# Stimulation Montage Achieves Balanced Focality and Intensity
###### Abstract  
Transcranial direct current stimulation (tDCS) is a non-invasive neuromodulation technique to treat brain disorders by using a constant, low current to stimulate targeted cortex regions. Compared to the conventional tDCS that uses two large pad electrodes, multiple electrode tDCS has recently received more attention. It is able to achieve better stimulation performance in terms of stimulation intensity and locality. In this paper, we first establish a computational model of tDCS, and then propose a novel optimization algorithm using a regularization matrix \(\lambda\) to explore the balance between stimulation intensity and locality. The simulation study is designed such that the performance of state-of-the-art algorithms and the proposed algorithm can be compared via quantitative evaluation. The results show that the proposed algorithm not only achieves desired intensity, but also smaller target error and better focality. Robustness analysis indicates that the results are stable within the ranges of scalp and cerebrospinal fluid (CSF) conductivities, while the skull conductivity is most sensitive and should be carefully considered in real clinical applications. t +
Footnote †: journal:  
0000-0001-4500-3222-2  
will enable multi-electrode systems to provide stimulation with high focality, accuracy, and intensity. So far, optimization-based methods are the most popular solution to assign injected current values. As an overdetermined problem, the Least Squares solution is a straightforward approach [20], which minimizes the second order error term. Considering the safety issue in clinical use, constraints are then added when applying the algorithm; thus, it can be referred to as the Constrained Least Squares method (CLS). Its optimal current pattern often produces relatively focal stimulation but low stimulation intensity; one possible explanation for this is that the target region is generally tiny compared to the whole brain. To overcome this challenge, the Least Squares method has been improved by assigning weight to balance the tiny target region and large non-target ones, in a technique called the Weighted Least Squares method [20; 21]. It is able to produce higher stimulation intensity; however, the weight factor must be given by the clinician, which is a non-trivial task. Another possible solution is to change the L2-norm of the error vector to an L1-norm approach. The L1-norm is applied to achieve more focal stimulation because the fidelity term based on the L1-norm is more robust and results in a non-uniform error distribution, which we have reported previously [22]. However, its very computationally expensive. Because of its computational drawbacks, we do not explore the effects of using the L1-norm in this investigation. Another developed technique optimizes for the intensity at the target region, and is named the Max Intensity (MI) method [17; 23]. This method tends to achieve high stimulation intensity, but is more likely to activate large non-target areas. Thus, this motivates the introduction of more constraints on non-target areas to improve the MI method [24; 25]. However, the additional constraints may lead to situations of no feasible solution set and, also, longer computational time. These improvements all indicate the key point behind this optimization problem--that is, to find ways of balancing the stimulation intensity and focality. One novel solution named Linearly Constrained Minimum Variance (LCMV) [20] adopts ideas from the beamforming problem. The algorithm has a hard constraint in that the stimulation intensity at the target region is enforced to be exactly equal to the desired one, while a cost function minimizes the energy of the non-target regions. This strategy is aimed to ensure the stimulation effectiveness, but has pitfalls. LCMV minimizes the effects on the non-target areas under the premise that the hard constraint is fulfilled.