In PhD-OCT, an OCT M-B scan is used to collect spatially resolved information on Brownian motion. No additional hardware is required beyond a phase-stable OCT system of sufficient speed to measure the temporal fluctuation. The time-dependent complex-valued autocorrelation, g
(1), of this signal follows an exponential decay for a diffusive, non-flowing sample. PhD-OCT fits the initial, linear portion of this curve.
\begin{equation}{g^{\left( 1 \right)}}\left( {{\rm{\Delta t\;}}} \right) = {e^{ - {\rm{\Gamma \Delta t\;}}}} \approx 1 - {{\rm{\Gamma }}_T}{\rm{\Delta t\;}}\end{equation}
where Δt is the time lag and Γ
T is the time constant of the exponential decorrelation. In the case of dilute particles in solution undergoing Brownian motion, the Stokes-Einstein equation applies:
\begin{equation}{{\rm{\Gamma }}_T} = Q\frac{{Tn_T^2}}{{{R_T}{\eta _T}}},\;Q = \frac{{8{\rm{\pi }}{k_b}}}{{3{\lambda ^2}}}\end{equation}
where T is temperature in Kelvin,
nT is refractive index of the sample,
RT is radius of the protein aggregate particles, assumed to be spherical, and η
T is the viscosity of the sample,
kb is the Boltzmann constant, and λ is the wavelength of the imaging system. Where Q is constant for an imaging setup. This equation can be used in DLS to calculate the hydrodynamic radius of polymer aggregates.
30 However, this equation assumes the protein solution to be dilute. In high-concentration solutions, such as the lens cytoplasm (20–50% protein by mass),
31 interactions between the polymers themselves (polymer-polymer interactions) dominate, rendering the viscosity and radius poorly suited metrics.
32–34 Because the lens cytoplasm has high protein density, −Γ
T is reported in this study without further calculation of particle size.