Measuring stone volume - three-dimensional software reconstruction or an ellipsoid algebra formula?
OBJECTIVE
To determine the optimal method for assessing stone volume, and thus stone burden, by comparing the accuracy of scalene, oblate, and prolate ellipsoid volume equations with three-dimensional (3D)-reconstructed stone volume. Kidney stone volume may be helpful in predicting treatment outcome for renal stones. While the precise measurement of stone volume by 3D reconstruction can be accomplished using modern computer tomography (CT) scanning software, this technique is not available in all hospitals or with routine acute colic scanning protocols. Therefore, maximum diameters as measured by either X-ray or CT are used in the calculation of stone volume based on a scalene ellipsoid formula, as recommended by the European Association of Urology.


METHODS
In all, 100 stones with both X-ray and CT (1-2-mm slices) were reviewed. Complete and partial staghorn stones were excluded. Stone volume was calculated using software designed to measure tissue density of a certain range within a specified region of interest. Correlation coefficients among all measured outcomes were compared. Stone volumes were analysed to determine the average 'shape' of the stones.


RESULTS
The maximum stone diameter on X-ray was 3-25 mm and on CT was 3-36 mm, with a reasonable correlation (r = 0.77). Smaller stones (<9 mm) trended towards prolate ellipsoids ('rugby-ball' shaped), stones of 9-15 mm towards oblate ellipsoids (disc shaped), and stones >15 mm towards scalene ellipsoids. There was no difference in stone shape by location within the kidney.


CONCLUSIONS
As the average shape of renal stones changes with diameter, no single equation for estimating stone volume can be recommended. As the maximum diameter increases, calculated stone volume becomes less accurate, suggesting that larger stones have more asymmetric shapes. We recommend that research looking at stone clearance rates should use 3D-reconstructed stone volumes when available, followed by prolate, oblate, or scalene ellipsoid formulas depending on the maximum stone diameter.
Department of Urology, Norfolk and Norwich University Hospitals NHS Foundation Trust, Norfolk, UK.
William
W
Finch
Richard
R
Johnston
Nadeem
N
Shaida
Andrew
A
Winterbottom
Oliver
O
Wiseman
D000465:Algorithms; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods; D021621:Imaging, Three-Dimensional; D007669:Kidney Calculi / Q000000981:diagnostic imaging / Q000473:pathology*; D008433:Mathematics; D011859:Radiography; D012984:Software
CT; X-ray; algebra; kidney; stone volume; urolithiasis