A Differential Equation–Based Epidemiological Model of Post-Operative Chronic Pain in Scoliosis Patients with Data-Driven Analysis

Authors

• Paige Zhu, Phillips AcademyFollow
• Padmanabhan Seshaiyer, George Mason UniversityFollow

Publication Date

7-2-2026

Keywords

idiopathic scoliosis, data science, chronic pain, post-operative

Disciplines

Mathematics | Non-linear Dynamics | Ordinary Differential Equations and Applied Dynamics | Partial Differential Equations | Physical Sciences and Mathematics | Science and Mathematics Education

Abstract

Chronic post-surgical pain (CPSP) is a common and often overlooked complication following surgical correction of idiopathic scoliosis, impacting long-term patient wellbeing despite improvements in surgical outcomes. This project introduces a novel epidemiological framework to model the progression of CPSP using a compartmental structure. By applying a coupled system of nonlinear differential equations, we simulate pain trajectories over time and assess the effectiveness of surgical interventions. The model is implemented for a single-cohort population and extended to a two-cohort design to compare outcomes between Posterior Spinal Fusion (PSIF) and Vertebral Body Tethering (VBT) procedures. Further stratification by patient age enables us to explore demographic influences on chronic pain dynamics. Stability analysis confirms the existence of disease-free equilibria, while numerical simulations provide insights into long-term recovery versus chronic outcomes. To address the lack of real patient data, synthetic datasets are generated and used to validate parameter recovery through Physics Informed Neural Networks (PINNs), which successfully infer model parameters under varying levels of noise while preserving the governing dynamics.

Recommended Citation

Zhu, Paige and Seshaiyer, Padmanabhan (2026) "A Differential Equation–Based Epidemiological Model of Post-Operative Chronic Pain in Scoliosis Patients with Data-Driven Analysis," CODEE Journal: Vol. 20: Iss. 2, Article 7.
Available at: https://scholarship.claremont.edu/codee/vol20/iss2/7