# A Mathematical Analysis of a Biomechanical Model for an Innovative Spinal Decompression and Correction System for the Conservative Treatment of Scoliosis

## TL;DR

This paper presents a biomechanical model to estimate optimal forces for treating scoliosis using a mathematical approach.

## Contribution

A novel biomechanical model based on Timoshenko beam theory is introduced for precise scoliosis treatment.

## Key findings

- A mathematical model was developed to estimate optimal controlling forces for scoliosis treatment.
- The model can be optimized for different scoliosis curve patterns using computed tomography data.
- The relationship between corrective force position and treatment effect was analyzed.

## Abstract

Scoliosis is a three-dimensional deformity of the spine that can lead to a series of physical and psychological problems. Appropriate controlling forces should be applied to prevent the curve’s progression and even correct the deformity. The aims of this study were to develop a biomechanical model that can quickly estimate the optimal positions and magnitudes of the controlling forces for treating scoliosis and to analyze the interaction between longitudinal traction and lateral forces. Based on the scoliotic curve information that was extracted and simulated from the computed tomography data of patients, a mathematical model of scoliosis was established via the Timoshenko beam theory. The model could be optimized to provide precise and effective treatment for patients with different scoliosis curve patterns. The relationship between the corrective force position, magnitude, and the treatment effect on scoliosis could be obtained using this model. This study provides a biomechanical theoretical basis for determining the magnitude, position, and sequence of applying controlling forces on spines for patients with scoliosis.