Beeler-Reuter Model for Ventricular Cells
This applet simulates the Beeler-Reuter model in a 1D cable or 1D ring of
any length between 0.5 cm and 20 cm.
Initiation by a stimulus, propagation, and complex dynamics such as discordant alternans can be studied.
To learn more about the model in a single cell, use the BR single cell applet.
- The Start button initiates the applet. An action potential can be produced
either by pressing the Apply S1 button or by clicking inside the panel with the
mouse, which will produce a stimulus that will generate an action potential if large enough.
The length can be changed at any time by using the Cable Length slider.
The new length is automatically indicated on
the horizontal axis (minimum length is 0.5 cm, maximum is 20 cm).
To observe AP initiation or propagation in more or less detail,
the simulation speed can be increased or decreased at any time by using the
Simulation Speed slider.
When initiating a stimulus using the Apply S1 button,
attributes of the stimulus can be set by using the Strength, Duration,
Length, and Position
The list box in the bottom
left corner is used to choose either a cable or a ring simulation.
Note: using a long cable before changing from a cable to a ring is recommended to prevent self-termination of the wave.
The list box in the bottom
right corner is used to choose either the original Beeler-Reuter (BR) model or
the what is commonly known as the Modified Beeler-Reuter (MBR) model, whose calcium
dynamics are twice as fast with consequent action potential duration and wavelength shortening.
The gna, gnac
and gs text-boxes are used to set the sodium and
calcium conductances used in the simulation.
The check boxes on the right indicate which variables are plotted.
The Reset button brings the membrane potential of all the cells back to the rest state.
The Stop button is used to stop the simulation at any time. The simulation can be resumed by using the
Continue button that replaces the Stop button when the simulation is stopped.
Click the Start button and then the
Apply S1 button to
generate an action potential propagating to the right. As
the wave propagates, enlarge the cable to about 16 cm using the
Cable Length slider at
the top right. When the wave front is
close to the right boundary, click the Stop
button and use the list box in the lower left corner to change the cable to
a ring, then click the Continue button.
This allows the wave to reenter, and after a few rotations around the ring
it will be a steady wave with a
fixed wavelength. Decrease the ring size slowly, and observe the formation
of discordant alternans at a length of 13 cm.
Repeat as above, but change the sodium and/or calcium conductances and find the
lengths at which alternans appear.
Reset using the Reset button and study the threshold for excitation as
a function of the stimulus parameters (strength, duration, and length) as well as
the sodium and calcium
Induce multiple waves by clicking inside the window with the mouse.
Each time the mouse is clicked, a voltage stimulus proportional to the
height of the mouse position within the simulation window is added to the voltage at the
location of the mouse along the cable. Try to block waves and induce a single reentrant wave along a ring.
The model can be found in the following reference: GW Beeler and H Reuter, J Physiol 1977; 268: 177-210.