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 osteonin-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.

The mechanoresponse of bone is closely related to the osteocyte lacunocanalicular network architecture

“…Circuit theory based on Kirchhoff’s first law was used to calculate the fluid flow velocity in each canaliculus of the network (for details of the model and parameter values used, see ref. 41 ). Describing the topology of the network by the directed edge-node incidence matrix , with elements equal to 1 (or −1) if edge points toward (or away from) node , and otherwise 0, conservation of fluid in the network (Kirchhoff’s first law) can be written as with , the volumetric flow rate through the edge , and , the source/sink contribution to the flow of node i .…”

“…Circuit theory based on Kirchhoff's first law was used to calculate the fluid flow velocity in each canaliculus of the network (for details of the model and parameter values used, see ref. 41). Describing the topology of the network by the directed edge-node incidence matrix A ji , with elements equal to 1 (or −1) if edge j points toward (or away from) node i, and otherwise 0, conservation of fluid in the network (Kirchhoff's first law) can be written as ∑ j A ji q j = f i with q j , the volumetric flow rate through the edge j, and f i , the source/sink contribution to the flow of node i. Exploiting the definition of the incidence matrix leads to Δp j = ∑ i A ji p i , where Δp j denotes the pressure difference over edge j, and p i , the pressure at node i. Darcy's law relates the pressure difference and volumetric flow rate within each edge, q j = C jj Δp j .…”

“…It was shown that the LCN architecture is spatially very heterogeneous ( 35 – 37 ) and changes with age ( 38 – 40 ). Combining such 3D imaging of the LCN with fluid flow calculations predicted substantial differences in the mechanoresponsiveness between different osteon types in human cortical bone ( 41 ).…”

“…5) A conversion of image data into a mathematical network was performed using a custom software ( 36 ). 6) Circuit theory was applied to calculate the load-induced fluid flow in each of the millions of imaged canaliculi ( 45 ), and a mechanical stimulus was inferred ( 41 ), which is used as a predictor of the mechanoresponse of the tibia.…”

Modeling cortical bone adaptation using strain gradients

“…The present study calculates bending-induced stain gradients in those directions along which the canaliculi or osteocyte cell processes are typically oriented. 30 A schematic representation of possible orientations of osteocyte cell processes or canaliculi embedded in the cortex is shown in Figure 1(d) based on Bruker Micro-CT Academy. 31 In addition, it is also expected that strain gradients/pressure gradients developed along canaliculi initiates fluid motion responsible for osteogenic activity at the bone surface.…”