Tortuosity of blood vessels

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

Answer 1

[Sean de Wolski]

http://www.mathworks.com/videos/medical-image-processing-with-matlab-81890.html

The second example might interest you.

[Tri Rowstenkowski]

@Sean de Wolski

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:

1. How to calculate the lengths of both actual branches and the imaginary straight lines between nodes
2. How do I mark the vessel branches (orange) and the branch nodes (yellow) as shown in the picture.
3. I am calculating "spinelength" as the sum of all pixels. How do I calculate individual branch lengths?
4. 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]

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.

Answer 2

[Maz M. Khansari]

Check this out https://www.mathworks.com/matlabcentral/fileexchange/72986-vessel-tortuosity-index-vti