Numerical and Experimental Investigation of Fluid Flow in the Bone Lacuno-Canalicular Network

Context

Bone is a porous, multiscale biological material in which fluid flow plays an important role in the mechanical response of the tissue. The lacuno-canalicular network (LCN), which is connected to the vascular network, constitutes a highly complex porous system at the submicrometric scale. However, fluid exchanges between the LCN and the vascular network, as well as the spatial heterogeneity of the LCN permeability, are still poorly understood and are often neglected in current numerical models.

The increase in intramedullary pressure (ImP) observed during mechanical loading suggests that the vascular network is not completely drained and may therefore contribute significantly to the fluid behavior within bone. A better understanding of fluid flow at both the vascular and LCN scales is consequently required to improve the numerical description of bone fluid transport during mechanical loading.

Objective of the PhD Thesis

The objective of this PhD thesis is to investigate fluid behavior within the vascular and lacuno-canalicular networks of bone through a combination of experimental characterization, computational homogenization, machine learning and numerical modeling.

The work will focus in particular on characterizing fluid flow within the vascular network during mechanical loading, estimating the spatial distribution of LCN permeability from realistic bone microstructures, and developing a numerical twin capable of describing fluid pressure and velocity within the bone matrix.

The numerical and experimental approaches will be developed in close interaction in order to improve the understanding of fluid exchanges between the LCN and vascular networks and to assess the influence of intramedullary pressure on bone fluid behavior.

Missions

• Characterization of fluid behavior at the vascular scale

An original experimental method based on X-ray tomography and particle velocimetry will be developed to characterize fluid motion within the bone vascular network during mechanical loading. The method will rely on an initial tomographic acquisition to characterize the three-dimensional architecture of the sample, followed by fast bi-planar radiographic acquisitions using the DTHE (Double Tomographe à Haute Energie) available at INSA Lyon.

A simplified and upscaled model of the vascular porosity will first be manufactured by 3D printing transparent polymer structures containing one or two vascular canals. This model will be used to optimize the experimental methodology and determine appropriate parameters, including the fraction and density of radio-opaque particles as a function of pore size and fluid properties.

An upscaled bone model based on µCT data will subsequently be developed to investigate both drained and undrained conditions. Once optimized, the method will be applied to real bone samples in order to characterize fluid behavior within realistic vascular architectures. The experimental results will provide boundary conditions for the numerical twin developed in the subsequent stage of the project.

• Estimation of LCN permeability from realistic geometries

The permeability of the LCN is a key parameter for numerical modeling of fluid flow in bone. While current models often rely on a single permeability value, the intrinsic permeability of the canaliculi is expected to vary spatially according to their location within the network.

A large dataset of 27 human femoral diaphysis bone samples, acquired using nano-CT at the ESRF, provides realistic three-dimensional descriptions of the LCN at a voxel size of 100 nm. Preliminary work has already enabled an estimation of LCN permeability from realistic canalicular morphologies using the Kozeny relationship.

The PhD student will develop a computational framework combining computational homogenization and machine learning to obtain fast and accurate predictions of effective bone permeability while limiting the need for computationally expensive direct numerical simulations (DNS).

The dataset will combine realistic porous morphologies with mechanical loading parameters and computational simulations of interstitial fluid flow. In particular, graph neural networks will be investigated to represent the interconnected canalicular system and predict effective transport properties from the underlying network architecture.

• Development of a numerical twin to investigate the influence of intramedullary pressure

Based on the experimental characterization of vascular fluid behavior and the homogenized description of LCN permeability, a numerical twin of the mechanical loading experiments will be developed.

The bone sample will be modeled as a biporous medium accounting for both vascular and LCN permeabilities. A poroelastic framework will be used to predict fluid pressure and flow during mechanical loading under controlled boundary conditions.

In close interaction with the experimental work, the model will be progressively simplified and calibrated to reproduce the experimental response, including pressure relaxation curves. The vascular network obtained from µCT data and the spatial distribution of LCN permeability obtained from the previous task will be incorporated into the model.

The local elastic properties of the bone matrix will also be estimated using micromechanical homogenization based on mineral density measurements obtained from tomography. The numerical model will reproduce the experimental boundary conditions and provide estimates of fluid velocity and pressure throughout the bone matrix during loading.

The final objective will be to quantify the respective contributions of intramedullary pressure and matrix deformation to fluid behavior within the LCN and vascular networks.

Le MSME a pour ambition d’apporter des contributions dans les domaines de la ville durable, de l’environnement, des matériaux et de la santé en se basant sur la synergie de compétences pointues en modélisation et simulation impliquant la mécanique, le transfert de chaleur et de matière, la biomécanique et la chimie théorique.

Cette association originale est à la base du développement de stratégies de recherche multi-échelles (de l’échelle atomique à celle des milieux continus) et pluridisciplinaires innovantes, dont les applications concernent les matériaux et structures du génie civil et du génie mécanique, la récupération d’énergie, la pollution de l’air, la micro et nano-fluidique, les tissus vivants et les implants.

Le laboratoire occupe une place particulière dans le paysage scientifique français par les thématiques développées dans ses équipes et les activités développées dans les thématiques transversales :

1- La chimie quantique, ou chimie in silico, pour l’étude de la structure électronique et la dynamique des noyaux (spectroscopie et réactivité) de systèmes moléculaires de petite et moyenne taille et les développements méthodologiques associés

2- La mécanique des milieux continus pour :
l’élaboration de méthodologies de modélisation et d’outils de simulation numérique permettant de mieux comprendre et maîtriser le comportement mécanique et physique des matériaux et des structures
la modélisation et la simulation des transferts de masse et de chaleur par convection
la modélisation et la simulation du comportement mécanique des matériaux vivants en prenant en compte divers niveaux structurels

3- La modélisation et la simulation multi-échelle, de la molécule aux systèmes macroscopiques où les changements d’échelle s’accompagnent d’un changement de physique.

Le MSME a été créé en 2008 et est devenu une unité mixte de recherche en 2010. Il se trouve sous la triple tutelle du CNRS, de l’UGE et de l’UPEC. Le laboratoire se compose de quatre équipes disciplinaires : chimie théorique, mécanique, transferts de chaleur et de matière et biomécanique.

Profile

• Master's degree in Mechanical Engineering, Biomedical Engineering, Computational Mechanics or a related field
• Strong background in mechanics and numerical modeling
• Interest in biomechanics, porous media and fluid–structure interactions
• Good analytical and problem-solving skills
• Ability to work independently while collaborating effectively within a multidisciplinary research team
• Good scientific writing and communication skills in English

Knowledge of the following would be an advantage

• Good knowledge of continuum mechanics and mechanics of materials
• Strong skills in numerical simulation and computational modeling
• Knowledge of finite element methods and/or computational fluid dynamics
• Experience with image-based modeling, µCT or 3D image processing would be an advantage
• Knowledge of machine learning, graph neural networks and/or computational homogenization would be appreciated
• Programming skills in Python, MATLAB, C++ or a similar language
• Ability to analyze and interpret experimental and numerical data
• Good command of written and spoken English
• Ability to work autonomously while demonstrating strong teamwork skills