# Laplace Solver

Author: Anton J Prassl anton.prassl@medunigraz.at

## Introduction

Computing Laplace-Dirichlet maps provide an elegant tool for describing the distance between defined boundaries. Specialized software routines exploiting these maps in order to assign ventricular fibers and sheets or to determine the set of elements to receive heterogeneous conductivities are frequently used in the carputils framework. To run the experiments of this example change directories as follows:

cd ${TUTORIALS}/02_EP_tissue/13_laplace ## Experimental Setup The geometry and the electrodes are defined as follows: ## Problem-specific openCARP Parameters The relevant part of the .par file for this example is shown below: experiment = 2 # perform Laplace solve only bidomain = 1 # ground electrode stimulus[0].x0 = -50. # par-file units are always microns! stimulus[0].xd = 100. stimulus[0].y0 = -50. stimulus[0].yd = 10100. stimulus[0].z0 = -50. stimulus[0].zd = 200. stimulus[0].stimtype = 3 # extracellular ground # stimulus electrode stimulus[1].x0 = -50. stimulus[1].xd = 10100. stimulus[1].y0 = -50. stimulus[1].yd = 100. stimulus[1].z0 = -50. stimulus[1].zd = 200. stimulus[1].stimtype = 2 # extracellular voltage stimulus[1].duration = 1. stimulus[1].strength = 1. # set isotropic conductivities everywhere num_gregions = 1 gregion[0].g_il = 1 gregion[0].g_it = 1 gregion[0].g_el = 1 gregion[0].g_et = 1 ## Experiment To run this experiment cd${TUTORIALS}/02_EP_tissue/3_laplace

Run

./run.py --visualize

Note

• Set uniform conductivities everywhere to not disturb the laplace solution
• Exclude any geometry parts (e.g. bath) you do not need the laplace solution for. meshtool<mesh-data-extraction> will help you to reintegrate any computed features back into its 'parent'.
• openCARP needs the bidomain flag to be set to 1. Otherwise the program will abort with a hint to change this specific setting.
• One may scale the values of the laplace solution through setting the stimulus strengths to e.g. 0 (stimulus[0], GND) and 1 (stimulus[1].strength) as shown above.
• The example collects stimulation nodes by defining an inclosing volume (x0,x0+xd,y0,y0+yd,z0,z0+zd). Alternatively, vertices can directly be addressed by including a vertex file<vertex-file>.

Expected result:

## Nodal Boundary Conditions

Instead of having to define a different stimulus for each different Dirichlet value, specific nodes can be assigned different values in one file. The relevant parameters to change are below:

stimulus[1].stimtype =     2    # extracellular voltage
stimulus[1].vtx_file =     BCs
stimulus[1].vtx_fcn  =     1
stimulus[1].strength =     1.

When stimulus[1].vtx_fcn is non-zero, the vtx_file, BCs.vtx in this case, has vertex adjustment format in which the nodal strength is specified along with the node number. The nodal strengths in the file are then multiplied by stimulus[1].strength.

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