Unified rheological modeling using fractal calculus for soft biological matter

Modeling soft biological matter has been a long-standing domain of interest due to its complex, multiscale nonlinear mechanical behavior, exhibiting unique power-law characteristics within its multiscale architecture. Fractional viscoelasticity has been widely used to capture its intricate characteristics but requires different models to describe solid- and fluid-like behavior. In this study, we employ fractal calculus, a local alternative to global fractional calculus with reduced mathematical and computational complexity, to develop fractal rheological viscoplastic models with independent time scaling for constitutive fractal elements. Generalized fractal models can capture the entire spectrum of physical behavior between solid- and fluid-like viscoelastic models, while having time-domain solutions, unlike their fractional counterparts. The proposed fractal viscoelastic self-similar hierarchical structures allow increased tunability of their local and global power-law behavior for multiscale modeling. With the mechanical characteristics of biological matter strongly associated with disease progression, the developed fractal framework provides a unified methodology for their rheological modeling, analysis, and simulation across the scales. From employing stiffness, fluidity, and other viscoplastic parameters as cancer biomarkers to providing detailed insights into the interplay of material fluidity, viscoelasticity, and plasticity for a wide variety of soft biological matter, the versatility of the proposed framework is established.