Multi-objective optimization via evolutionary algorithm (MOVEA) for high-definition transcranial electrical stimulation of the human brain

Designing a transcranial electrical stimulation (tES) strategy requires considering multiple objectives, such as intensity in the target area, focality, stimulation depth, and avoidance zone. These objectives are often mutually exclusive. In this paper, we propose a general framework, called multi-objective optimization via evolutionary algorithm (MOVEA), which solves the non-convex optimization problem in designing tES strategies without a predefined direction. MOVEA enables simultaneous optimization of multiple targets through Pareto optimization, generating a Pareto front after a single run without manual weight adjustment and allowing easy expansion to more targets. This Pareto front consists of optimal solutions that meet various requirements while respecting trade-off relationships between conflicting objectives such as intensity and focality. MOVEA is versatile and suitable for both transcranial alternating current stimulation (tACS) and transcranial temporal interference stimulation (tTIS) based on high definition (HD) and two-pair systems. We comprehensively compared tACS and tTIS in terms of intensity, focality, and steerability for targets at different depths. Our findings reveal that tTIS enhances focality by reducing activated volume outside the target by 60%. HD-tTIS and HD-tDCS can achieve equivalent maximum intensities, surpassing those of two-pair tTIS, such as 0.51 V/m under HD-tACS/HD-tTIS and 0.42 V/m under two-pair tTIS for the motor area as a target. Analysis of variance in eight subjects highlights individual differences in both optimal stimulation policies and outcomes for tACS and tTIS, emphasizing the need for personalized stimulation protocols. These findings provide guidance for designing appropriate stimulation strategies for tACS and tTIS. MOVEA facilitates the optimization of tES based on specific objectives and constraints, advancing tTIS and tACS-based neuromodulation in understanding the causal relationship between brain regions and cognitive functions and treating diseases. The code for MOVEA is available at https://github.com/ncclabsustech/MOVEA.