Although the effects of dehydration on the mechanical behavior of cortical bone are known, the underlying mechanisms for such effects are not clear. We hypothesize that the interactions of water with the collagen and mineral phases each have a unique influence on mechanical behavior. To study this, strength, toughness, and stiffness were measured with three-point bend specimens made from the mid-diaphysis of human cadaveric femurs and divided into six test groups: control (hydrated), drying in a vacuum oven at room temperature (21 °C) for 30 min and at 21, 50, 70, or 110 °C for 4 h. The experimental data indicated that water loss significantly increased with each increase in drying condition. Bone strength increased with a 5% loss of water by weight, which was caused by drying at 21 °C for 4 h. With water loss exceeding 9%, caused by higher drying temperatures (≥70 °C), strength actually decreased. Drying at 21 °C (irrespective of time in vacuum) significantly decreased bone toughness through a loss of plasticity. However, drying at 70 °C and above caused toughness to decrease through decreases in strength and fracture strain. Stiffness linearly increased with an increase in water loss. From an energy perspective, the water-mineral interaction is removed at higher temperatures than the water-collagen interaction. Therefore, we speculate that loss of water in the collagen phase decreases the toughness of bone, whereas loss of water associated with the mineral phase decreases both bone strength and toughness.

We estimate the correlation coefficient between two variables with repeated observations on each variable, using linear mixed effects (LME) model. The solution to this problem has been studied by many authors. Bland and Altman (1995) considered the problem in many ad hoc methods. Lam, Webb and O'Donnell (1999) solved the problem by considering different correlation structures on the repeated measures. They assumed that the repeated measures are linked over time but their method needs specialized software. However, they never addressed the question of how to choose the correlation structure on the repeated measures for a particular data set. Hamlett et al. (2003) generalized this model and used Proc Mixed of SAS to solve the problem. Unfortunately, their method also cannot implement the correlation structure on the repeated measures that is present in the data. We also assume that the repeated measures are linked over time and generalize all the previous models, and can account for the correlation structure on the repeated measures that is present in the data. We study how the correlation coefficient between the variables gets affected by incorrect assumption of the correlation structure on the repeated measures itself by using Proc Mixed of SAS, and describe how to select the correlation structure on the repeated measures. We also extend the model by including random intercept and random slope over time for each subject. Our model will also be useful when some of the repeated measures are missing at random.

The risk of bone fracture depends in part on tissue quality, not just the size and mass. This study assessed the postyield energy dissipation of cortical bone in tension as a function of age and composition. Specimens were prepared from tibiae of human cadavers in which male and female donors were divided into two age groups: middle aged (51 to 56 years, n ¼ 9) and elderly (72 to 90 years, n ¼ 8). By loading, unloading, and reloading a specimen with rest periods inserted in between, tensile properties at incremental strain levels were assessed. In addition, postyield toughness was estimated and partitioned as plastic strain energy related to permanent deformation, released elastic strain energy related to stiffness loss, and hysteresis energy related to viscous behavior. Porosity, mineral and collagen content, and collagen crosslinks of each specimen were also measured to determine the micro-and ultrastructural properties of the tissue. Age affected all the energy terms plus strength but not elastic stiffness. The postyield energy terms were correlated with porosity, pentosidine (a marker of nonenzymatic crosslinks), and collagen content, all of which varied significantly with age. General linear models suggested that pentosidine concentration and collagen content provided the best explanation of the age-related decrease in the postyield energy dissipation. Among them, pentosidine concentration had the greatest contribution to plastic strain energy and was the best explanatory variable of damage accumulation. ß

Lymph node status, PR status, tumor size, differentiation, race, and marital status are valuable for prognostication in breast cancer. The prognostic groups derived can provide guidance for clinical trial design, patient management, and future treatment policy.