# A new mathematical model for evaluating surface changes in the mid-abdominal sagittal plane after two-level pedicle reduction osteotomy in patients with ankylosing spondylitis

## TL;DR

This paper introduces a mathematical model to predict changes in abdominal surface area after a specific spinal surgery in patients with ankylosing spondylitis.

## Contribution

The study introduces a novel mathematical model using trigonometric functions to predict abdominal median sagittal plane changes after two-level PSO in AS patients.

## Key findings

- The mathematical model accurately predicted changes in the abdominal median sagittal plane area.
- There was no significant difference between predicted and actual area change rates.
- Postoperative measurements of LL, SVA, and GK showed significant changes compared to preoperative values.

## Abstract

The purpose of this study was to create a mathematical model to precalculate the acreage change in the abdominal median sagittal plane (ac-AMSP) of patients with ankylosing spondylitis (AS) for whom two-level pedicle subtraction osteotomy (PSO) was planned.

A single-centre retrospective review of prospectively collected data was conducted among 11 adults with AS. Acreage of the abdominal median sagittal plane (a-AMSP) was performed. The distances and angles between the osteotomy apexes, anterosuperior edge of T12, xiphoid process, superior edge of the pubis, and anterosuperior corner of the sacrum were measured on preoperative thoracolumbar computed tomography. A mathematical model was created using basic trigonometric functions in accordance with the abdominal parameters. Planned osteotomized vertebra angles (POVAs) were substituted into the mathematical model, and the predictive ac-AMSP (P-AC) was obtained. A paired sample t test was performed to determine the differences between the P-AC and actual ac-AMSP (A-AC) and between the predictive acreage change rate (P-CR) and actual acreage change rate (A-CR).

The mean age and GK were 44.4 ± 8.99 years and 102.9° ± 19.17°, respectively. No significant difference exists between A-CR and P-CR via mathematical modeling (p > 0.05). No statistically significant difference existed between POVA and actual osteotomized vertebra angles (AOVA) (p > 0.05). A statistically significant difference was observed between preoperative and postoperative measurements of LL, SVA, and GK variables (p < 0.001).

The novel mathematical model was reliable in predicting the ac-AMSP in AS patients undergoing two-level PSO.

The online version contains supplementary material available at 10.1186/s12893-023-02285-z.