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Updated: May 7, 2026
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Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
Published on: April 26, 2016
Measuring stone volume - three-dimensional software reconstruction or an ellipsoid algebra formula?
William Finch1, Richard Johnston, Nadeem Shaida
1Department of Urology, Norfolk and Norwich University Hospitals NHS Foundation Trust, Norfolk, UK.
BJU International
|September 24, 2013
Summary
Renal stone volume estimation accuracy varies by stone size and shape. Three-dimensional (3D) reconstruction is most accurate, but ellipsoid formulas (prolate, oblate, scalene) can be used based on stone diameter.
Area of Science:
- Urology
- Medical Imaging
- Nephrology
Background:
- Accurate kidney stone volume assessment is crucial for predicting treatment outcomes.
- Current methods often rely on maximum diameters and ellipsoid formulas, but their accuracy is debated.
- Three-dimensional (3D) reconstruction offers precise volume measurement but isn't universally available.
Purpose of the Study:
- To compare the accuracy of scalene, oblate, and prolate ellipsoid volume equations against 3D-reconstructed stone volume.
- To determine the optimal method for assessing renal stone volume and burden.
- To evaluate how stone shape influences volume calculation accuracy.
Main Methods:
- Reviewed 100 kidney stones using both X-ray and computed tomography (CT) imaging.
- Excluded complete and partial staghorn calculi.
- Calculated stone volumes using specialized software and analyzed stone shapes based on diameter.
Main Results:
- Stone shape varied with diameter: smaller stones (<9 mm) were prolate, medium (9-15 mm) oblate, and larger (>15 mm) scalene.
- Accuracy of ellipsoid formulas decreased with increasing stone diameter.
- No significant difference in stone shape was observed based on kidney location.
Conclusions:
- No single ellipsoid formula accurately estimates renal stone volume across all sizes.
- Larger stones exhibit more asymmetric shapes, reducing the accuracy of diameter-based calculations.
- Recommend 3D-reconstructed volumes when available; otherwise, use size-dependent ellipsoid formulas (prolate, oblate, or scalene).
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