M. Bashoor Zadeh, M. Bohner, G. Baroud (Sherbrooke, Canada – Bettlach, Switzerland)
INTRODUCTION: A mineral bone substitute is a resorbable porous structure to support healing of a damaged bone. Predicting the in-vivo behaviour of a mineral bone substitute is of significant importance to design an effective scaffold. Recently, a theoretical model has been developed [1] developed that estimates the cell-mediated resorption rate of a bone substitute by assuming that (i) the linear resorption of the solid surface is constant (ii) provided the surface can be reached by blood vessels and cells (interconnection diameter > 0.05mm). This study presents a numerical algorithm applied to bone substitutes with complex geometries. The substitutes were reconstructed using fuzzy image processing tools. The proposed algorithm is validated by comparing its results with the analytical results of a simple geometry and experimental data of a more complex scaffold.
METHODS: A porous bone substitute was first scanned by a micro-computed tomography system. The pores of the sample were then reconstructed using skeleton points that extracted based on the 3D fuzzy distance transform map and ridge detection method.
The resorption simulation was performed in two steps: (a) colonization of a pore by resorbing cells, (b) resorption of the bone substitute material. For the colonization step, it is required to enlarge (or create) the pores and interconnections to enable in-growth of blood vessels. Hence, at the skeleton points, the algorithm compares the size of pores and interconnections with the size of the blood vessels to find the new accessible pores for resorbing cells. Once the pore is invaded by resorbing cells, the next step is started to resorb the bone substitute material at the interface surface. In addition, resorbing the material leads to enlarge the pores and interconnections which are too small for blood vessels. These steps were repeated for each pore until the structure was fully resorbed.
RESULTS: Fig. 1 compares the simulation results of the algorithm against the analytical results of the theoretical model [1] for a simple cubical block with constant width of 5 mm and average inter-pore distance of 22 μm. Due to the proportionality of resorption time and total layer thickness resorbed for full resorption of scaffold material, a similar ratio was expected for all cases. The discrepancy among the results can be justified by the limitation of voxel size, especially for models with small pore radius (e.g. 100 and 200 μm).
Fig.1- Analytical and simulation results of FCC lattice of pores with various pore size.
Fig. 2 compares the simulation results against the experimental data presented in [2]. The correlation coefficient (R2) between experimental and simulation data is above 0.8. Consistent with experimental results, the algorithm indicates that the resorption rate decreases as the time marches. The fastest resorption rate is experienced at the beginning of the process.
Fig.2- Experimental and simulation data of real bone substitute structure.
CONCLUSION: The proposed algorithm estimates resorption process of mineral bone substitutes that helps to better understand the in-vivo behavior of them. The algorithm can also be used as a design tool to improve the geometrical parameters of bone substitutes.
ACKNOWLEDGMENT: The authors would like to thank S. Allen for the supports provided to optimize the resorption simulation code.
REFERENCES: 1. M. Bohner and F. Baumgart; Biomaterials 25 (2004) 3569-82.
2. M.C. von Doernberg, et al, Biomaterials 27 (2006) 5186-98.