SOFTWARE PACKAGE FOR ELECTROPHYSIOLOGICAL MODELING OF NEURONAL AND CARDIAC EXCITABLE CELLS

Summary

The software package described in this article is dedicated for educational and research purposes in the area of electrophysiological cell membrane properties modeling. The designed and created software package offers a selection of several models of nerve fibre membrane, cortical neuron models and various models of heart cells. The model properties and simulation conditions can be set interactively. Consequently, generation of an action potential (AP) on a particular membrane can be observed. The software allows computation and graphical visualization of actual time courses of model state variables, particularly the membrane potential, membrane currents and other model variables. Eventually, additional important characteristics are evaluated from the output data, such as AP duration (APD) of heart cells or AP frequency of cortical neurons.

Keywords:
electrophysiological modeling, software package, neuron, heart cell, cell membrane models, action potential

Introduction

Computational cell models are a very useful tool for better understanding of cell function, furthermore, they create powerful ability to predict cell behavior under different conditions. Models of excitable nerve, heart and muscle cells have been developed for more than half a century. This began with the well-known Hodgkin-Huxley model of the giant squid axon [4], and other cell type models then followed.

System description

Various models of nerve fibre membrane [1], [3], [4], [10], [11] cortical neuron models [11] – [13] and various models of heart cells [2], [5] – [9] are included in this software package:

Nerve fibre membrane models:

Hodgkin-Huxley model,

Frankenhaeuser-Huxley model,

Fitzhugh-Nagumo model,

Chiu-Ritchie-Rogart-Stagg-Sweeney model,

Schwarz-Eikhof model, and more;

Cortical neuron models:

Wilson regular spiking model,

Wilson fast spiking model,

Wilson bursting model, and more;

Heart ventricular cell models:

Luo-Rudy model,

Hund-Rudy dynamic model,

O'Hara-Rudy model, and more;

Other heart cell models include:

Michaels model of the sinoatrial (SA) node,

Nygren model of the atrial cell.

The cell type branch and consequently the cell model type is selected in the main window of the designed program (Fig. 2, Fig. 4). The following two main parameters can then be set: (1) the number of periods (period is denoting the cycle length) and (2) the duration of one period. 

A stimulation current of prescribed amplitude and duration is applied to the membrane during each period. LÉKAŘ Parameters related to stimulation current, as well as many other cell model parameters, such as intracellular and extracellular ion concentrations, ion channel characteristics and dimensional attributes can be changed in the “Model parameters” window. In the “Initial conditions” window, the user can view and change the values for the initial conditions of model state variables.

After pressing the “Compute” button, new computation is achieved with actual parameter settings. Results are graphically visualized on three panels: the upper panel shows the time course of the membrane potential, the middle one (“Subplot2”) shows the time course of the selected state variable, such as intracellular calcium concentration (Fig. 4) and the bottom one (“Subplot3”) shows the time course of selected membrane current or a different selected derived variable, as exemplified in the evaluated APD also in Figure 4. After pressing the “More info” button, a new window with a description of the particular cell model is opened.

Nerve fibre membrane models

The Hodgkin-Huxley model of an unmyelinated nerve fibre is one of the most often used models [4]. This model consists of only two types of voltagesensitive ion channels: the sodium channel and the potassium channel; which are represented by nonlinear conductances G_Na and G_K (in mS) in Figure 1. 

The stimulation current I_st (in μA) across the membrane is divided into the ionic current I_ionic and capacitive current through the membrane capacity C_m (in μF): 

The time change of the membrane potential (in mV) is then:

where i_ionic and ist are the current densities (in μA/cm²), cm is the membrane capacity per 1 cm² (in μF/cm²) and t is time (in ms). For the Hodgkin- Huxley model, the ionic current density is determined only by the sodium, potassium and leakage ion flows:

Cortical neurons

The cortical neurons generate a train of nerve impulses with frequency of 1 – 100 Hz or a burst-like activity of nerve impulses (Fig. 2, upper trace: bursts of APs generated by the Wilson bursting model) [12]. The cortical neuron membrane usually contains more types of ion channels than the nerve fibre membrane.

Using the developed software package, the influence of stimulation parameters and model parameters on the AP frequency may be observed (Fig. 2, lower trace).

Heart ventricular cells

The ventricular heart cells (myocytes) comprise many more types of membrane ion channels, ion pumps and exchangers, as depicted in Figure 3. These include channels for the L-type calcium current, the slow and rapid delayed rectifier potassium current, the calcium pump current and the sodium/potassium ATPase current.

Calcium ions play the primary role in the excitationcontraction coupling in myocytes. Advanced models of left ventricular myocytes, such as the Hund-Rudy dynamic model [5], and the O'Hara-Rudy dynamic model [9] contain different calcium buffers, including calmodulin and troponin, and also calcium ion fluxes through the sarcolemmal (cell) membrane and through the membrane of the sarcoplasmic reticulum (SR) which is the main reservoir of calcium ions.

In the software package, membrane and SR currents, ion concentrations and membrane potential parameters influenced by model parameters and other simulated conditions can be evaluated and observed. These include the AP duration depicted in the lower trace in Figure 4.

Conclusion

The presented software package can help researchers and students to understand the basic and more complex principles related to excitation in neuronal and cardiac cells. This knowledge poses the basis of the electrophysiology of the heart and the nervous system.

The described software package has been developed in the Matlab programming environment and it can be continuously extended by new models of various cell types. This software package can find a great number of applications in different branches of electrophysiological research.

Acknowledgement

The work has been supported by the Slovak Ministry of Education under grants VEGA 1/0987/12, VEGA 2/0210/10 and APVV-0513-10.

Elena Cocherová, Ph.D.

Institute of Electronics and Photonics,

Faculty of Electrical Engineering and Information

Technology Slovak University of Technology

Ilkovičova 3, 812 19 Bratislava

E-mail: elena.cocherova@stuba.sk

Phone: +421 2 60291174