An optimization approach for well-targeted transcranial direct current stimulation

TL;DR

This paper introduces a new optimization method for transcranial direct current stimulation (tDCS) that enhances targeting precision and safety by solving an optimal control problem with finite element discretization and advanced numerical algorithms.

Contribution

It presents a novel optimization framework for multi-array tDCS, including theoretical convergence proofs and practical simulation results demonstrating improved focality and target alignment.

Findings

Optimized current flow fields show higher focality.

Enhanced directional agreement to target vectors.

Method outperforms standard bipolar montages.

Abstract

Transcranial direct current stimulation is a non-invasive brain stimulation technique which modifies neural excitability by providing weak currents through scalp electrodes. The aim of this study is to introduce and analyze a novel optimization method for safe and well-targeted multi-array tDCS. For optimization, we consider an optimal control problem for a Laplace equation with Neumann boundary conditions with control and point-wise gradient state constraints. We prove existence and residual and objective convergence results for the proposed methods and provide computer simulation results in a highly realistic six-compartment geometry-adapted hexahedral head model. For discretization of the proposed minimization problem the finite element method is employed and the existence of at least one minimizer to the discretized optimization problem is shown. For numerical solution of the corresponding discretized problem we employ the alternating direction method of multipliers and comprehensively examine the cortical current flow field with regard to focality, target intensity and orientation. The numerical results reveal that the optimized current flow fields show significantly higher focality and, in most cases, higher directional agreement to the target vector in comparison to standard bipolar electrode montages.