The deterioration of the musculoskeletal system is a serious health concern for long term space missions. The accumulated information over the past decades of space flights showed that microgravity impacts significantly the musculoskeletal system with muscle atrophy and bone loss. Until now, it has been difficult to make reasonable predictions of the bone loss for prolonged space missions due to the lack of in-space experimental data and weak understanding of the mechanobiological bone mechanisms. On earth, the healthy musculoskeletal degradation is mainly age related with osteoporosis and delayed fracture healing. A better understanding of the bone mechanobiological functions could help us improve our model predictions of the musculoskeletal health system during long term space missions.We develop a numerical model able to predict the bone loss at the mesoscopic scale (bone trabecula) in microgravity. The model is able to correlate the calculated bone degradation mechanism with data available in the literature showing the effective bone density loss measured experimentally. An optimization algorithm is used for an average bone microstructure distribution and long-term prediction. Extrapolation is made to link the local bone loss at the structural scale with the corresponding effective bone strength. The first part of the paper details the extraction of the bone microstructure using micro-CT images and numerical model development. Next, the degradation and optimization schemes are detailed. Finally, some results are presented for long term degradation.

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.

3D reconstruction of heterogeneous materials from 2D images is essential for a precise characterization of their physical properties (mechanical, thermal, electrical and so on). For this, statistical descriptors such as two-point correlation function (TPCF), lineal path function (LPF), or two-point correlation cluster function (TPCCF) are frequently used. But the effective properties of the reconstructed microstructures are not always corresponding to the real ones as the statistical distribution functions may distribute the material microstructure in a different way from the original one. This is more pronounced for cellular and porous materials such as trabecular bone, fuel cell, and rocks where the connectivity between clusters is not well correlated to the one of real material and degrades the materials physical behavior predictions. This paper proposes a new statistical descriptor, called Quality of Connection function (QCF), able to determine the quality of connections between clusters and has detailed statistical information about the microstructure distribution. The proposed descriptor is tested on trabecular bone obtained from X-ray micro-computed tomography, and used as example of heterogeneous material having a complex microstructure. Effective properties such as Young Modulus were calculated for these microstructures and compared with real ones. The new descriptor shows improved capacity to describe the material microstructure distribution and prediction of its physical properties.