Using a sensitivity study to facilitate the design of a multi-electrode array to measure six cardiac conductivity values

• A multi-electrode array is designed to find six cardiac conductivities.
• A sensitivity study finds types of electrodes that need to be included.
• Electrodes that are sensitive to the conductivities have low values of potential.
• Based on this, alternative designs for the electrode array are considered.
• It is shown that six conductivities can be retrieved accurately.

When using the bidomain model to model the electrical activity of the heart, there are potentially six cardiac conductivity values involved: conductivity values in directions along and normal to the cardiac fibres with a sheet, as well as a conductivity value in the normal direction between the sheets, and these occur for both the extracellular and intracellular domains in the model. To date it has been common to assume that the two normal direction conductivity values are the same. However, recent work has demonstrated that six cardiac conductivity values, rather than four, are necessary for accurate modelling, which can then facilitate understanding of cardiovascular disease.To design a method to determine these conductivities, it is also necessary to design a suitable multi-electrode array, which can be used, in conjunction with an inversion technique, to retrieve conductivity values from measurements of potential made on the array. This work uses the results of a study, into the sensitivity of the measuring potentials to variability in the input conductivities, to facilitate the design of an array that could be used to retrieve six cardiac conductivity values, as well as fibre rotation angle.It is found that if an electrode in the array has a much lower value of potential than the other electrodes, then it tends to be much more sensitive to the input conductivities than the other electrodes. It also appears that inclusion of this type of electrode in the set of measuring electrodes is essential for accurately retrieving conductivity values. This technique is used to identify electrodes to be included in the array and using the final design it is demonstrated, using synthetic values of potential, that the six cardiac conductivity values, and the fibre rotation angle, can be retrieved very accurately.