Fractional-order differential model for knee implant recovery in smart health infrastructures

Abstract

Abstract Recovery from knee replacement surgery in conventional orthopaedic healthcare systems can be delayed due to high costs, pain, limited monitoring, and insufficient follow-up, which may hinder early detection of poor healing and inflammation. This study presents a smart orthopaedic healthcare model for knee replacement recovery, where integrated sensors support continuous monitoring and improve the rehabilitation process, thereby reducing delays associated with traditional care systems. A mathematical modelling approach based on compartmental modelling and fractional-order dynamics is used to represent delayed healing responses following total knee replacement surgery. The analysis shows that prolonged delays in monitoring and treatment can lead to unstable recovery patterns, resulting in fluctuations in knee function and inflammation levels. To improve recovery outcomes, the study demonstrates that intelligent sensing devices providing real-time feedback effectively reduce inflammation and enhance joint performance. Results show that when delays are minimised, near-complete restoration of knee function is achieved (≥ 98%), accompanied by optimal inflammation suppression and functional recovery. However, in the presence of delays, recovery remains substantially improved, particularly in terms of inflammation control (≈ 92%), although overall functional gains and recovery efficiency are comparatively reduced. Overall, this work highlights the importance of early inflammation management and feedback-assisted rehabilitation in maintaining knee stability and accelerating recovery. The proposed model provides a theoretical foundation for developing advanced rehabilitation strategies and intelligent device-assisted therapies in smart orthopaedic healthcare systems.