Model number

Cardiac Action Potential with Ca, K, and Na currents. Beeler-Reuter 1977 paper.


fig 1

Beeler-Reuter 1977, the first action potential model accounting for calcium currents. The Na current, iNa, is a variant of the Hodgkin Huxley Na current, modified by having a second inactivation variable j, The potassium current iK1 is inward rectifier. The ix1 current represents a summation of other K currents in the dog heart, and is somewhat empirical. The code is overly compact, to keep it on one page. Notation is provided after the program code. The Na and K concentrations are fixed, but Cai is variable: Ca influx with each excitation is counterbalanced by a slow "efflux" represented by an exponential return (time constant tauCa) toward the initial Cai.
Figure shown on right is plot 1 and plot 3 of "current" plot page. ix1 represents the current through x1 channel,(mA/cm^2) which is mainly potassium.

  • Missing file.

Beeler-Reuter 1977 (BR77) JSim Model Notes:

  • Vrest: = -80 mV: It was simplified here to allow the three ionic current to be totally distinct sections of code for the purposes of building modules for reconstructing cell models.
  • BR77 fig 2 is reproduced on plot "AP_Ca" plot 2 (lower)
  • BR77 fig 3 is reproduced on plot "current" plot 2 (right upper)
  • BR77 (Shown here) fig 4 is reproduced on plot "current" plot 1 (left upper) and plot "AP_Ca" (upper)
  • BR77 fig 5 h*j product is reproduced on plot "AP_Ca" plot 1 (upper) Conditions need to be changed using the Vclamp conditions described
  • BR77 fig 6 time course of f is reproduced on plot "AP_Ca" plot 1 (upper) of x1 (Shown here) is reproduced on plot "current" plot 3 (lower left)
  • BR77 fig 7: Upper: Change gbCa +/- 10% for the BR variable gbars. Change ixscale +/- 10% for BR ibar xi.
  • BR77 fig 8: Parset BRfig8 The influence of current during the early plateau phase is more evident in the Purkinje fibre than in the ventricular myocyte. To mimic the Purkinje fibre, double ixscale and halve iK1scale. For Iext, use fgen_8, to select the Pulse2 set up to give 2 pulses: the first is the same as the usual stimulus pulse, while the second (fgen_8.Pulse2.p2Amplitude) is varied from -0.04 to higher levels in 0.02 steps using the loops. Greater depolarization during the plateau now shortens the AP. Restore the orig parameter set: Runtime, Model params; then reset ixscale to 0.0008 and iK1scale to 0,00035. or alternatively go to: Par Set; Load project parameter set; select BR from popup window.
  • BR77 fig 12.Par set BRfig12. Effects of tetrodotoxin shutting down iNa. Turn off stimulus, setting Iext = 0 to see spontaneous APs. Diminish or knock out gbNa = 0 (_ block iNa). Increase the leak Na conductance, gNaC by 8-fold

Other Figures need to be added using Vclamp.


The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

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 Beeler GW Jr and Reuter H. Reconstruction of the action potential of ventricular
 myocardial fibres. J Physiol (Lond) 268: 177-210, 1977.

Others related:
 Bassingthwaighte JB and Reuter H. Calcium movements and excitation-contraction
 coupling in cardiac cells. In: Electrical Phenomena in the Heart, edited by
 DeMello WC. New York: Academic Press, Inc., 1972, pp 353-395.[Defines variables d and f kinetics]

 Bassingthwaighte JB, Beeler GW, Sidell PM, Reuter H, and Safford RE. A model
 for calcium movements and excitation-contraction coupling in cardiac cells.
 In: Regulation and Control in Physiological Systems, edited by Iberall AS and
 Guyton AC. Rochester, New York: Internat. Proc. Conf.Amer.Physiol.Soc,1973, pp 36-38.
 [Implements model of 1972 paper]

 Beeler GW Jr and Reuter H. Voltage clamp experiments on ventricular myocardial
 fibres. J Physiol 207: 165-190, 1970.

 Beeler GW Jr and Reuter H. Membrane calcium current in ventricular myocardial
 fibres. J Physiol 207: 191-209, 1970.

 Beeler GW Jr and Reuter H. The relation between membrane potential, membrane
 currents, and activation of contraction in ventricular myocardial fibres.
 J Physiol 207: 211-229, 1970.
Key terms
Cardiac electrophysiology
ionic currents
voltage clamp
dog canine heart
ventricular fibre
fiber action potential
Nernst potential
time and voltage-dependent time constants
cell physiology

Please cite in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

Model development and archiving support at provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.