Hierarchical internal variables reflecting microstructural properties: Application to cardiac muscle contraction

The formalism of internal state variables is proposed for describing the pr ocesses of deformation in muscles. Due to the complicated hierarchical micr ostructure of soft tissues where macroscopic stress states depend upon the sliding of molecules and ion concentrations, the internal variables are swi tched in successively forming a certain hierarchy, This hierarchy is a gene ral property for complicated materials with different microscopic processes influencing the macroscopic behaviour. Based on that property a novel conc ept of hierarchical internal variables is defined (up to the knowledge of a uthors first time) and embedded into the framework of the existing formalis m. The discussion based on an example of cardiac muscle contraction illustr ates the advantages of this approach.