Elastodynamic optimization of architectured scaffolds

Biomechanics team of the Multiscale Modeling and Simulation laboratory (MSME), Université Paris-Est Créteil, CNRS (UMR 8208), Créteil, France (https://msme.univ-gustave-eiffel.fr/presentation/equipe-biomeca)

Context

A currently explored strategy in tissue engineering consists in leveraging architectured scaffolds to replace and subsequently repair bone defects. Such a strategy is likely to improve the biomechanical properties of the bone substitute in terms of strength, bone in-growth, and adhesion, thereby strengthening the anchoring mechanisms of the scaffold with its surrounding biological environment. In particular, this emerging field is now made possible thanks to the resolution and customization allowed by recent advances in additive manufacturing.

From a mechanical perspective, an architectured scaffold can be considered as a network of pores -filled by soft tissue, fluid, voids, or a combination thereof- periodically distributed within a rigid matrix. The primary process at play after its insertion is the scaffold resorption, concurrently with the gradual bone in-growth within the pores, which occurs at a length scale of a few hundred micrometers. In this sense, the unit cells of the scaffold (~1 mm), which can evolve both in time and space, are similar to the periodic structures studied in the field of elastic metamaterials (in the MHz regime). This analogy suggests using concepts and tools developed for metamaterials, in order to analyze the acoustic response of architectured scaffolds. Ultimately, such an approach could lead to the development of innovative methods of nondestructive testing by ultrasound, which would allow for the evaluation of the mechanical properties of scaffolds, their spatial organization, and their composition, at different healing times.

Objectives

The main objective of this project is to establish optimization strategies for architectured media to improve both their mechanical properties (taking into account biomechanical constraints) and their acoustic signatures. Here, acoustic signatures refer to the ability of the architectured medium to modulate its ultrasonic response (e.g., in terms of scattering, dispersion, or attenuation), as a function of the evolution of its biomechanical environment over time (in-growth and mineralization of the bone tissue within pores, scaffold resorption, etc.). The main tasks of the candidate will be: (i)~the modeling and numerical simulation of the elastic wave propagation in periodic architectured media and (ii)~the optimization of the unit cell (geometry, material, porosity) to maximize the acoustic signatures based on biomechanical constraints. In particular, we will take advantage of triply periodic minimal surfaces, which are acknowledged to amplify both acoustic and biomechanical features, such as the broadening of prohibited frequency bands and the promotion of osseointegration. An experimental validation step on samples obtained by additive manufacturing is planned too.

It should be noted that this internship is proposed within the frame of a project entitled `Quasiperiodic architectured bio-materials for bone substitutes', which is funded by the French National Research Agency (ANR). As such, the successful candidate will have the opportunity to continue his research within the framework of a PhD thesis, the funding of which is assured.

Required skills

The candidate must have a strong background in Solid Mechanics or Acoustics, with a particular interest in elastic waves. Skills in mechanical modeling and numerical simulation are an asset. A taste for experimental work and interdisciplinary collaboration is desirable.