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Experiments have shown that external mechanical loading plays an important role in bone development and remodeling. In fact, recent research has provided evidence that osteocytes can sense such loading and respond by releasing biochemical signals (mechanotransduction, MT) that initiate bone degradation or growth. Many aspects on MT remain unclear, especially at the cellular level. Because of the extreme hardness of the bone matrix and complexity of the microenvironment that an osteocyte lives in, in vivo studies are difficult; in contrast, modeling and simulation are viable approaches. Although many computational studies have been carried out, the complex geometry that can involve 60+ irregular canaliculi is often simplified to a select few straight tubes or channels. In addition, the pericellular matrix (PCM) is usually not considered. To better understand the effects of these frequently neglected aspects, we use the lattice Boltzmann equations to model the fluid flow over an osteocyte in a lacuno-canalicular network in two dimensions. We focus on the influences of the number/geometry of the canaliculi and the effects of the PCM on the fluid wall shear stress (WSS) and normal stress (WNS) on an osteocyte surface. We consider 16, 32, and 64 canaliculi using one randomly generated geometry for each of the 16 and 32 canaliculi cases and three geometries for the 64 canaliculi case. We also consider 0%, 5%, 10%, 20%, and 40% pericellular matrix density. Numerical results on the WSS and WNS distributions and on the velocity field are visualized, compared, and analyzed. Our major results are as follows: (1) the fluid flow generates significantly greater force on the surface of the osteocyte if the model includes the pericellular matrix (PCM); (2) in the absence of PCM, the average magnitudes of the stresses on the osteocyte surface are not significantly altered by the number and geometry of the canaliculi despite some quantitative influence of the latter on overall variation and distribution of those stresses; and (3) the dimensionless stress (stress after non-dimensionalization) on the osteocyte surface scales approximately as the reciprocal of the Reynolds number and increasing PCM density in the canaliculi reduces the range of Reynolds number values for which the scaling law holds. 

Previous studies have shown that volatile organic compounds (VOCs) are potential biomarkers of breast cancer. An unanswered question is how urinary VOCs change over time as tumors progress. To explore this, BALB/c mice were injected with 4T1.2 triple negative murine tumor cells in the tibia. This typically causes tumor progression and osteolysis in 1–2 weeks. Samples were collected prior to tumor injection and from days 2–19. Samples were analyzed by headspace solid phase microextraction coupled to gas chromatography–mass spectrometry. Univariate analysis identified VOCs that were biomarkers for breast cancer; some of these varied significantly over time and others did not. Principal component analysis was used to distinguish Cancer (all Weeks) from Control and Cancer Week 1 from Cancer Week 3 with over 90% accuracy. Forward feature selection and linear discriminant analysis identified a unique panel that could identify tumor presence with 94% accuracy and distinguish progression (Cancer Week 1 from Cancer Week 3) with 97% accuracy. Principal component regression analysis also demonstrated that a VOC panel could predict number of days since tumor injection (R2 = 0.71 and adjusted R2 = 0.63). VOC biomarkers identified by these analyses were associated with metabolic pathways relevant to breast cancer. 

Abstract Breast cancer is the most common cancer detected in women and current screening methods for the disease are not sensitive. Volatile organic compounds (VOCs) include endogenous metabolites that provide information about health and disease which might be useful to develop a better screening method for breast cancer. The goal of this study was to classify mice with and without tumors and compare tumors localized to the mammary pad and tumor cells injected into the iliac artery by differences in VOCs in urine. After 4T1.2 tumor cells were injected into BALB/c mice either in the mammary pad or into the iliac artery, urine was collected, VOCs from urine headspace were concentrated by solid phase microextraction and results were analyzed by gas chromatography-mass spectrometry quadrupole time-of-flight. Multivariate and univariate statistical analyses were employed to find potential biomarkers for breast cancer and metastatic breast cancer in mice models. A set of six VOCs classified mice with and without tumors with an area under the receiver operator characteristic (ROC AUC) of 0.98 (95% confidence interval [0.85, 1.00]) via five-fold cross validation. Classification of mice with tumors in the mammary pad and iliac artery was executed utilizing a different set of six VOCs, with a ROC AUC of 0.96 (95% confidence interval [0.75, 1.00]).