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Total Lung Capacity form CT scan

Tags: Lung CT scan

Math topic: Numerical Integration Riemann Sums Volume through Integration Topic: Medical imaging

Total Lung Capacity form CT scan

The total lung capacity is estimated by computing the areas of the lungs in different slices and adding them up as a Riemann Sum.

See a scrollable of all 100 images in the wikimedia site

Data

All the data below is adapted and constructed from CT-scan images available at wikimedia. Images by Mikael Häggström, MD., CC0 1.0 Universal Public Domain Dedication. Date accessed: May 14, 2026.

Note on scale for the images: The original images have no exact scale data, but you can use an approximate scale of 0.287 mm/pixel,1 so each pixel ≈ 0.287² = 0.0824 mm².

Slice thickness: The slice thickness of the images is 3 mm.

  • zip file with 11 axial slices (every 10th slice of the series) for integration problems. Images are named by position (thorax_axial_003.jpg = slice 3).

  • lung_areas.csv: lung cross-sectional area for all 106 slices. Columns:

    • position: slice number, 1–106, head→foot
    • lung_pixels: number of pixels making up the lung cross-section
    • lung_area_cm2: total area in cm² (both lungs combined)
    • n_lung_regions: number of regions on the slice that make up the lung cross-section.

  1. The JPEGs carry no pixel-spacing metadata, but each has a burned-in FoV: 374 mm annotation, and the reconstructed image spans 1303 pixels in the frame: 374 mm ÷ 1303 px ≈ 0.287 mm/pixel (an estimate, not exact). ↩︎