The Physics and Safety of Intracortical Microstimulation

The charge-balanced biphasic pulse

ICMS delivers a charge-balanced biphasic pulse: a cathodic phase that depolarizes nearby membrane and triggers spikes, immediately followed by an equal-and-opposite anodic phase that reverses the electrochemistry and returns net charge to zero. Balancing is not a nicety — unrecovered charge drives irreversible reactions that corrode the electrode and damage tissue. The charge delivered in one phase is simply current times pulse width.

Q = I \cdot t_{\mathrm{pw}}

Charge per phase Q (in µC) is current I times pulse width t_{\mathrm{pw}}. It is the primary quantity that both drives activation and constrains safety.

Charge is simply the current multiplied by how long each pulse lasts — just like the amount of water you deliver equals the flow rate times how long the tap is open. This single number is what both makes neurons fire and decides whether the tissue stays safe.

Q: the charge delivered in one pulse (microcoulombs, µC) — think of it as the total amount of electricity pushed out.
I: the current — how hard the electricity is pushed (microamps, µA).
t_{\mathrm{pw}}: the pulse width — how long each single pulse lasts (milliseconds).

A current of I = 50 µA lasting t_{\mathrm{pw}} = 0.2 ms delivers Q = 50 \times 0.2 = 10 nanocoulombs of charge in that pulse.

How that charge crosses the electrode–tissue boundary matters. Capacitive (reversible) transfer charges the double layer without chemistry and is inherently safe; irreversible faradaic reactions (electrolysis, dissolution) are not. Staying inside the electrode's charge injection capacity — the charge it can deliver reversibly — is the goal, which is why materials like iridium oxide and PEDOT coatings are used: they enlarge the reversible budget dramatically.

Safety: charge and charge-density limits

Tissue damage tracks two quantities together, not one. Charge per phase Q sets how much total excitation you inject; charge density D = Q/A sets how concentrated it is at the electrode surface. A tiny electrode passing a modest current can still exceed safe density because its area A is small.

D = \frac{Q}{A} = \frac{I \, t_{\mathrm{pw}}}{A}

Charge density per phase (µC/cm²). Shrinking the electrode raises D for the same current — a core tension when you want many small, selective contacts.

Charge density is the charge squeezed onto each square centimetre of the electrode. Spread the same charge over a smaller electrode and the crowding shoots up — which is exactly why tiny, selective electrodes are the ones most at risk of harming tissue.

D: charge density per pulse (µC/cm²) — how concentrated the charge is.
Q: the charge per pulse, from the formula above.
A: the electrode's surface area (cm²) — the area the charge is spread over.

Halve the electrode area A while keeping the same charge Q, and the density D doubles.

\log_{10} D = k - \log_{10} Q

The Shannon–McCreery criterion: a damage boundary in the (Q, D) plane. Roughly k \approx 1.5 is conservative and k \approx 2.0 approaches injury — safe stimulation stays below the line.

This is a safety line, not a formula you plug a target into. It says: the more total charge you put into each pulse, the lower the density you are allowed to use. Drawn on log–log axes it is a straight downhill line, and safe stimulation stays below it.

D: charge density per pulse.
Q: charge per pulse.
k: the safety constant that sets where the line sits — about 1.5 is conservative, about 2.0 is already edging toward injury.

At k \approx 1.5 you keep a comfortable safety margin; pushing toward k \approx 2.0 means you are approaching the damage threshold.

Who gets activated: the current–distance law

A common misconception is that ICMS lights up a clean sphere of neurons around the tip. It does not. The current needed to activate an element grows roughly with the square of its distance from the electrode (the Stoney current–distance relation), so raising the amplitude expands recruitment nonlinearly.

I_{\mathrm{th}}(r) = I_0 + k_{\mathrm{cd}}\, r^{2} \quad\Longrightarrow\quad r_{\mathrm{act}} = \sqrt{\frac{I - I_0}{k_{\mathrm{cd}}}}

Threshold current rises with the square of distance r; equivalently the activation radius grows as \sqrt{I}, so the volume of tissue activated scales like (I - I_0)^{3/2}.

To wake up a neuron that sits twice as far from the electrode you need roughly four times the current — the cost grows with the square of distance. Turned around, the radius you can activate grows only like the square root of the current, so turning the current up does spread the volume of tissue activated outward, but with steadily diminishing reach.

I_{\mathrm{th}}(r): the threshold current needed to activate a neuron sitting a distance r from the electrode.
I_0: the baseline current needed right next to the electrode (r = 0).
k_{\mathrm{cd}}: the current–distance constant — how quickly the required current climbs as you move away.
r_{\mathrm{act}}: the activation radius — how far out neurons still get activated at a given current I.

With I_0 = 2 and k_{\mathrm{cd}} = 1, reaching a neuron at r = 3 needs I = 2 + 1 \times 3^2 = 11; doubling the reach to r = 6 would need I = 2 + 36 = 38.

Two subtleties make this even less tidy. First, axons and passing fibres have far lower thresholds than cell bodies, so ICMS preferentially recruits axonal elements — you often activate distant somata via their local axons, not the neurons physically nearest the tip. Second, recruitment is sparse and distributed: a scatter of activated elements interspersed with unactivated ones, not a solid volume. Both facts shape what percept a given electrode can evoke.

Detection thresholds and the usable window

The smallest stimulus a participant can reliably feel is the ICMS detection threshold — typically on the order of a few to a few-tens of microamps, though it varies widely with electrode, cortical site, pulse width and frequency. Shorter pulses need more current for the same effect, captured by a strength–duration curve.

I_{\mathrm{th}}(t_{\mathrm{pw}}) = I_{\mathrm{rh}}\left(1 + \frac{t_{\mathrm{ch}}}{t_{\mathrm{pw}}}\right)

Strength–duration (Weiss–Lapicque): I_{\mathrm{rh}} is the rheobase (asymptotic current for long pulses) and t_{\mathrm{ch}} the chronaxie (pulse width at twice rheobase). Short pulses cost more current but often deposit less charge.

The shorter the pulse, the more current you need to make the same neuron fire. Very long pulses settle onto a floor current (the rheobase); the chronaxie is the special pulse width where you need exactly twice that floor. Short-and-strong often deposits less total charge than long-and-weak — which is gentler on the tissue.

I_{\mathrm{rh}}: the rheobase — the floor current that even an infinitely long pulse still needs.
t_{\mathrm{ch}}: the chronaxie — the pulse width at which the required current is exactly twice the rheobase.
t_{\mathrm{pw}}: the pulse width you actually use.

When the pulse width equals the chronaxie (t_{\mathrm{pw}} = t_{\mathrm{ch}}), the threshold current is exactly twice the rheobase: I_{\mathrm{th}} = 2\, I_{\mathrm{rh}}.

Between detection at the bottom and pain, spread or damage at the top lies the usable stimulation window. Good feedback design lives entirely inside it — high enough to be felt clearly, low enough to stay safe and spatially selective. Guide 3 is about choosing what to put in that window.