Computing conduction velocity restitution


Section author: Jason Bayer <>

This tutorial demonstrates how to compute conduction velocity restitution in cardiac tissue.


Conduction velocity restitution is an important property of cardiac tissue. As pacing frequency is increased, conduction velocity will become slower. For this tutorial, the user will shown how to construct conduction velocity restitution curves to describe the conduction properties of cardiac tissue in response to various pacing protocols.

Problem setup

1D cable model

A 1.0 cm cable of epicardial ventricular myocytes is used to generate a CV restitution curve for a user defined pacing protocol. The model domain was discretized with linear finite elements with an average edge length of 0.01 cm.

Ionic model

This tutorial uses the most recent version of the ten Tusscher ionic model for human ventricular myocytes [Tusscher2006] that was modified for the study [Bayer2016] . This ionic model is labeled GTT2_fast in CARP’s LIMPET library.

Pacing protocol

The left side of the 1D cable model is paced with 5-ms-long stimuli at twice capture amplitude for an S1S2 restitution pacing protocol defined by the user inputs.The user sets the cycle length and number of beats for S1 pacing, and the range of cycle lengths to apply for the S2.

Conduction velocity

Activation times are computed for each S2 beat of the pacing protocol using the CARP option LATs (see tutorial X). CV is then computed along the cable by taking the difference in activation times at the locations 0.25 cm and 0.75 cm divided by the distance between the two points.


The following optional arguments are available (default values are indicated):

./ --help 
  --Gil               Default: 0.3650 S/m
                      Intracellular longitudinal tissue conductivity
  --Gel               Default: 1.3111 S/m
                      Extracellular longitudinal tissue conductivity
  --nbeats            Default: 5
                      Number of beats for S1 pacing at CI1
  --CI0               Default: 300 ms
                      Shortest S2 coupling interval
  --CI1               Default: 500 ms
                      S1 cycle length and longest S2 coupling interval
  --CIinc             Default: 25 ms
                      Decrement for time interval from CI1 to CI0

After running, the CI and CV are output into the ASCII file CVrestitution_GTT2_fast_bcl_…..

If the program is run with the --visualize option, the CV restitution curve in the file above will be plotted using pythons plotting functions.


  1. Determine the minimum S2 CI for the default parameters
  2. Determine the effect of decreasing Gil by 75% on the minimum S2 CI.
  3. Determine the effect of increasing Gil by 50% on the minimum S2 CI.

Solutions to the tasks

  1. The minimum CI for the default parameters is 325 ms.
./ --CI0 300 --visualize --np 2
  1. Reducing Gil by 75% slows down CV and shifts the minimum S2 CI to 300 ms.
./ --CI0 275 --Gil 0.09125 --visualize --np 2
  1. Increasing Gil by 50% speeds up CV and shifts the minimum S2 CI to 375 ms.
./ --CI0 275 --Gil 0.5475 --visualize --np 2


[Bayer2016]Bayer JD, Lalani GG, EJ Vigmond, SM Narayan, NA Trayanova. Mechanisms linking electrical alternans and clinical ventricular arrhythmia in human heart failure. Heart Rhythm, 13(9):1922-1931, 2016. [Pubmed]