Mechanical properties of meniscal circumferential fibers using an inverse finite element analysis approach

Effect of meniscus modelling assumptions in a static tibiofemoral finite element model: importance of geometry over material

Finite element studies of the tibiofemoral joint have increased use in research, with attention often placed on the material models. Few studies assess the effect of meniscus modelling assumptions in image-based models on contact mechanics outcomes. This work aimed to assess the effect of modelling assumptions of the meniscus on knee contact mechanics and meniscus kinematics. A sensitivity analysis was performed using three specimen-specific tibiofemoral models and one generic knee model. The assumptions in representing the meniscus attachment on the tibia (shape of the roots and position of the attachment), the material properties of the meniscus, the shape of the meniscus and the alignment of the joint were evaluated, creating 40 model instances. The values of material parameters for the meniscus and the position of the root attachment had a small influence on the total contact area but not on the meniscus displacement or the force balance between condyles. Using 3D shapes to represent the roots instead of springs had a large influence in meniscus displacement but not in knee contact area. Changes in meniscus shape and in knee alignment had a significantly larger influence on all outcomes of interest, with differences two to six times larger than those due to material properties. The sensitivity study demonstrated the importance of meniscus shape and knee alignment on meniscus kinematics and knee contact mechanics, both being more important than the material properties or the position of the roots. It also showed that differences between knees were large, suggesting that clinical interpretations of modelling studies using single geometries should be avoided.

In Situ Loading and Time-Resolved Synchrotron-Based Phase Contrast Tomography for the Mechanical Investigation of Connective Knee Tissues: A Proof-of-Concept Study

Articular cartilage and meniscus transfer and distribute mechanical loads in the knee joint. Degeneration of these connective tissues occurs during the progression of knee osteoarthritis, which affects their composition, microstructure, and mechanical properties. A deeper understanding of disease progression can be obtained by studying them simultaneously. Time-resolved synchrotron-based X-ray phase-contrast tomography (SR-PhC-µCT) allows to capture the tissue dynamics. This proof-of-concept study presents a rheometer setup for simultaneous in situ unconfined compression and SR-PhC-µCT of connective knee tissues. The microstructural response of bovine cartilage (n = 16) and meniscus (n = 4) samples under axial continuously increased strain, or two steps of 15% strain (stress-relaxation) is studied. The chondrocyte distribution in cartilage and the collagen fiber orientation in the meniscus are assessed. Variations in chondrocyte density reveal an increase in the top 40% of the sample during loading, compared to the lower half. Meniscus collagen fibers reorient perpendicular to the loading direction during compression and partially redisperse during relaxation. Radiation damage, image repeatability, and image quality assessments show little to no effects on the results. In conclusion, this approach is highly promising for future studies of human knee tissues to understand their microstructure, mechanical response, and progression in degenerative diseases.

Noninvasive identification of directionally-dependent elastic properties of soft tissues using full-field optical data

This paper introduces an innovative approach for elastic property characterization of soft tissues, having directional-dependent material behavior, via their vibration response measurement and interpretation. The full-field time-dependent surface displacements as a result of externally excited soft tissues are collected through digital image correlation (DIC). A developed analytical model, capturing the low-amplitude vibration behavior of anisotropic layered human skin with the incorporation of the influence of subcutaneous elasticity and inertia, is employed to accurately predict its resonant frequencies and pertaining displacement field images. An efficient solution approach for the model is implemented into an inverse algorithm to rapidly characterize the anisotropic elastic properties based on importing the vibration characteristics. To show the merit of the approach, a 3-D finite element (FE) simulation model was used to generate full-field data, detected and matched with a set of specific vibration modes via modal assurance criterion (MAC). The validity of the model implemented into the inverse characterization algorithm is demonstrated through a comparison of predicted vibration frequencies and mode-shapes simulated via the 3-D FE model for different cases with anisotropic elastic properties in different layers of the skin. It is shown that modes are influenced differently when anisotropic properties are introduced to the model. Thus, the established inverse characterization algorithm is capable of rapidly predicting the elastic material properties of anisotropic soft sheets with adequate accuracy.

Model Properties and Clinical Application in the Finite Element Analysis of Knee Joint: A Review

The knee is the most complex joint in the human body, including bony structures like the femur, tibia, fibula, and patella, and soft tissues like menisci, ligaments, muscles, and tendons. Complex anatomical structures of the knee joint make it difficult to conduct precise biomechanical research and explore the mechanism of movement and injury. The finite element model (FEM), as an important engineering analysis technique, has been widely used in many fields of bioengineering research. The FEM has advantages in the biomechanical analysis of objects with complex structures. Researchers can use this technology to construct a human knee joint model and perform biomechanical analysis on it. At the same time, finite element analysis can effectively evaluate variables such as stress, strain, displacement, and rotation, helping to predict injury mechanisms and optimize surgical techniques, which make up for the shortcomings of traditional biomechanics experimental research. However, few papers introduce what material properties should be selected for each anatomic structure of knee FEM to meet different research purposes. Based on previous finite element studies of the knee joint, this paper summarizes various modeling strategies and applications, serving as a reference for constructing knee joint models and research design.

Age influence on resistance and deformation of the human sutured meniscal horn in the immediate postoperative period

Introduction: To preserve knee function, surgical repair is indicated when a meniscal root disinsertion occurs. However, this surgery has not yet achieved complete recovery of the joint´s natural biomechanics, with the meniscus-suture interface identified as a potentially determining factor. Knowing the deformation and resistance behavior of the sutured meniscal horn and whether these properties are preserved as the patient ages could greatly contribute to improving repair outcomes. Methods: A cadaveric experimental study was conducted on human sutured menisci classified into three n = 22 age groups (young ≤55; 55 < middle-aged ≤75; 75 < old) were subjected to load-to-failure test by suture pulling. Meniscal thickness at the suture hole was measured and the applied traction force and tissue deformation in the suture area in the direction of traction were recorded during the test. The traction load that initiated the meniscal cut-out, F c , maximum load borne by the meniscus, F u , tissue stress at the cut-out initiation, S c , and equivalent stiffness modulus at the suture area, m s , were calculated. Results: At the tissue level, the resistance in terms of S c decrease with age (young: 47.2 MPa; middle-aged: 44.7 MPa; old: 33.8 MPa) being significantly different between the young and the old group (p = 0.015). Mean meniscal thickness increased with age (young: 2.50 mm; middle-aged: 2.92 mm; old: 3.38 mm; p = 0.001). Probably due to thickening, no differences in resistance were found at the specimen level, i.e., in F c (overall mean 58.2 N) and F u (overall mean 73.6 N). As for elasticity, m s was lower in the old group than in the young group (57.5 MPa vs. 113.6 MPa, p = 0.02) and the middle-aged one (57.5 MPa vs. 108.0 MPa, p = 0.04). Conclusion: Regarding the influence of age on the sutured meniscal horn tissue, in vitro experimentation revealed that meniscal horn specimens older than 75 years old had a more elastic tissue which was less resistant to cut-out than younger menisci at the suture hole area. However, a thickening of the meniscal horns with age, which was also found, leveled out the difference in the force that initiated the tear, as well as in the maximum force borne by the meniscus in the load-to-failure test.

Experimental validation for the interconversion between generalized Kelvin-Voigt and Maxwell models using human skin tissues

Mechanical properties of biological systems provide essential insights into their component, physiological function, and disease mechanism under various conditions, such as age, health, and other environmental factors. Viscoelasticity is one of the most important and investigated properties to study biomaterials, cells, and tissues, as they exhibit the characteristics of both fluid-like behavior, viscosity, and solid-like behavior, elasticity. Various mathematical models, such as the Kelvin-Voigt and Maxwell models, have been developed and practiced to estimate and extract viscoelastic properties. However, one of the inherent challenges with the use of these models is the poor transferability of mathematically estimated viscoelastic properties across different models, largely due to variations in constituent elements and their arrangements within each model. This issue impedes the interconversion of parameters of one model to another and complicates comparison across models. In this study, we demonstrate the equivalence between the generalized Maxwell and generalized Kelvin-Voigt models through two distinct approaches: indirect, Maxwell model-based Kelvin-Voigt model estimation and direct, curve fitting-based Kelvin-Voigt model estimation. We utilized human melanoma skin tissues to estimate viscoelastic properties using the Prony series. The estimated parameters and resulting viscoelastic properties revealed no significant difference between the two approaches and between the two patients. This study is the first experimental validation of the mathematical interconversion of the two models, signifying that this approach will enable an accurate and objective analysis and comparison of mechanical properties across various viscoelastic models.

Heterogeneity of dynamic shear properties of the meniscus: A comparison between tissue core and surface layers

Damage to the meniscus has been associated with excessive shear loads. Aimed at elucidating meniscus pathophysiology, previous studies have investigated the shear properties of the meniscus fibrocartilaginous core. However, the meniscus is structurally inhomogeneous, with an external cartilaginous envelope (tibial and femoral surface layers) wrapping the tissue core. To date, little is known about the shear behavior of the surface layers. The objective of this study was to measure the dynamic shear properties of the surface layers and derive empirical relations with their composition. Specimens were harvested from tibial and femoral surface layers and core of porcine menisci (medial and lateral, n = 10 each). Frequency sweep tests yielded complex shear modulus (G*) and phase shifts (δ). Mechanical behavior of regions was described by a generalized Maxwell model. Correlations between shear moduli with water and glycosaminoglycans content of the tissue regions were investigated. The femoral surface had the lowest shear modulus, when compared to core and tibial regions. A 3-relaxation times Maxwell model satisfactorily interpreted the shear behavior of all tissue regions. Inhomogeneous tissue composition was also observed, with water content in the surface layers being higher when compared with tissue core. Water content negatively correlated with shear properties in all regions. The lower measured shear properties in the femoral layer may explain the higher prevalence of meniscal tears on the superior surface of the tissue. The heterogenous behavior of the tissue in shear provides insight into meniscus pathology and has important implications for efforts to tissue engineer replacement tissues.

Effect of molecular weight and tissue layer on solute partitioning in the knee meniscus

Objective

Knee meniscus tissue is partly vascularized, meaning that nutrients must be transported through the extracellular matrix of the avascular portion to reach resident cells. Similarly, drugs used as therapeutic agents to treat meniscal pathologies rely on transport through the tissue. The driving force of diffusive transport is the gradient of concentration, which depends on molecular solubility. The meniscus is organized into a core region sandwiched between the tibial and femoral superficial layers. Structural differences exist across meniscal regions; therefore, regional differences in solubility are also hypothesized.

Methods

Samples from the core, tibial and femoral layers were obtained from 5 medial and 5 lateral porcine menisci. The partition coefficient (K) of fluorescein, 3 ​kDa and 40 ​kDa dextrans in the layers of the meniscus was measured using an equilibration experiment. The effect of meniscal compartment, layer, and solute molecular weight on K was analyzed using a three-way ANOVA.

Results

K ranged from a high of ∼2.9 in fluorescein to a low of ∼0.1 in 40 ​kDa dextran and was inversely related to the solute molecular weight across all tissue regions. Tissue layer only had a significant effect on partitioning of 40k Dex solute, which was lower in the tibial surface layer relative to the core (p ​= ​0.032).

Conclusion

This study provides insight into depth-dependent partitioning in the meniscus, indicating the limiting effect of the meniscus superficial layer on solubility increases with solute molecular size. This illustrates how the surface layers could potentially reduce the effectiveness of drug delivery therapies incorporating large molecules (>40 ​kDa).

Tensile energy dissipation and mechanical properties of the knee meniscus: relationship with fiber orientation, tissue layer, and water content

Introduction: The knee meniscus distributes and dampens mechanical loads. It is composed of water (∼70%) and a porous fibrous matrix (∼30%) with a central core that is reinforced by circumferential collagen fibers enclosed by mesh-like superficial tibial and femoral layers. Daily loading activities produce mechanical tensile loads which are transferred through and dissipated by the meniscus. Therefore, the objective of this study was to measure how tensile mechanical properties and extent of energy dissipation vary by tension direction, meniscal layer, and water content. Methods: The central regions of porcine meniscal pairs (n = 8) were cut into tensile samples (4.7 mm length, 2.1 mm width, and 0.356 mm thickness) from core, femoral and tibial components. Core samples were prepared parallel (circumferential) and perpendicular (radial) to the fibers. Tensile testing consisted of frequency sweeps (0.01-1Hz) followed by quasi-static loading to failure. Dynamic testing yielded energy dissipation (ED), complex modulus (E*), and phase shift (δ) while quasi-static tests yielded Young's Modulus (E), ultimate tensile strength (UTS), and strain at UTS (ε_UTS). To investigate how ED is influenced by the specific mechanical parameters, linear regressions were performed. Correlations between sample water content (φ_w) and mechanical properties were investigated. A total of 64 samples were evaluated. Results: Dynamic tests showed that increasing loading frequency significantly reduced ED (p < 0.05). Circumferential samples had higher ED, E*, E, and UTS than radial ones (p < 0.001). Stiffness was highly correlated with ED (R² > 0.75, p < 0.01). No differences were found between superficial and circumferential core layers. ED, E*, E, and UTS trended negatively with φ_w (p < 0.05). Discussion: Energy dissipation, stiffness, and strength are highly dependent on loading direction. A significant amount of energy dissipation may be associated with time-dependent reorganization of matrix fibers. This is the first study to analyze the tensile dynamic properties and energy dissipation of the meniscus surface layers. Results provide new insights on the mechanics and function of meniscal tissue.

Strain-Dependent Diffusivity of Small and Large Molecules in Meniscus

Due to lack of full vascularization, the meniscus relies on diffusion through the extracellular matrix to deliver small (e.g., nutrients) and large (e.g., proteins) to resident cells. Under normal physiological conditions, the meniscus undergoes up to 20% compressive strains. While previous studies characterized solute diffusivity in the uncompressed meniscus, to date, little is known about the diffusive transport under physiological strain levels. This information is crucial to fully understand the pathophysiology of the meniscus. The objective of this study was to investigate strain-dependent diffusive properties of the meniscus fibrocartilage. Tissue samples were harvested from the central portion of porcine medial menisci and tested via fluorescence recovery after photobleaching to measure diffusivity of fluorescein (332 Da) and 40 K Da dextran (D40K) under 0%, 10%, and 20% compressive strain. Specifically, average diffusion coefficient and anisotropic ratio, defined as the ratio of the diffusion coefficient in the direction of the tissue collagen fibers to that orthogonal, were determined. For all the experimental conditions investigated, fluorescein diffusivity was statistically faster than that of D40K. Also, for both molecules, diffusion coefficients significantly decreased, up to ∼45%, as the strain increased. In contrast, the anisotropic ratios of both molecules were similar and not affected by the strain applied to the tissue. This suggests that compressive strains used in this study did not alter the diffusive pathways in the meniscus. Our findings provide new knowledge on the transport properties of the meniscus fibrocartilage that can be leveraged to further understand tissue pathophysiology and approaches to tissue restoration.

Experiments and hyperelastic modeling of porcine meniscus show heterogeneity at high strains

Constitutive modeling of the meniscus is critical in areas like knee surgery and tissue engineering. At low strain rates, the meniscus can be described using a hyperelastic model. Calibration of hyperelastic material models of the meniscus is challenging on many fronts due to material variability and friction. In this study, we present a framework to determine the hyperelastic material parameters of porcine meniscus (and similar soft tissues) using no-slip uniaxial compression experiments. Because of the nonhomogeneous deformation in the specimens, a finite element solution is required at each step of the iterative calibration process. We employ a Bayesian calibration approach to account for the inherent material variability and a Bayesian optimization approach to minimize the resulting cost function in the material parameter space. Cylindrical specimens of porcine meniscus from the anterior, middle and posterior regions are tested up to 30% compressive strain and the Yeoh form of hyperelastic strain energy density function is used to describe the material response. The results show that the Yeoh form is able to accurately describe the compressive response of porcine meniscus and that the Bayesian calibration and optimization approaches are able to calibrate the model in a computationally efficient manner while taking into account the inherent material variability. The results also show that the shear modulus or the initial stiffness is roughly uniform across the different areas of the meniscus, but there is significant spatial heterogeneity in the response at high strains. In particular, the middle region is considerably stiffer at high strains. This heterogeneity is important to consider in modeling the response of the meniscus for clinical applications.