Fibril-reinforced Poroelastic Model Research Articles

Exploring the Multifaceted Dynamics of Cartilage: A Comparative Modeling Study

Cartilage numeric models play a vital role in advancing our understanding of cartilage mechanics, disease progression, and the development of clinical interventions. The aim of this study is to investigate the influence of different mathematical models on cartilage mechanical behavior over time. A comparative analysis was conducted across three scenarios: the single-phase, biphasic, and fibril-reinforced poroelastic models. To understand how cartilage behaves over time, a 1000-second ramp relaxation displacement was applied. The findings reveal that the single-phase model falls short of capturing the time-dependent characteristics of cartilage. Conversely, the inclusion of fluid and collagen fibrils within the cartilage model significantly enhances cartilage resilience and enables the cartilage to behave non-linearly. The results presented herein make a substantial contribution to a deeper and more holistic comprehension of cartilage's dynamic behavior under compressive loads, shedding light on the intricate interplay between fluid pressure and fibril reinforcement.

Comparison of different material models of articular cartilage in 3D computational modeling of the knee: Data from the Osteoarthritis Initiative (OAI)

The intricate properties of articular cartilage and the complexity of the loading environment are some of the key challenges in developing models for biomechanical analysis of the knee joint. Fibril-reinforced poroelastic (FRPE) material models have been reported to accurately capture characteristic responses of cartilage during dynamic and static loadings. However, high computational and time costs associated with such advanced models limit applicability of FRPE models when multiple subjects need to be analyzed. If choosing simpler material models, it is important to show that they can still produce truthful predictions. Therefore, the aim of this study was to compare depth-dependent maximum principal stresses and strains within articular cartilage in the 3D knee joint between FRPE material models and simpler isotropic elastic (IE), isotropic poroelastic (IPE) and transversely isotropic poroelastic (TIPE) material models during simulated gait cycle.When cartilage-cartilage contact pressures were matched between the models (15% allowed difference), maximum principal stresses in the IE, IPE and TIPE models were substantially lower than those in the FRPE model (by more than 50%, TIPE model being closest to the FRPE model), and stresses occurred only in compression in the IE model.Additional simulations were performed to find material parameters for the TIPE model (due to its anisotropic nature) that would yield maximum principal stresses similar to the FRPE model. The modified homogeneous TIPE model was in a better agreement with the homogeneous FRPE model, and the average and maximum differences in maximum principal stresses throughout the depth of cartilage were 7% and 9%, respectively, in the lateral compartment and 9% and 11% in the medial compartment.This study revealed that it is possible to match simultaneously maximum principal stresses and strains of cartilage between non-fibril-reinforced and fibril-reinforced knee joint models during gait. Depending on the research question (such as analysis of fibril strain necessitates the use of fibril-reinforced material models) or clinical demand (fast simulations with simpler material models), the choice of the material model should be done carefully.

Very early osteoarthritis changes sensitively fluid flow properties of articular cartilage

In this study, fibril-reinforced poroelastic (FRPE) modeling was used for rabbit knee after anterior cruciate ligament transection (ACLT) to assess how the mechanical properties of collagen, proteoglycans, and fluid in articular cartilage change in early osteoarthritis, and how site-specific these changes are.Unilateral ACLT was performed in eight skeletally mature, female New Zealand white rabbits. A separate control (CTRL) group consisted of knee joints of five non-operated rabbits. Animals were sacrificed at four weeks after ACLT and cartilage-on-bone samples from femoral groove, medial and lateral femoral condyles, and tibial plateaus were harvested. A stress–relaxation protocol in indentation geometry was applied and the FRPE model was fitted to the experimental force–time curve by minimizing the mean absolute error between experiment and simulation. The optimized parameters were: fibril network modulus (Ef), representing the collagen network; non-fibrillar matrix modulus (Enf), representing the PG matrix; and permeability (k), representing fluid flow.Permeability was increased significantly in the ACLT group compared to the CTRL group knees at all sites except for the medial tibial plateau. ACLT also caused a decrease in the Ef at all sites except for the medial and lateral tibial plateaus. The Enf of the ACLT group knees was altered only for the lateral femoral condyle.The results of this study suggest that early osteoarthritis primarily affects cartilage permeability and impairs the collagen network stiffness in a site-specific manner. These findings from early osteoarthritis indicate that fluid flow velocity in articular cartilage may change prior to quantifiable structural alterations in the tissue.

Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration

The understanding of load support mechanisms in cartilage has evolved with computational models that better mimic the tissue ultrastructure. Fibril-reinforced poroelastic models can reproduce cartilage behaviour in a variety of test conditions and can be used to model tissue anisotropy as well as assess stress and pressure partitioning to the tissue constituents. The goal of this study was to examine the stress distribution in the fibrillar and non-fibrillar solid phase and pressure in the fluid phase of cartilage in axisymmetric models of a healthy and osteoarthritic hip joint. Material properties, based on values from the literature, were assigned to the fibrillar and poroelastic components of cartilage and cancellous and subchondral compact bone regions. A cyclic load representing walking was applied for 25 cycles. Contact stresses in the fibrillar and non-fibrillar solid phase supported less than 1% of the contact force and increased only minimally with load cycles. Simulated proteoglycan depletion increased stresses in the radial and tangential collagen fibrils, whereas fibrillation of the tangential fibrils resulted in increased compressive stress in the non-fibrillar component and tensile stress in the radial fibrils. However neither had an effect on fluid pressure. Subchondral sclerosis was found to have the largest effect, resulting in increased fluid pressure, non-fibrillar compressive stress, tangential fibril stress and greater cartilage consolidation. Subchondral bone stiffening may play an important role in the degenerative cascade and may adversely affect tissue repair and regeneration treatments.

Poroelasticity of Cartilage at the Nanoscale

Atomic-force-microscopy-based oscillatory loading was used in conjunction with finite element modeling to quantify and predict the frequency-dependent mechanical properties of the superficial zone of young bovine articular cartilage at deformation amplitudes, δ, of ∼15 nm; i.e., at macromolecular length scales. Using a spherical probe tip (R ∼ 12.5 μm), the magnitude of the dynamic complex indentation modulus, |E∗|, and phase angle, φ, between the force and tip displacement sinusoids, were measured in the frequency range f ∼ 0.2–130 Hz at an offset indentation depth of δ0 ∼ 3 μm. The experimentally measured |E∗| and φ corresponded well with that predicted by a fibril-reinforced poroelastic model over a three-decade frequency range. The peak frequency of phase angle, fpeak, was observed to scale linearly with the inverse square of the contact distance between probe tip and cartilage, 1/d2, as predicted by linear poroelasticity theory. The dynamic mechanical properties were observed to be independent of the deformation amplitude in the range δ = 7–50 nm. Hence, these results suggest that poroelasticity was the dominant mechanism underlying the frequency-dependent mechanical behavior observed at these nanoscale deformations. These findings enable ongoing investigations of the nanoscale progression of matrix pathology in tissue-level disease.

Compressive and tensile properties of articular cartilage in axial loading are modulated differently by osmotic environment

Aims of the present study were to test the hypotheses that (1) the compressive properties of articular cartilage are affected more by changes in the medium ionic concentration than the tensile properties, (2) collagen network controls the compression–tension nonlinearity of articular cartilage, and (3) proteoglycan (PG) and collagen contents are primary determinants of the compressive and tensile properties of cartilage, respectively. These hypotheses were experimentally tested by axial compressive and tensile tests (perpendicular to the cartilage surface) of bovine articular cartilage samples immersed in 0.005 M ( n = 6), 0.15 M ( n = 12) and 1.0 M ( n = 6) saline solutions. Compressive and tensile behaviour was analyzed by a nonlinear fibril-reinforced poroelastic model. Tissue PG and collagen contents were measured using Fourier transform infrared imaging spectroscopy (FT-IRIS). The compressive modulus of cartilage varied significantly ( n = 6, p < 0.05) as the medium concentration changed. The tensile modulus changed significantly only as the medium concentration was reduced from 0.15 to 0.005 M ( n = 6, p < 0.05). The fibril-reinforced poroelastic model with stiff, nonlinear collagen fibrils predicted the experimentally measured compression–tension nonlinearity of cartilage. Tissue PG and collagen contents accounted for the compressive and tensile properties of cartilage.

Comparison of single-phase isotropic elastic and fibril-reinforced poroelastic models for indentation of rabbit articular cartilage

Classically, single-phase isotropic elastic (IE) model has been used for in situ or in vivo indentation analysis of articular cartilage. The model significantly simplifies cartilage structure and properties. In this study, we apply a fibril-reinforced poroelastic (FRPE) model for indentation to extract more detailed information on cartilage properties. Specifically, we compare the information from short-term (instantaneous) and long-term (equilibrium) indentations, as described here by IE and FRPE models. Femoral and tibial cartilage from rabbit (age 0–18 months) knees ( n=14) were tested using a plane-ended indenter (diameter=0.544 mm). Stepwise creep tests were conducted to equilibrium. Single-phase IE solution for indentation was used to derive instantaneous modulus and equilibrium (Young's) modulus for the samples. The classical and modified Hayes’ solutions were used to derive values for the indentation moduli. In the FRPE model, the indentation behavior was sample-specifically described with three material parameters, i.e. fibril network modulus, non-fibrillar matrix modulus and permeability. The instantaneous and fibril network modulus, and the equilibrium Young's modulus and non-fibrillar matrix modulus showed significant ( p<0.01) linear correlations of R 2=0.516 and 0.940, respectively (Hayes’ solution) and R 2=0.531 and 0.960, respectively (the modified Hayes’ solution). No significant correlations were found between the non-fibrillar matrix modulus and instantaneous moduli or between the fibril network modulus and the equilibrium moduli. These results indicate that the instantaneous indentation modulus (IE model) provides information on tensile stiffness of collagen fibrils in cartilage while the equilibrium modulus (IE model) is a significant measure for stiffness of PG matrix. Thereby, this study highlights the feasibility of a simple indentation analysis.

A fiber reinforced poroelastic model of nanoindentation of porcine costal cartilage: A combined experimental and finite element approach

Nanoindentation has shown promise as a mechanical characterization tool for orthopaedic biomaterials since it can probe the properties of small, heterogeneous, irregularly shaped tissue volumes in physiological environments. However, the majority of nanoindentation analyses have been limited to the determination of linear elastic and viscoelastic properties. Since biomaterials possess complex nonlinear, hydrated, time-dependent constitutive behavior, the objective of the present study is to explore the ability of nanoindentation to determine physiologically relevant material properties using a fibril reinforced poroelastic (FRPE) model. A further goal is to ascertain the sensitivity of nanoindentation load–displacement curves to different FRPE parameters, including the elastic properties of the nonfibrillar matrix, the composition and distribution of fibers, and nonlinearity in the fluid permeability. Porcine costal cartilage specimens are experimentally tested with nanoindentation load relaxation experiments at two different loading depths and loading rates. The FRPE material properties are extracted from comparisons to finite element simulations. The study demonstrates the behavior of the model in nanoindentation is distinct from bulk indentation; the static response of the nanoindentation is determined almost exclusively by the elastic properties of the nonfibrillar matrix and the volume fraction of fibers, while the transient response is dominated by the fluid permeability of the tissue. The FRPE model can accurately describe the time-dependent mechanical behavior of costal cartilage in nanoindentation, with good agreement between experimental and numerical curve fits ( R 2 = 0.98 ± 0.01 ) at multiple indentation depths and indentation rates.

COMPARISON OF INDENTATION MODELS OF ARTICULAR CARTILAGE

Classically, single-phase isotropic elastic (IE) model has been used for indentation analysis of articular cartilage (Hayes et al. 1972). The model significantly simplifies cartilage structure and properties. In this study, we apply a fibril reinforced poroelastic (FRPE) model (Soulhat et al. 1999) for indentation to extract more detailed information on cartilage properties. Specifically, we compare the information from short–term (instantaneous) and long-term (equilibrium) indentations, as described by IE and FRPE models.

Deep vertical collagen fibrils play a significant role in mechanics of articular cartilage

The primary orientation of collagen fibrils alters along the cartilage depth; being horizontal in the superficial zone, random in the transitional zone, and vertical in the deep zone. Commonly used confined and unconfined (when with no underlying bone) testing configurations cannot capture the mechanical role of deep vertical fibril network. To determine this role in cartilage mechanics, an axisymmetric nonlinear fibril-reinforced poroelastic model of tibial cartilage plateaus was developed accounting for depth-dependent properties and distinct fibril networks with physical material properties. Both creep and relaxation indentation models were analyzed which results were found equivalent in the transient period but diverged in post-transient periods. Vertical fibrils played a significant role at the transient period in dramatically increasing the stiffness of the tissue and in protecting the solid matrix against large distortions and strains at the subchondral junction. This role, however, disappeared both with time and at loading rates slower than those expected in physiological activities such as walking. The vertical fibrils demonstrated a chevron-type deformation pattern that was further accentuated with time in creep loading. Damages to deep vertical collagen fibril network or their firm anchorage to the bone, associated with bone bruises, for example, would weaken the transient stiffness and place the tissue at higher risk of failure particularly at the deep zone.

332 繊維束構造を考慮したモデルによる再生軟骨の圧縮特性の数値解析(GS-11:再生組織・細胞(2),一般セッション,学術講演)

332 繊維束構造を考慮したモデルによる再生軟骨の圧縮特性の数値解析(GS-11:再生組織・細胞(2),一般セッション,学術講演)

A fibril reinforced nonhomogeneous poroelastic model for articular cartilage: inhomogeneous response in unconfined compression

The depth dependence of material properties of articular cartilage, known as the zonal differences, is incorporated into a nonlinear fibril-reinforced poroelastic model developed previously in order to explore the significance of material heterogeneity in the mechanical behavior of cartilage. The material variations proposed are based on extensive observations. The collagen fibrils are modeled as a distinct constituent which reinforces the other two constituents representing proteoglycans and water. The Young's modulus and Poisson's ratio of the drained nonfibrillar matrix are so determined that the aggregate compressive modulus for confined geometry fits the experimental data. Three nonlinear factors are considered, i.e. the effect of finite deformation, the dependence of permeability on dilatation and the fibril stiffening with its tensile strain. Solutions are extracted using a finite element procedure to simulate unconfined compression tests. The features of the model are then demonstrated with an emphasis on the results obtainable only with a nonhomogeneous model, showing reasonable agreement with experiments. The model suggests mechanical behaviors significantly different from those revealed by homogeneous models: not only the depth variations of the strains which are expected by qualitative analyses, but also, for instance, the relaxation-time dependence of the axial strain which is normally not expected in a relaxation test. Therefore, such a nonhomogeneous model is necessary for better understanding of the mechanical behavior of cartilage.