Multiscale Numerical Methods for Modeling Biofluid Dynamics Across Cellular to Organ-Level Scales

Abstract

The multiscale modeling of biofluid dynamics presents a formidable challenge due to the inherent complexity of physiological systems, where interactions span molecular, cellular, tissue, and organ-level scales. This paper systematically examines advanced numerical methodologies tailored to address these cross-scale phenomena, focusing on their mathematical underpinnings, computational trade-offs, and physiological fidelity. We critically evaluate continuum-based approaches, such as the Navier-Stokes equations with hybrid viscoelastic constitutive models, against discrete particle methods, including dissipative particle dynamics and lattice Boltzmann formulations. Special emphasis is placed on interface-capturing techniques like the immersed boundary method and arbitrary Lagrangian-Eulerian frameworks for resolving fluid-structure interactions in deformable biological tissues. Furthermore, we analyze homogenization strategies for bridging cellular-scale phenomena—such as endothelial shear stress sensing—to macroscopic hemodynamic simulations. A comparative assessment of monolithic versus partitioned coupling schemes reveals critical insights into numerical stability and scalability for large-scale vascular simulations. The discussion extends to recent advances in data-driven surrogate modeling, which synergize reduced-order physics with machine learning to alleviate computational bottlenecks. By contextualizing these approaches against experimental validations in vascular flow and pulmonary dynamics, this work provides a rigorous framework for selecting appropriate multiscale strategies based on accuracy, efficiency, and target physiological observables.