The Human Meniscus Behaves as a Functionally Graded Fractional Porous Medium under Confined Compression Conditions

Implications of using simplified finite element meshes to identify material parameters of articular cartilage

The objective of this work was to determine the effects of using simplified finite element (FE) mesh geometry in the process of performing reverse iterative fitting to estimate cartilage material parameters from in situ indentation testing. Six bovine tibial osteochondral explants were indented with sequential 5 % step-strains followed by a 600 s hold while relaxation force was measured. Three sets of porous viscohyperelastic material parameters were estimated for each specimen using reverse iterative fitting of the indentation test with (1) 2D axisymmetric, (2) 3D idealized, and (3) 3D specimen-specific FE meshes. Variable material parameters were identified using the three different meshes, and there were no systematic differences, correlation to basic geometric features, nor distinct patterns of variation based on the type of mesh used. Implementing the three material parameter sets in a separate 3D FE model of 40 % compressive strain produced differences in von Mises stresses and pore pressures up to 25 % and 50 %, respectively. Accurate material parameters are crucial in any FE model, and parameter differences influenced by idealized assumptions in initial material property determination have the potential to alter subsequent FE models in unpredictable ways and hinder the interpretation of their results.

Development of Improved Confined Compression Testing Setups for Use in Stress Relaxation Testing of Viscoelastic Biomaterials

The development of cell-based biomaterial alternatives holds significant promise in tissue engineering applications, but it requires accurate mechanical assessment. Herein, we present the development of a novel 3D-printed confined compression apparatus, fabricated using clear resin, designed to cater to the unique demands of biomaterial developers. Our objective was to enhance the precision of force measurements and improve sample visibility during compression testing. We compared the performance of our innovative 3D-printed confined compression setup to a conventional setup by performing stress relaxation testing on hydrogels with variable degrees of crosslinking. We assessed equilibrium force, aggregate modulus, and peak force. This study demonstrates that our revised setup can capture a larger range of force values while simultaneously improving accuracy. We were able to detect significant differences in force and aggregate modulus measurements of hydrogels with variable degrees of crosslinking using our revised setup, whereas these were indistinguishable with the convectional apparatus. Further, by incorporating a clear resin in the fabrication of the compression chamber, we improved sample visibility, thus enabling real-time monitoring and informed assessment of biomaterial behavior under compressive testing.

On the characteristics of natural hydraulic dampers: An image-based approach to study the fluid flow behaviour inside the human meniscal tissue

The meniscal tissue is a layered material with varying properties influenced by collagen content and arrangement. Understanding the relationship between structure and properties is crucial for disease management, treatment development, and biomaterial design. The internal layer of the meniscus is softer and more deformable than the outer layers, thanks to interconnected collagen channels that guide fluid flow. To investigate these relationships, we propose an integrated approach that combines Computational Fluid Dynamics (CFD) with Image Analysis (CFD-IA). We analyze fluid flow in the internal architecture of the human meniscus across a range of inlet velocities (0.1 mm/s to 1.6 m/s) using high-resolution 3D micro-computed tomography scans. Statistical correlations are observed between architectural parameters (tortuosity, connectivity, porosity, pore size) and fluid flow parameters (Re number distribution, permeability). Some channels exhibit Re values of 1400 at an inlet velocity of 1.6 m/s, and a transition from Darcy's regime to a non-Darcian regime occurs around an inlet velocity of 0.02 m/s. Location-dependent permeability ranges from 20-32 Darcy. Regression modelling reveals a strong correlation between fluid velocity and tortuosity at high inlet velocities, as well as with channel diameter at low inlet velocities. At higher inlet velocities, flow paths deviate more from the preferential direction, resulting in a decrease in the concentration parameter by an average of 0.4. This research provides valuable insights into the fluid flow behaviour within the meniscus and its structural influences. 3D models and image stack are available to download at https://doi.org/10.5281/zenodo.10401592. STATEMENT OF SIGNIFICANCE: The meniscus is a highly porous soft tissue with remarkable properties of load transfer and energy absorption. We give insight on the mechanism of energy absorption from high resolution uCT scans, never presented before, and a new method which combine CFD and image. The structure is similar to a sandwich structure with a stiff outside layer and a soft internal layer made of collagen channels oriented in a preferential direction guiding the fluid flow, enabling it to accommodate deformation and dissipate energy, making it a potentially optimized damping system. We investigate architectural/ fluid flow parameters- fluid regimes relationship, which is of interest of the readers working on designing suitable biomimetic systems that can be adopted for replacement.

The biomechanical properties of human menisci: A systematic review

Biomechanical characterization of meniscal tissue ex vivo remains a critical need, particularly for the development of suitable meniscus replacements or therapeutic strategies that target the native mechanical properties of the meniscus. To date, a huge variety of test configurations and protocols have been reported, making it extremely difficult to compare the respective outcome parameters, thereby leading to misinterpretation. Therefore, the purpose of this systematic review was to identify test-specific parameters that contribute to uncertainties in the determination of mechanical properties of the human meniscus and its attachments, which derived from common quasi-static and dynamic tests in tension, compression, and shear. Strong evidence was found that the determined biomechanical properties vary significantly depending on the specific test parameters, as indicated by up to tenfold differences in both tensile and compressive properties. Test mode (stress relaxation, creep, cyclic) and configuration (unconfined, confined, in-situ), specimen shape and dimensions, preconditioning regimes, loading rates, post-processing of experimental data, and specimen age and degeneration were identified as the most critical parameters influencing the outcome measures. In conclusion, this work highlights an unmet need for standardization and reporting guidelines to facilitate comparability and may prove beneficial for evaluating the mechanical properties of novel meniscus constructs. STATEMENT OF SIGNIFICANCE: The biomechanical properties of the human meniscus have been studied extensively over the past decades. However, it remains unclear to what extent both test protocol and specimen-related differences are responsible for the enormous variability in material properties. Therefore, this systematic review analyzes the biomechanical properties of the human meniscus in the context of the underlying testing protocol. The most sensitive parameters affecting the determination of mechanical properties were identified and critically discussed. Currently, it is of utmost importance for scientists evaluating potential meniscal scaffolds and biomaterials to have a control group rather than a direct comparison to the literature. Standardization of both test procedures and reporting requirements is needed to improve and accelerate the development of meniscal replacement constructs.

Breast simulation pipeline: From medical imaging to patient-specific simulations

BACKGROUND

Breast-conserving surgery is the most acceptable operation for breast cancer removal from an invasive and psychological point of view. Before the surgical procedure, a preoperative MRI is performed in the prone configuration, while the surgery is achieved in the supine position. This leads to a considerable movement of the breast, including the tumor, between the two poses, complicating the surgeon's task.

METHODS

In this work, a simulation pipeline allowing the computation of patient-specific geometry and the prediction of personalized breast material properties was put forward. Through image segmentation, a finite element model including the subject-specific geometry is established. By first computing an undeformed state of the breast, the geometrico-material model is calibrated by surface acquisition in the intra-operative stance.

FINDINGS

Using an elastic corotational formulation, the patient-specific mechanical properties of the breast and skin were identified to obtain the best estimates of the supine configuration. The final results are a shape-fitting closest point residual of 4.00 mm for the mechanical parameters Ebreast=0.32 kPa and Eskin=22.72 kPa, congruent with the current state-of-the-art. The Covariance Matrix Adaptation Evolution Strategy optimizer converges on average between 5 to 30 min depending on the initial parameters, reaching a simulation speed of 20 s. To our knowledge, our model offers one of the best compromises between accuracy and speed.

INTERPRETATION

Satisfactory results were obtained for the estimation of breast deformation from preoperative to intra-operative configuration. Furthermore, we have demonstrated the clinical feasibility of such applications using a simulation framework that aims at the smallest disturbance of the actual surgical pipeline.

Parameter Identification of the Fractional-Order Mathematical Model for Convective Mass Transfer in a Porous Medium

Fractional calculus is an essential tool in studying new phenomena in hydromechanics and heat and mass transfer, particularly anomalous hydromechanical advection-dispersion considering the fractal nature of the porous medium. They are valuable in solving the urgent problem of convective mass transfer in a porous medium (e.g., membranes, filters, nozzles, convective coolers, vibrational prillers, and so on). Its solution allows for improving chemical engineering and technology workflows, refining process models for obtaining porous granular materials, realizing the convective cooling of granular and grain materials, and ensuring the corresponding apparatuses' environmental safety. The article aims to develop a reliable convective mass transfer model for a porous medium and proposes a practical approach for its parameter identification. As a result, a general scientific and methodological approach to parameter identification of the fractional convective mass transfer model in a porous medium was proposed based on available experimental data. It mainly used Riemann-Liouville fractional time and coordinate derivatives. The comprehensive application of the Laplace obtained the corresponding general solution transform with respect to time and a coordinate, the Mittag-Leffler function, and specialized functions. Different partial solutions in various application case studies proved this solution. Moreover, the algorithm for practically implementing the developed approach was proposed to evaluate parameters for the considered model by evaluation data. It was reduced to the two-parameter model and justified by the available experimental data.

On the fractional transversely isotropic functionally graded nature of soft biological tissues: Application to the meniscal tissue

This paper focuses on the origin of the poroelastic anisotropic behaviour of the meniscal tissue and its spatially varying properties. We present confined compression creep test results on samples extracted from three parts of the tissue (Central body, Anterior horn and Posterior horn) in three orientations (Circumferential, Radial and Vertical). We show that a poroelastic model in which the fluid flow evolution is ruled by non-integer order operators (fractional Darcy's law) provides accurate agreement with the experimental creep data. The model is validated against two additional sets of experimental data: stress relaxation and fluid loss during the consolidation process measured as weight reduction. Results show that the meniscus can be considered as a transversely isotropic poroelastic material. This behaviour is due to the fluid flow rate being about three times higher in the circumferential direction than in the radial and vertical directions in the body region of the meniscus. The 3D fractional poroelastic model is implemented in the finite element software to estimate the weight loss during the confined compression tests.

Region- and layer-specific investigations of the human menisci using SHG imaging and biaxial testing

In this paper, we examine the region- and layer-specific collagen fiber morphology via second harmonic generation (SHG) in combination with planar biaxial tension testing to suggest a structure-based constitutive model for the human meniscal tissue. Five lateral and four medial menisci were utilized, with samples excised across the thickness from the anterior, mid-body, and posterior regions of each meniscus. An optical clearing protocol enhanced the scan depth. SHG imaging revealed that the top samples consisted of randomly oriented fibers with a mean fiber orientation of 43.3 ^o . The bottom samples were dominated by circumferentially organized fibers, with a mean orientation of 9.5 ^o . Biaxial testing revealed a clear anisotropic response, with the circumferential direction being stiffer than the radial direction. The bottom samples from the anterior region of the medial menisci exhibited higher circumferential elastic modulus with a mean value of 21 MPa. The data from the two testing protocols were combined to characterize the tissue with an anisotropic hyperelastic material model based on the generalized structure tensor approach. The model showed good agreement in representing the material anisotropy with a mean r ² = 0.92.

On the microstructurally driven heterogeneous response of brain white matter to drug infusion pressure

Delivering therapeutic agents into the brain via convection-enhanced delivery (CED), a mechanically controlled infusion method, provides an efficient approach to bypass the blood–brain barrier and deliver drugs directly to the targeted focus in the brain. Mathematical methods based on Darcy’s law have been widely adopted to predict drug distribution in the brain to improve the accuracy and reduce the side effects of this technique. However, most of the current studies assume that the hydraulic permeability and porosity of brain tissue are homogeneous and constant during the infusion process, which is less accurate due to the deformability of the axonal structures and the extracellular matrix in brain white matter. To solve this problem, a multiscale model was established in this study, which takes into account the pressure-driven deformation of brain microstructure to quantify the change of local permeability and porosity. The simulation results were corroborated using experiments measuring hydraulic permeability in ovine brain samples. Results show that both hydraulic pressure and drug concentration in the brain would be significantly underestimated by classical Darcy’s law, thus highlighting the great importance of the present multiscale model in providing a better understanding of how drugs transport inside the brain and how brain tissue responds to the infusion pressure. This new method can assist the development of both new drugs for brain diseases and preoperative evaluation techniques for CED surgery, thus helping to improve the efficiency and precision of treatments for brain diseases.