Monitoring osteoarthritis: A simple mathematical model

Abstract

Osteoarthritis (OA) is a kind of joint inflammation which can be ascribed to the age, obesity, gender, depression, genetic predisposition, and cyclic or heavy cartilage loading. There is no definitive treatment for OA; hence, as far as possible the best practical resort is the prevention. We herein propose a simple mathematical model that receives the age, obesity, gender,and overloading by considering the impact of cartilage self-repair and predicts the cartilage damage. Python programming language using Numpy library was used for modeling and solver module. Assuming body mass index (BMI) > 27, we assumed that with the damage to cartilage increases by 6.5% with an increase of each BMI unit, whereas for a BMI <27 the cartilage damage can be ignored. The model predicted that the critical damge occurs is between ages of 44 and 64. In this timeframe, damage to the cartilage increases by 10%, which is roughly in line with the clinical data. Moreover, the impact of gender on the cartilage damage is not pronounced. The proposed simple mathematical model helps physiotherapists to privide themselves with a possibility of a timely rough prediction of the cartilage damage and probably making smarter decisions for invasive interventions.