Confined and unconfined articular cartilage mechanics: Effect of creep duration on estimations of mechanical properties

Abstract

Recent findings suggest that cartilage mechanical function may be a biomarker for early osteoarthritis (OA) pathology. Thus, the development of methodologies for in-vivo applications has expanded. However, when creep tests are performed, inconsistency in applied stress and testing duration impede meaningful comparisons. Therefore, this study investigates the impact of creep duration on cartilage mechanics through ex-vivo confined and unconfined compression experiments on healthy bovine cartilage samples (n = 20), subjected to 1 MPa stress for 5 h. A Zener model was fitted to unconfined data and a nonlinear biphasic model was fitted to confined data using durations ranging from 15 min to 5 h. Mechanical properties were compared against the full 5-h dataset to determine relative errors (RE) associated with insufficient creep duration. Based on our findings, we aim to establish a common ground for both in vivo and ex vivo environments. Both unconfined (R² = 0.96 ± 0.02) and confined (R² = 0.997 ± 0.003) models fitted the data well over 5 h. For confined creep tests, the aggregate modulus (H_A) was 0.34 ± 0.12 MPa after 5 h and 0.27 ± 0.12 MPa after 1 h (RE ∼ 20 %), while initial permeability (k₀) increased from 0.17 × 10⁻¹⁵ m⁴N⁻¹s⁻¹ to 0.56 × 10⁻¹⁵ m⁴N⁻¹s⁻¹ (RE ∼ 49 %). The Zener model estimated the initial (E₁) and steady-state (E₂) modulus to be 3.6 ± 0.7 MPa and 3.2 ± 0.3 MPa after 5 h, respectively. After 1 h, these values were 4.7 ± 1.0 MPa (RE ∼ 29 %) and 3.2 ± 0.3 MPa (RE ∼ 2 %). A larger RE (∼57 %) was observed for the relaxation time constant (τ) determined after 5 h (1688 ± 556 s) and 1 h (781 ± 170 s) with the Zener model. The benefit of extended creep duration diminished after 1–1.5 h for confined compression and 2 h for unconfined compression for non-rate dependent stiffness parameters (i.e., H_A, E₁, E₂). This aligned well with the predefined equilibrium criteria of less than 0.6 μm/min, with equilibrium reached at 71 ± 23 min for confined experiments and 94 ± 25 min for unconfined experiments. In contrast, for parameters controlling the nonlinear material response (i.e., τ, k_0, M), 4 h were required for unconfined compression and 1.5 h for confined compression to achieve RE ∼ 10 %. Thus, insufficient creeping duration resulted in large RE, especially for strain-dependent parameters. Therefore, it is recommended to use a clear equilibrium definition when conducting ex vivo experiments. In the context of clinically viable testing duration (i.e., 45–60 min) RE was ∼20 % for the predicted aggregate modulus and ∼10 % for the nonlinear permeability coefficient. While these errors appear substantial, they may still estimate cartilage mechanics within reasonable limits given the associated variability in healthy and OA cartilage characteristics. Therefore, within a limited timeframe, it could be possible to estimate mechanical properties using in vivo creep experiments that may serve as biomarkers for early OA.