Example b2123 - coupled bidomain - torso This example solves the bidomain equation through to a point where an activation wave is well established and then iterates between the extracellular and the boundary element problem to get the epicardial fluxes to match. The heart is a FE mesh. The torso consists of a BE mesh for the body surface and also a BE mesh around the epicardium.
# Example b2123 - coupled bidomain - torso
# Assign region and class variables
# =================================
# Command updated by fixcom.sh on Wed Aug 23 17:50:04 NZT 2000
# Old command: assign variable BEM 1 # Region 1 is a boundary element mesh
$BEM = 1 # Region 1 is a boundary element mesh
# Command updated by fixcom.sh on Wed Aug 23 17:50:04 NZT 2000
# Old command: assign variable GRID 2 # Region 2 is grid points over a FEM mesh
$GRID = 2 # Region 2 is grid points over a FEM mesh
# Command updated by fixcom.sh on Wed Aug 23 17:50:04 NZT 2000
# Old command: assign variable LAPLACE 1 # Class 1 is the generalised Laplace equation
$LAPLACE = 1 # Class 1 is the generalised Laplace equation
# Command updated by fixcom.sh on Wed Aug 23 17:50:04 NZT 2000
# Old command: assign variable TMEMBRANE 2 # Class 2 is the transmembrane potential
$TMEMBRANE = 2 # Class 2 is the transmembrane potential
# Command updated by fixcom.sh on Wed Aug 23 17:50:04 NZT 2000
# Old command: assign variable EXTCELLR 3 # Class 3 is the extracellular potential
$EXTCELLR = 3 # Class 3 is the extracellular potential
# Command updated by fixcom.sh on Wed Aug 23 17:50:04 NZT 2000
# Old command: assign variable EXTUPDATE 4 # Class 4 is used for the extracellular matrix with
$EXTUPDATE = 4 # Class 4 is used for the extracellular matrix with
# flux boundary conditions.
# Define the problem
# ==================
# Read in parameters and reallocate arrays
fem define para;r;2dheart;example
# Define 2 regions
fem define regi;r;2dheart;example
# Define a 2d cubic-linear and a 1d cubic basis
fem define base;r;2dheart;example
# Define the problem geometry
fem define node;r;ref;example reg all
fem define elem;r;ref;example reg all
# Generate a grid scheme over the FE mesh
fem define grid;r;2dheart;example reg $GRID
# Use default fibre angles
fem define fibr;d reg $GRID
fem define elem;r;ref;example fibre reg $GRID
# Compute global grid point coordinates and generate metric tensors
fem update grid geom reg $GRID
fem update grid metric reg $GRID
fem group grid external as boundary reg 2
# Define the generalised Laplace equation
fem define equa;r;torsoslice;example reg $BEM class $LAPLACE lock
# Define the grid equations (Fitzhugh-Nagumo ionic current model)
fem define equa;r;fhn2;example reg $GRID class $TMEMBRANE,$EXTCELLR,$EXTUPDATE lock
# Define the material properties of the 2 meshes
fem define mate;r;torsoslice;example reg $BEM class $LAPLACE
fem define mate;r;fhn;example reg $GRID class $TMEMBRANE,$EXTCELLR
fem define cell;r;fhn;example reg $GRID class $TMEMBRANE,$EXTCELLR
# Update the grid material according to the fibre angles
fem update grid mate reg $GRID class $TMEMBRANE,$EXTCELLR
# Define potentials on the heart, no flux on torso
fem define init;r;torsoslice;example reg $BEM class $LAPLACE
# Define initial activation from the middle of the septum
fem define init;r;2dheart;example reg $GRID class $TMEMBRANE,$EXTCELLR
# Define the solution procedure for the 2 problems
fem define solv;r;torsoslice;example reg $BEM class $LAPLACE
fem define solv;r;2dheart;example reg $GRID class $TMEMBRANE
fem define solv;r;2dheart2;example reg $GRID class $EXTCELLR
fem define solv;r;2dheart3;example reg $GRID class $EXTUPDATE
# Solve the problem
# =================
# Solve the bidomain problem for 10ms (1000 iterations)
fem solve to 10 reg $GRID class $TMEMBRANE,$EXTCELLR,$EXTUPDATE
# Update the potential and the arc length derivative of potential
# at the nodes on the heart from the extracellular solution
fem update node potential reg $BEM,$GRID
# Solve the generalised Laplace equation
fem solve reg $BEM class $LAPLACE
# Check the boundary fluxes to see of they match
fem update node potential reg $BEM,$GRID check
# Loop to converge boundary fluxes
# ================================
# Command updated by fixcom.sh on Wed Aug 23 17:50:04 NZT 2000
# Old command: DO A=1..4
for $A ( 1..4 )
{
# Using the the flux and derivative values from the BE problem
# interpolate to find a flux value at each epicardial grid point.
# Solve the extracellular update equation using these flux values.
fem solve iterate 1 reg $GRID,$BEM class $TMEMBRANE,$EXTCELLR,$EXTUPDATE,$LAPLACE
# Update the potential and the arc length derivative of potential
# at the nodes on the heart from the new extracellular solution
fem update node potential reg $BEM,$GRID
# Resolve the generalised Laplace problem
fem solve reg $BEM class $LAPLACE
# Check to see what the difference in the bounday fluxes are
fem update node potential reg $BEM,$GRID check
# Command updated by fixcom.sh on Wed Aug 23 17:50:04 NZT 2000
# Old command: ENDDO
}
# Draw the results to the screen
# ==============================
# Open a 2d graphics window
fem define window;c
# Draw the extracellular potential field over the grid point mesh
fem dr field grid 1 zmin=-21 zmax=9 noscale reg $GRID class $EXTCELLR
# Draw the resultant potential field on the body surface
fem dr field zmin=-21 zmax=9 noscale reg $BEM class $LAPLACE elem 16..27
# Draw white lines to show the FE heart mesh
fem dr lines reg 2 rgb=white
Name Modified Size
example_b2123.com 20-Nov-2001 5.0k 2dheart.ipbase 10-Apr-2000 2.5k 2dheart.ipgrid 06-Mar-2003 4.4k 2dheart.ipinit 10-Apr-2000 1.8k 2dheart.ippara 12-Nov-2002 5.9k 2dheart.ipregi 10-Apr-2000 93 2dheart.ipsolv 13-Apr-2007 1.8k 2dheart.ipsolv.old 10-Apr-2000 1.5k 2dheart2.ipsolv 13-Apr-2007 1.8k 2dheart2.ipsolv.old 10-Apr-2000 1.5k 2dheart3.ipsolv 13-Apr-2007 1.8k 2dheart3.ipsolv.old 10-Apr-2000 1.5k fhn.ipcell 10-Apr-2000 3.4k fhn.ipmate 10-Apr-2000 1.7k fhn.ipmate_cell_old 10-Apr-2000 5.2k fhn2.ipequa 26-May-2003 4.5k output.com 10-Apr-2000 107 ref.ipelfb 10-Apr-2000 5.6k ref.irelem 10-Apr-2000 18k ref.irnode 10-Apr-2000 29k ref_old.irelem 10-Apr-2000 18k torsoslice.ipcell 10-Apr-2000 633 torsoslice.ipequa 26-May-2003 6.4k torsoslice.ipinit 10-Apr-2000 6.0k torsoslice.ipmate 10-Apr-2000 633 torsoslice.ipmate_cell_old 10-Apr-2000 633 torsoslice.ipsolv 13-Apr-2007 1.5k
Name Modified Size
examples_b_b2_b21_b212_b2123.tar.gz 14-Apr-2007 22k
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Input last modified: Fri Apr 13 10:38:26 2007