Uncertainty Quantification in Numerical Simulations of Biofluid Flows: Methods and Applications

Abstract

Biofluid flows within the human body are often characterized by intricate geometries, variable material properties, and complex boundary conditions. These factors introduce considerable uncertainties into numerical simulations, requiring robust strategies to analyze and quantify possible variations in predicted flow parameters. While deterministic simulations have provided significant insights into physiological processes, recent efforts have increasingly emphasized the importance of incorporating uncertainty to improve predictive accuracy and guide clinical decision-making. This discussion offers a structured examination of how different methods can capture variability in transport phenomena, fluid-structure interactions, and boundary conditions, while ensuring consistency and computational efficiency. Special attention is paid to how stochastic parameterization in hemodynamics can help refine the quantification of flow rates, pressure gradients, and wall shear stresses under uncertain or imprecise data constraints. The overall goal is to highlight approaches that enhance confidence in simulation outcomes, thereby bolstering clinical relevance and translation to patient-specific scenarios. By integrating rigorous mathematical tools, advanced modeling techniques, and scalable computational strategies, this work demonstrates a pathway to more robust and physiologically realistic biofluid flow simulations. The subsequent sections focus on conceptual foundations, practical formulations, solution methodologies, and interpretive guidelines, leading to new avenues for precision medicine and improved understanding of critical flow phenomena.