  The interest in the extracellular vesicles (EVs) is rapidly growing as they
became reliable biomarkers for many diseases. For this reason, fast and
accurate techniques of EVs size characterization are the matter of utmost
importance. One increasingly popular technique is the Nanoparticle Tracking
Analysis (NTA), in which the diameters of EVs are calculated from their
diffusion constants. The crucial assumption here is that the diffusion in NTA
follows the Stokes-Einstein relation, i.e. that the Mean Square Displacement
(MSD) of a particle grows linearly in time (MSD $\propto t$). However, we show
that NTA violates this assumption in both artificial and biological samples,
i.e. a large population of particles show a strongly sub-diffusive behaviour
(MSD $\propto t^\alpha$, $0<\alpha<1$). To support this observation we present
a range of experimental results for both polystyrene beads and EVs. This is
also related to another problem: for the same samples there exists a huge
discrepancy (by the factor of 2-4) between the sizes measured with NTA and with
the direct imaging methods, such as AFM. This can be remedied by e.g. the
Finite Track Length Adjustment (FTLA) method in NTA, but its applicability is
limited in the biological and poly-disperse samples. On the other hand, the
models of sub-diffusion rarely provide the direct relation between the size of
a particle and the generalized diffusion constant. However, we solve this last
problem by introducing the logarithmic model of sub-diffusion, aimed at
retrieving the size data. In result, we propose a novel protocol of NTA data
analysis. The accuracy of our method is on par with FTLA for small
($\simeq$200nm) particles. We apply our method to study the EVs samples and
corroborate the results with AFM.
