# Adjusting wavelength to experimental data

See code in GitLab.
Author: Jason Bayer jason.bayer@ihu-liryc.fr

This tutorial demonstrates how to adjust parameters in tissue simulations to match experimental data for conduction velocity, action potential duration, and wavelength. To run the experiments of this tutorial change directories as follows:

## Experimental data

The mapping of electrical activity with optical imaging on the epicardium of human ventricles provides an accurate measurement of CV 1 and APD 2 . The data from these studies is shown below and were recorded during baseline pacing with a cycle length of 1000 ms.

Tissue state $$CV_{l}$$ (cm/s) $$CV_{t}$$ (cm/s) $$APD_{80}$$ (ms) $${\lambda}_{l}$$ (cm) $${\lambda}_{t}$$ (cm)

Nonfailing

92

22

340

34

8

## 1D cable model

A 1.5 cm cable of epicardial ventricular myocytes is used to initially adjust CV and APD to experimentally derived values. The model domain was discretized with linear finite elements with an average edge length of 0.02 cm.

## 2D sheet model

A 1.5 cm x 1.5 cm sheet of epicardial tissue is used to verify CV and APD derived in the 1D cable model. The model domain is discretized using quadrilateral element finite elements with an average edge length of 0.02 cm, and a longitudinal fiber direction in each element parallel to the X-axis of the sheet. The mesh was generated using the command below according to the mesher tutorial.

./mesher -size[0] 1.5 -size[1] 1.5 -size[2] 0.0 -resolution[0] 200.0 -resolution[1] 200.0 -resolution[2] 0.0

## Ionic model

For this example, we use the most recent version of the ten Tusscher ionic model for human ventricular myocytes 3 that was modified for the study 4 . This ionic model is labeled GTT2_fast in openCARP's LIMPET library. After a quick literature search, one will find that the slow outward rectifying potassium current $$I_{K_{s}}$$ is heterogeneous across the human ventricular wall 5 . Therefore, the maximal conductance $$G_{K_{s}}$$ of $$I_{K_{s}}$$ is adjusted in order to match the APD=340 ms derived experimentally. Note, the default value for $$G_{K_{s}}$$ in epicardial ventricular myocytes is 0.392 nS/pF.

## Pacing protocol

The left side of the 1D cable model and the center of the 2D sheet model is paced with 5-ms-long stimuli at twice capture amplitude for a cycle length and number of beats chosen by the user.

## Conduction velocity

To determine initial conditions for the tissue conductivities along ($$\sigma_{il}$$, $$\sigma_{el}$$) and transverse ($$\sigma_{it}$$, $$\sigma_{et}$$) the fibers in the models, tuneCV is used as described in the tutorial Tuning Conduction Velocities. The commands to obtain the two conductivities are listed below.

./tuneCV --converge true --tol 0.0001 --velocity 0.92 --model GTT2_fast --sourceModel monodomain --resolution 200.0

./tuneCV --converge true --tol 0.0001 --velocity 0.22 --model GTT2_fast --sourceModel monodomain --resolution 200.0

The initial conductivities resulting from tuneCV are $$\sigma_{il}=0.3544$$ S/m, $$\sigma_{el}=1.27$$ S/m, $$\sigma_{it}=0.024$$ S/m, and $$\sigma_{et}=0.0862$$ S/m.

To compute CV, activation times are computed for the last beat of the pacing protocol using the openCARP option LATs (see tutorial on electrical mapping), with activation time recorded at the threshold crossing of -10 mV. CV is then computed along the cable by taking the difference in activation times at the locations 1.0 cm and 0.5 cm divided by the distance between the two points. For the sheet model, CV is computed along the longitudinal and transverse fiber directions by taking the difference in activation times at the locations illustrated in the figure below. Specifically, $$CV_{l}$$ = 0.25/(L2-L1) and $$CV_{t}$$ = 0.25/(T2-T1). The locations of L1 and T1 are 0.25 cm away from the tissue center, and L2 and T2 are 0.5 cm away from the tissue center.

## Action potential duration

Activation potential duration is computed at 80% repolarization ($$APD_{80}$$) according to [Bayer2016]. This is achieved by using the igbutils function igbapd as illustrated below.

./igbapd --repol=80 --vup=-10 --peak-value=plateau ./vm.igb 

## Usage

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

./run.py --help
--dimension         Options: {cable,sheet}, Default: cable
Choose cable for quick 1D parameter adjustments,
then the 2D sheet to verify the adjustments.
--GKs               Default: 0.392  nS/pF
Maximal conductance of IKs
--Gil               Default: 0.3544 S/m
Intracellular longitudinal tissue conductivity
--Gel               Default: 1.27 S/m
Extracellular longitudinal tissue conductivity
--Git               Default: 0.024 S/m
Intracellular transverse tissue conductivity
--Get               Default: 0.0862 S/m
Extracellular transverse tissue conductivity
--nbeats            Default: 3
Number of beats for pacing protocol. This number
should be much larger to achieve steady-state
--bcl               Default: 1000
Basic cycle length for pacing protocol
--timess            Default: 1000
Time before applying pacing protocol

After running run.py, the results for APD, CV, and ($$\lambda$$) can be found in the file adjustment_results.txt within the output subdirectory for the simulation.

If the program is ran with the --visualize option, meshalyzer will automatically load the $$V_m(t)$$ for the last beat of the pacing protocol. Output files for activation and APD are also produced for each simulation and can be found in the output directory and loaded into meshalyzer.

1. Determine the value for IKs to obtain the experimental value for APD in the cable.
2. Place this value in the sheet model to verify the model is behaving in the same manner as the simple cable model.
3. Determine a set of Gil and Gel (keep ratio for Gil/Git the same) so that both the longitudinal and transverse wavelengths are less than 8 cm.

1. A GKs=0.25 nS/pF is needed to obtain the APD of 340 ms.
./run.py --GKs 0.25 --dimension cable
1. The following command produces the same APD in the sheet model.
./run.py --GKs 0.25 --dimension sheet
1. The following commands produce longitudinal and transverse wavelengths less than 8 cm.
./run.py --GKs 0.25 --Gil 0.02 --Git 0.0135 --dimension cable

./run.py --GKs 0.25 --Gil 0.02 --Git 0.0135 --dimension sheet

References

1. Glukhov AV, Fedorov VV, Kalish PW, Ravikumar VK, Lou Q, Janks D, Schuessler RB, Moazami N, Efimov IR. Conduction remodeling in human end-stage nonischemic left ventricular cardiomyopathy. Circulation, 125(15):1835-1847, 2012. [Pubmed]↩︎

2. Glukhov AV, Fedorov VV, Lou Q, Ravikumar VK, Kalish PW, Schuessler RB, Moazami N, and Efimov IR. Transmural dispersion of repolarization in failing and nonfailing human ventricle. Circ Res, 106(5):981-991, 2010. [Pubmed]↩︎

3. ten Tusscher KHWJ, Panfilov AV. Alternans and spiral breakup in a human ventricular tissue model. Am J Physiol Heart Circ Physiol, 291(3):H1088-H1100, 2006. [Pubmed]↩︎

4. 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]↩︎

5. Pereon Y, Demolombe S, Baro I, Drouin E, Charpentier F, Escande D. Differential expression of kvlqt1 isoforms across the human ventricular wall. Am J Physiol Heart Circ Physiol, 278(6):H1908-H1915, 2000. [Pubmed]↩︎

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