Small signal impedance of heart cell membranes

Theoretical Aspects of Resting-State Cardiomyocyte Communication for Multi-Nodal Nano-Actuator Pacemakers

The heart consists of billions of cardiac muscle cells-cardiomyocytes-that work in a coordinated fashion to supply oxygen and nutrients to the body. Inter-connected specialized cardiomyocytes form signaling channels through which the electrical signals are propagated throughout the heart, controlling the heart's beat to beat function of the other cardiac cells. In this paper, we study to what extent it is possible to use ordinary cardiomyocytes as communication channels between components of a recently proposed multi-nodal leadless pacemaker, to transmit data encoded in subthreshold membrane potentials. We analyze signal propagation in the cardiac infrastructure considering noise in the communication channel by performing numerical simulations based on the Luo-Rudy computational model. The Luo-Rudy model is an action potential model but describes the potential changes with time including membrane potential and action potential stages, separated by the thresholding mechanism. Demonstrating system performance, we show that cardiomyocytes can be used to establish an artificial communication system where data are reliably transmitted between 10 s of cells. The proposed subthreshold cardiac communication lays the foundation for a new intra-cardiac communication technique.

Incorporating inductances in tissue-scale models of cardiac electrophysiology

In standard models of cardiac electrophysiology, including the bidomain and monodomain models, local perturbations can propagate at infinite speed. We address this unrealistic property by developing a hyperbolic bidomain model that is based on a generalization of Ohm's law with a Cattaneo-type model for the fluxes. Further, we obtain a hyperbolic monodomain model in the case that the intracellular and extracellular conductivity tensors have the same anisotropy ratio. In one spatial dimension, the hyperbolic monodomain model is equivalent to a cable model that includes axial inductances, and the relaxation times of the Cattaneo fluxes are strictly related to these inductances. A purely linear analysis shows that the inductances are negligible, but models of cardiac electrophysiology are highly nonlinear, and linear predictions may not capture the fully nonlinear dynamics. In fact, contrary to the linear analysis, we show that for simple nonlinear ionic models, an increase in conduction velocity is obtained for small and moderate values of the relaxation time. A similar behavior is also demonstrated with biophysically detailed ionic models. Using the Fenton-Karma model along with a low-order finite element spatial discretization, we numerically analyze differences between the standard monodomain model and the hyperbolic monodomain model. In a simple benchmark test, we show that the propagation of the action potential is strongly influenced by the alignment of the fibers with respect to the mesh in both the parabolic and hyperbolic models when using relatively coarse spatial discretizations. Accurate predictions of the conduction velocity require computational mesh spacings on the order of a single cardiac cell. We also compare the two formulations in the case of spiral break up and atrial fibrillation in an anatomically detailed model of the left atrium, and we examine the effect of intracellular and extracellular inductances on the virtual electrode phenomenon.

Electrical resonance with voltage-gated ion channels: perspectives from biophysical mechanisms and neural electrophysiology

Electrical resonance, providing selective signal amplification at preferred frequencies, is a unique phenomenon of excitable membranes, which has been observed in the nervous system at the cellular, circuit and system levels. The mechanisms underlying electrical resonance have not been fully elucidated. Prevailing hypotheses attribute the resonance to voltage-gated ion channels on the membrane of single neurons. In this review, we follow this line of thinking to summarize and analyze the biophysical/molecular mechanisms, and also the physiological relevance of channel-mediated electrical resonance.

Parametric resonance and amplification in excitable membranes. The Hodgkin-Huxley model

It has previously been shown by different investigators that the excitable membrane shows a resonant sensitivity to periodic external perturbations, but its Q-factor is, as a rule, low. The present paper analyses the possible ways of increasing the membrane Q, using a model of the Hodgkin-Huxley type. It is found, in particular, that it can be increased considerably by modulating periodically the membrane capacitance or the activation and inactivation rate constants of ionic channels, with a frequency of about 2 fo (fo being the fundamental frequency of damped oscillations in the membrane), the extent of modulation not exceeding the critical value 2/Q. In this case, a significant parametric amplification of the membrane current takes place. If the modulation coefficient is above 2/Q, the membrane can display a parametric resonance that causes stable self-oscillations in the potential with a frequency approximately fo. The conditions for the realization of parametric amplification and resonance in biological membranes are discussed.

Linear impedance studies of voltage-dependent conductances in tissue cultured chick heart cells

Plateau and pacemaker currents from tissue cultured clusters of embryonic chick heart cells were studied in the time domain, using voltage-clamp steps, and in the frequency domain, using a wide-band noise input superimposed on a steady holding voltage. In the presence of tetrodotoxin to block the sodium channel, a depolarizing voltage step into the plateau range elicited: (a) a rapid (approximately equal to 2 ms) activation of the slow inward current; (b) a subsequent slower (approximately equal to 25 ms) decline in the slow inward current; and (c) activation of a very slow (5 to 10 s) outward current. Impedance studies in this voltage range could clearly resolve two voltage-dependent processes, which appeared to correspond to points b and c above because of their voltage dependence, pharmacology, and time constants. A correlate of point a was also probably present but difficult to resolve owing to the fast time constant of activation for the slow inward channel. At voltages negative to -50 mV a new voltage-dependent process could be resolved, which, because of its voltage dependence and time constant, appeared to represent the pacemaker channel (also termed If or IK2). In the Appendix, linear models of voltage-dependent channels and ion accumulation/depletion are derived and these are compared with our data. Most of the above-mentioned processes could be attributed to voltage-dependent channels with kinetics similar to those observed in time domain, voltage-clamp studies. However, the frequency domain correlate of the decline of the slow inward current was incompatible with channel gating, rather, it appears accumulation/depletion of calcium may dominate the decline in this preparation.

Linear electrical properties of isolated cardiac cells

A frequency domain equivalent circuit analysis of isolated ventricular cells indicated the presence of an internal membrane structure which has a total capacitance four- to sixfold larger than the surface membrane. The internal membrane was mainly attributed to the sarcoplasmic reticulum since other morphological studies have shown that its area is many-fold larger than that of the surface membrane. Corresponding estimates from the transverse tubular system indicate an area less than that of the surface; thus this structure is not a likely candidate for the observed internal capacitance. Measurements in hypertonic solutions showed that the access resistance to the internal membrane reversibly increased as the tonicity was elevated. Freeze-fractured electron microscopic studies confirmed that hypertonic solutions increased the volume of transverse tubular system, which thus appears to have little relation to the access resistance. The most probable source of the access resistance is the diadic junction to the sarcoplasmic reticulum, which therefore would electrically couple it to the surface membrane.

Cable theory in neurons with active, linearized membranes

This investigation aims at exploring some of the functional consequences of single neurons containing active, voltage dependent channels for information processing. Assuming that the voltage change in the dendritic tree of these neurons does not exceed a few millivolts, it is possible to linearize the non-linear channel conductance. The membrane can then be described in terms of resistances, capacitances and inductances, as for instance in the small-signal analysis of the squid giant axon. Depending on the channel kinetics and the associated ionic battery the linearization yields two basic types of membrane: a membrane modeled by a collection of resistances and capacitances and membranes containing in addition to these components inductances. Under certain specified conditions the latter type of membrane gives rise to a membrane impedance that displays a prominent maximum at some nonzero resonant frequency fmax. We call this type of membrane quasi-active, setting it apart from the usual passive membrane. We study the linearized behaviour of active channels giving rise to quasi-active membranes in extended neuronal structures and consider several instances where such membranes may subserve neuronal function: 1. The resonant frequency of a quasi-active membrane increases with increasing density of active channels. This might be one of the biophysical mechanisms generating the large range over which hair cells in the vertebrate cochlea display frequency tuning. 2. The voltage recorded from a cable with a quasi-active membrane can be proportional to the temporal derivative of the injected current. 3. We modeled a highly branched dendritic tree (delta-ganglion cell of the cat retina) using a quasi-active membrane. The voltage attenuation from a given synaptic site to the soma decreases with increasing frequency up to the resonant frequency, in sharp contrast to the behaviour of passive membranes.(ABSTRACT TRUNCATED AT 400 WORDS)