M4 · Phosphene simulator

It grows. Cortical magnification M(r) drops with eccentricity, and sigma_deg = radius_to_sigma * sqrt(I/K) / M(r). Smaller M -> bigger apparent size for the same current. This is why peripheral phosphenes appear large and blob-like, while foveal ones are crisp dots.

Bigger. K is the current-spread constant (uA/mm^2). A smaller K means the same current spreads over a larger cortical area, activating more tissue -> larger phosphene radius -> larger sigma.

Foveated provides finer central details and uniform provides finer peripheral ones. With the same N electrodes, foveated placement crowds them near the fovea, where sigma is also smaller, producing crisper central vision. Uniform placement gives the periphery the same density as the fovea but each phosphene is small in the centre and large in the periphery.

They sweep outward (small steps in cortex = huge eccentricity changes in the periphery), and they grow (cortical magnification drops, so each electrode covers more degrees of visual angle). This is the engineering case for foveated electrode placement: phosphenes are cheap and large in the periphery, scarce and small in the fovea.

The abstract shapes (square + disc, letter "E", grating bars, diagonal line) stay legible — their information lives in a few large, high-contrast regions that survive coarse sampling by the electrode lattice. The natural photographs (kitten, scene) do not: most of the recognisable signal in a real image lives in fine edges and texture that fall below the inter-electrode spacing, so they alias into a blobby mess that no longer reads as the original object.

The overall silhouette — a roughly round bright blob with two triangular ear notches against a darker background. Individual features (eyes, whiskers, fur texture, fur boundaries) are essentially gone: they sit inside that blob at spatial scales finer than the lattice can resolve. The same point generalises to faces: a pure intensity-based forward pass is a poor match whenever identity is carried by the geometry of internal features rather than by the outer silhouette. To carry that information you would need a representation that first extracts feature locations (eyes, mouth, ear tips) and renders those explicitly, instead of sampling raw pixel brightness.

Not really. The Canny preset gives you the edge map of the scene, which is the right kind of information — building outlines, rooflines, window frames — but once it is resampled onto the electrode lattice the edges come out as disconnected dots rather than continuous contours. There is no signal that says "these two phosphenes belong to the same line"; the visual system has to guess. For sparse arrays this guess fails on buildings because their identifying features are exactly long straight edges, which the lattice fragments into ambiguous point clouds. Denser arrays (push N electrodes up) help, but the underlying problem — no perceptual grouping cue between phosphenes — remains.

The fade is not the stim turning off — it is adaptation. The dashed yellow line plotted on top of the brightness curve is the mean trace state \(B\), and you can see it rising as soon as stimulation starts. The trace adds onto the rheobase in the leak term, so the effective amplitude (I − rheobase − trace) shrinks as the trace grows. Charge per second drops, activation drops, brightness fades — even though \(I_{\mathrm{stim}}\) has not moved. The fall in brightness mirrors the rise in the dashed line.

Switching to disable trace zeroes \(B\) out of the equations entirely. Now the leak is just the rheobase, the effective amplitude stays constant, and the brightness saturates and stays there for the whole stim window — a flat plateau instead of a curve that bends down. That flat behaviour is what you would see in an idealised, non-adapting cortex; the trace is the one ingredient that turns the simulator's output into something that matches what real cortical implants do.

It postpones and smooths both the rise and the fall. At the yaml default the activation integrator is essentially instantaneous: brightness jumps to its peak in one frame when stim starts, and drops back in one frame when stim ends. Raising the slider keeps a larger fraction of \(A\) alive from frame to frame, so the cell takes more frames to build up to its peak and more frames to drain back to zero. The corners of the curve become rounded ramps; the trace-driven fade in the middle is still there, but now layered on top of a softer rise and a gentler tail.

Because dynaphos puts a hard activation threshold in front of the sigmoid (Eq. 10): brightness is only emitted when \(A > A_{\mathrm{th}}\) (yaml: \(9.14\times10^{-8}\)). Below that cut-off, the simulator returns exactly zero — no phosphene at all, regardless of how small a positive activation the equations would otherwise yield. This matches what is observed in human implant data: there is a minimum charge below which the percept simply does not appear; you do not get a "very faint" phosphene that fades smoothly to nothing.

The Stim ON until frame slider is the divider line. Up to frame ~60 the implant is delivering current; after that, \(I_{\mathrm{stim}} = 0\) and the cell is just relaxing on its own. That gives you two qualitatively different regions in the plot.

Frames ~0–60 (stim ON, after the initial rise) — adaptation. With \(\tau_A \approx 0.83\,\mathrm{s}\) the activation now needs many frames to climb, so you see a soft ramp up. Then the brightness peaks and starts curving back down even though the current has not moved. The dashed yellow trace line is climbing in parallel: it adds to the leak, the effective amplitude \((I_{\mathrm{stim}} - I_0 - B)\) shrinks, charge per second drops, activation drops. This is the trace-driven adaptation regime — same input, falling output.

Frames ~60 onwards (stim OFF) — pure activation decay. The moment stim turns off, \(I_{\mathrm{stim}} = 0\) so \(I_{\mathrm{eff}} = 0\) and no new charge is injected. The trace is irrelevant here — it cannot eat into a current that is already zero. Activation simply leaks away at rate \(1/\tau_A\), and the brightness falls along an exponential tail purely set by the activation_decay slider. The dashed trace line is still high (it decays on \(\tau_B\), thousands of seconds), but it has no effect on the brightness any more — the curve is owned entirely by \(A\)'s leak.

So the trick is: anything that bends downward while stim is still on is the trace; anything that falls after the stim-ON boundary is the activation integrator emptying out.

The peripheral one. Cortical magnification shrinks as eccentricity grows — the cortex devotes far more surface area per visual degree to the centre of the visual field than to the edges. The same disc of activated tissue therefore covers a wider patch of visual angle in the periphery, so the phosphene comes out bigger and less crisp. Near the fovea, magnification is large, and the same current paints a small, sharp dot.

Concentrate them around the fovea (the "foveated" layout in Section 02). Two things line up there: (1) cortical magnification is largest, so each phosphene is naturally smallest and sharpest, and (2) that is where the user actually looks when they want to read or identify something. Spreading electrodes evenly across the field wastes budget on the periphery, where phosphenes are big and blurry anyway and where fine detail is rarely needed.

Because the information that identifies a natural image lives in fine edges and textures — spatial frequencies above what the electrode lattice can carry. By the time the image is resampled onto a few hundred phosphenes, those high-frequency cues are gone. The abstract targets are different: their identity lives in a few big, high-contrast regions (a solid block, a bold letter stroke, a coarse bar pattern). Coarse sampling preserves that just fine, so the shape still reads. Phosphene arrays are a low-resolution carrier; natural images carry their meaning above that carrier's bandwidth.

The trace. It is a slow internal "fatigue" state that accumulates while the cell is being stimulated, and it adds onto the leak current alongside the rheobase. As the trace grows, the effective amplitude (the part of the stim current that survives the leak) shrinks, the charge per second delivered to the cell shrinks with it, and the activation that drives brightness drops. The input has not moved, but the cell's response has — that is the adaptation. The activation state on its own would just plateau at a constant brightness; the trace is what bends the curve back down.

The first threshold is the rheobase. It is subtracted from the stim current before any charge is computed — if the stim current is below it, the cell receives no charge at all. The second is the activation threshold: even when charge is being delivered, the simulator only renders a phosphene if the accumulated activation state climbs above this cut-off. So yes — there is a band of currents above the rheobase where charge is being delivered but the activation never reaches the perception threshold, and the screen stays black. The rheobase gates charge delivery; the activation threshold gates whether you actually see anything.