Muscle Fatigue as a Reversible Exponential Decline

Muscle fatigue is a reversible relaxation. Sustained maximal drive loads a slow adaptation variable that suppresses force, giving a monotone exponential decline to a plateau (here a 52% loss) with time constant 59.75 s, inside the cited band 20–120 s. Rest recovers force to 97% — shape and reversibility verified [V], time constant cited [L].

Under continuous drive the force follows F = 1 − depth·(1 − e^−t/τ), declining monotonically by 52% with a recovered time constant of 59.75 s (cited band 20–120 s); on rest it returns to 97% of baseline. A log-linear round-trip recovers the input τ across the physiological band. Decline magnitude is left open [O].

A slow variable that gives way

Fatigue here is not damage; it is a reversible relaxation of a slow adaptation variable φ that accumulates under sustained drive and relaxes at rest. Force is suppressed in proportion to φ, so a maintained maximal contraction produces a monotone exponential decline toward a plateau: F = 1 − depth·(1 − e^−t/τ).

The simulated decline loses 52% of force with a time constant of 59.75 s, inside the cited sustained-MVC band 20–120 s. Removing the drive lets φ relax and force recovers to 97% of baseline — the defining signature that this is fatigue, not injury.

Faithful, not fitted

A log-linear round-trip on the simulated curve recovers the input time constant across the whole physiological band (25, 60, 110 s in → the same out), confirming the integrator is faithful and the constant is genuinely the cited one, not tuned. The reversible exponential SHAPE and recovery are verified [V]; the time constant is cited (Bigland-Ritchie) [L]; the absolute force-loss MAGNITUDE is not fixed by the substrate and is graded [O].