Application of Hertzian contact theory to predict cartilage overload in the osteoarthritic and anterior-cruciate-ligament-deficient knee: A biomechanical analysis.

Abstract

Altered tibiofemoral contact mechanics contribute to cartilage degeneration in knee osteoarthritis (OA) and anterior cruciate ligament (ACL) deficiency. Predicting focal cartilage overload is challenging due to biomechanical complexity. Hertzian contact theory, though simplified, provides a physically robust framework to estimate stress distributions from geometry and material properties. To apply Hertzian theory to model tibiofemoral contact pressures and areas in healthy, osteoarthritic, and ACL-deficient knees, and assess its capability to identify patterns linked to cartilage degeneration. A Hertzian-based model was built for three conditions using standardized cartilage properties (E = 10 MPa, ν = 0.45) and representative sagittal radii of curvature. A 700-N vertical load simulated single-leg stance. Peak contact pressure, contact area, and stress patterns were computed. Sensitivity analyses varied modulus, curvature, and load. Outputs were compared qualitatively with anatomical degeneration regions reported in imaging studies. Compared with the healthy model (3.21 MPa; 258.3 mm²), OA showed a 26.2 % higher peak pressure and 14.2 % smaller contact area; ACL deficiency showed a 33.3 % increase in peak pressure and 19.3 % reduction in area. OA overload localized medially, ACL deficiency shifted posteriorly. Geometry changes had greater influence on contact mechanics than stiffness or load changes. Hertzian theory captures key biomechanical changes in OA and ACL deficiency, identifying clinically relevant overload zones. This simplified approach underscores the dominant role of joint geometry and supports practical biomechanical risk assessment.