2014/07/22 by Martin Lysy, Lysy, Martin, Natesh S. Pillai +11 · 1 citation
Chemistry · Engineering · Mathematics · Medicine · #62P10 (Primary) #Applications (stat.AP) #Electrostatics and Colloid Interactions #FOS: Computer and information sciences #Fractional Differential Equations Solutions #Inhalation and Respiratory Drug Delivery #Microfluidic and Bio-sensing Technologies
paper · pdf · doi:10.48550/arxiv.1407.5962
openalex publication_date 2014/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
State-of-the-art techniques in passive particle-tracking microscopy provide\nhigh-resolution path trajectories of diverse foreign particles in biological\nfluids. For particles on the order of 1 micron diameter, these paths are\ngenerally inconsistent with simple Brownian motion. Yet, despite an abundance\nof data confirming these findings and their wide-ranging scientific\nimplications, stochastic modeling of the complex particle motion has received\ncomparatively little attention. Even among posited models, there is virtually\nno literature on likelihood-based inference, model comparisons, and other\nquantitative assessments. In this article, we develop a rigorous and\ncomputationally efficient Bayesian methodology to address this gap. We analyze\ntwo of the most prevalent candidate models for 30 second paths of 1 micron\ndiameter tracer particles in human lung mucus: fractional Brownian motion (fBM)\nand a Generalized Langevin Equation (GLE) consistent with viscoelastic theory.\nOur model comparisons distinctly favor GLE over fBM, with the former describing\nthe data remarkably well up to the timescales for which we have reliable\ninformation.\n