# Passive viscoelastic response of striated muscles

## TL;DR

This paper develops a novel second-order rheological model for the passive viscoelastic response of striated muscles, incorporating long-range interactions and validated with frog muscle data.

## Contribution

It introduces a new second-order continuum model for muscle mechanics derived from a stochastic micromodel, improving upon previous first-order approaches.

## Key findings

- Model shows excellent agreement with experimental data
- Second-order equation captures complex muscle behavior
- Microscopic parameters accurately predict macroscopic response

## Abstract

Muscle cells with sarcomeric structure exhibit highly nontrivial 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. Instead of the first order rheological equation, anticipated by A.V. Hill on the phenomenological grounds, we obtain a novel second order equation. We use the values of the microscopic parameters for frog muscles to show that the proposed rheological model is in excellent quantitative agreement with physiological experiments.