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Neurovascular Coupling & BOLD Signal (2D)

2D balloon-model lab: solve the Buxton hemodynamic equations live on canvas, tune stimulus amplitude, duration, transit time τ and the Grubb exponent α, and watch the fMRI BOLD response curve — inflow, blood volume, deoxyhemoglobin and BOLD — form in real time.

Neuroscience & Biophysics2DAdvanced60 FPS📱 Mobile-adapted⇄ 3D version

This 2D companion solves the same Buxton balloon-model equations as the 3D version on a flat, readable canvas chart rather than an orbiting scene. A neural stimulus of adjustable amplitude and duration drives inflow f_in; the coupled ODEs then convert that inflow into blood volume v and deoxyhemoglobin content q, whose combination produces the BOLD signal that fMRI scanners actually detect. A side panel exposes the stimulus amplitude and duration alongside the vascular transit time τ and Grubb exponent α, while the chart plots all four synchronized time-courses — f_in, v, q and BOLD — over a rolling 30-second window, with a shaded stimulus band making the multi-second lag between neural firing and its hemodynamic echo directly visible, along with the characteristic post-stimulus undershoot.

⚙ Under the hood

2D balloon-model lab: neural stimulus amplitude and duration drive an inflow pulse f_in, integrated together with blood volume v and deoxyhemoglobin content q via explicit Euler at a fixed 20 ms sub-step, producing the BOLD signal ΔS/S₀ ≈ V₀(k₁(1−q) + k₂(1−q/v) + k₃(1−v)) plotted live alongside the other three time-courses.

BOLD signalneurovascular couplingballoon modelfMRIcerebral blood flow

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install