Tortuosity of blood vessels
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Hi all,
I need to find the tortuosity index of a skeletonized blood vessel (attached text file for x y coordinates) using total squared curvature approach. it's a bit difficult for a matlab beginner like me. I do not have any experience with this kind of equation at all. Can anyone help me creating a function just for this purpose? Thanks
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Accepted Answer
Sean de Wolski
on 17 Oct 2014
The second example might interest you.
2 Comments
Tri Rowstenkowski
on 9 Feb 2021
Edited: Tri Rowstenkowski
on 9 Feb 2021
Hello Sean,
I am trying to calculate the Tortuosity of blood vessels. (Vessel tortuosity is calculated as the sum of branch lengths divided by the sum of imaginary straight lines).
I have the following questions:
- How to calculate the lengths of both actual branches and the imaginary straight lines between nodes
- How do I mark the vessel branches (orange) and the branch nodes (yellow) as shown in the picture.
- I am calculating "spinelength" as the sum of all pixels. How do I calculate individual branch lengths?
- Any suggestions in preprocessing would be appreciated.
I followed https://www.mathworks.com/videos/medical-image-processing-with-matlab-81890.html video and read the https://www.mathworks.com/matlabcentral/answers/522378-how-to-measure-the-diameter-along-the-length-of-an-object#answer_429784 post. Any help would be highly appreciated. Thank you.
clc;
clear;
close all
% Read the image
I=imread('VAD.png');
figure,imshow(I)
%convert it to gray scale
I_gray=rgb2gray(I);
%Sharpen the image
b = imsharpen(I_gray,'Amount',8);
h = fspecial('average', [3 3]);
b = imfilter(b, h);
%choose brighter objects
Bina=b>150
figure,imshow(Bina);
se = strel('cube',3)
erodedBW = imerode(Bina,se);
%Remove small objects from binary image
BW2 = bwareaopen(Bina,100)
figure,imshow(BW2);
skelImage = bwskel(BW2, 'MinBranchLength', 10);
MinBranchLength = round(sum(skelImage(:))/2)
skelImage = bwskel(BW2,'MinBranchLength',MinBranchLength);
figure,imshow(skelImage)
endpointImage = bwmorph(skelImage, 'endpoints');
[rows, columns] = find(endpointImage)
spineLength = sum(skelImage(:))
straightLineDistance = sqrt((columns(2) - columns(1))^2 + (rows(2) - rows(1))^2)
tortuosity = spineLength / straightLineDistance
Sean de Wolski
on 11 Feb 2021
Your calculation for spinelength assumes that pixels of any connectivity are equivalently far apart which is not true. You need to account for corner connected v. edge connected. bwdistgeodesic will do this for you (metric of every point to an end point). Then take the max value of that.
More Answers (1)
Maz M. Khansari
on 15 Oct 2019
Check this out https://www.mathworks.com/matlabcentral/fileexchange/72986-vessel-tortuosity-index-vti
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