Optimisation of conductivities from 2D mapping study

Example_B2112

This study is based on a data set obtained from a 2D epicardial mapping study by Peng Chen at Cedars Sinai Medical Center, LA. The data set is stored in peng4.signal, and contains potential recordings at 509 surface electrodes on canine myocardium, and can be viewed using Emap. The only change to this data was to reject electrode 225 as it distorted the results.

The wavefront proceeds fairly constantly for approximately the first 40ms, and then activated the entire remaining region almost simultaneously. This is due to the 3D nature of the tissue slice, and as we are only interested in 2D conductivities, the first 15 columns and 19 rows of electrodes only were used (cornered by electrodes 1 and 393). The activation times were converted from Emap to a data file using /usr/local/bin/sig2ipdata and the (very poor quality!) C source code is available at http://www.esc.auckland.ac.nz/People/Students/Sands/sig2ipdata.c.

From observation of the activation map, the fibre direction was assumed to be constantly zero throughout the region. Similarly from observation, the stimulus points were determined as the closest grid points to electrodes 148,169,190 and 211.

The optimiser goes through the following sequence:

NAGMINA:	fem define initial;w;optimise
NAGMINA:	fem define solve;w;optimise
OPTI: 		DO LOOP 
FUNCT2:		   fem update optimisation	
FUNCT2:		   fem update grid material	
FUNCT2:		   fem define initial;r;optimise
FUNCT2:		   fem define solve;r;optimise
FUNCT2:		   fem solve
FUNCT2:		   fem evaluate residuals wrt mat_params view
OPTI: 		UNTIL residual is minimised

Activation time is calculated as the time of greatest change in Vm, and the residuals compare this to the activation time at the electrode.