## Electrophysiology Equation Editor Example

Contents

### Description

- This example guides the user through the process of using the Electrophysiology Ionic Model Editor to create an ionic model that uses the modified Fitz-Hugh Nagumo equations for excitable media. Once created, the model is used to simulate cardiac action potential propagation in a 2-D mesh.

### Start Continuity

- Launch the Continuity Client
On the About Continuity startup screen

check the

**Electrophysiology**box under`Use Modules:`

### Load Problem

Select the cont6 file for this tutorial ( 2D_MFHN_setup.cont6 )

- This file contains the mesh for this problem, but does not have an ionic model specified.

### Create the Ionic Model

Electrophysiology→Edit→Ionic Model...

In the

`Select Model`tab, make sure that`<<add new model>>`is selected.Proceed to the next tab,

`Edit Properties`In the

`File Name`box, type a name for the model, something like`EP_my_MFHN`.**DO NOT NAME IT**`EP_MFHN`, as this file already exists.- Enter a short model description if you wish

Proceed to the next tab,

`Edit Equations`- The equations for the MFHN model are as follows, note that we will only be putting the ODE's in the equation editor, the PDE is of the general form that is solved by Continuity's FE routines.

- To start, we will insert stimulus information that will allow time- and location-dependent stimulus of the tissue
To insert an equation, click

`Insert Variable`on the lower left of the form.Change the variable name to

`stim_end`in the`Name`box and press**ENTER**(click`OK`in the dialog box that pops up)Change the button that says

`Constant`to`Temporary Variable`Click

`Insert→Template`on the upper left menu bar, note that in the`equation`box the following appears:`stim_end = t`Copy and paste the following expression into the

`equation`box:`stim_end = <stim_start> + <stim_dur>`Click

`Insert Variable`againIn the

`Name`box, type`i_stim`and press**ENTER**In the

`equation`box, replace the existing contents with the following (it might be best to maximize your browser window to see the correct line break formatting):IF(t.GE.<stim_start> .AND. t.LE.stim_end .AND. <stim_dur>.ne.0.d0) THEN i_stim = <stim_mag> ENDIF

In the

`Variable List`, click on**V**. This variable is predefined automatically to be the the`Spatially Coupled Variable`, and in this case is analogous to the transmembrane voltage. To match with the literature, we will change the variable name to**u**:In the

`Name`box, change**V**to**u**and press**ENTER**, click`OK`if a dialog box pops up.In the

`Equation`box, type in the first ODE shown above, but adding an additional term for the stimulus current as follows:`du_dt = c1*u*(u-a)*(1-u)-c2*u*v+i_stim`Now we'll add the second equation. Click on

`Insert Variable`In the

`Name`box, type**v**Change the box that says

`Spatially-Coupled Variable`to`State Variable`Go to Insert→Template and click

`OK`if a dialog box pops upIn the

`Equation`box, type the second ODE:`dv_dt = b*(u-d*v)`

Now we must add the necessary constants contained in the equations, namely

**a, b, c1, c2, and d**:

Click the

`Insert Variable`button.Change the button that says

`Independent Variable`to`Constant`In the

`Name`box, enter**a**and press**ENTER**Select

`Insert→Template`. You will see the entry`parameter(a = 0.0)`appear in the`equation`boxIn the

`equation`box change**a=0.0**to**a=0.13**Type a description in the

`description`box if you wishTo add the remaining constants, repeat the above steps starting with clicking on

`Insert Variable`.The order that the variables appear in the list is important. Since u and v depend on all the constants and temporary variables, they should appear

**after**those variables. Select u, and click**Shift down**to move u to the very bottom. Then do the same with v.Now click the

`View code`tab to see the automatically-generated FORTRAN subroutine containing the model equations.Click on the

`Compile`tabClick the

`Save file`button to save your work up to this pointIn the drop-down menu to the right of the

`Compile`button, change the server to`be-5511-2.ucsd.edu (webservice)`Click on the

`Compile`button. Compiling will take about 35 seconds to complete

Click on the

`Set Initial Values`tab. In this tab, we'll set up the initial values for the state variables.In the

`Variable List`click on**u**Find the button next to

`For default values use`and change it from`Value`to`Field 5`In the

`Variable List`click on**v**Change the number in the box next to the button that says

`Value`from 1 to**0.0**

Now proceed to the

`Set parameters`tab. Notice that the parameters tab contains six values. The first three are automatically generated and represent the diffusion coefficients for the problem, one for each of the fiber coordinate directions. The other three were automatically generated from the equations we entered - anything in the equations tab contained in angle brackets (<stim_start> for example) is generated in this list as a parameter automatically.For each of the diffusion coefficients, change their default value to

**field 1**Click on

`stim_start`in the list of parameters. This specifies the time in ms of the start of the stimulus current. Change its value to be**1.0**Click on

`stim_dur`in the list of parameters. This specifies the duration of the stimulus in ms. Change its value to be**3.0**Click on

`stim_mag`in the list of parameters. This specifies the magnitude of the stimulus current. In this case, we want the stimulus to be non-zero for certain nodes, and zero everywhere else. We have already defined a field in the nodes form containing this spatially-varying property. This is contained in field 4, so change the button next to`For default values use`to be`field 4`

- At this point, the model is completely defined, but must be saved before submitting.
Return to the

`Compile`tab, and click the`Save file`button

Finally, go to the last tab,

`Submit`and click the`Submit`button to close the form.

### Send and calculate mesh

Click the

**surfaces**radio buttonClick

**Render**to display mesh surface

### Solve for action potential propagation

- Electriophysiology→Calculate→Constraints...
Click

**OK**

- At this point you should save the file for future modifications
- Electriophysiology→Solve→Initialize...
Electriophysiology→Solve→Integration...

Verify that

`Start Time`is**0.0**Set

`Duration`to**50**Set

`Step Size`to**0.1**Go to the

`Solutions`tabFor

`Display solution every`, choose**10**steps

Click

**OK**and wait for the solver to complete its job (observe progress in the Python shell)

### Rendering and output

Electriophysiology→Render→Solution...

Change the

`Min Value`to**0.0**and`Max Value`to**1.0**Click

**OK**- Wait for the rendering to complete all frames before proceeding (observe status in Python shell)

- When the 50 animation frames have been computed, you should see an animation in Continuity of the action propagation.