When there is a description of a circuit or circuit elements, you see even some of the smartest people become all glazed over, as if the words current or Ohm's Law inexplicably creates a block in understanding (I must admit, the same thing happens to me with probability math, I just can't get my head around it). The concepts of basic circuit theory are indeed simple, and luckily the circuit theory of basic tDCS is indeed straightforward. I will do my best to dispel some confusion about current flow, brain currents, and anode and cathode.
Consider the drawing below, a simple tDCS setup using current regulating diodes. Firstly, this is a DC circuit, none of the values are changing with time. After it is powered up and reached a steady state, it keeps that value. A current can only occur if there is a closed loop, and since there is only one loop, there can only be one current (I).
In most tDCS circuits a current regulating device is used. That means even with varying input voltage (i.e. as the battery changes) and with varying load (i.e. if the head resistance changes due to drying of the sponges or movement changing the electrode position) the current will still remain the same. Now you see why simple current regulating devices (in this case a Current Regulating Diode (CRD)) are perfectly suited for tDCS. What this means that as long as you have a bias voltage, and an appropriate load, the current will be 1mA, and the current will only flow in one direction.
There is confusion about current direction. We electrical engineers like to use current (because algebraic equations can be used to calculate current and voltage), and in the DC situation, current always flows from positive (+) to negative (-). Not to confuse anybody, but charge (and electrons) flow in the opposite direction but that is not relevant here because all circuit elements are best described using current.
All the math you need for this discussion is Ohms law, V = I x R or I = V/R. What that means is if there is a smaller resistance, the current will be greater and also if there is a resistance and there is a current, there is a voltage drop over that resistance. OK back to tDCS.
Looking at the tDCS schematic above, the 2k Ohm resistor is there to limit the current; if the CRD fails, and there is 18V at the head. The head resistance will vary due to numerous things, but a good range is 2kOhm to 6kOhm. For worst case, use 2 kOhm. So if there is 18V at the head, and the current regulator is not working, then the maximum current can be 4.5mA (18V/4kOhm). The 2kOhm will also limit the current in fail mode or normal mode if the electrodes are shorted together. During normal functioning, you can short them together and the CRD is still happy to produce 1mA into a 2kOhm load. This also protects the electronics. Obviously shorting together is not something that happens at the head but when the electrodes are taken off or fall off the head when still on and come together on the table or desk.
With tDCS nomenclature, the current flows through the Anode, the positive electrode, through the head to the Cathode, negative electrode (forget electrochemistry, diodes etc.). I, like many people, have wondered how much current really goes through the brain. Since the dura mater, connective tissue, and the skull will be more resistive than the fluid just under the skin you would think that most of the current travels tangentially under the scalp but obviously some current goes in to the brain. What I have read is that the closer together the electrodes, the more current travels under the scalp (which makes sense).
From a physiological view, it is more complicated. The head is not a true resistor (but for the circuit design, it works to make this assumption), as the skin, connective tissue, skull and then brain have a non uniform electrical characteristic. For the effect on the brain, research scientists are more concerned with current density and achieving the best current density. Hence another reason why the nice uniform current density of the sponge electrode is the best choice. The drawing below shows an imaging of current density with a 2mA DC stimulation. The red is the section where current is flowing into the brain and blue is the section where current is flowing out of the brain.
Lastly you can calculate the current density by dividing the current of stimulation by the area of the electrode, but just knowing that there is a sufficient size electrode, the correct connection between electrode and scalp, and limiting the stimulation level to 2 mA, then the current density is not a concern.
