cytocalc.microrheology module

Functions for extracting viscoelasticity from microrheology measurements

cytocalc.microrheology._msd_to_g_star_evans(times: ndarray[tuple[int, ...], dtype[float]], msd: ndarray[tuple[int, ...], dtype[float]], radius: float, viscosity: float = 0, **kwargs)[source]

Extract G* from MSD using Evans’ method

cytocalc.microrheology._msd_to_g_star_mason(times: ndarray[tuple[int, ...], dtype[float]], msd: ndarray[tuple[int, ...], dtype[float]], radius: float, **kwargs)[source]

Extract G* from MSD using Mason’s method

  1. Mason, T. G. Estimating the viscoelastic moduli of complex fluids using the generalized Stokes–Einstein equation. Rheol. Acta 39, 371–378 (2000).

cytocalc.microrheology.msd_to_g_star(times: ndarray[tuple[int, ...], dtype[float]], msd: ndarray[tuple[int, ...], dtype[float]], radius: float, viscosity: float = 0, method: str = 'evans', **kwargs)[source]

Extracts Complex Shear Modulus G* (in Pa) from the MSD of a probe.

Mason’s method: Approximate G* using a truncated power-law expansion. Ref: _msd_to_g_star_mason()

  1. Mason, T. G. Estimating the viscoelastic moduli of complex fluids using the generalized Stokes–Einstein equation. Rheol. Acta 39, 371–378 (2000).

Evans’ method: Extract G* using a DTFT on the creep compliance J(t). Ref: _msd_to_g_star_mason()

  1. Evans, R. M. L., Tassieri, M., Auhl, D. & Waigh, T. A. Direct conversion of rheological compliance measurements into storage and loss moduli. Phys. Rev. E 80, 012501 (2009).

Parameters:

  • times – npt.NDArray[float], an array of timepoints (unit: s)

  • msd – npt.NDArray[float], an array of MSD values (unit: um^2)

  • radius – float, radius of the bead (unit: um)

  • viscosity – (for Evans’ method only) float, viscosity of medium (unit: pN.s/um^2)

  • method – str, method to use for extracting G*. Must be one of [“evans”, “mason”]

Returns:

npt.NDArray[float], npt.NDArray[complex], an array of omegas (unit: Hz), an array of G* (G’ + iG’’) (unit: Pa)