# Utilizing Kernel Density Estimation and Butterfly Diagram to Characterize the Gait Variability in the Fallers: A Cross‐Sectional Study

## TL;DR

This study uses kernel density estimation and butterfly diagrams to analyze gait patterns and identify instability in elderly individuals who fall.

## Contribution

The study introduces KDE and COP symmetry index to quantify variability in butterfly diagrams for fall risk assessment.

## Key findings

- Fallers had a significantly higher COP symmetry index compared to non-fallers.
- KDE revealed more variability patterns in fallers (three patterns) than in non-fallers (two patterns).
- No significant differences were found in step width, step length, or COP distances between fallers and non-fallers.

## Abstract

The butterfly diagram is an effective tool for visualizing gait patterns and identifying potential areas of instability in the elderly individuals who fall. Nevertheless, there is a lack of comprehensive exploration regarding the quantification of variability at the intersections in butterfly diagrams. We proposed the utilization of kernel density estimation (KDE) and center of pressure (COP) symmetry index to analyze the spatial probability distribution of intersections in butterfly diagrams and to characterize the variability of gait patterns in elderly fallers.

Twenty active elderly individuals (including both fallers and non‐fallers) volunteered to participate in this study. Initially, the self‐selected walking speed of each subject was assessed using a treadmill. Subsequently, each participant walked for a duration of 60 s. The bilateral toe‐off (TO) and initial contact (IC) points of the butterfly diagram were identified for the computation of the COP symmetry index and the intersections of bilateral TO‐IC. Following this, the intersections within the walking window were utilized to assess their density and variability through Kernel density estimation.

Fallers exhibited a significantly greater COP symmetry index (mean = 0.09, SD = 0.55), than non‐fallers (mean = 0.58, SD = 0.56; sig. = 0.03, η2 = 0.09). No significant differences were found in step width, step length, or COP distances (p > 0.05). KDE revealed distinct variability patterns: non‐fallers showed two patterns (A, B), while fallers displayed three (C, D, E), suggesting greater gait instability in fallers.

KDE and COP symmetry analysis appeared to effectively quantify gait variability, offering insights into fall risk factors and potential intervention targets for elderly women.