Elastic wave propagation in periodic and quasiperiodic architectured materials with applications to bone scaffold monitoring

Scientific 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 [1].

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 regard, 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 [2]. 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 [3]. This study has been conceived and funded within the framework of the QBone research project, conducted in collaboration between the Laboratoire Modélisation et Simulation Multi Echelle (Université Paris-Est Créteil), the Institut Jean Le Rond d’Alembert (Sorbonne Université), and the Institut Mondor pour la Recherche Biomédicale (Université Paris-Est Créteil).

PhD Project

The main objective of this project is to establish optimisation strategies for architectured materials 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 [4]), as a function of the evolution of its biomechanical environment over time (in-growth and mineralisation of bone tissue within pores, scaffold resorption, etc.).

The main research activities include the:

• Numerical modelling of elastic wave propagation in periodic and quasi-periodic architectured materials and metamaterials;
• Extraction and analysis of acoustic signatures based on frequency bandgaps or other relevant acoustic features;
• Development of optimisation tools linking geometry, material properties and ultrasonic responses;
• Construction of a digital twin of scaffolds informed by growth and remodelling models (from other partners of the QBone project);
• Transfer of optimised designs towards an experimental validation in a laboratory-controlled environment.

References

[1] A. A. Zadpoor, Biomater. Sci., 8(1):18–38, 2020. [2] G. Rosi et al., Int. J. Solids Struct., 305:113059, 2024. [3] M. Gattin et al., Appl. Acoust., 217:109844, 2024. [4] M. Gattin et al., Ultrasonics, 131:106951, 2023.

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)

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.