BIOMECHANICS, BIOENGINEERING AND MATHEMATICAL BIOLOGY Seminar

PROGRAM

Predavanja možete pratiti i online putem MITEAM stranice Seminara iz Biomehanike, bioinžinjeringa i matematičke biologije: https://miteam.mi.sanu.ac.rs/asset/pkPCEADMcffpGhjaQ

Plan rada Seminara iz Biomehanike, bioinžinjeringa i matematičke biologije za DECEMBAR 2025.

Ponedeljak 29.12.2025. u 16:00, Pariske Komune bb, Niš i Online
Andjelka Hedrih, Mathematical Institute SANU, Belgrade, Serbia
FRACTALS IN MEDICINE AND BIOLOGY
Fractal patterns—manifestations of statistical self-similarity across spatial and temporal scales—are pervasive in living organisms and critically shape the architecture and function of tissues and organs. In many cases, the behavior of such systems is more accurately captured using fractional calculus to describe memory-dependent processes, anomalous diffusion, viscoelasticity, and long-range interactions that cannot be addressed by classical integer-order models. To characterize a variety of biofractal structures a theory of oscillations, chaos theory, fractal geometry, and fractional differential equations are often used. In this talk we will provide several examples from the literature: the fractal branching of the pulmonary airway tree, the dendritic and axonal arborization patterns in neuronal circuits, and the fractal morphology of trabecular bone, which contributes to load distribution and mechanical resilience as well as some of our findings regarding the oscillatory model of mitotic spindle. For each of these systems, fractional-order models—such as fractional diffusion equations, fractional Kelvin–Voigt viscoelastic models, and fractional-order impedance formulations—have provided improved fits to empirical data and deeper insight into physiological regulation. In pathological conditions characteristic deviations from healthy fractal patterns are observed. At the microscopic scale, fractal analyses of chromatin architecture and DNA organization reveal that cancer progression is accompanied by a breakdown of normal fractal hierarchy. Additionally, fractional-order oscillatory models of mitotic spindle dynamics have been used to describe anomalous rotational and vibrational behaviors observed in dividing cancer cells. The importance of fractal principles in both health and disease will be discussed.