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Smooth gradient heterogeneities (ionic adjustment)

Author: Patrick Boyle pmjboyle@gmail.com

This tutorial details how to assign a gradient of cell-scale properties using the adjustments interface.

Problem Setup

This example will run one simulation using a 2D sheet model (1 cm x 1 cm) in which all elements and nodes are in the same imp_region[] and gregion[] but heterogeneity in cell-scale dynamics is imposed at the cell scale in gradient patterns using the adjustments interface.

By default, \(I_{Kr}\) is modulated from 0x to 5x from left to right and \(I_{to}\) is modulated from 0x to 5x from bottom to top. Both gradients are linear. The resulting pattern of excitation is shown below:

The stars are colour-coded and indicate the approximate locations from which the action potential traces shown below were extracted:

As expected, \(I_{to}\) modulation leads to an abolished notch along the bottom edge of the sheet but an exaggerated notch along the top edge. \(I_{kr}\) modulation in the sheet leads to a progressive shortening of action potential duration from left to right as more repolarizing current becomes available to the cells.

Usage

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

./run.py
  --help 

    --xgrad_var         Options:
  {GCaL,Gks,Gkr,Gto}, Default: Gkr

                        parameter that should be varied along the left-to-right (X) gradient

    --xgrad_left_scf    Default:
  0.0

                        scaling factor at left side of the X gradient

    --xgrad_right_scf   Default:
  5.0

                        scaling factor at right side of the Y gradient

    --xgrad_flip        left
  becomes right, right becomes left

  

    --ygrad_var         Options:
  {GCaL,Gks,Gkr,Gto}, Default: Gto

                        parameter that should be varied along the bottom-to-top (Y) gradient

    --ygrad_bottom_scf  Default:
  0.0

                        scaling factor at bottom of Y gradient

    --ygrad_top_scf     Default:
  5.0

                        scaling factor at top of Y gradient

    --ygrad_flip        down
  becomes up, up becomes down

If the program is run with the --visualize option, meshalyzer will automatically load the \(V_m(t)\) sequence corresponding to the run simulation. Output files for activation and repolarisation sequences as well as APD are produced for each simulation and can be found in the output directory and loaded into meshalyzer.

The --xgrad[...] and --ygrad[...] parameters can be modified to impose different gradients in the x and y directions (i.e., left-to-right and bottom-to-top, respectively) in four different parameters: \(g_{CaL}\), \(g_{Ks}\), \(g_{Kr}\), and \(g_{to}\), which correspond to the L-type \(Ca^{2+}\), slow delayed rectifier \(K^{+}\), rapid delayed rectifier \(K^{+}\), and transient outward \(K^{+}\) currents, respectively.

Notes and Precautions

• The --xgrad_var and --ygrad_var parameters should not be set to the same value, otherwise the simulation will not behave as expected.
• The -adjustments[] interface in CARP can only be used to modify cell-scale properties that correspond to a state variable in the ionic model being used.

Use the --imp-info argument of bench to find out which variables are eligible to bet set on a nodal basis. There are actually two types of variables listed as state variables, (1) actual state variables which describe the ionic model state and evolve with each time step, and (2) model parameters which affect behaviour but do not change. Thus, state variables can be intialized on a nodal basis. Parameters which can be set on a nodal basis must be listed as parameters, i.e., being listed up top, as well as being listed as state variables. For example, in the case of the converted_TT2 ionic model used in this example, the following are parameters which can be set nodally:

>
  bench --imp=converted_TT2 --imp-info

  converted_TT2:

  [...]

        State
  variables:

                                GCaL

                                 Gkr

                                 Gks

                                 Gto

Under the Hood

In the parameter file, the following options are used to adjust nodal values. First, if you wish to adjust N variables:

num_adjustments = N

For each adjustment structure, i.e., adjustment[0], ..., adjustment[N-1], the following fields are set:

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05D_Region_Reunification 06_eikonal