Tortuosity

image0

All freehand or polyline dimension lines with at least three points are analysed for tortuosity. Draw a line along the centre or edge of each vessel from end to end.

Two tortuosity methods are used:

Tort0

This is a simple tortuosity measure of the ratio of vessel length to chord length, where chord length is the shortest straight line length between the two end points.

image1

This is a dimensionless measure.

Tort1

This uses a method described in: Enrico Grisan, Marco Foracchia, Alfredo Ruggeri. A novel method for automatic evaluation of retinal vessel tortuosity. Proceedings of the 25th Annual International Conference of the IEEE EMBS, Cancun, Mexico, 2003

image2

The dimension line is split into N curves. The start/end of each curve is found by a change in curvature on the line. Then sum of the ratios of curve length to chord length ( Li / Si ) is used to determine total tortuosity.

Dimensions are 1 / length i.e. µm-1

Configuration ini file settings are used to reduce noise:

[tortuosity]
minlength=10
minangle=5
mincurvelength=20.0
log=0

where:

minlength

Minimum length (in µm) before testing for change of angle

minangle

Minimum change of angle (in degrees). Only angle changes above this value are considered.

mincurvelength

Minimum curve length (in µm) between changes in curve.

log

0= no logging. 1= log angle and length calculations to the log file.

These configuration settings are read each time a CapiScope image file is opened. If you want to experiment changing these values, edit the ini file (same base filename and folder as the executable, e.g. c:\KKTechnolgy\CapiScope\kkcapiuSC.ini ).

Result Output

Individual Tortuosity results are shown in the “Dimension List”. Tort1n is the number of curves used in the tortuosity calculation. The Dimension List window is displayed by the menu “Windows”, “Dimension List”.

The Dimension list can be saved using “File”, “Save”. The file is a standard “csv” comma separated variable text file which can be opened in Excel or OpenOffice.

The total tortuosity for the whole image is calculated by using the image3 toolbar button or the “=” key.

Data in the “Image Results” window can be selected, copied and pasted into other applications such as Excel.

image4 Changes in curvature direction are shown as black diamonds on the dimension lines. There might be more marks than indicated by the tort1n value since the curvelength value might be less than the configuration minimum for some of them.