Passive viscoelastic response of striated muscles. Issue 16 (7th April 2022)

• Record Type: Journal Article
• Authors: Staniscia, Fabio; Truskinovsky, Lev
• Is Part Of: Soft matter. Volume 18:Issue 16(2022)
• Page Start: 3226
• Page End: 3233
• Publication Date: 2022-04-07
• Subjects: Soft condensed matter -- Periodicals; 530.413
• DOI: 10.1039/d1sm01527c
• Languages: English
• ISSNs: 1744-683X

Abstract

Abstract : We derive, starting from a microscopic model of the sarcomere and using methods of statistical mechanics, a rheological spring-dashpot model which explains the short time (few milliseconds) muscle fibre behaviour. Abstract : Muscle cells with sarcomeric structure exhibit highly non trivial passive mechanical response. The difficulty of its continuum modeling is due to the presence of long-range interactions transmitted by extended protein skeleton. To build a rheological model for muscle 'material', we use a stochastic micromodel, and derive a linear response theory for a half-sarcomere, which can be extended to the whole fibre. Instead of the first order rheological equation, anticipated by Hill on the phenomenological grounds, we obtain a novel second order equation which shows that tension depends not only on its current length and the velocity of stretching, but also on its acceleration. Expressing the model in terms of elementary rheological elements, we show that one contribution to the visco-elastic properties of the fibre originates in cross-bridges, while the other can be linked to inert elements which move in the sarcoplasm. We apply this model to explain the striking qualitative difference between the relaxation in experiments involving perturbation of length vs. those involving perturbation of force, and we use the values of the microscopic parameters for frog muscles to show that the model is in excellent quantitative agreement with physiological experiments.