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.
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Sepsis is characterized by an overactive, dysregulated inflammatory response that drives organ dysfunction and often results in death. Mathematical modeling has emerged as an essential tool for understanding the underlying complex biological processes. A system of four ordinary differential equations (ODEs) was developed to simulate the dynamics of bacteria, the pro- and anti-inflammatory responses, and tissue damage (whose molecular correlate is damage-associated molecular pattern [DAMP] molecules and which integrates inputs from the other variables, feeds back to drive further inflammation, and serves as a proxy for whole-organism health status). The ODE model was calibrated to experimental data from E. coli infection in genetically identical rats and was validated with mortality data for these animals. The model demonstrated recovery, aseptic death, or septic death outcomes for a simulated infection while varying the initial inoculum, pathogen growth rate, strength of the local immune response, and activation of the pro-inflammatory response in the system. In general, more septic outcomes were encountered when the initial inoculum of bacteria was increased, the pathogen growth rate was increased, or the host immune response was decreased. The model demonstrated that small changes in parameter values, such as those governing the pathogen or the immune response, could explain the experimentally observed variability in mortality rates among septic rats. A local sensitivity analysis was conducted to understand the magnitude of such parameter effects on system dynamics. Despite successful predictions of mortality, simulated trajectories of bacteria, inflammatory responses, and damage were closely clustered during the initial stages of infection, suggesting that uncertainty in initial conditions could lead to difficulty in predicting outcomes of sepsis by using inflammation biomarker levels.more » « less
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Abstract Objective To incorporate chronic vascular adaptations into a mathematical model of the rat hindlimb to simulate flow restoration following total occlusion of the femoral artery.
Methods A vascular wall mechanics model is used to simulate acute and chronic vascular adaptations in the collateral arteries and collateral‐dependent arterioles of the rat hindlimb. On an acute timeframe, the vascular tone of collateral arteries and distal arterioles is determined by responses to pressure, shear stress, and metabolic demand. On a chronic timeframe, sustained dilation of arteries and arterioles induces outward vessel remodeling represented by increased passive vessel diameter (arteriogenesis), and low venous oxygen saturation levels induce the growth of new capillaries represented by increased capillary number (angiogenesis).
Results The model predicts that flow compensation to an occlusion is enhanced primarily by arteriogenesis of the collateral arteries on a chronic time frame. Blood flow autoregulation is predicted to be disrupted and to occur for higher pressure values following femoral arterial occlusion.
Conclusions Structural adaptation of the vasculature allows for increased blood flow to the collateral‐dependent region after occlusion. Although flow is still below pre‐occlusion levels, model predictions indicate that interventions which enhance collateral arteriogenesis would have the greatest potential for restoring flow.
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Abstract Objective The development of earlier and less invasive treatments for peripheral arterial disease requires a more complete understanding of vascular responses following a major arterial occlusion. A mechanistic model of the vasculature of the rat hindlimb is developed to predict acute (immediate) changes in vessel diameters and smooth muscle tone following femoral arterial occlusion.
Methods Vascular responses of collateral arteries and distal arterioles to changes in pressure, shear stress, and metabolism are assessed before and after occlusion. The effects of exercise are also simulated and compared with venous flow measurements from WKY rats.
Results The model identifies collateral arteries as the primary contributors to flow compensation following occlusion. Increasing the number of capillaries has minimal effect on blood flow while increasing the number of collateral arteries significantly increases flow, since the primary site of resistance shifts upstream to the collateral arteries following occlusion. Despite significant collateral dilation, calf flow remains below pre‐occlusion levels and the deficit becomes more severe with increased activity.
Conclusions Although unable to compensate fully for an occlusion, the model demonstrates the importance of the shear response in collateral arteries and the metabolic response in the distal microcirculation in acute adaptations to a major arterial occlusion.
