Caractérisation géométrique par la logique floue et simulation de la résorption cellulairement assistée de substituts poreux pour tissus osseux par microtomographie à rayons X

The objective of this thesis is to provide an improved characterization of porous scaffolds. A more focused objective is to provide a computational model simulating the cell mediated resorption process of resorbable bone substitutes. The thesis is structured in three scientific manuscripts. The first manuscript used fuzzy-based image treatment methods to analyse images generated by micro-computed tomography. From the literature, it is known that the fuzzy-based method helps to improve the accuracy of the characterization, in particular for scaffolds featuring a relatively small pore size. In addition, a new algorithm was introduced to determine both pore and interconnection sizes. The surface area of bone substitutes was quantified by using marching cube algorithm. Besides, the so-called Lattice Boltzmann method was used to characterize the permeability of the investigated scaffolds. Scaffolds made of [béta]-tricalcium phosphate ([béta]-Ca[subscript 3](PO[subscript 4])[subscript 2]) and presenting a constant porosity and four variable pore sizes were examined. The average pore size (diameter) of the four bone substitute groups (denominated with a letter from group A to D) was measured to be 170.3«1.7, 217.3«5.2, 415.8«18.8 and 972.3«10.9 [micro]m. Despite this significant change in pore size, the pore interconnection size only increased slightly, in the range of 61.7 to 85.2 [micro]m. The average porosity of the four groups was 52.3«1.5 %. The surface density of scaffolds decreased from 11.5 to 3.3 mm[superscript -1], when the pore size increased. The results revealed that the permeability of scaffolds is in the same order of magnitude and increased from 1.1?10[superscript -10] to 4.1?10[superscript -10] m[superscript 2] with increasing the pore size. The second manuscript was devoted to the use of subvoxelization algorithm and high-resolution scanner, in an attempt to further improve the accuracy of the results, in particular, of the small pore scaffolds. As expected, an increase of the image resolution from 15 to 7.5 [micro]m significantly eased the segmentation process and hence improved scaffold characterization. Subvoxelization also improved the results specifically in terms of interconnection sizes. Specifically, much smaller interconnection sizes were yielded after applying the subvoxelization process. For example, the mean interconnection size of small pore size groups, group A and B, dropped from 63 to 20 and 30 [micro]m, respectively. Furthermore, due to more details obtained from subvoxelization and high-resolution scanning, additional effects so called"boundary effects" were observed. The boundary effects can yield misleading results in terms of interconnection sizes. The means to reduce these effects were proposed. The third manuscript focused on the simulation and understanding of cell mediated resorption of bone graft substitutes. A computer model was developed to simulate the resorption process of four bone substitute groups. [mu]CT data and new"image processing" tools such as labelling and skeletonization were combined in an algorithm to perform the steps of resorption simulation algorithm. The proposed algorithm was verified by comparing simulation results with the analytical results of a simple geometry and biological in vivo data of bone substitutes. A correlation coefficient between the simulation results and both analytical and experimental data, was found to be larger than 0.9. Local resorption process revealed faster resorption in external region specifically at earlier resorption time. This finding is in agreement with the in vivo results. Two definitions were introduced to estimate the resorption rate; volume resorption rate and linear resorption rate. The volume resorption rate was proportional to accessible surface and decreased when the pore size increased, while the linear resorption rate was proportional to thickness of material and increased with increasing the pore size. In addition, the simulation results revealed no effect of resorption direction on resorption behaviour of substitutes. However, the resorption rate of small pore size samples was decreased with increasing the minimum interconnection size required for cell ingrowth, to 100 [micro]m. This thesis combined novel"image processing" tools and subvoxelization method to improve the characterization of porous bone substitutes used in the bone repair process. The improved characterization allowed a more accurate simulation process. The simulation data were consistent with previously obtained biological data of the same group and allows understanding the local resorption process. The available tools and results are expected to help with the design of optimal substitute for bone repair."--Résumé abrégé par UMI

Assessing cortical bone mechanical properties using collagen proton fraction from ultrashort echo time magnetization transfer (UTE-MT) MRI modeling.

Cortical bone shows as a signal void when using conventional clinical magnetic resonance imaging (MRI). Ultrashort echo time MRI (UTE-MRI) can acquire high signal from cortical bone, thus enabling quantitative assessments. Magnetization transfer (MT) imaging combined with UTE-MRI can indirectly assess protons in the organic matrix of bone. This study aimed to examine UTE-MT MRI techniques to estimate the mechanical properties of cortical bone. A total of 156 rectangular human cortical bone strips were harvested from the tibial and femoral midshafts of 43 donors (62 ± 22 years old, 62 specimens from females, 94 specimens from males). Bone specimens were scanned using UTE-MT sequences on a clinical 3 T MRI scanner and on a micro-computed tomography (μCT) scanner. A series of MT pulse saturation powers (400°, 600°, 800°) and frequency offsets (2, 5, 10, 20, 50 kHz) was used to measure the macromolecular fraction (MMF) utilizing a two-pool MT model. Failure mechanical properties of the bone specimens were measured using 4-point bending tests. MMF from MRI results showed significant strong correlations with cortical bone porosity (R = -0.72, P < 0.01) and bone mineral density (BMD) (R = +0.71, P < 0.01). MMF demonstrated significant moderate correlations with Young modulus, yield stress, and ultimate stress (R = 0.60-0.61, P < 0.01). These results suggest that the two-pool UTE-MT model focusing on the organic matrix of bone can potentially serve as a novel tool to detect the variations of bone mechanical properties and intracortical porosity

Caractérisation géométrique par la logique floue et simulation de la résorption cellulairement assistée de substituts poreux pour tissus osseux par microtomographie à rayons X

The objective of this thesis is to provide an improved characterization of porous scaffolds. A more focused objective is to provide a computational model simulating the cell mediated resorption process of resorbable bone substitutes. The thesis is structured in three scientific manuscripts. The first manuscript used fuzzy-based image treatment methods to analyse images generated by micro-computed tomography. From the literature, it is known that the fuzzy-based method helps to improve the accuracy of the characterization, in particular for scaffolds featuring a relatively small pore size. In addition, a new algorithm was introduced to determine both pore and interconnection sizes. The surface area of bone substitutes was quantified by using marching cube algorithm. Besides, the so-called Lattice Boltzmann method was used to characterize the permeability of the investigated scaffolds. Scaffolds made of [béta]-tricalcium phosphate ([béta]-Ca[subscript 3](PO[subscript 4])[subscript 2]) and presenting a constant porosity and four variable pore sizes were examined. The average pore size (diameter) of the four bone substitute groups (denominated with a letter from group A to D) was measured to be 170.3«1.7, 217.3«5.2, 415.8«18.8 and 972.3«10.9 [micro]m. Despite this significant change in pore size, the pore interconnection size only increased slightly, in the range of 61.7 to 85.2 [micro]m. The average porosity of the four groups was 52.3«1.5 %. The surface density of scaffolds decreased from 11.5 to 3.3 mm[superscript -1], when the pore size increased. The results revealed that the permeability of scaffolds is in the same order of magnitude and increased from 1.1?10[superscript -10] to 4.1?10[superscript -10] m[superscript 2] with increasing the pore size. The second manuscript was devoted to the use of subvoxelization algorithm and high-resolution scanner, in an attempt to further improve the accuracy of the results, in particular, of the small pore scaffolds. As expected, an increase of the image resolution from 15 to 7.5 [micro]m significantly eased the segmentation process and hence improved scaffold characterization. Subvoxelization also improved the results specifically in terms of interconnection sizes. Specifically, much smaller interconnection sizes were yielded after applying the subvoxelization process. For example, the mean interconnection size of small pore size groups, group A and B, dropped from 63 to 20 and 30 [micro]m, respectively. Furthermore, due to more details obtained from subvoxelization and high-resolution scanning, additional effects so called"boundary effects" were observed. The boundary effects can yield misleading results in terms of interconnection sizes. The means to reduce these effects were proposed. The third manuscript focused on the simulation and understanding of cell mediated resorption of bone graft substitutes. A computer model was developed to simulate the resorption process of four bone substitute groups. [mu]CT data and new"image processing" tools such as labelling and skeletonization were combined in an algorithm to perform the steps of resorption simulation algorithm. The proposed algorithm was verified by comparing simulation results with the analytical results of a simple geometry and biological in vivo data of bone substitutes. A correlation coefficient between the simulation results and both analytical and experimental data, was found to be larger than 0.9. Local resorption process revealed faster resorption in external region specifically at earlier resorption time. This finding is in agreement with the in vivo results. Two definitions were introduced to estimate the resorption rate; volume resorption rate and linear resorption rate. The volume resorption rate was proportional to accessible surface and decreased when the pore size increased, while the linear resorption rate was proportional to thickness of material and increased with increasing the pore size. In addition, the simulation results revealed no effect of resorption direction on resorption behaviour of substitutes. However, the resorption rate of small pore size samples was decreased with increasing the minimum interconnection size required for cell ingrowth, to 100 [micro]m. This thesis combined novel"image processing" tools and subvoxelization method to improve the characterization of porous bone substitutes used in the bone repair process. The improved characterization allowed a more accurate simulation process. The simulation data were consistent with previously obtained biological data of the same group and allows understanding the local resorption process. The available tools and results are expected to help with the design of optimal substitute for bone repair."--Résumé abrégé par UMI

Pore-scale analysis of Newtonian flow in the explicit geometry of vertebral trabecular bones using lattice Boltzmann simulation

The geometric and transport properties of trabecular bone are of particular interest for medical engineers active in orthopaedic applications and more specifically in hard tissue implantations. This article resorts to computational methods to provide some understanding of the geometric and transport properties of vertebral trabecular bone. A fuzzy distance transform algorithm was used for geometric analysis on the pore scale, and a lattice Boltzmann method (LBM) for the simulation of flow on the same scale. The transport properties of bone including the pressure drop, elongation, and shear component of dissipated energy, and the tortuosity of the bone geometry were extracted from the results of the LBM flow simulations. Whenever suitable, dimensionless numbers were used for the analysis of the data. The average pore size and distribution of the bone were found to be 746μm and between 75 and 2940μm, respectively. The permeability of the flow in the cavities of the specific bone sample was found to be 5.05×10-8 m2 for the superior—inferior direction which was by a factor of 1.5—1.7 higher than the permeability in the other two anatomical directions (anterior—posterior). These findings are consistent with experimental results found 3 years prior independently. Tortuosity values approached 1.05 for the superior—inferior direction, and 1.13 and 1.11 for the other two perpendicular directions. The low tortuosities result mainly from the large bone porosity of 0.92. The flow on the pore scale seems to be shear dominated but 30 per cent of the energy dissipation was because of elongational effects. The converging and diverging geometry of the bone explains the significant elongation and deformation of the fluid elements. The transition from creeping flow (the Darcy regime), which is of interest to vertebral augmentation and this study, to the laminar region with significant inertia effects took place at a Reynolds number of about 1—10, as usual for porous media. Finally, the authors wish to advise the readers on the significant computational requirements to be allocated to such a virtual test bench

Ultrashort echo time magnetization transfer (UTE-MT) imaging of cortical bone

Magnetization transfer (MT) imaging is one way to indirectly assess pools of protons with fast transverse relaxation. However, conventional MT imaging sequences are not applicable to short T2 tissues such as cortical bone. Ultrashort echo time (UTE) sequences with TE values as low as 8μs can detect signals from different water components in cortical bone. In this study we aim to evaluate two-dimensional UTE-MT imaging of cortical bone and its application in assessing cortical bone porosity as measured by micro-computed tomography (μCT) and biomechanical properties. In total, 38 human cadaveric distal femur and proximal tibia bones were sectioned to produce 122 rectangular pieces of cortical bone for quantitative UTE-MT MR imaging, μCT, and biomechanical testing. Off-resonance saturation ratios (OSRs) with a series of MT pulse frequency offsets (Δf) were calculated and compared with porosity assessed with μCT, as well as elastic (modulus, yield stress, and strain) and failure (ultimate stress, failure strain, and energy) properties, using Pearson correlation and linear regression. A moderately strong negative correlation was observed between OSR and μCT porosity (R2=0.46-0.51), while a moderate positive correlation was observed between OSR and yield stress (R2=0.25-0.30) and failure stress (R2=0.31-0.35), and a weak positive correlation (R2=0.09-0.12) between OSR and Young's modulus at all off-resonance saturation frequencies. OSR determined with the UTE-MT sequence provides quantitative information on cortical bone and is sensitive to μCT porosity and biomechanical function