Viscoelastic properties of sodium hyaluronate and their mathematical optimization in intra-articular injections: a predictive model for enhancing clinical efficacy

Objective To develop and validate a biomechanical and mathematical model capable of predicting the clinical efficacy of intra-articular sodium hyaluronate injections (HA) in osteoarthritis (OA), by aligning viscoelastic properties of HA formulations with joint-specific mechanical demands and patient phenotypes. Design A predictive simulation model based on linear viscoelastic theory and non-Newtonian fluid mechanics was constructed to replicate intra-articular HA behavior during physiologic gait cycles. Input variables included HA-specific parameters (molecular weight, concentration, viscosity), joint-specific mechanics (loading frequency, anatomical volume), and patient factors (BMI, Kellgren–Lawrence grade, activity level). Three-dimensional finite element models (FEM) of the knee, hip, and shoulder were developed to assess HA distribution, mechanical damping, and synovial retention. Model predictions were validated retrospectively against clinical outcomes (WOMAC scores at 3 months) in 126 knee OA patients treated with single-injection HA. Partial least squares regression was used to evaluate predictive accuracy. Results An optimal viscoelastic window was identified (G′ = 120–220 Pa, η = 50–120 Pa·s, tan δ = 0.4–0.6), associated with superior joint coverage, damping capacity, and intra-articular residence. Formulations within this window yielded significantly higher clinical improvement (≥30% WOMAC reduction; OR 2.18; 95% CI: 1.42–3.37; p 0.01). Predictive accuracy of the model was confirmed ( R 2 = 0.61; RMSE = 7.8). Clinical benefit was most pronounced in KL II–III patients with preserved joint mechanics and moderate-to-high activity levels. Simulations also demonstrated the need for joint-specific tailoring of HA volume and stiffness, particularly in the hip and shoulder. Conclusion This study provides a validated, patient-specific, and joint-adaptive model for optimizing HA viscosupplementation in OA. The findings support a shift from empirical selection to precision-based rheological personalization of HA therapy, enhancing treatment outcomes and biomechanical integration.