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

Few studies have examined calcaneal volume because of the difficulty of calculating it. The aim of this study was to generate a formula that can provide an approximate calcaneal volume through simple mathematical calculations based on measurements taken from plain radiographs.

The study was carried out on 216 dry calcanei from the adult population of Anatolia. The volumes were calculated using Archimedes' water displacement method aided by a new technique for temporarily coating dry bones. On lateral radiographs, the following were measured: 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, and 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, which is commonly used in machine learning.

The mean volume was 55.8 mL, with a standard deviation of 11.7. After evaluation using machine learning techniques, multiple linear regression was determined to be the most effective model, 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.

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