Hierarchical Internal Variables Reflecting Microstructural Properties: Application to Cardiac Muscle Contraction

The formalism of internal state variables is proposed for describing the processes of deformation in muscles. Due to the complicated hierarchical microstructure of soft tissues where macroscopic stress states depend upon the sliding of molecules and ion concentrations, the internal variables are switched in successively forming a certain hierarchy. This hierarchy is a general property for complicated materials with different microscopic processes influencing the macroscopic behaviour. Based on that property a novel concept of hierarchical internal variables is defined (up to the knowledge of authors first time) and embedded into the framework of the existing formalism. The discussion based on an example of cardiac muscle contraction illustrates the advantages of this approach.