The point spread function of the human head and its implications for transcranial current stimulation

Area of Science:

• Neuroscience
• Biophysics
• Computational Modeling

Background:

• Transcranial current stimulation (tCS) requires accurate electric field modeling.
• Current models range from simple to complex, individualized approaches.
• A need exists for an accessible benchmark model for general population studies.

Purpose of the Study:

• To derive a computationally efficient and accessible forward model for tCS.
• To establish a linear system relating scalp currents to brain electric fields.
• To enable both forward and backward problem solutions in tCS.

Main Methods:

• Derivation of a closed-form linear system for electric potential computation.
• Utilizing spherical harmonic (Fourier) domain analysis.
• Spherical convolution of scalp current distribution with a derived point spread function.

Main Results:

• A simple scalar multiplication relates scalp current density to brain electric potential in the spherical harmonic domain.
• The derived model allows easy computation of electric fields for known scalp currents.
• The model facilitates determination of scalp currents needed for desired electric fields (backward problem).

Conclusions:

• The developed model offers a simplified and accessible method for tCS electric field computation.
• This approach is valuable for general population studies and designing optimal stimulation montages.
• The model aids in both predicting stimulation effects and designing targeted brain interventions.