergy of membrane currents) and Calcium Clock (internal oscillations of calcium concentration). To date, no ionic model is able to reproduce in silico the autonomous activity found in cultured NRVMs. The present project aims to fill this gap.Methods. A non-automatic NRVM ionic model (Korhonen-Tavi, 2009) is modified according to documented Voltage and Calcium Clocks mathematical formulations. The myocytes are cultured for 48 hours at low density, allowing cells to remain single on dishes. Autonomous action potentials (APs) are measured with patch clamp method, and calcium transients (CTs) with Fluo-4 AM fluorescence imaging. Experimental variables (spontaneous rate, AP amplitude and duration, CT decay time course) are extracted and compared to the output of the model. Results. Insertion of Voltage Clock (upregulation of If and ICaL, and downregulation of IK1 and Ito) into the model showed the presence of automaticity with the characteristic slow late diastole depolarization. The maximum activation frequencies (0,7Hz) reached only the lower frequency range documented experimentally and found in the litterature (0,4 to 6Hz). Conclusion. Limitations in the rate of automaticity found emphasise the importance of exploring the Calcium Clock mechanism whose insertion may lead to higher spontaneous rates. In the future, a bifurcation analysis will give some insights on the dynamical mechanisms behind pacemaker generation in cultured NRVMs.