Excitation wavefront propagation from point stimulus in canine ventricular myocardium.

Example b221: Excitation wavefront propagation from point stimulus in canine ventricular myocardium.

An eikonal equation is used to model propagation of the region of excitation in a model of canine ventricular myocardium with 60 tri-cubic Hermite elements. The solution describes the excitation time of the tissue following a point basal endocardial stimulus.

The solution method is described in:
Karl A. Tomlinson, Peter J. Hunter, and Andrew J. Pullan (2002), "A Finite Element Method for an Eikonal Equation Model of Mycardial Excitation Wavefront Propagation", SIAM J. Appl. Math., 63(1), 324-350.
and Karl Tomlinson's PhD thesis.

The comfile run by this example is as follows:

fem define parameters;r;petrov-heart;example

fem define coordinates;r;rect3D-c0;example    #3D rect. Cart. with atleast C0 continuity 
fem define bases;r;herm3;example         #tri-cubic hermite bases and others
# geometry:
fem define node;r;heart;example        #99 nodes
fem define element;r;heart;example     #60 elements
# fibres:
fem define fibre;r;heart;example
fem define element;r;heart;example fibre
# miscellaneous fields:
# 1st field is tri-cubic Hermite, used in the solution process for continuity.
# 2nd field determines versions for dep. var.
# cm does not really provide a place to specify the interpolation
# of the dependent variable (activation time in this case) so
# a scalar field (the 2nd) is set up to describe this information.
fem define field;r;c0;example
fem define element;r;c0;example field
# orthotropic eikonal equation, solved with Petrov-Galerkin FEM
fem define equation;r;eik-ort-pet;example
fem define material;r;heart;example       #material parameters
fem define initial;r;lv-free;example   #left ventricular free wall initiation
fem update field eikonal            #calculate continuity field 1
fem update gauss eikonal timing     #calculate gauss point stuff
fem define solve;r;eik-an;example      #analytical derivatives for Newton method
# A continuation method is used here to use a linear (diffusion) problem to
# provide an initial guess of the solution to a non-linear problem
# (eikonal-diffusion).  When the increment parameter is 0 there is no eikonal
# term in the equation.  When the parameter is 1 then the equation is the full
# non-linear problem.  In-between the non-linear term is smaller.

# iterate 1 is specified during the continutation process so as to only do one
# iteration in the Newton method at each step as an accurate solution is only
# required in the final solve.

fem solve iterate 1 increment 0.01; # one iteration with 100x diffusion
if( $TESTING )
  { # check application of boundary conditions
    fem define initial;w;lv-free-iter1
  }

if( 0 )
  { # skip gradual reduction in diffusion to save some time
    fem solve iterate 1 increment 0.03;
    fem solve iterate 1 increment 0.07;
    fem solve iterate 1 increment 0.1;
    fem solve iterate 1 increment 0.14;
    fem solve iterate 1 increment 0.2;
    fem solve iterate 1 increment 0.3;
    fem solve iterate 1 increment 0.4;
    fem solve iterate 1 increment 0.5;
    fem solve iterate 1 increment 0.7;
    # fem solve increment 0.7
    # fem define initial;w;lv-free-0.7;example
  } else
  { # Read in precalculated solution at 1.4x diffusion
    fem define initial;r;lv-free-0.7;example;
  }

fem solve iterate 1 increment 0.8         #one iteration with 1.25x diffusion
fem solve iterate 1 increment 0.9         #one iteration with 1.1x diffusion
fem solve increment 1                     #solve with correct diffusion

# Output results for cmgui
fem export node;heart as heart
fem export elem;heart as heart
fem export node;heart-sol field as heart_sol
fem export elem;heart-sol field as heart_sol

if( $TESTING )
  {
    fem list node;solution solution
  }

Files used by this example are:

Name                 Modified     Size

example_b221.com     16-Mar-2007  3.0k
c0.ipelfd            10-Apr-2000   29k
c0.ipfiel            10-Apr-2000   71k
eik-an.ipsolv        16-Aug-2010  2.3k
eik-an.ipsolv.old    13-Apr-2007  2.1k
eik-ort-pet.ipequa   10-Apr-2000  1.0k
heart.ipelem         10-Apr-2000   58k
heart.ipelfb         10-Apr-2000   27k
heart.ipfibr         03-Dec-2003   49k
heart.ipmate         10-Apr-2000  1.4k
heart.ipnode         10-Apr-2000  245k
herm3.ipbase         10-Apr-2000   14k
lv-free-0.7.ipinit   04-Dec-2003   96k
lv-free.ipinit       03-Dec-2003   13k
petrov-heart.ippara  12-Nov-2002  5.9k
rect3D-c0.ipcoor     10-Apr-2000  688 
viewsol.com          03-Dec-2003  1.2k

Download the entire example:

Name                           Modified     Size

examples_b_b2_b22_b221.tar.gz  17-Aug-2010  104k

Testing status by version:

	Status	Tested	Real time (s)
i686-linux
cm	Success	Sun Mar 6 00:05:00 2016	5
cm-debug	Success	Sat Mar 5 00:32:09 2016	20
mips-irix
cm	Success	Sun Aug 19 02:26:24 2007	52
cm-debug	Success	Wed Aug 15 02:13:15 2007	112
cm-debug-clear-malloc	Success	Sat Aug 18 02:36:18 2007	126
cm-debug-clear-malloc7	Success	Mon Aug 20 02:39:42 2007	128
cm64	Success	Sun Aug 19 02:25:44 2007	53
cm64-debug	Success	Tue Aug 21 02:15:58 2007	119
cm64-debug-clear-malloc	Success	Thu Apr 1 11:23:11 2004	57
rs6000-aix
cm	Success	Wed Mar 4 01:11:36 2009	5
cm-debug	Success	Mon Mar 2 01:12:23 2009	23
cm64	Success	Wed Mar 4 01:11:36 2009	5
cm64-debug	Success	Tue Mar 3 01:18:51 2009	22
x86_64-linux
cm	Success	Sun Mar 6 00:01:20 2016	5
cm-debug	Success	Sat Mar 5 00:03:35 2016	13

Testing status by file:

cmiss_test.log

i686-linux
Success	cm:	cmiss_test.log.retain.
Success	cm-debug:	cmiss_test.log.retain.
mips-irix
Success	cm:	cmiss_test.log.retain.
Success	cm-debug:	cmiss_test.log.retain.
Success	cm-debug-clear-malloc:	cmiss_test.log.retain.
Success	cm-debug-clear-malloc7:	cmiss_test.log.retain.
Success	cm64:	cmiss_test.log.retain.
Success	cm64-debug:	cmiss_test.log.retain.
Success	cm64-debug-clear-malloc:	cmiss_test.log.retain.
rs6000-aix
Success	cm:	cmiss_test.log.retain.
Success	cm-debug:	cmiss_test.log.retain.
Success	cm64:	cmiss_test.log.retain.
Success	cm64-debug:	cmiss_test.log.retain.
x86_64-linux
Success	cm:	cmiss_test.log.retain.
Success	cm-debug:	cmiss_test.log.retain.

lv-free-iter1.ipinit

i686-linux
Success	cm:	ndiff test: no significant differences with generic answer.
Success	cm-debug:	ndiff test: no significant differences with generic answer.
mips-irix
Success	cm:	ndiff test: no significant differences with generic answer.
Success	cm-debug:	ndiff test: no significant differences with generic answer.
Success	cm-debug-clear-malloc:	ndiff test: no significant differences with generic answer.
Success	cm-debug-clear-malloc7:	ndiff test: no significant differences with generic answer.
Success	cm64:	ndiff test: no significant differences with generic answer.
Success	cm64-debug:	ndiff test: no significant differences with generic answer.
Success	cm64-debug-clear-malloc:	ndiff test: no significant differences with generic answer.
rs6000-aix
Success	cm:	ndiff test: no significant differences with generic answer.
Success	cm-debug:	ndiff test: no significant differences with generic answer.
Success	cm64:	ndiff test: no significant differences with generic answer.
Success	cm64-debug:	ndiff test: no significant differences with generic answer.
x86_64-linux
Success	cm:	ndiff test: no significant differences with generic answer.
Success	cm-debug:	ndiff test: no significant differences with generic answer.

solution.opnode

i686-linux
Success	cm:	ndiff test: no significant differences with generic answer.
Success	cm-debug:	ndiff test: no significant differences with generic answer.
mips-irix
Success	cm:	ndiff test: no significant differences with generic answer.
Success	cm-debug:	ndiff test: no significant differences with generic answer.
Success	cm-debug-clear-malloc:	ndiff test: no significant differences with generic answer.
Success	cm-debug-clear-malloc7:	ndiff test: no significant differences with generic answer.
Success	cm64:	ndiff test: no significant differences with generic answer.
Success	cm64-debug:	ndiff test: no significant differences with generic answer.
Success	cm64-debug-clear-malloc:	ndiff test: no significant differences with generic answer.
rs6000-aix
Success	cm:	ndiff test: no significant differences with generic answer.
Success	cm-debug:	ndiff test: no significant differences with generic answer.
Success	cm64:	ndiff test: no significant differences with generic answer.
Success	cm64-debug:	ndiff test: no significant differences with generic answer.
x86_64-linux
Success	cm:	ndiff test: no significant differences with generic answer.
Success	cm-debug:	ndiff test: no significant differences with generic answer.

Html last generated: Sun Mar 6 05:51:15 2016

Input last modified: Mon Aug 16 11:26:28 2010

CMISS Help / Examples / b / b2 / b22 / b221