We provide a comment to our paper “Comparative Sensitivity Analysis of Muscle Activation Dynamics,” Computational and Mathematical Methods in Medicine (2015), 16 pages, Article ID 585409, DOI 10.1155/2015/585409 [1], where we stated an erroneous form of Hatze’s activation dynamics that is not applicable to non-steady-state muscle processes. However, as we only considered steady-state situations, all results and consequences still hold true. The authors would like to apologize for any inconvenience caused.
In his consecutive work [2–4], Hatze introduced the dynamics of changes in activity q (activation dynamics) for skeletal muscle fibers in response to neural stimulation σ as a multilevel process, with γ being the relative free calcium ion concentration and lCE the length of the contractile element (CE). In [4, Eqns. 3.27, 3.29, and 3.30], this process is summarized as follows: (1)γ˙=m·σ-γ,γ0=γ0,ρlCE=ρc·lρ-1lρ·lCE,opt/lCE-1,qlCE,γ=q0+ρlCE·γν1+ρlCE·γν.
In our main article [1, Eqn. (5)], we had reformulated the above equation system (1) as (2)q˙=ν·m1-q0·σ·ρlCE·1-q1+1/ν·q-q01-1/ν-1-q·q-q0,in an effort to eliminate the state variable γ in favor of q. However, the specific formulation in (2) holds only true in the steady-state case l˙CE=0. This is because the transformation [5, Eqns. 3.21–3.24] was erroneously done by (3)q˙=∂q∂γγ˙rather than properly taking the total derivative(4)q˙=∂q∂γγ˙+∂q∂lCEl˙CEfor the total time derivative of q.
In our framework only steady-state muscle conditions were investigated; that is, l˙CE=0, such that the second term of the right hand side in (4) vanishes. Hence, the situation from (2) holds throughout the article. In non-steady-state isometric contractions, this second term seems to be of reversed sign to the first, but with a considerably smaller absolute value; compare [6].
Acknowledgments
The authors would like to thank Maria Hammer for drawing attention to their computational error.
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