MC-tES in Zeffiro Interface: Sparse Optimized and Regularized Stimulus

Abstract

This thesis aims to describe the mathematical methodology of multi-channel transcranial electrical stimulation (MC-tES) and its computational implementation in the open Matlab-based Zeffiro Interface (ZI) toolbox. The goal is to extend the current solver capabilities of ZI, and by using the solver implementation, among other things, to enlighten the process of finding a focal optimized, and preferably sparse, current pattern, as well as to provide the necessary codes for further software development. The present implementation covers both forward and inverse MC-tES solver. The former inherits for ZI’s finite element method based forward solver for electroencephalography. Here the mathematical framework of this solver is described and its connection to MC-tES explained. The application of the complete electrode model boundary conditions ensures the high accuracy of the model at the vicinity of the current-injecting electrodes. The inverse problem is approached via L1-regularized optimization and the dual-simplex linear programming algorithm. The performance of the implementation is evaluated in numerical experiments in which the volume current density caused by the stimulus is steered using a synthetic 10 nAm source with a reference extent of 253 mm3 as a target. A rough initial range for the regularization and tolerance parameter is found with somatosensory, visual and auditory cortex as the reference target areas, using a realistic multi-layered head model discretized with 1 mm accuracy.