Analysing a Reported Experiment That May Demonstrate the Interplay of Fluid Velocity and Pore Pressure in Bone Adaptation

Existing models suggest that osteogenesis occurs in regions of the elevated stimuli, such as peak strain, high fluid velocity, and pore pressure. However, an in vivo study shows that cantilever loading-induced osteogenesis is prominent only at the anterio-lateral side of the mid-diaphyseal section of a mouse tibia, despite an equal magnitude of strain, fluid velocity, and pore pressure at the medial-posterior surface, located just opposite to it. This indicates that the magnitude of individual stimuli alone is not sufficient, as these stimuli appear to interact to induce new bone formation. The present work aims to investigate this interplay by analysing the above-mentioned in vivo study, and developing an improved mathematical model to predict new bone formation.

A poroelastic model was developed using finite element analysis. The tensile side of the bone section was found to have predominantly negative pore-pressure, which stretches the cell processes radially. In contrast, the compressive side predominantly exhibits positive pore pressure, which compresses the osteocyte processes radially. According to the literature, fluid flow applies drag forces on the tethering fibres of osteocytes, resulting in radial stretching of the cell processes, similar to the effect of negative pressure. Accordingly, the net radial displacement due to the combined effect of fluid flow and pore pressure is expected to be greater at the anterio-lateral site compared with the medio-posterior site. We hypothesize that this mechanism leads to new bone formation at the anterio-lateral side only.

To test this hypothesis, a Fourier series was used to approximate pore pressure as well as fluid velocity. In line with the literature, effective negative pressure due to fluid flow was assumed to be proportional to the fluid velocity. The strains induced by these stimuli were analytically computed assuming viscoelastic behaviour. The viscoelastic dissipation energy density due to the combined effect was then computed. The mineral apposition rate (MAR) was assumed to be proportional to the square root of the dissipation energy density above a reference value, consistent with the literature.

The present work provides evidence that fluid velocity and pore pressure are not only critical stimuli for new bone formation but that their interaction governs the process. This insight advances existing knowledge and may help in designing interventions for treating bone loss.