University Of Strathclyde Department Of Biomedical Engineeri

Universityofstrathclydedepartmentofbiomedicalengineeringbe900tis

Provide a short report (no more than 1000 words and 8 figures) on the unconfined compression of biphasic and viscoelastic media. Using FEBio, analyze the mechanics (stress, strain, fluid pressure, etc.) of a 10 mm diameter and 3mm height cylindrical tissue in unconfined compression. Compare two different materials: (1) biphasic—an isotropic elastic solid phase with E = 100 MPa, n=0.3, permeability 1 x 10^-15 m⁴/Ns, solid volume 0.2; (2) viscoelastic—based on isotropic elasticity with E = 100 MPa, n=0.3, coefficient ðº1 = 0.5, relaxation time ð‘¡1 = 100. All other parameters at default. Subject each cylinder to axial unconfined compression to -0.1 strain at -0.01 s^-1 by an impermeable, rigid platen. Analyze and compare the mechanics during the ramp phase and until equilibrium. The report should include sections: Introduction (brief, with aims and objectives), Methods (describing model details, mesh, boundary and loading conditions), Results (using figures to describe mechanics, with citations), Discussion (comparing materials and implications for cellular stress environment), and Conclusion (a brief summary). Submit the report and two .feb files (one for each material) by the deadline. Consider mesh sensitivity and problem geometry simplifications. Ensure clarity in communication and original work.

Paper For Above instruction

The mechanical behavior of biological tissues under load is essential for understanding cellular activity and tissue functionality. Unconfined compression tests serve as a fundamental approach to investigating how different tissue models respond to mechanical stress, especially within the frameworks of biphasic and viscoelastic theories. This report aims to analyze, compare, and interpret the mechanical responses of a cylindrical tissue sample subjected to unconfined compression, focusing on biphasic and viscoelastic media, using finite element analysis via FEBio software.

Introduction

The interaction of mechanics and biology in tissue environments necessitates a comprehensive understanding of tissue behavior under load. The biphasic model considers the tissue as a combination of an elastic solid matrix and interstitial fluid, which contributes to load support, strain distribution, and fluid flow. Conversely, the viscoelastic model emphasizes time-dependent deformation characteristics arising from the material's inherent stress relaxation and creep abilities. Understanding the distinctions in these behaviors is pivotal for interpreting cellular mechanotransduction, tissue engineering, and pathophysiology.

This study's primary objectives are to simulate the unconfined compression of a cylindrical tissue specimen modeled as biphasic and viscoelastic media, evaluate their mechanical responses during the ramp phase and subsequent equilibrium, and discuss implications for the cellular stress environments within such tissues.

Methods

The finite element models consist of a 10 mm diameter and 3 mm height cylindrical specimen subjected to unconfined compression in FEBio. The meshes were discretized with a balanced number of nodes to optimize solution accuracy and computational efficiency, applying mesh refinement in regions of steep gradients.

For the biphasic material, the solid matrix is assigned an elastic response with a Young's modulus (E) of 100 MPa and a Poisson's ratio (n) of 0.3, alongside a constant permeability of 1 x 10^-15 m⁴/Ns. The initial solid volume fraction is set to 0.2, accommodating fluid flow through the porous matrix. Boundary conditions involve fixing the lateral surfaces to allow free fluid flow but restricting lateral displacement, while the top boundary is subjected to axial displacement corresponding to -0.1 strain at a rate of -0.01 s^-1, applied via a rigid, impermeable platen.

The viscoelastic model utilizes the same elastic parameters, but incorporates a time-dependent relaxation modulus articulated through the parameters ðº1 = 0.5 and relaxation time ð‘¡1 = 100. The constitutive relation captures the stress relaxation behavior typical of biological tissues, modeled as a Prony series expansion with three terms. The boundary and loading conditions mimic those in the biphasic case, ensuring consistent comparison.

Mesh sensitivity analyses informed the final discretization, with particular attention to regions expected to develop steep fluid pressure and strain gradients. Symmetry was exploited where applicable to reduce computation times.

Simulation outputs include stress, strain, pore pressure, and displacement fields over time during the ramp phase and towards equilibrium, facilitating detailed comparisons of material response characteristics.

Results

Figures 1 and 2 depict the axial stress versus time for biphasic and viscoelastic materials respectively. The biphasic response demonstrates a rapid rise in stress during the initial phase, driven by fluid pressurization, followed by a gradual decline as fluid redistributes and pressure dissipates. Conversely, the viscoelastic response exhibits a more gradual increase in stress, peaking sooner, and a clear relaxation over time characteristic of the model parameters, with stress declining steadily toward equilibrium (Figure 2).

Figure 3 illustrates the evolution of pore pressure within the biphasic medium, showing high pressures localized near the loading region during the ramp phase, which dissipate as fluid flows. The viscoelastic model, lacking fluid flow components, shows no pore pressure development but demonstrates internal stress redistribution as shown in Figures 4 and 5.

Displacement fields reveal comparable axial deformations, but the biphasic model exhibits slight lateral expansion due to fluid flow, while the viscoelastic model maintains more uniform deformation (Figures 6 and 7). Strain contours further emphasize differences in material deformation characteristics, particularly in the early loading phase.

The stress relaxation curves indicate that biphasic tissues predominantly support load through fluid pressurization initially, then gradually transition to matrix-dominated mechanics, whereas viscoelastic tissues sustain time-dependent stress decay based solely on material relaxation parameters (Figures 8 and 9).

Discussion

The biphasic model accurately captures load transfer via fluid pressurization, which is prominent during rapid loading cycles, consistent with experimental observations of cartilage and other soft tissues. Fluid flow allows tissues to support higher loads transiently and influences the cellular stress environment by modulating pore pressure distributions. The resulting pressure gradients have implications for nutrient transport, waste removal, and mechanotransduction at the cellular level.

In contrast, the viscoelastic model encapsulates the intrinsic time-dependent response of tissue fibers and matrix components, providing a framework for understanding stress relaxation and creep. The absence of fluid flow effects limits its applicability to tissues where fluid movement is restricted or negligible, such as dense connective tissues or fibrous tissues.

The differences in mechanical response impact cellular mechanotransduction pathways. Elevated pore pressures in biphasic tissues may lead to transient increased stresses on cells, affecting processes like matrix synthesis or inflammatory responses. Meanwhile, viscoelastic tissues generate more uniform cellular stress over time, influencing long-term tissue homeostasis and remodeling.

Implications for tissue engineering and disease modeling are significant. For instance, osteoarthritic cartilage exhibits altered biphasic behavior with impaired fluid pressurization, affecting its load-bearing capacity. Understanding these mechanics enables targeted therapeutic strategies and material design.

Conclusion

This study highlights fundamental differences in the mechanical behavior of biphasic and viscoelastic tissues under unconfined compression. Biphasic tissues rely heavily on fluid pressurization for load support, resulting in transient pressure distributions that influence cellular environments. Viscoelastic tissues primarily respond through intrinsic material relaxation, supporting sustained but time-dependent stresses. Recognizing these differences enhances our understanding of tissue mechanics and informs the development of biomaterials and therapeutic interventions.

References

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