Sensorimotor-Rhythm 2D Cursor BCI (Wolpaw & McFarland, 2004)
Measured by Wolpaw & McFarland · PNAS 101(51) (2004)
Inputs
The measured or assumed values behind the calculations, each with its source.
- N = 8
- Eight target locations on the screen periphery; the user drove a cursor from the center to a block-randomized target via sensorimotor-rhythm (mu/beta) modulation, i.e. continuous 2D control, not a discrete classifier.
- MT = 2.75 s
- Mean movement time to reach a target, averaged over the four users (individual means 1.9, 3.9, 3.3, 1.9 s). Best users reached targets in ~1.9 s.
- W = 4.9 % of workspace
- Target size as a fraction of the workspace (the paper's precision figure); exact pixel geometry was not published, so the amplitude/width ratio below is an estimate.
- P = 0.82
- Mean fraction of targets reached within the 10 s allowed, averaged over users (89%, 70%, 78%, 92%).
Strictest ITR
Each scoring method is an upper bound on the channel, so the headline is the strictest (smallest) one for this entry. Use the score selector on the home page to view any single method across entries.
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Bits per selection (Wolpaw formula)
B = log2(N) + P*log2(P) + (1-P)*log2((1-P)/(N-1)) = log2(8) + 0.82*log2(0.82) + 0.18*log2(0.18/7) = 1.815 bits / selection
Term 1 is the information if every choice were correct; terms 2-3 subtract the bits lost to the error rate, assumed spread evenly over the other N-1 targets.
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Selections per second
T = 2.75 s/selection -> 1 / 2.75 = 0.364 selections/s
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Information transfer rate
ITR = B * selections/s = 1.815 * 0.364 = 0.66 bits/s
What counts as a bit depends on the action space. The number of distinguishable actions and how likely each one is are design choices of the task, not the sensing hardware. The same modality can present a fixed set of targets, a set pruned per step by a grammar or language model, or a continuous control space. Each of these changes how many actions are live and how the probability mass is spread, and therefore the information per selection. Read the action space below before comparing headline numbers across entries.
Action space
What the user can produce at each step, and how those options are distributed.
- Structure
- Continuous control space
- Size
- Continuous
- Prior
- Uniform: all actions assumed equally likely
- Notes
- A continuous 2D cursor driven by sensorimotor-rhythm modulation (left/right-hand and rest motor imagery): the canonical non-invasive cursor BCI, and the paper that showed scalp EEG can approach invasive cursor control. The paper reports an eight-target center-out task, so the reference follows the Wolpaw-style target-acquisition estimate over those cued endpoints. The Fitts estimate is kept as a geometry-based check, but the paper does not publish pixel geometry or endpoint scatter, so that calculation rests on inferred target size and amplitude.
Comparability The strictest bound here is a Wolpaw-style target-acquisition estimate over cued endpoints. This is a continuous cursor task, so compare it carefully with the Fitts-bounded pointing entries: the number reflects the published target set and completion rate, not a full Fitts effective-width throughput.
Other bounds considered for the headline
Also valid upper bounds for this entry and eligible to be the headline. They just came out looser than the strictest above. Pick any of these in the home-page score selector.
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Information per movement (index of difficulty)
ID = log2(A/W + 1); target W ≈ 4.9% of workspace, amplitude A ≈ 45% (center to periphery) → A/W ≈ 9.2 → ID ≈ 3.35 bits/movement
ESTIMATE: the paper reports size/precision as a fraction of the workspace but not pixel geometry, so A/W is inferred from the center-out layout. This is one of two load-bearing assumptions in the entry.
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Throughput = information ÷ movement time
mean MT ≈ 2.75 s → TP ≈ 3.35 / 2.75 ≈ 1.22 bits/s (best users ~1.8 bits/s at MT ≈ 1.9 s)
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Discount for completion rate
× 0.82 (mean fraction of targets reached within the 10 s limit) → ≈ 1.00 bits/s
This is a COMPLETION discount, not a Fitts effective-width adjustment: the paper publishes no endpoint scatter (SDx), so the index of difficulty uses nominal width and the 82% is targets reached in time, not a spatial-miss rate. Accuracy is therefore folded as a simple throughput multiplier (the same fallback used for the Neuralink cursor), not via the standard We = 4.133·SDx.
Other score types
Bounds the atlas keeps out of the default strictest headline: as-reported figures, alternate task conditions, or raw-channel ceilings that shouldn't win the headline by default. Each still carries a score type, so the home-page selector ranks this entry on it when you choose that type. Read its derivation before comparing across entries.
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Achieved-bitrate credit per correct acquisition
N = 8 cued targets → log2(N − 1) = log2(7) = 2.81 bits per net-correct selection (field-standard achieved bitrate, e.g. Webgrid; Nuyujukian 2015, which introduced the metric, used log2(N)).
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Net-correct acquisition rate
incorrect = 0, so net-correct = 0.82 of attempts at one per 2.75 s → 0.82 / 2.75 = 0.298 correct/s.
Misses are 10 s timeouts, not wrong-target selections, so there are no false selections to net against. Same reached-in-time basis (P = 0.82, mean movement time 2.75 s) as the entry's Fitts and Wolpaw calcs. Unlike the Wolpaw figure it credits log2(N − 1) per correct acquisition rather than the mutual information, so it runs looser.
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Achieved bitrate
2.81 bits × 0.298 correct/s = 0.84 bits/s.
Source
- Authors
- Wolpaw & McFarland
- Publication
- PNAS 101(51), 2004
- Paper
- 10.1073/pnas.0403504101