Nicolas Bochud (MSME, Université Paris-Est)

Tracking the evolution of ultrasonic signatures of multiphase architectured media:
An application to biomechanics

N. Bochud¹, M. Gattin¹, Q. Grossman², D. Ruffoni², G. Rosi¹, and S. Naili¹

1. Univ Paris Est Creteil, Univ Gustave Eiffel, CNRS, UMR 8208, MSME, F-94010 Créteil, France
2. Mechanics of Biological and Bioinspired Materials Laboratory, Department of Aerospace
and Mechanical Engineering, University of Liège, B-4000 Liège, Belgium

Currently explored strategies in tissue engineering take advantage of architectured scaffolds to replace
damaged bone tissue, and this mainly for two reasons. First, as compared to bulk implants, architectured
scaffolds are suspected to enhance biomechanical properties in terms of strength, bone in-growth, and
adhesion to bone tissue. Second, their use is also expected to help reducing the stress shielding phenomenon
by decreasing the mismatch of properties between the bone substitute and its biological environment, for
instance by optimizing the material distribution across the scaffold. From a mechanical viewpoint, tissue
engineering scaffolds can be considered as multiphase architectured media, which consist of periodic arrays
of soft inclusions (tissue, fluid, voids, or some combination thereof) embedded in a hard scaffold matrix. The
primary process at play after their 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. Thereby, their
mechanical behavior is function of the properties of the constituent phases, their respective volume
fractions, and the topology of the unit cell, all of which being time dependent (at the biological time scale of
several weeks). Such complex scenario requires the development of monitoring strategies to assess the
mechanical performance of scaffolds, while preserving their structural integrity.

Interestingly, from an acoustic viewpoint, architectured scaffolds act as bulk phononic crystal analogs,
and should therefore support elastic wave propagation in the megahertz (MHz) regime, whose frequency-
dependent nature is acknowledged to arise from a combination of internal resonances of the unit cells and
wave interferences (Bragg scattering). In this talk, I will report on the reflection and transmission of elastic
waves propagating through water-immersed architectured samples in the MHz regime, which exhibit a
periodic organization at a length scale of a few hundred micrometers. Experimental outcomes, which span a
range of scaffold-like samples engineered to mimic the expected variations that take place in a biological
environment (e.g., varying volume fraction of the constituent phases, stiffening of the inclusions), will be
systematically compared with modeled predictions. A particular attention will be given to critical modeling
considerations, such as the behavior in reflection, the interaction of Bloch waves with the viscoelastic
properties of the constituent phases, as well as the role of modal conversion at the interface between the
homogeneous incident medium and the architectured one. Altogether, the reported results will show that
specific ultrasonic signatures associated with elastic wave propagation in periodic media, encompassing
phenomena such as dispersion, attenuation, and bandgaps, could offer valuable insights towards the
nondestructive monitoring of micro-architectured media like scaffolds.

[1] M. Gattin, N. Bochud, G. Rosi, Q. Grossman, D. Ruffoni, and S. Naili. Ultrasound characterization of the
viscoelastic properties of additively manufactured photopolymer materials. J. Acoust. Soc. Am., 152(3):
1901–1912, 2022.

[2] M. Gattin, N. Bochud, G. Rosi, Q. Grossman, D. Ruffoni, and S. Naili. Ultrasonic bandgaps in viscoelastic
1D-periodic media: Mechanical modeling and experimental validation. Ultrasonics, 131: 106951, 2023.

[3] M. Gattin, N. Bochud, Q. Grossman, D. Ruffoni, G. Rosi, and S. Naili. Ultrasound monitoring of multiphase
architectured media: Bandgap tracking via the measurement of the reflection coefficient. Appl. Acoust., 217:
109844, 2024.