Refining anticipation of degraded bone microstructures during osteoporosis based on statistical homogenized reconstruction method via quality of connection function

Abstract

Nowadays, osteoporosis disease that is related to aging has become a proliferating problem in worldwide society. It is therefore crucial to understand its evolution and predict this phenomenon precisely for different types of bone and volume fractions with adequate mathematical model. The application of statistical reconstruction method would be a helpful tool to predict osteoporosis for the simplified bone microstructures. To model osteoporosis evolution over time, in a first step, we propose to degrade the volume fraction with a mathematical model to reach any determined volume fraction between the initial condition and the degraded one with a statistical interpolation. In a second step, the degraded microstructure will be optimized using a statistical descriptor. The final optimized microstructures will be discussed as a function of the effective mechanical properties. The capability of quality of connection and two-point correlation functions (TPCFs) in 3D models and their application in the optimization of reconstructed interpolated models are going to be demonstrated. Finally, we will demonstrate and discuss the advantages of using the Quality of Connection Function (QCF) as a replacement of TPCF over the sole statistical descriptor named TPCF. We will show that QCF descriptor is better than TPCF only to find the optimized reconstructed models in a determined volume fraction.

A New Statistical Descriptor for the Physical Characterization and 3D Reconstruction of Heterogeneous Materials

“…Future works include evaluating the capability of QCF to adequately reconstruct 3D microstructures accounting for the heterogeneous distribution. This work was started in Famouri et al (2021), who showed that the microstructures chosen by QCF in the reconstruction process of 3D trabecular bone were more accurate compared to the one chosen by TPCF.…”

Prediction of Cortical Bone Thickness Variations in the Tibial Diaphysis of Running Rats

“…For this reason, some models have tried to bridge the different scales of bone remodeling (see, e.g., [15][16][17][18]). However, the limited knowledge of bone mechanobiological functioning remains a gap difficult to bridge to validate these models on human patients, particularly when accounting for patient dependency [19][20][21]. It is possible, at the macroscopic scale, to integrate more complex mechanical behavior in order to try accessing the local microstructure distribution that influences the bone density variation, either with or without an implant [22][23][24][25][26][27].…”

Prediction of bone microstructures degradation during osteoporosis with fuzzy cellular automata algorithm

“…Around macroscopic bone stimulus described generally in Hart [15], Giorgio et al [16] applied to specific microstructured media [17], many researches include the range of adaptative response [18][19][20][21], more physiological approaches [22], optimal response [23][24][25], including viscous and diffusive phenomena [26,27], and cellular automata (CA) [28]. Lately, Famouri et al [29] and Bagherian et al [30] developed a statistical function called quality of connection to more accurately predict the microstructure evolution of bone during osteoporosis based on its volume fraction. But the difficulty lies in the fact that the use of classical continuum mechanics fails when trying to model the local bone mechanobiological effects, particularly at a cellular level, since the continuity of the material is not realistic anymore [31][32][33].…”