2025/12/11 by Serhii V Marchenko, Marchenko, Serhii V
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Biological Physics (physics.bio-ph) #FOS: Biological sciences #FOS: Physical sciences #Quantitative Methods (q-bio.QM) #physics.bio-ph #q-bio.QM
paper · pdf · doi:10.48550/arxiv.2512.13720
arxiv created 2026/07/29 · arxiv updated 2026/07/31
Small deviations during nominally isometric loading can be separated into a sustained mean offset and fluctuations about that offset. We develop a local quasi-static model that connects these video-accessible kinematic quantities to metabolic energy. Muscle activation is eliminated through joint-moment equilibrium, and the resulting metabolic power is reduced to a smooth function of a locally invertible muscle-length coordinate. For the deviation \(x(t)=ℓ(t)-ℓ0\), the reduced energy satisfies Emet[ℓ] = P0T + C1ΔAℓ + C2M2,ℓ + R3, |R3| ≤ KT‖x‖L^∞(0,T)3, where \(ΔAℓ=∫0T x(t) dt\) is signed deviation absement and \(M2,ℓ=∫0T x(t)2 dt\) is the second raw integral moment. Equivalently, if \(μ_ℓ\) and \(σ_ℓ2\) are the mean and variance of the observed length deviation, then \(ΔAℓ=Tμ_ℓ\) and \(M2,ℓ=T(μ_ℓ2+σ_ℓ2)\). A video-based protocol can therefore estimate the required predictors without differentiating the recorded trajectory. Within the autonomous quasi-static model, periodic variation does not require a separate cycle-specific predictor: its mean contributes through absement and its dispersion through the second moment. This moment-based protocol, rather than the Taylor expansion alone, provides the experimentally testable result: residual dependence on frequency after control for the first two moments would identify the limit of the quasi-static reduction.