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Objective. Understanding how current reaches the brain during transcranial electrical stimulation (tES) underpins efforts to rationalize outcomes and optimize interventions. To this end, computational models of current flow relate applied dose to brain electric field. Conventional tES modeling considers distinct tissues like scalp, skull, cerebrospinal fluid (CSF), gray matter and white matter. The properties of highly conductive CSF are especially important. However, modeling the space between skull and brain as entirely CSF is not an accurate representation of anatomy. The space conventionally modeled as CSF is approximately half meninges (dura, arachnoid, and pia) with lower conductivity. However, the resolution required to describe individual meningeal layers is computationally restrictive in an MRI-derived head model. Emulating the effect of meninges through CSF conductivity modification could improve accuracy with minimal cost.

Approach. Models with meningeal layers were developed in a concentric sphere head model. Then, in a model with only CSF between skull and brain, CSF conductivity was optimized to emulate the effect of meningeal layers on cortical electric field for multiple electrode positions. This emulated conductivity was applied to MRI-derived models.

Main results. Compared to a model with conventional CSF conductivity (1.65 S m−1), emulated CSF conductivity (0.85 S m−1) produced voltage fields better correlated with intracranial recordings from epilepsy patients.

Significance. Conventional tES models have been validated using intracranial recording. Residual errors may nonetheless impact model utility. Because CSF is so conductive to current flow, misrepresentation of the skull-brain interface as entirely CSF is not realistic for tES modeling. Updating the conventional model with a CSF conductivity emulating the effect of the meninges enhances modeling accuracy without increasing model complexity. This allows existing modeling pipelines to be leveraged with a simple conductivity change. Using 0.85 S m−1 emulated CSF conductivity is recommended as the new standard in non-invasive brain stimulation modeling.


This is the authors' manuscript of a work originally published in the Journal of Neural Engineering, available at

This work is made available under the terms of a CC BY NC ND license



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