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A mixture theory-based finite element formulation for the study of biodegradation of poroelastic scaffolds

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Abstract

Surgical implants, known as Tissue Engineered Nerve Guides (TENGs) are often inserted to provide alignment and mechanical support to broken or damaged nerves. These implants are designed to be poroelastic and biodegradable, and the ideal rate of degradation would be that equal to the rate of regrowth of the recovering nerve. Inspired by the design of these TENGs, we develop a mixture theory based mathematical model to simulate the degradation of a poroelastic solid immersed in a fluid bath. The temporal evolution of the solid’s mechanical and transport properties is also modeled. The model comprises of the degrading solid, the degradation reaction products, and the fluid in which the solid is immersed. The resultant governing equations are formulated in an Arbitrary Lagrangian–Eulerian (ALE) framework. The weak formulation of the partial differential equations (PDEs) so derived is numerically implemented using a finite element method (FEM). The numerical model is studied for stability and convergence rates using the Method of Manufactured Solutions.

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Notes

  1. This notation is typical in the fluid mechanics literature (cf. [11]). In the continuum mechanics literature, the operation in question is typically denoted by \(( \nabla _{{\mathbf {x}}}{\mathbf {v}} ){\mathbf {u}}\) (cf. [7, 19]).

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Acknowledgements

This work was supported by the U.S. National Science Foundation (CMMI 1537008).

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Authors and Affiliations

  1. Center for Neural Engineering, W-321 Millenium Science Complex, The Pennsylvania State University, University Park, PA, 16802, USA

    Priyanka Patki

  2. Center for Neural Engineering, W-315 Millenium Science Complex, The Pennsylvania State University, University Park, PA, 16802, USA

    Francesco Costanzo

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  1. Priyanka Patki
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Correspondence to Priyanka Patki.

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Patki, P., Costanzo, F. A mixture theory-based finite element formulation for the study of biodegradation of poroelastic scaffolds. Comput Mech 66, 351–371 (2020). https://doi.org/10.1007/s00466-020-01854-w

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