Mathematical Modeling of Vancomycin Release from Poly-L-Lactic Acid-Coated Implants

This study aimed to develop a mathematical model to predict the release profile and antibacterial efficacy of a vancomycin delivery system integrated with poly(L-lactic acid)-coated bone implants specifically designed for bone plates. Using Fickian diffusion principles within an ANSYS-CFX computational fluid dynamic model, we validated the model against our in vitro vancomycin release and agar diffusion studies, as well as previously published in vivo data, confirming the reliability of the model. The model predictions demonstrated the effectiveness of the system in inhibiting bacterial growth in surrounding tissue with no observed toxicity, with a peak vancomycin concentration of 0.95 mg/ml at 6 hours, followed by a decrease to levels that remained effective for antibacterial activity. Furthermore, a sensitivity analysis revealed that the model is particularly sensitive to the half-life of vancomycin, with a maximum sensitivity index of 0.8, indicating its greater impact on the prediction accuracy than the diffusion coefficient, which has a maximum sensitivity index of 0.5. Therefore, precise input of vancomycin's half-life is critical for accurate predictions. These findings offer substantial support for the efficacy of the local delivery system as a promising therapeutic approach against implant-associated infections.