Personalized electric field simulations of deformable large TMS coils based on automatic position and shape optimization

Background

Transcranial Magnetic Stimulation (TMS) therapies use both focal and unfocal coil designs. Unfocal designs often employ bendable windings and moveable parts, making realistic simulations of their electric fields in inter-individually varying head sizes and shapes challenging. This hampers comparisons of the various coil designs and prevents systematic evaluations of their dose-response relationships.

Objective

Introduce and validate a novel method for optimizing the position and shape of flexible coils taking individual head anatomies into account. Evaluate the impact of realistic modeling of flexible coils on the electric field simulated in the brain.

Methods

Accurate models of four coils (Brainsway H1, H4, H7; MagVenture MST-Twin) were derived from computed tomography data and mechanical measurements. A generic representation of coil deformations by concatenated linear transformations was introduced and validated. This served as basis for a principled approach to optimize the coil positions and shapes, and to optionally maximize the electric field strength in a region of interest (ROI).

Results

For all four coil models, the new method achieved configurations that followed the scalp anatomy while robustly preventing coil-scalp intersections on N=1100 head models. In contrast, setting only the coil center positions without shape deformation regularly led to physically impossible configurations. This also affected the electric field calculated in the cortex, with a median peak difference of ∼16%. In addition, the new method outperformed grid search-based optimization for maximizing the electric field of a standard figure 8 coil in a ROI with a comparable computational complexity.

Conclusion

Our approach alleviates practical hurdles that so far hampered accurate simulations of bendable coils. This enables systematic comparison of dose-response relationships across the various coil designs employed in therapy.

Highlights

• automatic positioning and shape optimization of large deformable TMS coils

• ensures adherence to the head anatomy and prevents coil-head intersections

• enable automatic electric field maximization in target brain regions

• outperforms grid search for standard flat coils

• provides accurate computational models of four coils used in clinical practice