Effects of pacemaker currents on creation and modulation of human ventricular pacemaker: theoretical study with application to biological pacemaker engineering

Bifurcations and Proarrhythmic Behaviors in Cardiac Electrical Excitations

The heart is a hierarchical dynamic system consisting of molecules, cells, and tissues, and acts as a pump for blood circulation. The pumping function depends critically on the preceding electrical activity, and disturbances in the pattern of excitation propagation lead to cardiac arrhythmia and pump failure. Excitation phenomena in cardiomyocytes have been modeled as a nonlinear dynamical system. Because of the nonlinearity of excitation phenomena, the system dynamics could be complex, and various analyses have been performed to understand the complex dynamics. Understanding the mechanisms underlying proarrhythmic responses in the heart is crucial for developing new ways to prevent and control cardiac arrhythmias and resulting contractile dysfunction. When the heart changes to a pathological state over time, the action potential (AP) in cardiomyocytes may also change to a different state in shape and duration, often undergoing a qualitative change in behavior. Such a dynamic change is called bifurcation. In this review, we first summarize the contribution of ion channels and transporters to AP formation and our knowledge of ion-transport molecules, then briefly describe bifurcation theory for nonlinear dynamical systems, and finally detail its recent progress, focusing on the research that attempts to understand the developing mechanisms of abnormal excitations in cardiomyocytes from the perspective of bifurcation phenomena.

Reciprocal interaction between IK1 and If in biological pacemakers: A simulation study

Pacemaking dysfunction (PD) may result in heart rhythm disorders, syncope or even death. Current treatment of PD using implanted electronic pacemakers has some limitations, such as finite battery life and the risk of repeated surgery. As such, the biological pacemaker has been proposed as a potential alternative to the electronic pacemaker for PD treatment. Experimentally and computationally, it has been shown that bio-engineered pacemaker cells can be generated from non-rhythmic ventricular myocytes (VMs) by knocking out genes related to the inward rectifier potassium channel current (IK1) or by overexpressing hyperpolarization-activated cyclic nucleotide gated channel genes responsible for the "funny" current (If). However, it is unclear if a bio-engineered pacemaker based on the modification of IK1- and If-related channels simultaneously would enhance the ability and stability of bio-engineered pacemaking action potentials. In this study, the possible mechanism(s) responsible for VMs to generate spontaneous pacemaking activity by regulating IK1 and If density were investigated by a computational approach. Our results showed that there was a reciprocal interaction between IK1 and If in ventricular pacemaker model. The effect of IK1 depression on generating ventricular pacemaker was mono-phasic while that of If augmentation was bi-phasic. A moderate increase of If promoted pacemaking activity but excessive increase of If resulted in a slowdown in the pacemaking rate and even an unstable pacemaking state. The dedicated interplay between IK1 and If in generating stable pacemaking and dysrhythmias was evaluated. Finally, a theoretical analysis in the IK1/If parameter space for generating pacemaking action potentials in different states was provided. In conclusion, to the best of our knowledge, this study provides a wide theoretical insight into understandings for generating stable and robust pacemaker cells from non-pacemaking VMs by the interplay of IK1 and If, which may be helpful in designing engineered biological pacemakers for application purposes.

Dynamical mechanisms of phase-2 early afterdepolarizations in human ventricular myocytes: insights from bifurcation analyses of two mathematical models

Early afterdepolarization (EAD) is known as a cause of ventricular arrhythmias in long QT syndromes. We theoretically investigated how the rapid (I_Kr) and slow (I_Ks) components of delayed-rectifier K⁺ channel currents, L-type Ca²⁺ channel current (I_CaL), Na⁺/Ca²⁺ exchanger current (I_NCX), Na⁺-K⁺ pump current (I_NaK), intracellular Ca²⁺ (Ca_i) handling via sarcoplasmic reticulum (SR), and intracellular Na⁺ concentration (Na_i) contribute to initiation, termination, and modulation of phase-2 EADs, using two human ventricular myocyte models. Bifurcation structures of dynamical behaviors in model cells were explored by calculating equilibrium points, limit cycles (LCs), and bifurcation points as functions of parameters. EADs were reproduced by numerical simulations. The results are summarized as follows: 1) decreasing I_Ks and/or I_Kr or increasing I_CaL led to EAD generation, to which mid-myocardial cell models were especially susceptible; the parameter regions of EADs overlapped the regions of stable LCs. 2) Two types of EADs (termination mechanisms), I_Ks activation-dependent and I_CaL inactivation-dependent EADs, were detected; I_Ks was not necessarily required for EAD formation. 3) Inhibiting I_NCX suppressed EADs via facilitating Ca²⁺-dependent I_CaL inactivation. 4) Ca_i dynamics (SR Ca²⁺ handling) and Na_i strongly affected bifurcations and EAD generation in model cells via modulating I_CaL, I_NCX, and I_NaK Parameter regions of EADs, often overlapping those of stable LCs, shifted depending on Ca_i and Na_i in stationary and dynamic states. 5) Bradycardia-related induction of EADs was mainly due to decreases in Na_i at lower pacing rates. This study demonstrates that bifurcation analysis allows us to understand the dynamical mechanisms of EAD formation more profoundly.

NEW & NOTEWORTHY

We investigated mechanisms of phase-2 early afterdepolarization (EAD) by bifurcation analyses of human ventricular myocyte (HVM) models. EAD formation in paced HVMs basically depended on bifurcation phenomena in non-paced HVMs, but was strongly affected by intracellular ion concentrations in stationary and dynamic states. EAD generation did not necessarily require I_Ks.

Quantitative Decomposition of Dynamics of Mathematical Cell Models: Method and Application to Ventricular Myocyte Models

Mathematical cell models are effective tools to understand cellular physiological functions precisely. For detailed analysis of model dynamics in order to investigate how much each component affects cellular behaviour, mathematical approaches are essential. This article presents a numerical analysis technique, which is applicable to any complicated cell model formulated as a system of ordinary differential equations, to quantitatively evaluate contributions of respective model components to the model dynamics in the intact situation. The present technique employs a novel mathematical index for decomposed dynamics with respect to each differential variable, along with a concept named instantaneous equilibrium point, which represents the trend of a model variable at some instant. This article also illustrates applications of the method to comprehensive myocardial cell models for analysing insights into the mechanisms of action potential generation and calcium transient. The analysis results exhibit quantitative contributions of individual channel gating mechanisms and ion exchanger activities to membrane repolarization and of calcium fluxes and buffers to raising and descending of the cytosolic calcium level. These analyses quantitatively explicate principle of the model, which leads to a better understanding of cellular dynamics.

SEM, TEM, and IHC Analysis of the Sinus Node and Its Implications for the Cardiac Conduction System

More than 100 years after the discovery of the sinus node (SN) by Keith and Flack, the function and structure of the SN have not been completely established yet. The anatomic architecture of the SN has often been described as devoid of an organized structure; the origin of the sinus impulse is still a matter of debate, and a definite description of the long postulated internodal specialized tract conducting the impulse from the SN to the atrioventricular node (AVN) is still missing. In our previously published study, we proposed a morphologically ordered structure for the SN. As a confirmation of what was presented then, we have added the results of additional observations regarding the structural particularities of the SN. We investigated the morphology of the sinus node in the human hearts of healthy individuals using histochemical, immunohistochemical, optical, and electron microscopy (SEM, TEM). Our results confirmed that the SN presents a previously unseen highly organized architecture.

Contribution of quantitative changes in individual ionic current systems to the embryonic development of ventricular myocytes: a simulation study

Early embryonic rodent ventricular cells exhibit spontaneous action potential (AP), which disappears in later developmental stages. Here, we used 3 mathematical models-the Kyoto, Ten Tusscher-Panfilov, and Luo-Rudy models-to present an overview of the functional landscape of developmental changes in embryonic ventricular cells. We switched the relative current densities of 9 ionic components in the Kyoto model, and 160 of 512 representative combinations were predicted to result in regular spontaneous APs, in which the quantitative changes in Na(+) current (I Na) and funny current (I f) made large contributions to a wide range of basic cycle lengths. In all three models, the increase in inward rectifier current (I K1) before the disappearance of I f was predicted to result in abnormally high intracellular Ca(2+) concentrations. Thus, we demonstrated that the developmental changes in APs were well represented, as I Na increased before the disappearance of I f, followed by a 10-fold increase in I K1.

Effect of hyperpolarization-activated current I(f) on robustness of sinoatrial node pacemaking: theoretical study on influence of intracellular Na(+) concentration

To elucidate the effects of hyperpolarization-activated current I(f) on robustness of sinoatrial node (SAN) pacemaking in connection with intracellular Na(+) concentration (Na(i)) changes, we theoretically investigated 1) the impacts of I(f) on dynamical properties of SAN model cells during inhibition of L-type Ca(2+) channel currents (I(CaL)) or hyperpolarizing loads and 2) I(f)-dependent changes in Na(i) and their effects on dynamical properties of model cells. Bifurcation analyses were performed for Na(i)-variable and Na(i)-fixed versions of mathematical models for rabbit SAN cells; equilibrium points (EPs), limit cycles (LCs), and their stability were determined as functions of model parameters. Increasing I(f) conductance (g(f)) shrank I(CaL) conductance (g(CaL)) regions of unstable EPs and stable LCs (rhythmic firings) in the Na(i)-variable system but slightly broadened that of rhythmic firings at lower g(f) in the Na(i)-fixed system. In the Na(i)-variable system, increased g(f) yielded elevations in Na(i) at EPs and during spontaneous oscillations, which caused EP stabilization and shrinkage in the parameter regions of unstable EPs and rhythmic firings. As g(f) increased, parameter regions of unstable EPs and stable LCs determined for hyperpolarizing loads shrank in the Na(i)-variable system but were enlarged in the Na(i)-fixed system. These findings suggest that 1) I(f) does not enhance but rather attenuates robustness of rabbit SAN cells via facilitating EP stabilization and LC destabilization even in physiological g(f) ranges; and 2) the enhancing effect of I(f) on robustness of pacemaker activity, which could be observed at lower g(f) when Na(i) was fixed, is actually reversed by I(f)-dependent changes in Na(i).

Roles of sarcoplasmic reticulum Ca2+ cycling and Na+/Ca2+ exchanger in sinoatrial node pacemaking: Insights from bifurcation analysis of mathematical models

To elucidate the roles of sarcoplasmic reticulum (SR) Ca2+ cycling and Na+/Ca2+ exchanger (NCX) in sinoatrial node (SAN) pacemaking, we have applied stability and bifurcation analyses to a coupled-clock system model developed by Maltsev and Lakatta ( Am J Physiol Heart Circ Physiol 296: H594-H615, 2009). Equilibrium point (EP) at which the system is stationary (i.e., the oscillatory system fails to function), periodic orbit (limit cycle), and their stability were determined as functions of model parameters. The stability analysis to detect bifurcation points confirmed crucial importance of SR Ca2+ pumping rate constant ( Pup), NCX density ( kNCX), and L-type Ca2+ channel conductance for the system function reported in previous parameter-dependent numerical simulations. We showed, however, that the model cell does not exhibit self-sustained automaticity of SR Ca2+ release at any clamped voltage and therefore needs further tuning to reproduce oscillatory local Ca2+ release and net membrane current reported experimentally at −10 mV. Our further extended bifurcation analyses revealed important novel features of the pacemaker system that go beyond prior numerical simulations in relation to the roles of SR Ca2+ cycling and NCX in SAN pacemaking. Specifically, we found that 1) NCX contributes to EP instability and enhancement of robustness in the full system during normal spontaneous action potential firings, while stabilizing EPs to prevent sustained Ca2+ oscillations under voltage clamping; 2) SR requires relatively large kNCX and subsarcolemmal Ca2+ diffusion barrier (i.e., subspace) to contribute to EP destabilization and enhancement of robustness; and 3) decrementing Pup or kNCX decreased the full system robustness against hyperpolarizing loads because EP stabilization and cessation of pacemaking were observed at the lower critical amplitude of hyperpolarizing bias currents, suggesting that SR Ca2+ cycling contributes to enhancement of the full system robustness by modulating NCX currents and promoting EP destabilization.

Biological pacemaker created by percutaneous gene delivery via venous catheters in a porcine model of complete heart block

BACKGROUND

Pacemaker-dependent patients with device infection require temporary pacing while the infection is treated. External transthoracic pacing is painful and variably effective, while temporary pacing leads are susceptible to superinfection.

OBJECTIVE

To create a biological pacemaker delivered via venous catheters in a porcine model of complete heart block, providing a temporary alternative/adjunct to external pacing devices without additional indwelling hardware.

METHODS

Complete atrioventricular (AV) nodal block was induced in pigs by radiofrequency ablation after the implantation of a single-chamber electronic pacemaker to maintain a ventricular backup rate of 50 beats/min. An adenoviral vector cocktail (K(AAA) + H2), expressing dominant-negative inward rectifier potassium channel (Kir2.1AAA) and hyperpolarization-activated cation channel (HCN2) genes, was injected into the AV junctional region via a NOGA Myostar catheter advanced through the femoral vein.

RESULTS

Animals injected with K(AAA) + H2 maintained a physiologically relevant ventricular rate of 93.5 ± 7 beats/min (n = 4) compared with control animals (average rate, 59.4 ± 4 beats/min; n = 6 at day 7 postinjection; P <.05). Backup electronic pacemaker utilization decreased by almost 4-fold in the K(AAA) + H2 group compared with the control (P <.05), an effect maintained for the entire 14-day window. In contrast to the efficacy of gene delivery into the AV junctional region, open-chest, direct injection of K(AAA) + H2 (or its individual vectors) into the ventricular myocardium failed to elicit significant pacemaker activity.

CONCLUSIONS

The right-sided delivery of K(AAA) + H2 to the AV junctional region provided physiologically relevant biological pacing over a 14-day period. Our approach may provide temporary, bridge-to-device pacing for the effective clearance of infection prior to the reimplantation of a definitive electronic pacemaker.

Nonlinear dynamics in cardiology

The dynamics of many cardiac arrhythmias, as well as the nature of transitions between different heart rhythms, have long been considered evidence of nonlinear phenomena playing a direct role in cardiac arrhythmogenesis. In most types of cardiac disease, the pathology develops slowly and gradually, often over many years. In contrast, arrhythmias often occur suddenly. In nonlinear systems, sudden changes in qualitative dynamics can, counterintuitively, result from a gradual change in a system parameter-this is known as a bifurcation. Here, we review how nonlinearities in cardiac electrophysiology influence normal and abnormal rhythms and how bifurcations change the dynamics. In particular, we focus on the many recent developments in computational modeling at the cellular level that are focused on intracellular calcium dynamics. We discuss two areas where recent experimental and modeling work has suggested the importance of nonlinearities in calcium dynamics: repolarization alternans and pacemaker cell automaticity.

Onset of atrial arrhythmias elicited by autonomic modulation of rabbit sinoatrial node activity: a modeling study

Neuronal modulation of the sinoatrial node (SAN) plays a crucial role in the initiation and maintenance of atrial arrhythmias (AF), although the exact mechanisms remain unclear. We used a computer model of a rabbit right atrium (RA) with a heterogeneous SAN and detailed ionic current descriptions for atrial and SAN myocytes to explore reentry initiation associated with autonomic activity. Heterogeneous acetylcholine (ACh)-dependent ionic responses along with L-type Ca current (I(Ca,L)) upregulation were incorporated in the SAN only. During control, activation was typical with the leading pacemaker site located close to the superior vena cava or the intercaval region. With cholinergic stimulation, activation patterns frequently included caudal shifts of the leading pacemaker site and occasional double breakouts. The model became increasingly arrhythmogenic for the ACh concentration >20 nM and for large I(Ca,L) conductance. Reentries obtained included counterclockwise rotors in the free wall, clockwise reentry circulating between the SAN and free wall, and typical flutter. The SAN was the cause of reentry with a common leading sequence of events: a bradycardic beat with shifting in the caudal direction, followed by a premature beat or unidirectional block within the SAN. Electrotonic loading, and not just overdrive pacing, squelches competing pacemaker sites in the SAN. Cholinergic stimulation concomitant with I(Ca,L) upregulation shifts leading pacemaker site and can lead to reentry. A heterogeneous response to autonomic innervation, a large myocardial load, and an extensive SAN in the intercaval region are required for neurally induced SAN-triggered reentry.

Different distribution of Cav3.2 and Cav3.1 transcripts encoding T-type Ca(2+) channels in the embryonic heart of mice

We investigated the distribution of T-type Ca(2+) channel mRNAs in the mouse embryonic heart. Cav3.2, but not Cav3.1, was expressed in the E8.5 embryonic heart along with cardiac progenitor markers (Nkx2.5, Tbx5, Isl-1) and contractile proteins (alpha and beta MHC). In the E10.5 heart, the distribution of Cav3.1 mRNA was confirmed in the AV-canal and overlapped with that of MinK or Tbx2. Cav3.2 mRNA was observed not only in the AV-canal but also in the outflow tract, along with MinK and Isl-1, indicating the expression of Cav3.2 in the secondary heart field. Thus, Cav3.2 may contribute to the development of the outflow tract from the secondary heart field in the embryonic heart, whereas Cav3.1 may be involved in the development of the cardiac conduction-system together with Cav3.2.

Roles of hyperpolarization-activated current If in sinoatrial node pacemaking: insights from bifurcation analysis of mathematical models

To elucidate the roles of hyperpolarization-activated current (I(f)) in sinoatrial node (SAN) pacemaking, we theoretically investigated 1) the effects of I(f) on stability and bifurcation during hyperpolarization of SAN cells; 2) combined effects of I(f) and the sustained inward current (I(st)) or Na(+) channel current (I(Na)) on robustness of pacemaking against hyperpolarization; and 3) whether blocking I(f) abolishes pacemaker activity under certain conditions. Bifurcation analyses were performed for mathematical models of rabbit SAN cells; equilibrium points (EPs), periodic orbits, and their stability were determined as functions of parameters. Unstable steady-state potential region determined with applications of constant bias currents shrunk as I(f) density increased. In the central SAN cell, the critical acetylcholine concentration at which bifurcations, to yield a stable EP and quiescence, occur was increased by smaller I(f), but decreased by larger I(f). In contrast, the critical acetylcholine concentration and conductance of gap junctions between SAN and atrial cells at bifurcations progressively increased with enhancing I(f) in the peripheral SAN cell. These effects of I(f) were significantly attenuated by eliminating I(st) or I(Na), or by accelerating their inactivation. Under hyperpolarized conditions, blocking I(f) abolished SAN pacemaking via bifurcations. These results suggest that 1) I(f) itself cannot destabilize EPs; 2) I(f) improves SAN cell robustness against parasympathetic stimulation via preventing bifurcations in the presence of I(st) or I(Na); 3) I(f) dramatically enhances peripheral cell robustness against electrotonic loads of the atrium in combination with I(Na); and 4) pacemaker activity of hyperpolarized SAN cells could be abolished by blocking I(f).

Decreased intercellular coupling improves the function of cardiac pacemakers derived from mouse embryonic stem cells

The aim of this study was to determine if embryonic stem cell derived cardiomyocyte aggregates (ESdCs) can act as pacemakers in spontaneously active cardiomyocyte preparations when their connexin isoform expression is tuned toward a more sinus nodal phenotype. Using microelectrode array recordings (MEAs), we demonstrate that mouse ESdCs establish electrical coupling with spontaneously active cardiomyocyte preparations (HL-1 monolayer) and obtain pacemaker dominance. WT- and Cx43(-/-)-ESdCs comparably established intercellular coupling with cardiac host tissue (Cx43(-/-): 86% vs. WT: 91%). Although both aggregates had a 100% success rate in pacing quiescent cardiac preparations, Cx43(-/-)-ESdCs had an increased likelihood of gaining pacemaker dominance (Cx43(-/-): 40% vs. WT: 13%) in spontaneously active preparations. No differences in size, beating frequency, V(m), or differentiation were detected between WT- and Cx43(-/-)-ESdCs but the intercellular coupling resistance in Cx43(-/-)-ESdCs was significantly increased (Cx43(-/-): 1.2nS vs. WT: 14.8nS). Lack of Cx43 prolonged the time until Cx43(-/-)-ESdCs established frequency synchronization with the host tissue. It further hampered the excitation spread from the cardiomyocyte preparation into the ESdC. However rectifying excitation spread in these co-cultures could not be unequivocally identified. In summary, ESdCs can function as dominant biological pacemakers and Cx43 expression is not a prerequisite for their electrical integration. Maintenance of pacemaker dominance depends critically on the pacemaker's gap junction expression benefiting those with increased intercellular coupling resistances. Our results provide important insight into the design of biological pacemakers that will benefit the use of cardiomyocytes for cell replacement therapy.

Genesis and regulation of the heart automaticity

The heart automaticity is a fundamental physiological function in higher organisms. The spontaneous activity is initiated by specialized populations of cardiac cells generating periodical electrical oscillations. The exact cascade of steps initiating the pacemaker cycle in automatic cells has not yet been entirely elucidated. Nevertheless, ion channels and intracellular Ca(2+) signaling are necessary for the proper setting of the pacemaker mechanism. Here, we review the current knowledge on the cellular mechanisms underlying the generation and regulation of cardiac automaticity. We discuss evidence on the functional role of different families of ion channels in cardiac pacemaking and review recent results obtained on genetically engineered mouse strains displaying dysfunction in heart automaticity. Beside ion channels, intracellular Ca(2+) release has been indicated as an important mechanism for promoting automaticity at rest as well as for acceleration of the heart rate under sympathetic nerve input. The potential links between the activity of ion channels and Ca(2+) release will be discussed with the aim to propose an integrated framework of the mechanism of automaticity.

Regional difference in dynamical property of sinoatrial node pacemaking: role of na+ channel current

To elucidate the regional differences in sinoatrial node pacemaking mechanisms, we investigated 1), bifurcation structures during current blocks or hyperpolarization of the central and peripheral cells, 2), ionic bases of regional differences in bifurcation structures, and 3), the role of Na(+) channel current (I(Na)) in peripheral cell pacemaking. Bifurcation analyses were performed for mathematical models of the rabbit sinoatrial node central and peripheral cells; equilibrium points, periodic orbits, and their stability were determined as functions of parameters. Structural stability against applications of acetylcholine or electrotonic modulations of the atrium was also evaluated. Blocking L-type Ca(2+) channel current (I(Ca,L)) stabilized equilibrium points and abolished pacemaking in both the center and periphery. Critical acetylcholine concentration and gap junction conductance for pacemaker cessation were higher in the periphery than in the center, being dramatically reduced by blocking I(Na). Under hyperpolarized conditions, blocking I(Na), but not eliminating I(Ca,L), abolished peripheral cell pacemaking. These results suggest that 1), I(Ca,L) is responsible for basal pacemaking in both the central and peripheral cells, 2), the peripheral cell is more robust in withstanding hyperpolarizing loads than the central cell, 3), I(Na) improves the structural stability to hyperpolarizing loads, and 4), I(Na)-dependent pacemaking is possible in hyperpolarized peripheral cells.

Creating a cardiac pacemaker by gene therapy

While electronic cardiac pacing in its various modalities represents standard of care for treatment of symptomatic bradyarrhythmias and heart failure, it has limitations ranging from absent or rudimentary autonomic modulation to severe complications. This has prompted experimental studies to design and validate a biological pacemaker that could supplement or replace electronic pacemakers. Advances in cardiac gene therapy have resulted in a number of strategies focused on beta-adrenergic receptors as well as specific ion currents that contribute to pacemaker function. This article reviews basic pacemaker physiology, as well as studies in which gene transfer approaches to develop a biological pacemaker have been designed and validated in vivo. Additional requirements and refinements necessary for successful biopacemaker function by gene transfer are discussed.