## 4 Discussion  
Capacitive effects are known to be important for stimulating electrodes [26]. Typically, such electrodes are either Faradaic (where a chemical reaction occurs at the interface between the wire and the tissue) or capacitive (where charging or discharging a charged double layer at the electrode surface allows the stimulating current to enter the tissue). Figure 8: (**a**) The current, \(I\), applied to the wire as a function of time, \(t\), and (**b**) the peak tissue electric field intensity, \(E\), as a function of position, \(x\), at time 0.7 us. However, these electrodes typically connect the stimulating circuit to a grounded tissue space. In other words, the electrode capacitance is in series with the wire injecting the stimulating current, and a second grounded electrode is required to provide the return path for the current. Our case is different. The wire capacitance is distributed in parallel along the length of the wire. Capacitive current passes out of the wire at one end and returns back into the wire at the other end. In essence, one end of the wire acts as the cathode and the other end as the anode. This is a very different circuit than used when analyzing most stimulating electrodes; no separate ground electrode is required. Our model resembles, in fact, an undersea telegraph cable or an axon within a nerve more than the usual stimulating electrode. This model shows that a wire passing a sinusoidal current with a frequency of 3 kHz and amplitude of 1 mA produces an electric field in the surrounding tissue of about 4 mV/m. This value of \(E\) is small compared to the value required for excitation of neurons in the brain. [PERSON] found that the transmembrane potential produced in a single neuron in an electric field of 10 V/m can polarize a neuron by 6 to 8 mV, implying that the threshold is in the order of 10 V/m, or 10,000 mV/m [20]. Our value of \(E\) is about 2500 less than this threshold. Therefore, the electric field induced by capacitive coupling for a 1 mA, 3 kHz current should be well below the strength needed for neural excitation. In their calculations, [PERSON] et al. used a nominal value of 1 mA for the current, but in their experiments, they found thresholds in the order of 40 mA [18]. A current of 40 mA would increase our calculated electric field up to 160 mV/m, bringing the stimulus closer to the expected threshold, within a factor of about 60. For long, straight axons, the \"activating function\" dE/dx is often used as the source of electrical stimulation rather than the electric field itself. However, in the brain where axons bend and terminate, the electric field is more appropriate. The differences between these mechanisms are discussed in detail in [27]. [PERSON] et al. assumed the electric field in the tissue was caused by magnetic stimulation, and calculated its amplitude to be about 1000 mV/m [18]. However, using arguments like those presented by [PERSON] and [PERSON] [19], the electric field produced by magnetic stimulation should be in the order of  
\[E\approx\frac{\mu_{o}}{4\pi}\frac{dI}{dt}\approx\frac{\mu_{o}}{4\pi}\ I_{o}2\pi f \tag{13}\]  
where \(\mu_{o}\) is the permeability of free space (4\(\pi\)\(\times\) 10\({}^{-7}\) V s/(A m)). For \(I_{o}\) = 1 mA and \(f\) = 3 kHz, \(E\) should be in the order of 0.002 mV/m, which is nearly a factor of a million smaller than the value [PERSON] et al. calculated. (We have no explanation for why their calculation gave such a large value because we do not have access to their computer code; the computer code for our magnetic stimulation calculation is given in [19].) In this case, the electric field from magnetic stimulation (0.002 mV/m) is more than a thousand times smaller than the electric field from capacitive coupling (4 mV/m), implying that capacitive coupling is the dominant mechanism.