Machine learning-based estimation of Calcaneus volume using plain radiographic morphometry.

Background: Few studies exist on Calcaneus volume due to calculation difficulties. The aim of this study is to generate a formula that can give the approximate volume of a Calcaneus through simple mathematical calculations based on measurements taken from plain radiographs.

Materials and methods: The study was carried out on 216 dry calcanei from the adult population in Anatolia. The volumes were calculated using Archimedes' water displacement method aided by a new technique for temporarily coating dry bones. On lateral radiographs: maximum anteroposterior length (max AP l), maximum body length (max body l), body height (body h), minimum body height (min body h), facies articularis cuboidaea height, Böhler's angle, angle of Gissane; on axial radiographs: maximum posterior transverse width (max post w) and minimum posterior transverse width (min post w) were measured. The formula was derived using Python 3.12, commonly used in machine learning.

Results: The mean volume was 55.8 mL, with a standard deviation of 11.7. After evaluating with machine learning techniques, the multiple linear regression model was determined to be the most effective, and the formula was identified as follows: Volume (mL) = 0.96 × max AP l (mm) + 0.40 × max body l (mm) - 0.29 × body h (mm) + 0.76 × min body h (mm) + 0.14 × max post w (mm) + 0.48 × min post w (mm) - 7.49.

Conclusions: The proposed formula can serve as an index for future studies on Calcaneus volume, and the methods we used may be helpful for similar studies, particularly on dry bones.