Experimental and computational studies of strain–conduction velocity relationships in cardiac tissue

Velocity of electrical conduction in cardiac tissue is a function of mechanical strain. Although strain-modulated velocity is a well established finding in experimental cardiology, its underlying mechanisms are not well understood. In this work, we summarized potential factors contributing to strain–velocity relationships and reviewed related experimental and computational studies. We presented results from our experimental studies on rabbit papillary muscle, which supported a biphasic relationship of strain and velocity under uni-axial straining conditions. In the low strain range, the strain–velocity relationship was positive. Conduction velocity peaked with 0.59 m/s at 100% strain corresponding to maximal force development. In the high strain range, the relationship was negative. Conduction was reversibly blocked at 118±1.8% strain. Reversible block occurred also in the presence of streptomycin. Furthermore, our studies revealed a moderate hysteresis of conduction velocity, which was reduced by streptomycin. We reconstructed several features of the strain–velocity relationship in a computational study with a myocyte strand. The modeling included strain-modulation of intracellular conductivity and stretch-activated cation non-selective ion channels. The computational study supported our hypotheses, that the positive strain–velocity relationship at low strain is caused by strain-modulation of intracellular conductivity and the negative relationship at high strain results from activity of stretch-activated channels. Conduction block was not reconstructed in our computational studies. We concluded this work by sketching a hypothesis for strain-modulation of conduction and conduction block in papillary muscle. We suggest that this hypothesis can also explain uni-axially measured strain–conduction velocity relationships in other types of cardiac tissue, but apparently necessitates adjustments to reconstruct pressure or volume related changes of velocity in atria and ventricles.     

Mechanoelectric feedback leads to conduction slowing and block in acutely dilated atria: a modeling study of cardiac electromechanics

Atrial fibrillation, a common cardiac arrhythmia, is promoted by atrial dilatation. Acute atrial dilatation may play a role in atrial arrhythmogenesis through mechanoelectric feedback. In experimental studies, conduction slowing and block have been observed in acutely dilated atria. In the present study, the influence of the stretch-activated current (I(sac)) on impulse propagation is investigated by means of computer simulations. Homogeneous and inhomogeneous atrial tissues are modeled by cardiac fibers composed of segments that are electrically and mechanically coupled. Active force is related to free Ca(2+) concentration and sarcomere length. Simulations of homogeneous and inhomogeneous cardiac fibers have been performed to quantify the relation between conduction velocity and I(sac) under stretch. In our model, conduction slowing and block are related to the amount of stretch and are enhanced by contraction of early-activated segments. Conduction block can be unidirectional in an inhomogeneous fiber and is promoted by a shorter stimulation interval. Slowing of conduction is explained by inactivation of Na(+) channels and a lower maximum upstroke velocity due to a depolarized resting membrane potential. Conduction block at shorter stimulation intervals is explained by a longer effective refractory period under stretch. Our observations are in agreement with experimental results and explain the large differences in intra-atrial conduction, as well as the increased inducibility of atrial fibrillation in acutely dilated atria.     

Effects of Mechano-Electric Feedback on Scroll Wave Stability in Human Ventricular Fibrillation

Recruitment of stretch-activated channels, one of the mechanisms of mechano-electric feedback, has been shown to influence the stability of scroll waves, the waves that underlie reentrant arrhythmias. However, a comprehensive study to examine the effects of recruitment of stretch-activated channels with different reversal potentials and conductances on scroll wave stability has not been undertaken; the mechanisms by which stretch-activated channel opening alters scroll wave stability are also not well understood. The goals of this study were to test the hypothesis that recruitment of stretch-activated channels affects scroll wave stability differently depending on stretch-activated channel reversal potential and channel conductance, and to uncover the relevant mechanisms underlying the observed behaviors. We developed a strongly-coupled model of human ventricular electromechanics that incorporated human ventricular geometry and fiber and sheet orientation reconstructed from MR and diffusion tensor MR images. Since a wide variety of reversal potentials and channel conductances have been reported for stretch-activated channels, two reversal potentials, −60 mV and −10 mV, and a range of channel conductances (0 to 0.07 mS/µF) were implemented. Opening of stretch-activated channels with a reversal potential of −60 mV diminished scroll wave breakup for all values of conductances by flattening heterogeneously the action potential duration restitution curve. Opening of stretch-activated channels with a reversal potential of −10 mV inhibited partially scroll wave breakup at low conductance values (from 0.02 to 0.04 mS/µF) by flattening heterogeneously the conduction velocity restitution relation. For large conductance values (>0.05 mS/µF), recruitment of stretch-activated channels with a reversal potential of −10 mV did not reduce the likelihood of scroll wave breakup because Na channel inactivation in regions of large stretch led to conduction block, which counteracted the increased scroll wave stability due to an overall flatter conduction velocity restitution.     

Mechanisms of conduction slowing during myocardial stretch by ventricular volume loading in the rabbit

Acute ventricular loading by volume inflation reversibly slows epicardial electrical conduction, but the underlying mechanism remains unclear. This study investigated the potential contributions of stretch-activated currents, alterations in resting membrane potential, or changes in intercellular resistance and membrane capacitance. Conduction velocity was assessed using optical mapping of isolated rabbit hearts at end-diastolic pressures of 0 and 30 mmHg. The addition of 50 microM Gd3+ (a stretch-activated channel blocker) to the perfusate had no effect on slowing. The effect of volume loading on conduction velocity was independent of changes in resting membrane potential created by altering the perfusate potassium concentration between 1.5 and 8 mM. Bidomain model analysis of optically recorded membrane potential responses to a unipolar stimulus suggested that the cross-fiber space constant and membrane capacitance both increased with loading (21%, P = 0.006, and 56%, P = 0.004, respectively), and these changes, when implemented in a resistively coupled one-dimensional network model, were consistent with the observed slowing (14%, P = 0.005). In conclusion, conduction slowing during ventricular volume loading is not attributable to stretch-activated currents or altered resting membrane potential, but a reduction of intercellular resistance with a concurrent increase of effective membrane capacitance results in a net slowing of conduction.     

Anisotropic conduction block and reentry in neonatal rat ventricular myocyte monolayers

Anisotropy can lead to unidirectional conduction block that initiates reentry. We analyzed the mechanisms in patterned anisotropic neonatal rat ventricular myocyte monolayers. Voltage and intracellular Ca (Ca(i)) were optically mapped under the following conditions: extrastimulus (S1S2) testing and/or tetrodotoxin (TTX) to suppress Na current availability; heptanol to reduce gap junction conductance; and incremental rapid pacing. In anisotropic monolayers paced at 2 Hz, conduction velocity (CV) was faster longitudinally than transversely, with an anisotropy ratio [AR = CV(L)/CV(T), where CV(L) and CV(T) are CV in the longitudinal and transverse directions, respectively], averaging 2.1 ± 0.8. Interventions decreasing Na current availability, such as S1S2 pacing and TTX, slowed CV(L) and CV(T) proportionately, without changing the AR. Conduction block preferentially occurred longitudinal to fiber direction, commonly initiating reentry. Interventions that decreased gap junction conductance, such as heptanol, decreased CV(T) more than CV(L), increasing the AR and causing preferential transverse conduction block and reentry. Rapid pacing resembled the latter, increasing the AR and promoting transverse conduction block and reentry, which was prevented by the Ca(i) chelator 1,2-bis oaminophenoxy ethane-N,N,N',N'-tetraacetic acid (BAPTA). In contrast to isotropic and uniformly anisotropic monolayers, in which reentrant rotors drifted and self-terminated, bidirectional anisotropy (i.e., an abrupt change in fiber direction exceeding 45°) caused reentry to anchor near the zone of fiber direction change in 77% of monolayers. In anisotropic monolayers, unidirectional conduction block initiating reentry can occur longitudinal or transverse to fiber direction, depending on whether the experimental intervention reduces Na current availability or decreases gap junction conductance, agreeing with theoretical predictions.     

Membrane Characteristics of the Canine Papillary Muscle Fiber

Passive and active responses to intracellular and extracellular stimulation were studied in the canine papillary muscle. The electrotonic potential produced by extracellular polarization with the partition chamber method fitted the time course and the spatial decay expected from the cable theory (the time constant, 3.3 msec; the space constant, 1.2 mm). Contrariwise, spatial decay of the electrotonic potentials produced by intracellular polarization was very short and did not fit the decay curve expected for a simple cable, although only a small difference of time course in the electrotonic potentials produced by intracellular and extracellular polarizations was observed. A similar time course might result from the fact that when current flow results from intracellular polarization, the input resistance is less dependent on the membrane resistance. The foot of the propagated action potential rose exponentially with a time constant of 1.1 msec and a conduction velocity of 0.68 m/sec. The membrane capacity was calculated from the time constant of the foot potential and the conduction velocity to be 0.76 µF/cm². The responses of the papillary muscle membrane to intracellular stimulation differed from those to extracellular stimulation applied with the partition method in the following ways: higher threshold potential, shorter latency for the active response, linearity of the current-voltage relationship, and no reduction in the membrane resistance at the crest of the action potential during current flow.     

A Discrete Electromechanical Model for Human Cardiac Tissue: Effects of Stretch-Activated Currents and Stretch Conditions on Restitution Properties and Spiral Wave Dynamics

We introduce an electromechanical model for human cardiac tissue which couples a biophysical model of cardiac excitation (Tusscher, Noble, Noble, Panfilov, 2006) and tension development (adjusted Niederer, Hunter, Smith, 2006 model) with a discrete elastic mass-lattice model. The equations for the excitation processes are solved with a finite difference approach, and the equations of the mass-lattice model are solved using Verlet integration. This allows the coupled problem to be solved with high numerical resolution. Passive mechanical properties of the mass-lattice model are described by a generalized Hooke''s law for finite deformations (Seth material). Active mechanical contraction is initiated by changes of the intracellular calcium concentration, which is a variable of the electrical model. Mechanical deformation feeds back on the electrophysiology via stretch-activated ion channels whose conductivity is controlled by the local stretch of the medium. We apply the model to study how stretch-activated currents affect the action potential shape, restitution properties, and dynamics of spiral waves, under constant stretch, and dynamic stretch caused by active mechanical contraction. We find that stretch conditions substantially affect these properties via stretch-activated currents. In constantly stretched medium, we observe a substantial decrease in conduction velocity, and an increase of action potential duration; whereas, with dynamic stretch, action potential duration is increased only slightly, and the conduction velocity restitution curve becomes biphasic. Moreover, in constantly stretched medium, we find an increase of the core size and period of a spiral wave, but no change in rotation dynamics; in contrast, in the dynamically stretching medium, we observe spiral drift. Our results may be important to understand how altered stretch conditions affect the heart''s functioning.     

A Simulation Study of the Role of Mechanical Stretch in Arrhythmogenesis during Cardiac Alternans

The deformation of the heart tissue due to the contraction can modulate the excitation, a phenomenon referred to as mechanoelectrical feedback (MEF), via stretch-activated channels. The effects of MEF on the electrophysiology at high pacing rates are shown to be proarrhythmic in general. However, more studies need to be done to elucidate the underlying mechanism. In this work, we investigate the effects of MEF on cardiac alternans, which is an alternation in the width of the action potential that typically occurs when the heart is paced at high rates, using a biophysically detailed electromechanical model of cardiac tissue. We observe that the transition from spatially concordant alternans to spatially discordant alternans, which is more arrhythmogenic than concordant alternans, may occur in the presence of MEF and when its strength is sufficiently large. We show that this transition is due to the increase of the dispersion of conduction velocity. In addition, our results also show that the MEF effects, depending on the stretch-activated channels’ conductances and reversal potentials, can result in blocking action potential propagation.     

Simulation of high-frequency sinusoidal electrical block of mammalian myelinated axons

High frequency alternating current (HFAC) sinusoidal waveforms can block conduction in mammalian peripheral nerves. A mammalian axon model was used to simulate the response of nerves to HFAC conduction block. Sinusoidal waveforms from 1 to 40 kHz were delivered to eight simulated axon diameters ranging from 7.3 to 16 μm. Conduction block was obtained between 3 to 40 kHz. The minimum peak to peak current at which block was obtained, defined as the block threshold, increased with increasing frequency. Block threshold varied inversely with axon diameter. Upon initiation, the HFAC waveform produced one or more action potentials. These simulation results closely parallel previous experimental results of high frequency motor block of the rat sciatic and cat pudendal nerve. During HFAC block, the axons showed a dynamic steady state depolarization of multiple nodes, strongly suggesting a depolarization mechanism for HFAC conduction block. Action Editor: Karen Sigvardt     

Inference of motor unit recruitment order in voluntary and electrically elicited contractions

The relationship between surface myoelectric signal parameters and the level of voluntary or electrically elicited contractions was studied in 32 experiments on the tibialis anterior muscle of 22 healthy human subjects. Contractions were performed at 20 and 80% of the maximum voluntary contraction torque. Two levels of stimulation current were used, yielding, respectively, a maximum M wave and an M wave approximately 30% of the maximum. A four-bar electrode probe was used to detect single- and double-differential signals from which mean and median frequency of the power spectrum and average muscle fiber conduction velocity were estimated. Measurements obtained from voluntary contractions showed a positive correlation between contraction levels and both conduction velocity and spectral parameters. Conduction velocity increased by 21.2 +/- 10.9% when voluntary contraction level increased from 20 to 80% of the maximal value. Spectral parameters increased by similar amounts. Tetanic electrical stimulation was applied to a muscle motor point for 20 s via surface electrodes. Rectangular current pulses with 0.1-ms width and frequencies of 20, 25, 30, 35, and 40 Hz were used. Four types of behavior were observed with increasing stimulation level: 1) the two spectral parameters and conduction velocity both increased with stimulation in 15 experiments, 2) the two spectral parameters decreased and conduction velocity increased in 8 experiments, 3) the two spectral parameters and conduction velocity both decreased in 6 experiments, and 4) the two spectral parameters increased and conduction velocity decreased in 3 experiments. Conduction velocity increased with increasing stimulation current in 72% of the experiments, indicating a recruitment order similar to that of voluntary contractions, although it decreased in the other 28% of the cases, indicating a reverse order of recruitment. Contrary to what is observed in direct stimulation of nerves, motor units are not in general recruited in reverse order of size during electrical stimulation of a muscle motor point. This discrepancy may be the result of geometric factors or a lack of correlation between axonal branch diameter and the diameter of the parent motoneuron axon. Changes of conduction velocity and spectral parameters in opposite directions may be the result of the combined effect of the motor unit recruitment order and of the different tissue filtering function associated with the geometric location of the recruited motor units within the muscle.     

Optical recording of action potential propagation in demyelinated frog nerve.

Conduction in focally demyelinated frog nerves has been measured optically using potential-sensitive dyes. Absorption changes were recorded with an array of photodiodes positioned in the image plane of a microscope. Both the amplitude and conduction velocity of the optical signals decreased in the demyelinated region. Conduction was improved after exposure to the potassium channel blocking agent 4-aminopyridine.     

Experimental study of the conducted action potential in cardiac Purkinje strands

Conduction velocity is a complex physiological process that integrates the active and passive properties of the excitable cell. The relations between these properties in determining the conduction velocity are not intuitively obvious, and models have been used frequently to illustrate important relationships. To study the relationships of important parameters and to evaluate commonly used models, we changed conduction velocity experimentally in sheep cardiac Purkinje strands by reducing extracellular Na systematically. Cable analyses were also performed to obtain passive membrane and cable properties. Resting membrane resistance and capacitance did not change, nor did core resistance. Active properties measured in addition to conduction velocity included maximal upstroke velocity, action potential height, time constant of the foot, peak inward current, and upstroke power. With reduction in extracellular Na, all of these parameters of the action potential changed nonlinearly and not in direct proportion to the change in conduction velocity. The only simple relation found was a linear relationship between maximal upstroke velocity and peak inward current, normalized by the capacity of the foot. Models based on the cable equation and the wave equation offer a basis for quantitative analysis of conduction, and these data can be used to test the models.     

Subtle Paranodal Injury Slows Impulse Conduction in a Mathematical Model of Myelinated Axons

This study explores in detail the functional consequences of subtle retraction and detachment of myelin around the nodes of Ranvier following mild-to-moderate crush or stretch mediated injury. An equivalent electrical circuit model for a series of equally spaced nodes of Ranvier was created incorporating extracellular and axonal resistances, paranodal resistances, nodal capacitances, time varying sodium and potassium currents, and realistic resting and threshold membrane potentials in a myelinated axon segment of 21 successive nodes. Differential equations describing membrane potentials at each nodal region were solved numerically. Subtle injury was simulated by increasing the width of exposed nodal membrane in nodes 8 through 20 of the model. Such injury diminishes action potential amplitude and slows conduction velocity from 19.1 m/sec in the normal region to 7.8 m/sec in the crushed region. Detachment of paranodal myelin, exposing juxtaparanodal potassium channels, decreases conduction velocity further to 6.6 m/sec, an effect that is partially reversible with potassium ion channel blockade. Conduction velocity decreases as node width increases or as paranodal resistance falls. The calculated changes in conduction velocity with subtle paranodal injury agree with experimental observations. Nodes of Ranvier are highly effective but somewhat fragile devices for increasing nerve conduction velocity and decreasing reaction time in vertebrate animals. Their fundamental design limitation is that even small mechanical retractions of myelin from very narrow nodes or slight loosening of paranodal myelin, which are difficult to notice at the light microscopic level of observation, can cause large changes in myelinated nerve conduction velocity.     

Predicting human disease-associated circRNAs based on locality-constrained linear coding

Circular RNAs (circRNAs) are a new kind of endogenous non-coding RNAs, which have been discovered continuously. More and more studies have shown that circRNAs are related to the occurrence and development of human diseases. Identification of circRNAs associated with diseases can contribute to understand the pathogenesis, diagnosis and treatment of diseases. However, experimental methods of circRNA prediction remain expensive and time-consuming. Therefore, it is urgent to propose novel computational methods for the prediction of circRNA-disease associations. In this study, we develop a computational method called LLCDC that integrates the known circRNA-disease associations, circRNA semantic similarity network, disease semantic similarity network, reconstructed circRNA similarity network, and reconstructed disease similarity network to predict circRNAs related to human diseases. Specifically, the reconstructed similarity networks are obtained by using Locality-Constrained Linear Coding (LLC) on the known association matrix, cosine similarities of circRNAs and diseases. Then, the label propagation method is applied to the similarity networks, and four relevant score matrices are respectively obtained. Finally, we use 5-fold cross validation (5-fold CV) to evaluate the performance of LLCDC, and the AUC value of the method is 0.9177, indicating that our method performs better than the other three methods. In addition, case studies on gastric cancer, breast cancer and papillary thyroid carcinoma further verify the reliability of our method in predicting disease-associated circRNAs.     

Gap junction uncoupling and discontinuous propagation in the heart. A comparison of experimental data with computer simulations.

The effects of octanol on longitudinal propagation in guinea pig papillary muscles were measured by intracellular microelectrodes. These data were compared with alterations in conduction induced by stepwise removal of gap junction channels in computer simulations of propagation based on a discontinuous cable model. Octanol reduced the velocity (theta) of propagating action potentials (APs) from 53.2 +/- 3.5 to less than 6.6 +/- 2.1 cm/s before block occurred. The maximal rate of rise (Vmax) changed in a biphasic manner, increasing from 133.1 +/- 5.4 in controls to 201.7 +/- 11.0 V/s when theta was 20.5 +/- 2.8 cm/s, and then declining to less than 58.6 +/- 15.2 V/s just before block. The input resistance and time constant of the AP foot increased, and the ascending limb of phase-plane loops became increasingly nonlinear and notched during octanol treatment. All effects of octanol reversed upon washout. A strand of cardiac tissue was modeled as a discontinuous cable composed of 40 cells, each with 10 isopotential membrane segments described by Beeler-Reuter kinetics, and coupled by a variable number of gap junction channels (156 pS). Decreasing the number of channels from 40,000 to 400 to 60 slowed conduction from 62.6 to 16.4 to 3.1 cm/s. As noted in the experimental data, Vmax increased from 103 to 130 and then fell to less than 96 V/s. The AP foot increased and became nonexponential. Distinct notches developed during phase 1 of the APs at slower propagation velocities in the experiments and simulations. The close similarities between the experimental and theoretical data obtained in this study supports the applicability of a discontinuous cable model for describing longitudinal propagation in the heart.     

Differences between the channels, currents and mechanisms of conduction slowing/block and accommodative processes in simulated cases of focal demyelinating neuropathies

To clarify the differences between the mechanisms of conduction slowing/block and accommodative processes in focal demyelinating neuropathies, this computational study presents the kinetics of the ionic, transaxonal and transmyelin currents defining the intracellular and electrotonic potentials in different segments of human motor nerve fibres. The computations use our previous double cable model of the fibres. The simulated fibres have focal demyelination of internodes, paranodes or both together. The intracellular potentials are defined mainly by the Na(+) current, as the contribution of the K(+) fast and K(+) slow currents to the total nodal ionic current is negligible. The paranodal demyelinations cause an increase in the transaxonal current and a decrease in the transmyelin current at the paranodal segments. However, there is an inverse relationship between the transaxonal and transmyelin currents at the same segments in the cases of internodal demyelination. The internodal ionic channels beneath the myelin sheath do not contribute to the intracellular potentials, but they show a high sensitivity to long-lasting pulses. The slow components of the electrotonic potentials depend on the activation of the channel types in the nodal or internodal axolemma, whereas the fast components of the potentials are determined mainly by the passive cable responses. However, the current kinetics changes (defining the investigated electrotonic changes) are relatively weak. The study summarizes the results from these modelling investigations on the mechanisms underlying the conduction slowing/block and accommodative processes in focal demyelinating neuropathies such as Guillain-Barré syndrome and multifocal motor neuropathy.     

A cleft model for cardiac Purkinje strands.

Conduction of the action potential in cardiac muscle is complicated by its multicellular structure, with narrow intercellular clefts and cell-to-cell coupling. A model is developed from anatomical data to describe cardiac Purkinje strands of variable diameter and different internal arrangements of cells. The admittance of the model is solved analytically and fit to results of cable analysis. Using the extracted specific membrane and cell electrical parameters (Rm = 13 K omega cm2, Cm = 1.5 mu F/cm2, Ri = 100 mu cm, and Re = 50 omega cm), the model correctly predicted conduction velocity and filling of capacitance at the onset of a voltage step. The analysis permits more complete studies of the factors controlling conduction velocity; for instance, the effect on conduction velocity of a capacity in the longitudinal current circuit is discussed. Predictions of the impedance and phase angle were also made. Measurements of the frequency dependence of phase angle may provide a basis for separating cleft membrane properties from those of the surface membrane and may aid the measurement of nonlinear membrane properties in muscle.     

On the cable theory of nerve conduction

Conduction of an impulse in the nonmyelinated nerve fiber is treated quantitatively by considering it as a direct consequence of the coexistence of two structurally distinct regions, resting and active, in the fiber. The profile of the electrical potential change induced in the vicinity of the boundary between the two regions is analyzed by using the cable equations. Simple mathematical formulae relating the conduction velocity to the electrical parameters of the fiber are derived from the symmetry of the potential profile at the boundary. The factors that determine the conduction velocity in the myelinated nerve fiber are reexamined.     

Slow Conduction in Cardiac Muscle: A Biophysical Model

Mechanisms of slow conduction in cardiac muscle are categorized and the most likely identified. Propagating action potentials were obtained experimentally from a synthetically grown strand of cardiac muscle (around 50 μm by 30 mm) and theoretically from a one-dimensional cable model that incorporated varying axial resistance and membrane properties along its length. Action potentials propagated at about 0.3 m/s, but in some synthetic strands there were regions (approximately 100 μm in length) where the velocity decreased to 0.002 m/s. The electrophysiological behavior associated with this slow conduction was similar to that associated with slow conduction in naturally occurring cardiac muscle (notches, Wenckebach phenomena, and block). Theoretically, reasonable changes in specific membrane capacitance, membrane activity, and various changes in geometry were insufficient to account for the observed slow conduction velocities. Conduction velocities as low as 0.009 m/s, however, could be obtained by increasing the resistance (r_i) of connections between the cells in the cable; velocities as low as 0.0005 m/s could be obtained by a further increase in r_i made possible by a reduction in membrane activity by one-fourth, which in itself decreased conduction velocity by only a factor of 1/1.4. As a result of these findings, several of the mechanisms that have been postulated, previously, are shown to be incapable of accounting for delays such as those which occur in the synthetic strand as well as in the atrioventricular (VA) node.