On bone adaptation due to venous stasis

Abstract

This paper addresses the question of whether or not interstitial fluid flow due to the blood circulation accounts for the observed periosteal bone formation associated with comprised venous return (venous stasis). Increased interstitial fluid flow induced by increased intramedullary pressure has been proposed to account for the periosteal response in venous stasis. To investigate the shear stresses acting on bone cell processes due to the blood circulation-driven interstitial fluid flow, a poroelastic model is extended to the situation in which the interstitial fluid flow in an osteon is driven by the pulsatile extravascular pressure in the osteonal canal as well as by the applied cyclic mechanical loading. Our results show that under normal conditions, the pulsatile extravascular pressure in the osteonal canal due to cardiac contraction (10mm Hg at 2Hz) and skeletal muscle contraction (30mm Hg at 1Hz) induce peak shear stresses on the osteocyte cell processes that are two orders of magnitude lower than those induced by physiological mechanical loading (100 microstrain at 1Hz). In venous stasis the induced peak shear stress is reduced further compared to the normal conditions because, although the mean intramedullary pressure is increased, the amplitude of its pulsatile component is decreased. These results suggest that the interstitial fluid flow is unlikely to cause the periosteal bone formation in venous stasis. However, the mean interstitial fluid pressure is found to increase in venous stasis, which may pressurize the periosteum and thus play a role in periosteal bone formation.

Fig. 1

(a) A cross-section of an osteon with an outer radius r_o and an inner radius r_i. A cyclic mechanical loading with a uniform stress σ = −σ_o sin ωt is applied axially to the osteon. At the interior surface, the extravascular fluid pressure is assumed to be cyclic (p = p_b sin(Ωt + Ψ)+p₀) due to the heart beat, while the boundary condition at the cement line (the outer surface) is that of no leakage of bone fluid (∂p/∂r = 0). Osteocytes encased in the mineralized matrix are linked together with each other and with the osteoblasts lining the central canal surface via cell processes located in the canalicular channels. (b) A schematic model of a longitudinal cross-section of a canaliculus. The cell process is located in the center of the canaliculus. A pericellular fiber matrix fills the fluid space between the cell process (radius a) and the canalicular wall (radius b). The spacing between the fibers is Δ. The lacunar-canalicular porosity permeability is calculated from these structural parameters and the interstitial fluid pressure within the osteon is calculated using poroelasticity theory. Because of the presence of cytoskeletal actin bundles within the cell process, the circumferential deformation of the cell process is predicted to be less than 5% for physiological loading and thus is neglected in this model (You et al., 2001a). The shear stress induced by the canalicular fluid flow is calculated on the surface of the cell process.

Fig. 2

The spatial distribution profiles of the interstitial fluid pressure in the radial coordinate from the osteonal canal surface (R = 0.2) to the cement line (R = 1) depend on the type of the loading (mechanical or blood flow) and the loading frequency. (a) The normalized amplitude of the fluid pressure induced by mechanical loading $(p_1^{\text{amp}}/{\sigma }_0)$ increases radially from the canal to the cement line. The induced fluid pressure is much higher at 20 Hz than at 1 Hz across the osteon. (b) The normalized amplitude of the blood-induced fluid pressure $(p_{\mathrm{b}}^{\text{amp}}/p_{\mathrm{b}})$ decreases both across the osteon radius and with increasing frequency of the pulsatile extravascular pressure due to blood circulation. At 1 Hz, the pulsatile pressure within the osteonal canal can propagate to the whole osteon nearly uniformly with less than 5% decay in magnitude. At 20 Hz, the pulsatile pressure decreases rapidly from the canal to the cement line, with the amplitude of the pulsatile pressure at the cement line only 50% of that in the canal.

Fig. 3

The spatial distribution of the shear stress on the cell process membrane induced by (a) mechanical loading and (b) pulsatile extravascular pressure due to blood circulation. Since the fluid pressure gradients are proportional to shear stresses, the spatial distribution of the fluid pressure gradients has the same pattern (profile) as shown here. Two typical mechanical strains are considered; one is related to locomotion (100 microstrain (με) at 1 Hz) and the other is associated with posture (10 microstrain at 20 Hz). The two extravascular pressures in the osteonal canal considered are a normal pulse pressure due to the heart beat (10 mm Hg at 2 Hz), and an increased pressure induced by repeated skeletal muscle contraction and release (30 mm Hg at 1 Hz). The peak shear stresses and the fluid pressure gradients induced by both mechanical loading and blood circulation are located at the inner canal surface of the osteon.