Population Vector Decoding of Motor Cortex Spikes

Intended Reach Direction

Direction θ 0°

Neural Population

Electrode channels (N) 100

Tuning depth (modulation) 70%

Trial-to-trial noise 30%

Decoder Output

Decoded angle

0.0°

Angular error

0.0°

Pop. vector |V|

0.00

Mean firing rate

0.0 Hz

How it works

Each simulated motor-cortex neuron i has a fixed preferred direction (PD) spread around the circle, wired to an intracortical microelectrode. Its trial-averaged firing rate follows the cosine tuning law found by Georgopoulos et al. (1982) in real reaching-task recordings:

r_i(θ) = b0 + b1 · cos(θ − PD_i)

where θ is the true movement direction, b0 the baseline rate and b1 the tuning depth. On every trial each channel emits a spike count drawn from a Poisson process with mean r_i(θ)·T (T = 1 window), so the population is noisy exactly like real recordings. The classic population vector algorithm decodes θ back out of the spike counts by summing each channel's preferred-direction unit vector, weighted by how far its count exceeds baseline:

V = Σ_i (c_i − b0)·(cosPD_i, sinPD_i)
θ_decoded = atan2(V_y, V_x)

The decoded arrow (magenta) should track the true target arrow (white); the gap between them is the angular error the readout reports. This exact algorithm — a weighted vector sum over a tuned neural population — is the basis of real intracortical BCIs (e.g. Utah-array systems) that let paralyzed users steer a cursor or robotic arm with thought alone.

Channels (N) — how many electrodes contribute to the decode; fewer channels (simulating array dropout/scarring) makes the estimate noisier.
Tuning depth — how strongly each neuron's rate depends on direction; low depth means the signal is buried in baseline firing.
Noise — extra Poisson-count variability layered on top, mimicking session-to-session recording instability.
New Trial — redraws all spike counts for the same target, showing decode variability across repeated trials.

True direction Decoded (population vector) Active electrode (spiking)

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