A fractional stochastic theory for interfacial polarization of cell aggregates

TL;DR

This paper develops a fractional stochastic model to describe the interfacial polarization in cell aggregates, capturing complex distributions and anomalous relaxation phenomena with a flexible, time-domain framework.

Contribution

It introduces a novel fractional stochastic approach that models cellular polarization distributions and dynamics, extending traditional methods to include fractional derivatives for anomalous relaxation.

Findings

Polarization densities follow skewed and symmetric t-distributions.

A reduced order model accurately predicts mean and variance of dipole moments.

Fractional derivatives are necessary to explain observed anomalous relaxation phenomena.

Abstract

We present a theoretical framework to model the electric response of cell aggregates. We establish a coarse representation for each cell as a combination of membrane and cytoplasm dipole moments. Then we compute the effective conductivity of the resulting system, and thereafter derive a Fokker-Planck partial differential equation that captures the time-dependent evolution of the distribution of induced cellular polarizations in an ensemble of cells. Our model predicts that the polarization density parallel to an applied pulse follows a skewed t-distribution, while the transverse polarization density follows a symmetric t-distribution, which are in accordance with our direct numerical simulations. Furthermore, we report a reduced order model described by a coupled pair of ordinary differential equations that reproduces the average and the variance of induced dipole moments in the aggregate. We extend our proposed formulation by considering fractional order time derivatives that we find necessary to explain anomalous relaxation phenomena observed in experiments as well as our direct numerical simulations. Owing to its time-domain formulation, our framework can be easily used to consider nonlinear membrane effects or intercellular couplings that arise in several scientific, medical and technological applications.