Network architecture strongly influences the fluid flow pattern through the lacunocanalicular network in human osteons

Abstract

A popular hypothesis explains the mechanosensitivity of bone due to osteocytes sensing the load-induced flow of interstitial fluid squeezed through the lacunocanalicular network (LCN). However, the way in which the intricate structure of the LCN influences fluid flow through the network is largely unexplored. We therefore aimed to quantify fluid flow through real LCNs from human osteons using a combination of experimental and computational techniques. Bone samples were stained with rhodamine to image the LCN with 3D confocal microscopy. Image analysis was then performed to convert image stacks into mathematical network structures, in order to estimate the intrinsic permeability of the osteons as well as the load-induced fluid flow using hydraulic circuit theory. Fluid flow was studied in both ordinary osteons with a rather homogeneous LCN as well as a frequent subtype of osteons-so-called osteon-in-osteons-which are characterized by a ring-like zone of low network connectivity between the inner and the outer parts of these osteons. We analyzed 8 ordinary osteons and 9 osteon-in-osteons from the femur midshaft of a 57-year-old woman without any known disease. While the intrinsic permeability was 2.7 times smaller in osteon-in-osteons compared to ordinary osteons, the load-induced fluid velocity was 2.3 times higher. This increased fluid velocity in osteon-in-osteons can be explained by the longer path length, needed to cross the osteon from the cement line to the Haversian canal, including more fluid-filled lacunae and canaliculi. This explanation was corroborated by the observation that a purely structural parameter-the mean path length to the Haversian canal-is an excellent predictor for the average fluid flow velocity. We conclude that osteon-in-osteons may be particularly significant contributors to the mechanosensitivity of cortical bone, due to the higher fluid flow in this type of osteons.

Keywords: Canaliculi; Fluid flow; Human osteon; Lacuna; Lacunocanalicular network; Osteocyte.

Fig. 1

Overview of the experimental workflow from left to right: a A section was cut from the midshaft of a human femur and stained with rhodamine before embedding. b A 2D overview image of whole specimen was made using confocal laser scanning microscopy (CLSM) in order to identify ordinary osteons and osteon-in-osteons. 3D image stacks of the selected osteons were taken using CLSM. c The cement line (red 3D surface) and Haversian canal (blue 3D surface) in each osteon were marked as boundaries for the computational models. Both surfaces appear as areas and not as lines due to the considered depth of the image. d The 3D CLSM images were converted into networks consisting of edges (lines representing the canaliculi) and nodes (spheres where canaliculi intersect). A fluid flow analysis was then performed on these networks. Colors of spheres in d represent the node pressure, while the darkness of the lines represents the canalicular fluid flow velocity

Fig. 2

Projections of the 3D lacunocanalicular network of a an ordinary osteon and b osteon-in-osteon. These binary intensity projections along the imaging depth z-direction were made by taking the thresholded confocal microscopy image stacks with a projection value of 1 (red) if a voxel is part of the LCN and otherwise 0 (white). In the CLSM images osteon-in-osteons can be distinguished from ordinary osteons by an inner ring, which is almost free of canaliculi. The few areas where canaliculi bridge the inner osteon and the outer osteon are indicated with arrows. c Quantified backscattered electron image (qBEI) of the same osteon-in-osteon showing quantitatively the local calcium content of the bone. The osteon-in-osteon type is visible by a difference in calcium content between the inner and the outer osteon

Fig. 3

Pressure pattern images were made by plotting color-coded spheres at the location of each node of the network for a representative ordinary osteon (left) and osteon-in-osteon (right) (same osteons as in Fig. 2). The fluid flow was modeled with two approaches. Approach 1) A pressure difference of 13 kPa between cement line and Haversian canal was applied to an ordinary osteon (a) and an osteon-in-osteon (b). Approach 2) Fluid flow was forced out of the ordinary osteon (c) and osteon-in-osteon (d) as water is squeezed out of a steadily compressed sponge (i.e., constant homogeneous strain rate). The difference in pressure patterns between the two osteon types is a direct result of a difference in LCN topology. The much higher pressure in d) (note the different color scale) is partly caused by the much lower permeability of this osteon-in-osteon

Fig. 4

Pressure profiles plotted as a function of the normalized distance (Haversian canal = 0, cement line = 1). The profiles were obtained, firstly, by presenting for each node the values of its position (given by a value between 0 and 1 as normalized distance) and its pressure. Secondly, the data of all nodes in this scatter plot (plot not shown) were transformed in the shown profiles by using a local regression algorithm (locally weighted scatterplot smoothing, LOWESS). a and c Show the pressure profile for all 8 ordinary osteons; b and d show pressure profiles for all 9 osteon-in-osteons. In a and b the dashed line serves as a reference of a linear decrease of the applied pressure. In the background of d the gray values indicate the density of data points of the scatter plot for the osteon-in-osteon of Fig. 3d. The corresponding LOWESS fit is shown by the thicker red line. This kind of representation was chosen to highlight the spatial heterogeneity of the pressure distribution in this case, which can be only poorly rendered by a LOWESS fit

Fig. 5

The fluid flow patterns in the lacunocanalicular network are projections of the network in the style of a road map, where in addition to the color code edges with higher fluid flow velocity are rendered thicker. Edges with vanishing fluid flow velocity are not shown. a and b show the fluid flow patterns resulting from approach 1 in an ordinary osteon and a osteon-in-osteon, respectively; c and d the resulting fluid flow patterns using approach 2. The difference in fluid flow patterns between the two osteon types is a direct result of a difference in LCN topology

Fig. 6

Comparison of average fluid flow velocities. Each data point in the plots represents one osteon. a Comparison between fluid flow velocity in the outer half (CL for half close to cement line) and the inner half (HC for half close to Haversian canal) of the ordinary osteons. The box extends from the first to third quartile, the red line shows the median, and the whiskers extend from the box to show the full range of the data. b Relationship between average fluid flow velocity and mean path length to the Haversian canal. Different models were used to fit the data (black lines). For approach 1 the average fluid flow velocity is inversely related with the average shortest path length. For approach 2 the fluid flow velocity is linearly related with average shortest path length

Fig. 7

The cumulative probability distributions of fluid shear stresses at the cell process surfaces in the canaliculi are plotted for ordinary osteons (blue) and osteon-in-osteons (red) for the case of strenuous exercise (solid lines) and normal daily activities (dashed lines). Fluid flow velocities were calculated using model approach 2 and from the velocities shear forces were obtained using Eq. (10). All lines show the mean percentage of canaliculi with a shear stress larger than the value on the x-axis. The 99% confidence intervals of the mean are shown in the faintly colored bands around the lines. Confidence intervals are the same for both cases and are, therefore, omitted for the dashed lines to improve readability. The gray area above 0.4 Pa illustrates the range of shear stresses where osteocytes showed osteogenic responses to fluid shear stress in in vitro experiments (Bacabac et al. ; Bakker et al. ; Jacobs et al. ; Klein-Nulend et al. 1995)