Computational mesoscale framework for biological clustering and fractal aggregation

Hierarchical clustering due to diffusion and reaction is a widespread occurrence in natural phenomena, displaying fractal behavior with non-integer size scaling. The study of this phenomenon has garnered interest in both biological systems such as morphogenesis and blood clotting, and synthetic systems such as colloids and polymers. The modeling of biological clustering can be difficult, as it can occur on a variety of scales and involve multiple mechanisms, necessitating the use of various methods to capture its behavior. Here, we propose a novel framework, the generalized-mesoscale-clustering (GMC), for the study of complex hierarchical clustering phenomena in biological systems. The GMC framework incorporates the effects of hydrodynamic interactions, bonding, and surface tension, and allows for the analysis of both static and dynamic states of cluster development. The framework is applied to a range of biological clustering mechanisms, with a focus on blood-related clustering from fibrin network formation to platelet aggregation. Our study highlights the importance of a comprehensive characterization of the structural properties of the cluster, including fractal dimension, pore-scale diffusion, initiation time, and consolidation time, in fully understanding the behavior of biological clustering systems. The GMC framework also provides the potential to investigate the temporal evolution and mechanical properties of the clusters by tracking bond density and including hydrodynamic interactions.