Source codes to supplement the manuscript titled "Mathematical modelling of inflammatory process and obesity in osteoarthritis"

The following folders are included in this compressed supplement material:

• Codes_Bifurcations
• Codes_Codimension2 Bifurcations
• Codes_Evolution of Inflammation
• Codes_LSA
• Codes_Sensitivity of ExFunction
• lib_model
• Supporting Information

This material contains source codes according to the model information described in the manuscript. All of the codes were generated by MATLAB (R2022b, The Math Works, Inc., Natick, MA, USA).

Osteoarthritis (OA) is prevalent in obese people due to the inflamed adipose tissue surrounding the joints. The increase in obesity level upregulates adipokines enhancing inflammation. Whilst a few main inflammatory mediators including cytokines and adipokines have been identified, the multi-effects of obesity and exercise on OA inflammation are elusive. This study aimed to develop a five-variable mathematical model elucidating the dynamics of OA inflammation associated with obesity and physical activity. Within this model, pro- and anti-inflammatory cytokines, adipokines, matrix metalloproteinases and fibronectin fragments interact to regulate the inflammatory process. The damage of cartilage is considered crucial to stimulate the production of fibronectin fragments, subsequently leading to chronic inflammation. The adipokine production is dependent on the obesity level measured by body mass index (BMI). Hill functions are used to describe the interactions (stimulation and inhibition) between mediators and the nonlinear impacts of physical activity level on adiposity. The dynamics of this inflammation system was verified and analysed through bifurcation diagrams. Results indicate that a high BMI reduces the bistability of the system up to a BMI value of 33 for which inflammation is persistent in the non-dimensionalised model. In codimension-2 bifurcations, parameters of adipokine production can govern the transition of system behaviours. This shows the variability of individuals susceptible to OA inflammation related to obesity. The minimum damage leading to persistent inflammation is decreased as BMI increases and the correlation is nonlinear, which suggests a significant rise in OA risk with a high level of obesity. Additionally, the simulations of multiple physical activity intervention strategies suggest that physical activity can minimise and postpone inflammation by downregulating adipokines within a window period after injury. This novel computational model describes the roles of obesity and physical activity in OA inflammation, providing a mathematical framework to evaluate the risk of OA inflammation from the perspective of obesity.