Development of a numerical model representing antibacterial composite material

Background :

Dental implants are a major treatment solution for tooth replacement. Peri-implant infections are a very common complication due to ongoing exposure to infectious germs [1]. The main reason for this is inadequate decontamination of the implant surface. In this context, injectable composite materials offer an interesting clinical approach. The concept is based on the use of osteoconductive composite biomaterials combined with antibacterial molecules (generally antibiotics). The aim of this thesis project is to develop an osteoconductive antibacterial composite material (ACM). In addition to the challenges concerning the formulation of the ACM, its implementation and its experimental characterisation, the aim of this project is to develop a mathematical and numerical model that faithfully represents the physics and biological evolution in the material.

This is a fundamental aspect of controlling the use of these materials and adapting their composition to different patients.

Objectives et méthodology

In conjunction with the REGOS team, RMeS, UMR 1229 INSERM/Nantes Université/CHU (PHU4), the aim of this thesis project is to develop a multi-physics mathematical model (mechanics, diffusion, transport, chemistry) capable of accurately representing the phenomena taking place within MCAs and to implement it numerically in order to be able to make predictions that will enable the composition of the material to be optimised.

The planned methodology is as follows: :

•  Initially, a literature review and discussions with members of the REGOS team will be used to determine the main physical phenomena involved, their couplings and the mathematical models that can be used to represent them.
• An initial hierarchy of 1D models of increasing complexity will then be formulated, based on the thermodynamics of irreversible processes [2]. At each stage, these models will be validated numerically against reference solutions.
  The model obtained will take into account the different species involved and will be able to characterise their different kinetics. Couplings between physicochemistry and mechanics can be introduced at a later stage [3].
• This model will then be validated experimentally using the results obtained by the REGOS, PMN and BIOMEC teams (physico-chemistry, mechanics, rheology, cytocompatibility, osteoinduction). The numerical robustness of the model will also be assessed at this stage, including its sensitivity to the physical input parameters.
• Finally, the extension of the model will then be studied in the multi-dimensional case (2D, 3D) in order to get closer to physical reality in terms of geometric complexity. To do this, we will use the finite element method, based on the FEniCSx library. The accuracy, robustness and numerical efficiency of the model will be reassessed by comparison with the experimental campaign carried out previously.

[1] Rakic M, Galindo-Moreno P, Monje A. et al. How frequent does peri-implantitis occur? A systematic review and meta-analysis. Clin Oral Investig. 2018, 22(4):1805-1816.

[2] De Anda Salazar J., Développement de modèles variationnels et de stratégies algorithmiques pour les problèmes couplés. Thèse de doctorat, Ecole Centrale de Nantes (2019).

[3] Ganghoffer J.-F., Rahouadj R., Boisse J. et al., Phase field approaches of bone remodeling based on TIP, Journal of Non-Equilibrium Thermodynamics, 41 (2016), 49-75.

Partnership :

This project is part of a multi-disciplinary context and will be conducted in conjunction with :

• The REGOS team, RMeS, UMR 1229 INSERM/Nantes Université/CHU (PHU4)
• The PMN team, Institut des Matériaux de Nantes, UMR 6502 CNRS/Nantes Université
• GeM’s MECNUM et BIOMEC Thematic research units, UMR 6183 CNRS/Nantes Université/Ecole Centrale de Nantes

Location and supervision :
The thesis work will be carried out at the GeM institute (Civil and Mechanical Engineering Research Institute), on the Ecole Centrale de Nantes campus, in close collaboration with the project partners.

Centrale Nantes provides initial and continuing education for engineers in the scientific, technological and economic fields, as well as in the social and human sciences. It provides research training leading to doctorates and other national postgraduate degrees.

Centrale Nantes conducts fundamental and applied research in scientific and technical fields. It contributes to the development of the results obtained, to the dissemination of scientific and technical information and to international cooperation.

On its campus, the school has 2,200 students (engineering students, continuing education students, masters and doctoral students) and 400 research staff, including 150 teacher-researchers and researchers who belong to research laboratories.

GeM is a joint Research Center of Centrale Nantes, University of Nantes and CNRS (French National Research Center). It brings together the expertise of the Nantes Saint-Nazaire area in the field of civil engineering, mechanics of materials and processes, modeling and simulation in structural mechanics.

GeM gathers around 240 people, with 80 faculty members, 50 administrative and support staff, around 100 doctoral students and 10 post-doc.

GeM is also involved at Master level, and offers several Master programs in mechanics, civil engineering, and marine technology.

The research activities at GeM aim to develop innovative manufacturing processes, simulation tools suited for the design of parts, engineering structures and products lifecycle management, taking into account the influence of severe loadings and environmental actions.

Master 2 in mechanics, biomechanics, mechanical engineering, applied mathematics, interest in numerical approaches.