Statistical Challenges in Microrheology

TL;DR

This paper discusses the statistical challenges in analyzing microrheology data, focusing on the generalized Langevin equation model for particle dynamics in complex fluids, highlighting current methods and open problems for statisticians.

Contribution

It identifies key statistical challenges in microrheology, reviews existing inferential approaches, and emphasizes the need for advanced statistical methods for the generalized Langevin equation.

Findings

Highlights the complexity of particle diffusion in viscoelastic fluids.

Reviews current statistical inference methods for microrheology.

Points out open problems and future directions for statisticians.

Abstract

Microrheology is the study of the properties of a complex fluid through the diffusion dynamics of small particles, typically latex beads, moving through that material. Currently, it is the dominant technique in the study of the physical properties of biological fluids, of the material properties of membranes or the cytoplasm of cells, or of the entire cell. The theoretical underpinning of microrheology was given in Mason and Weitz (Physical Review Letters; 1995), who introduced a framework for the use of path data of diffusing particles to infer viscoelastic properties of its fluid environment. The multi-particle tracking techniques that were subsequently developed have presented numerous challenges for experimentalists and theoreticians. This paper describes some specific challenges that await the attention of statisticians and applied probabilists. We describe relevant aspects of the physical theory, current inferential efforts and simulation aspects of a central model for the dynamics of nano-scale particles in viscoelastic fluids, the generalized Langevin equation.