Tortuosity of blood vessels

Tri Rowstenkowski - 2022-02-12T10:51:10+00:00

Question: Tortuosity of blood vessels

Hello,   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 the euclidean distance between their end points).   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.   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  

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Expert Answer

Prashant Kumar answered . 2025-11-20

To calculate the tortuosity of blood vessels and achieve your objectives, follow these steps:

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1. Input Data and Preprocessing

You need an image or data representation of the blood vessels. If the image is raw:

• Apply a contrast enhancement to highlight vessels.
• Use edge detection techniques (e.g., Canny or Sobel) to extract the vessel structure.
• Use skeletonization to reduce the vessels to a one-pixel-wide skeleton (e.g., bwmorph in MATLAB or skeletonize in Python).

MATLAB example for preprocessing:

 

% Read and preprocess the image
img = imread('vessel_image.jpg'); % Replace with your image path
gray_img = rgb2gray(img); % Convert to grayscale
enhanced_img = imadjust(gray_img); % Contrast enhancement

% Binary image and skeletonization
binary_img = imbinarize(enhanced_img);
skeleton = bwmorph(binary_img, 'skel', Inf);

% Display skeletonized image
imshow(skeleton);
title('Skeletonized Vessel Structure');

2. Calculate Actual and Euclidean Lengths

• Actual Length (Branch Length): Count the number of pixels along the skeleton for each branch.
• Euclidean Length: Compute the Euclidean distance between branch endpoints.

To achieve this:

1. Identify branch nodes (points where vessels bifurcate).
2. Label the segments between branch nodes.
3. Compute the pixel count and endpoint distances for each segment.

MATLAB example:

 

% Label branch nodes and endpoints
branch_points = bwmorph(skeleton, 'branchpoints');
end_points = bwmorph(skeleton, 'endpoints');

% Find connected components (segments)
[labeled_segments, num_segments] = bwlabel(skeleton);

% Calculate lengths
branch_lengths = zeros(num_segments, 1);
euclidean_lengths = zeros(num_segments, 1);

for i = 1:num_segments
    % Extract individual segment
    segment = (labeled_segments == i);
    
    % Calculate actual length (number of pixels)
    branch_lengths(i) = sum(segment(:));
    
    % Identify endpoints of the segment
    [rows, cols] = find(segment);
    endpoints = find(end_points & segment);
    if length(endpoints) == 2
        [r1, c1] = ind2sub(size(segment), endpoints(1));
        [r2, c2] = ind2sub(size(segment), endpoints(2));
        % Calculate Euclidean distance
        euclidean_lengths(i) = sqrt((r2 - r1)^2 + (c2 - c1)^2);
    end
end

% Calculate tortuosity
tortuosity = sum(branch_lengths) / sum(euclidean_lengths);
fprintf('Tortuosity: %.2f\n', tortuosity);

3. Marking Branches and Nodes

Use bwlabel or connected component analysis to label branches and overlay markings for nodes and branches.

MATLAB example:

% Mark branch nodes and endpoints
imshow(skeleton);
hold on;
[y_branch, x_branch] = find(branch_points);
plot(x_branch, y_branch, 'yo', 'MarkerSize', 10, 'LineWidth', 2); % Yellow branch nodes

[y_end, x_end] = find(end_points);
plot(x_end, y_end, 'ro', 'MarkerSize', 10, 'LineWidth', 2); % Red endpoints

title('Branch Nodes (Yellow) and Endpoints (Red)');
hold off;

4. Improving Skeleton for Accuracy

To improve accuracy:

1. Remove small spurs using bwmorph(img, 'spur', n) to clean small noise.
2. Smooth skeleton using morphological operations or spline fitting.
3. Manually inspect or validate branch nodes for unusual bifurcations.

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Summary

• Use skeletonization to simplify the vessel structure.
• Detect branch nodes and endpoints using morphological operations.
• Calculate actual and Euclidean lengths for segments.
• Compute tortuosity as the ratio of actual length to Euclidean length.
• Visualize nodes and segments to validate the results.

Let me know if you'd like further clarification or additional details!

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