Conference Agenda

Introduction

Dynamic elastography is a fundamental technique to study the local mechanical property of the tissues, such as cornea. It is based on in-vivo tracking of shear waves propagation as a result of a transient stimulation. In quasi-incompressible materials, as the cornea, the shear waves are 150 times slower than the compressional waves. The quasi-incompressible behavior and the double-scale of the phenomena make the FE approximation difficult. We used an efficient scheme to obtain a reliable modelling of transient elastography measurements in incompressible pre-loaded tissues, and we applied to the cornea to reproduce a typical dynamic elastography experiment, on cornea with and without defects.

Method

Wave propagation in cornea can be treated as a linear perturbation of an already loaded material, under the assumption that the wave amplitude is small. The specificity of the biological tissues is the complexity of their mechanical response of tissue, which is almost incompressible, hyperelastic and anisotropic.

We performed a linearization of the elastic problem around the prestressed state. The linearized rigidity has then 2 components: a material one, due to the non-linearity of the constitutive law, and a geometric one, associated with the prestress. For the material constitutive law, we used a microsphere model including the contributions of the isotropic matrix, the collagen lamellae and the quasi-incompressibility of the tissue (Giraudet et al. 2022).

The simulations were done using a mesh reproducing the geometry of the cornea (Pandolfi et al. 2008). The static non-linear problem is solved through a classical iterative method. The wave propagation simulation presents a challenge due to the quasi-incompressible behavior: the time-step is controlled by the velocity of the fastest wave, the compression one, while we are interested in the slow, shear, waves. To overcome this difficulty, we use a fully explicit numerical method (Merlini et al. 2025), based on high-order spectral elements, mass-lumping together with Gauss-Lobatto quadrature rule and an inf-sup stable mixed formulation, and a relaxation of the CFL condition through the use of Chebyshev polynomials.

Results

We observe that the fibers have a limited effect on the main wave velocity, despite the increase of stiffness in the cornea. This may be due to our approximation with they are mainly in-plane, which is consistent with cornea observations, even if some out-of-plane orientations are reported (Petsche et al. 2013). However, they impact significantly a faster wave, with a much lower amplitude.

The IOP and the associated prestress has a significant impact on the velocity of the main wave: the wave is faster on a cornea under pressure than in a cornea in which the IOP has been suppressed.

The introduction of a mechanical defect leads to a significant alteration of the shape of the wave front, indicating that this method can be used for the early detections of pathologies such as keratoconus.

References

- C. Giraudet et al., JMBBM, 129:105121, 2022.

- A. Pandolfi et al., J Biomech Eng, 130: 061006, 2008.

- G. Merlini et al., Waves, submitted 2024.

- S. Petsche et al., BMMB, 12:1101–1113, 2013

Biodegradable magnesium (Mg) implants offer an attractive alternative to permanent metallic devices by gradually dissolving as natural bone regenerates, thereby reducing long‐term complications. However, predicting the degradation behavior of Mg and its interaction with surrounding tissues remains a significant challenge. In our work, we present a novel multiscale computational framework that couples a nonlocal peridynamic corrosion model with a bone healing and remodeling model. The peridynamic model accurately captures the time-dependent degradation of Mg by simulating its progressive dissolution and macroscopic volume loss, while dynamically linking the release of Mg ions to local biological responses. This ion release directly influences osteoblast differentiation and subsequent mineralization of the bone matrix, providing new insights into the connection between implant degradation and tissue regeneration. While our primary focus is on quantifying the biocorrosion of Mg and its immediate impact on bone healing, our framework also lays the groundwork for future integration of soft tissue biomechanics to further enhance implant-tissue integration. This coupled model serves as a robust tool for designing next-generation biodegradable implants and optimizing their mechanical performance and biocompatibility. Our findings promise to advance implant design strategies by linking degradation kinetics with tissue growth, thereby facilitating a more predictive and personalized approach to clinical treatment and opening avenues for interdisciplinary research in biomechanics and regenerative medicine.

The mechanical response of human spinal dura mater under higher strain rates remains incompletely characterized, despite the critical protective role of this fibrous membrane. In the present investigation, samples were harvested from six human donors with a mean age of 79.33 years and prepared in a longitudinal orientation along the spinal axis. Dog-bone-shaped specimens were subjected to uniaxial tensile loading at nominal strain rates of 0.5, 10, and 25 s⁻¹ using a custom-built testing apparatus. Parameters such as elastic modulus, ultimate tensile strength (UTS), and stretch at failure were evaluated potential rate-related effects. Morphometric measurements indicated that posterior specimens exhibited statistically greater thickness and cross-sectional area than anterior ones. However, no definitive increase in mechanical strength was observed on that basis alone.

Strain-rate-dependent stiffening of the dura mater was recorded, with statistically higher elastic modulus values measured at 10 and 25 s⁻¹ relative to 0.5 s⁻¹. At 25 s⁻¹, the mean elastic modulus exceeded 265 MPa, compared to approximately 172 MPa at 0.5 s⁻¹. Ultimate tensile stress values showed overlapping standard deviations but trended toward higher mean levels at 10 s⁻¹. Furthermore, failure stretch appeared slightly lower at 25 s⁻¹, suggesting a reduced ability to sustain elongation under rapid loading conditions. These observations align with previously noted viscoelastic phenomena in other collagenous tissues and underscore the importance of testing spinal dura mater at physiologically and clinically relevant strain rates.

A visco-hyperelastic constitutive framework was used to capture the nonlinear and time-dependent properties of the dura. This approach incorporated transversely isotropic material behavior, reflecting the predominant collagen fiber orientation in the craniocaudal direction, along with rate-dependent viscous terms. Excellent correlations were achieved between the proposed material model and the experimental stress–stretch data across the tested strain rates, as confirmed by high coefficients of determination (adjusted R² > 0.98) and low error metrics.

These results expand the existing knowledge base by characterizing human spinal dura mater at strain rates relevant to high-speed trauma. Inclusion of the derived constitutive model in finite element analyses is anticipated to enhance the biofidelity of human body models, particularly in automotive crashworthiness research or other high-impact applications. In addition, the demonstrated regional geometric differences suggest that more targeted investigations, including biaxial experiments and correlation with tissue microstructure, may further elucidate localized mechanical variations. Overall, the findings highlight the pronounced rate-dependent stiffening of spinal dura mater and contribute essential data for improved simulation of dynamic spinal loading scenarios. Such observations underscore the clinical importance of understanding how rapid loading events may compromise the dural barrier. Further integration of microstructural analyses, including collagen fiber mapping, may clarify the relationship between regional tissue composition and local mechanical outcomes.

1. Introduction

Eye movements are essential for visual integration, from fixational eye movements to saccades. Several studies have shown dependence between eye movements and ocular tissues strain (Demer, 2016). Integration of large eye movements in Finite Element Model (FEM) was previously addressed on simplified geometries (Karimi et al., 2017). Predicting activations parameters within a continuum extra ocular muscle model is a challenge since in-vivo measures are difficult. We propose a FEM that includes sclera, optic nerve and horizontal rectus muscles to implement new range of movements.

2. Methods

We retrieved an Abaqus assembly from a study on the ocular adduction by active extraocular muscle (EOM) contraction (Jafari et al., 2021). We assumed all tissues except the EOMs to be homogeneous, isotropic, incompressible, and hyperelastic based on previous modelisation (Jafari et al., 2021). A user subroutine models muscle contraction via EOM material properties. The quasi-incompressible strain energy density formulation captures both active and passive muscle behaviors (Grasa & Calvo, 2021). Muscle fibers anisotropy is accounted with an active stretch along the muscle fibers.

3. Results and discussion

Based on previous methodologies (Karimi et al., 2017), the model will be validated to reproduce horizontal saccadic movements where tensions in extra-ocular muscles have been quantified. Activations of the rectus muscles for saccadic movements exceeding previous range of motion are established. The principal strains will be quantified for saccadic movements in the peripapillary sclera.

4. Conclusions

Simulations of movements and corresponding activations will be extended through inverse simulations based on movements captured with an eye tracker. Positions implying important strains will be assessed, based on previous quantification of strains in eyes (Demer, 2016; Jafari et al, 2024).

Acknowledgements:

We thank S. Jafari and J. Demer for the Abaqus assembly and the 3D mesh.

Funding:

This project was partially funded by the French National Agency of Research and Technology via the convention Cifre 2023/0280. Several authors are employees of EssilorLuxottica.

References:

Demer, J. L. (2016). Optic Nerve Sheath as a Novel Mechanical Load on the Globe in Ocular Duction. Investigative Opthalmology & Visual Science, 57(4), 1826. doi: 10.1167/iovs.15-18718

Karami, A., Eghtesad, M., & Haghpanah, S. A. (2017). Prediction of muscle activation for an eye movement with finite element modeling. Computers in Biology and Medicine, 89, 368‑378. doi: 10.1016/j.compbiomed.2017.08.018

Jafari, S., Lu, Y., Park, J., & Demer, J. L. (2021). Finite Element Model of Ocular Adduction by Active Extraocular Muscle Contraction. Investigative Opthalmology & Visual Science, 62(1), 1. doi: 10.1167/iovs.62.1.1

Grasa, J., & Calvo, B. (2021). Simulating Extraocular Muscle Dynamics. A Comparison between Dynamic Implicit and Explicit Finite Element Methods. Mathematics, 9(9), 1024. doi: 10.3390/math9091024

Hernia is a physiological condition that significantly impacts patients’ quality of life, where there is an organ prolapse through the wall of the cavity that is normally contained, due to a weakness or opening, mainly of the abdominal wall. Surgical treatment for hernias often involves the use of specialized meshes to support the abdominal wall. While this method is highly effective, it frequently leads to complications such as pain, infections, inflammation, adhesions, and even the need for revision surgeries. According to the Food and Drug Administration (FDA), hernia recurrence rates can reach up to 11%, surgical site infections occur in up to 21% of cases, and chronic pain incidence ranges from 0.3% to 68%. These statistics highlight the urgent need to improve mesh technologies to minimize such complications.
In this study, a preliminary innovative melt-electrowritten mesh with antistatic properties from hernia repair is presented. Melt Electrowriting is a promising technique, which allows a precise deposition of thin fibers, mimicking the fibrillar component of the native extracellular matrix. The study investigated the effect of incorporating the antistatic agent Hostastat ® FA 38 (HT) at concentrations of 0.03, 0.06, and 0.1 wt% on the fiber diameter and mechanical properties of Polycaprolactone (PCL) meshes. The addition of HT reduced fiber diameter by 14–17%, 39–45%, and 65–66%, depending on the mesh geometry (square or sinusoidal, both with a 1.5 mm pore size). The reduced fiber diameter correlated with increased tensile strength and Young’s Modulus, as verified through uniaxial tensile testing. Comparisons between PCL/HT and pure PCL meshes with similar diameters and geometries confirmed the enhanced mechanical properties of PCL/HT meshes. Cytotoxicity tests, using the resazurin assay, indicated no cytotoxic effects at any HT concentration. Both sterilization methods (Ethanol + UV and UV only) showed no significant differences in results. These findings demonstrate that incorporating HT into PCL meshes produces thinner, more stable filaments with improved mechanical performance and no cytotoxicity, making them a promising material for applications such as hernia repair. Future studies on polymer-additive interactions could further optimize their mechanical and biological properties.

Keywords: Hernia Repair; Biodegradable Mesh Implants; Melt Electrowriting; Antistatic Agent; Cytotoxicity