Electrical Mapping
Module: tutorials.02_EP_tissue.08_lats.run
Section author: Fernando Campos <fernando.campos@kcl.ac.uk>
This tutorial demonstrates how to compute local activation times (LATs) and action potential durations (APDs) of cells in a cardiac tissue.
The wavelength of the cardiac impulse, given by the product of conduction velocity (CV) and refractory
period, is of utmost importance for the study of arrhythmia mechanisms. The assessment of the CV as
well as the refractory period of the cardiac action potential (AP) relies on the determination of
activation and repolarization times, respectively. Experimentally, these are usually calculated based
on 1) transmembrane voltages measured by glass micro-electrodes or in optical
mapping; or 2) extracellular potentials
measured at the surface of the tissue.
The estimation of activation/repolarization times is based on an event detector that records the
instants when the selected event type occurs. Local activation time (LAT), for instance, is usually
taken as the time of maximum or the minimum
:
Fig. 106 Action potential in an uncoupled cell. Upper panel: transmembrane potential
and its time derivative
. Lower panel: extracellular potential
and its time derivative
. LAT is usually taken as the time of maximum
or the minimum
.
Instead of using derivatives, LATs can also been estimated by the crossing of a threshold value provided
that the chosen value reflects the sodium channel activation since they are responsible for the rising
phase of AP. One could, for instance, pick the time instant when crosses -10 mV
with a positive slope. Equally, one could look for crossing of
with a negative
slope to detect repolarization events. AP duration (APD) can then be computed as the difference between
repolarization and activation times. The detection of activation (
) and repolarization
(
) times based on threshold crossing is illustrated below:
This example will run a simulation using a 2D sheet model (1 cm x 1 cm). A transmembrane stimulus
current of 100 uA/cm^2 is applied for a period of 1 ms at the middle of the left side of the tissue.
A ground electrode is placed at the opposite side of the stimulating electrode. Simulation of electrical
activity is based on the bidomain equations. Cellular dynamics cardiac myocytes within the tissue are
described using the Modified Beeler-Router Drouhard-Roberge (MBRDR) model. Activation times are obtained
either from or
using a threshold crossing method, whereas
repolarization can only be obtained by threshold crossing from
. Estimation of
repolarization times from
is out of the scope of this tutorial.
To run this tutorial :
cd tutorials/08_lats
./run.py --help
The following optional arguments are available (default values are indicated):
--quantity Quantity/variable/signal used to compute activation time
Options: {vm,phie}
Default: vm
--act-threshold The threshold value for determining activation from :math:`V_{\mathrm m}` or :math:`\phi_{\mathrm e}`
Default: -10 mV
--rep-threshold The threshold value for determining repolarization from :math:`V_{\mathrm m}
Default: -70 mV
--show-APDs Visualize APDs instead of LATs
If the program is run with the --visualize
option, meshalyzer will automatically load the computed
activation sequence (LATs). If the --show_APDs
is given, then the computed APDs will be loaded:
Visualize LATs:
./run.py --visualize
Visualize APDs:
./run.py --show-APDs
Differences between activation sequences computed from or
and/or with different thresholds can be appreciated with meshalyzer (
--visualize
). The activation
sequence for the default parameters looks like this:
Fig. 108 Activation sequence computed from (
--act-threshold=-10
) obtained after
delivering a stimulus current in the middle of the left side tissue.
Note
Fig. 109 Activation sequence computed from (
--act-threshold=-10
) obtained
after delivering a stimulus current in the middle of the left side tissue.
Note
The computed APDs using the default parameters looks like this (use --show-APDs
instead of --visualize
):
The relevant parameters used in the tissue-scale simulation are shown below:
# Number of events to detect
-num_LATs = 2
# Event 1: activation
-lats[0].ID = 'ACTs'
-lats[0].all = 0
-lats[0].measurand = 0
-lats[0].threshold = -10
-lats[0].mode = 0
# Event 2: repolarization
-lats[1].ID = 'REPs'
-lats[1].all = 0
-lats[1].measurand = 0
-lats[1].threshold = -70
-lats[1].mode = 1
num_LATs referes to the number of events we want to detect. In this tutorial there are two events:
activation and repolarization. -lats[0] are options to compute activation while -lats[1] are options
to compute repolarization. -lats[].ID is the name of output file; -lats[].all tells CARP if it should
detect only the first event (-lats[].all = 0), i.e. first beat, of all of them (-lats[].all = 1);
-lats[].measurand refers to the quantity: (0) or
(1);
-lats[].threshold is the threshold value for determining the event; finally, -lats[].mode tells CARP
to look for threshold crossing with a either a positive or negative slope.