# Quantitative Analysis of Stress–Stretch Curves in Canine Lumbar Vertebrae Using Modified Logistic Functions

## TL;DR

This study uses a modified logistic function to accurately model the stress-stretch behavior of canine vertebrae, aiding in understanding bone mechanics.

## Contribution

A modified logistic function is introduced for precise modeling of stress-stretch curves in canine vertebrae.

## Key findings

- The modified logistic function achieved an R² value near 0.999 for most stress-stretch curves.
- The model provides an accurate description of the mechanical behavior of canine vertebrae under external loading.

## Abstract

Background: The mechanical characteristics of bone are crucial for comprehending its functionality and response to different load conditions, which are essential for advancing medical treatments, implants, and prosthetics. By employing mathematical modeling to analyze the mechanical properties of bone, we can assess stress and deformation under both normal and abnormal conditions. This analysis offers valuable perspectives on potential fracture risks, the effects of diseases, and the effectiveness of various treatments. Therefore, researchers are attempting to find an adequate mathematical description of the mechanical properties of bone. Methods: Experimental stress–stretch external loading curves were obtained through investigations of canine vertebrae. The obtained experimental curves were fitted using the SciPy Python library with a slightly modified logistic function (logistic function plus additional const). Results: The resulting coefficient of determination R2 (R squared) for most curves was near 0.999, indicating that an appropriate fitting function was selected for the description of the experimental stress–stretch curves. Conclusions: The stress–stretch behavior of canine vertebrae can be described using a logistic function modified by adding additional parameters for the most accurate fitting results.