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Flow Calculation

In order to determine flow speed and direction, all possible cross-correlations are calculated at a distance of two fibers within three inner fiber rings. All correlations in the same direction are averaged, resulting in six correlation curves (30°, 90°, ..., 330°; by our definition, 0° means vertical flow direction). All six curves are fitted globally with the following model:

Parameter

Description

v

The flow speed (fit parameter).

ϕ

The angle between the flow and the vector connecting the fibers in this group of cross-correlations (fit parameter).

r0

The apparent distance between the fibers (calibration parameter).

Gdiff(τ)

The diffusion term (2D or 3D), see Fit Calculation.

Other parameters are defined as for the fit calculations, see Fit Calculation.

Flow Speed Classification

The calculated flow speed values are classified depending on the diffusion time of the analyzed fluorophore and also based on statistical quality of the flow correlation curves:

Flow Type

Criterium

No Flow

v <= 3*CI

Slow

(v > 3*CI) & (τflow > 3*τd)

Moderate

(v > 3*CI) & (τd < τflow < 3*τd)

Fast

(v > 3*CI) & (τflow < τd)

where τflow = r0/v and CI is the flow speed confidence interval.

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