Key result
A novel concept of hierarchical internal variables was defined and embedded into the existing formalism to describe the processes of deformation in cardiac muscle contraction.
Introduces a novel mathematical formalism using hierarchical internal variables to better model the complex microstructural properties of cardiac muscle contraction.
No immediate clinical impact; leaves open whether hierarchical variables enhance cardiac contraction models.
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.
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Engelbrecht et al. (2000) studied Cardiac muscle contraction. Hierarchical internal variables formalism was evaluated. A novel concept of hierarchical internal variables was defined and embedded into the existing formalism to describe the processes of deformation in cardiac muscle contraction.
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