Physics

Areas and Current

Although the current flows from the anode to the cathode, the strongest electric field occurs near the electrode surface, though currents may affect deeper brain structures depending on electrode configuration. 

This is because most of the electric gradient lies under the electrode. As the current travels through the brain tissue, it disperses and weakens, leading to reduced effects in regions farther from the electrodes. 

The current density depends on the size of the electrodes and their distance apart (smaller electrodes create a more concentrated and precise current, but over smaller regions). Some advanced techniques, like high-definition tDCS (HD-tDCS), improve targeting by using smaller, multiple electrodes,    reducing but not completely avoiding stimulation of  nearby areas.

Electrical currents - ions

Electrical currents involve the movement of charged particles. In conductors like wires, currents involve electron movement (flow), whilst in biological systems, current involve ion movement.

When you place an anode, the surface of the electrode will attract negative ions to it like Cl-, and repel positive ions like Na+. Therefore, the inside of neurons become less negative, approaching 0mV, which facilitates depolarization. 

On the other hand, the negatively charged electrode (cathode) will make the surface near itself more negative, attracting ions like Na+, and leaving the inside of the neurons more negative and therefore leading to hyperpolarization, where the neuron is less likely to fire.   

It is important to note, that while Cl- and Na+ influence charge distribution, Na+ and K+ dynamics primarily drive action potential generation (see here). However, they influence and change the distribution of charges, this makes the channels at the membrane of neurons more or less likely to open and close. 

For example, the resting potential is maintained by the Na⁺/K⁺ pump, which pumps 3 Na⁺ ions out and 2 K⁺ ions in, keeping the inside of the neuron more negative compared to the outside. The influence of this pump and other channels determines the voltage gradient.

Cl- ions are less relevant to action potentials, however they primarily act through GABAergic inhibition: GABA is a transmitter which opens membrane channels allowing Cl- to flow into the cell and hyperpolarize it. Although this remains of second importance for the AP compared to Na+ and K+.  

Position of electrodes

Current density calculations show that increasing the distance between the electrodes decreases the current shunted through the scalp and increases the current density in depth.

Current density, calculated as I/A (current divided by electrode area), determines stimulation intensity. Increasing the area of the electrode decreases the current density at the electrode surface, while increasing the applied current increases the current density.

When you increase the distance between the two electrodes, it changes the path the current takes to travel between them. This increases the likelihood that more current passes through deeper brain structures instead of shunting across the scalp. 

The current flow model says that current will go through the path of less resistance: If two electrodes are placed closer together, the current will travel around the head and pass via the skin instead of entering the brain. 

As electrode distance increases, deeper brain tissues offer less resistance compared to the skull, facilitating deeper current penetration. One needs to find a balance, as a too high increase of the distance leads to dispersion. 

Advanced software models map current pathways through different tissues, helping optimize electrode placement for targeted stimulation.

As there are too many formulas to add on a website, I attached a pdf which explains more in detail some of the physics topics which could be useful:

Table of Contents in document:

Physics of TES

Areas and Current over view

Electrical currents - ions

Electric currents- electrons

Energy and potentials

Membrane Voltage

Membranes and Circuits

Electric shock and too high currents