Impact of volume calculation formulae on volume estimation accuracy of different shaped objects: an in vitro ultrasound and CT study

Abstract

Background In image-assisted volume estimation, the volume of the object is calculated with a formula, using linear measurements of the objects. Since the volume estimation accuracy is thought to be influenced by the shape of the object, the volume estimation error would be related to the calculation formula used. Purpose To evaluate the volume estimation accuracy of selected volume calculation formulae, for different shaped objects. Material and Methods Globular (n = 5), elongated (n = 5), and near-spherical shaped plastic objects (n = 5), filled with water were subjected to ultrasound (US) and computed tomography (CT) in February 2018, to obtain the length, width, depth, and estimated volumes (EV). The volume was calculated manually using prolate, ellipsoid, and Lambert formulae. The actual volume (AV), EV, and calculated volumes were compared. Results The AV was in the range of 10–445 mL. The reliability of measurements was high as assessed by the intra-class variability (Cronbach’s alpha = 0.992). The EV has shown a high correlation to AV (US: ρ = 0.914, P < 0.001; CT: ρ = 0.943, P < 0.001; ellipsoid: ρ = 0.876, P < 0.001; prolate: ρ = 0.891, P < 0.001; Lambert: ρ = 0.876, P < 0.001). Regardless of the shape, the highest and lowest estimation accuracies were reported for prolate (bias = −0.7) and Lambert formulae (bias = +23.3), respectively. By any method, the globular objects were estimated with the highest accuracy: (US [bias = −0.31]; CT [bias = −0.14]; ellipsoid [bias = −1.5]; prolate [bias = −0.7]; Lambert [bias = 32.9]); and elongated objects were estimated with the lowest accuracy: (US [bias = −17.5]; CT [bias = −32.6]; ellipsoid [bias = −18.4]; prolate [bias = −0.3]; Lambert [bias = 11.4]). Conclusion The shape of the object and the calculation formula used has an impact on the volume estimation accuracy.