On the influence of microscopic architecture elements to the global viscoelastic properties of soft biological tissue

In this work we introduce a 2D minimal model of random scale-invariant network structures embedded in a matrix to study the influence of microscopic architecture elements on the viscoelastic behavior of soft biological tissue. Viscoelastic properties at a microscale are modeled by a cohort of basic elements with varying complexity integrated into multi-hierarchic lattice obeying self-similar geometry. It is found that this hierarchy of structure elements yields a global nonlinear frequency dependent complex-valued shear modulus. In the dynamic range of external frequency load, the modeled shear modulus proved sensitive to the network concentration and viscoelastic characteristics of basic elements. The proposed model provides a theoretical framework for the interpretation of dynamic viscoelastic parameters in the context of microstructural variations under different conditions.