# Development of a novel evaluation method by mathematical anatomy for foot bone alignment displacement using x-ray radiographs

## TL;DR

This paper introduces a new method using mathematical anatomy and x-ray images to evaluate foot bone alignment, which could improve the assessment of foot deformities.

## Contribution

A novel geometric shape analysis method using 2D-FFT for evaluating foot bone alignment in x-ray radiographs is developed.

## Key findings

- 2D-FFT images show distinct directional power spectra for normal, low, and high arched feet.
- The method reflects the bone arrangement of metatarsal and tarsal bones effectively.
- The technique has potential for assessing medial longitudinal arch and predicting patient prognosis.

## Abstract

The major methods of evaluating the foot arch in clinical practice in patients with foot deformities are medial longitudinal arch measurement using body surface somatometry and radiographic morphometry. Although these methods are widely used, they are considered problematic in terms of differences in scores between the methods. In this study, we developed a new geometric shape analysis method for the bony arrangement of the foot using the two-dimensional fast Fourier transform (2D-FFT), which incorporates mathematical anatomy using x-ray radiographs. Lateral radiographs of the foot bones were obtained using ImageJ2 provided by the National Institutes of Health. The 2D-FFT images show the characteristic directional power spectrum extending from low to high frequencies in the first and third quadrants on the normal, low and high arched foot respectively. The current method of reflecting the bone arrangement status of the metatarsal and tarsal bones may have the potential to establish a new radiographic evaluation method for assessing abnormal foot–bone alignment. As a result, the foot bone 2D-FFT method can be useful in assessing the medial longitudinal arch and predicting the prognosis of these patients.