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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.