Model-free estimation in scattering analysis of microscopy

2026-05-28

AI Summary

This work addresses the limitations of conventional particle tracking methods, which rely on manual parameter tuning and struggle to produce stable mean squared displacement (MSD) estimates across the full lag-time range in dense or low-contrast microscopy videos. To overcome these challenges, the authors propose MF-AIUQ, a model-free scattering analysis framework that directly infers MSD from raw microscopy videos without requiring particle localization or trajectory linking. Built upon the cumulant theorem linking the intermediate scattering function to MSD, MF-AIUQ integrates probabilistic modeling with marginal maximum likelihood estimation and introduces a novel logarithmic Fourier-space uniform sampling strategy to significantly reduce computational complexity while preserving accuracy. Experiments demonstrate that MF-AIUQ yields smooth, robust MSD estimates over the entire time domain across diverse simulated stochastic processes and three distinct experimental systems, making it particularly suitable for scenarios where tracking fails or prior physical models are unavailable.

Abstract

The mean squared displacement (MSD) of particles or probes is commonly estimated from microscopy videos using particle tracking approaches, which rely on tuning parameters manually, and are often unstable over the entire lag time range, especially in dense or low-contrast situations. In this work, we propose model-free ab initio uncertainty quantification (MF-AIUQ), a model-free method for scattering analysis of microscopy video based on a probabilistic framework, which estimates MSD without isolating particles and linking their trajectories. Based on the relationship between the intermediate scattering function (ISF) and the MSD derived from the cumulant theorem, MF-AIUQ estimates the MSD values by the marginal maximum likelihood estimator. To reduce the computational cost, the likelihood function is approximated by a subset of Fourier-transformed intensities. These intensities are equally spaced at the logarithmic values of Fourier basis functions and lag time points. We found that the ISF is smooth in this logarithmic input space, and the information of the ISF can be captured by this subset of inputs. We examine the method through simulation studies covering several representative stochastic processes and three experimental systems: a Newtonian fluid for evaluating performance in optically dense and bright-field settings, a gelation system with an evolving MSD shape, and snail mucin, a viscoelastic biopolymer, for modulus estimation. Across these studies, MF-AIUQ provides smooth and stable MSD estimates over the full lag time range and serves as a useful complementary approach in settings where particle tracking is unreliable or a parametric model of MSD is unavailable or unverifiable.

Problem

• mean squared displacement
• particle tracking
• scattering analysis
• microscopy
• uncertainty quantification

Innovation

• model-free
• mean squared displacement
• intermediate scattering function
• uncertainty quantification
• microscopy video analysis