Multiscale finite element modeling of mechanical strains and fluid flow in osteocyte lacunocanalicular system

Abstract

Osteocytes form over 90% of the bone cells and are postulated to be mechanosensors responsible for regulating the function of osteoclasts and osteoblasts in bone modeling and remodeling. Physical activity results in mechanical loading on the bones. Osteocytes are thought to be the main mechanosensory cells in bone. Upon load osteocytes secrete key factors initiating downstream signaling pathways that regulate skeletal metabolism including the Wnt/β-catenin signaling pathway. Osteocytes have dendritic structures and are housed in the lacunae and canaliculi within the bone matrix. Mechanical loading is known to have two primary effects, namely a mechanical strain (membrane disruption by stretching) on the lacunae/cells, and fluid flow, in the form of fluid flow shear stress (FFSS), in the space between the cell membranes and the lacuna-canalicular walls. In response, osteocytes get activated via a process called mechanotransduction in which mechanical signals are transduced to biological responses. The study of mechanotransduction is a complex subject involving principles of engineering mechanics as well as biological signaling pathway studies. Several length scales are involved as the mechanical loading on macro sized bones are converted to strain and FFSS responses at the micro-cellular level. Experimental measurements of strain and FFSS at the cellular level are very difficult and correlating them to specific biological activity makes this a very challenging task. One of the methods commonly adopted is a multi-scale approach that combines biological and mechanical experimentation with in silico numerical modeling of the engineering aspects of the problem. Finite element analysis along with fluid-structure interaction methodologies are used to compute the mechanical strain and FFSS. These types of analyses often involve a multi-length scale approach where models of both the macro bone structure and micro structure at the cellular length scale are used. Imaging modalities play a crucial role in the development of the models and present their own challenges. This paper reviews the efforts of various research groups in addressing this problem and presents the work in our research group. A clear understanding of how mechanical stimuli affect the lacunae and perilacunar tissue strains and shear stresses on the cellular membranes may ultimately lead to a better understanding of the process of osteocyte activation.

Keywords: Finite element model; Fluid flow shear stress; Lacunae; Mechanotransduction; Osteocyte; Perilacunar matrix; Strain.

Figure 1:

Confocal fluorescence microscope false-color images of a single 3D ROI in a bone sample from a 16 wo male C57Bl6 mouse ulna taken at 40x. The lacunocanalicular fluid space was labeled by injection with lysine-fixable dextran-conjugated Texas Red dye, revealing lacunae and canaliculi. Osteocytes were labeled with DiO (green) which identifies plasma membranes in cell bodies and dendrites. Nuclei were labeled with DAPI (cyan).

Figure 2:

3D confocal images were taken at a magnification of 40x. The ivory color represents bone. The bone, LCN, and osteocyte membranes are semi-transparent in this image. The nuclei were labeled with DAPI, shown in blue, and X-Gal precipitate, which indicates activation of the osteocytes) is depicted in yellow. The nuclei and precipitate are opaque in this image, and typically appear tinted by the pink (LCN) and green (osteocyte) colors that surround them.

Figure 3:

FE modeling and analysis begins with defining a mask of a 3D image (top left), followed by generating a surface mesh to fit the mask. The surface mesh is converted to a volume mesh (top right panel shows the volumes of the lacunae and bottom left shows the volume mesh of the bone), which can be processed and analyzed to compute displacements, strains, and other data of interest while simulating application of a load on the model (bottom right).

Figure 4:

A) Velocity streamlines in the fluid in the space between the osteocyte and the lacunar wall and B) the FFSS on the osteocyte cell membranes and dendrite surfaces