Computational Fluid Dynamics Analysis of the Bone Marrow in Cancellous Bone as a Non-Newtonian Fluid
Authors: Ohta Makoto , Sakuma Wataru , Nakayama Toshio , Anzai Hitomi , Ito Makoto , Sado Katsuyuki , Nakamura Shuji 
Published: February 2017

Stem cells in the bone marrow (BM) are used as regenerative treatment for leukemia. They are usually harvested by puncturing the cancellous bone in the ilium of the donor with a needle. However, this process can cause severe burden to the donor because of its inefficiency; the bone may require 50–100 punctures to obtain enough stem cells.
Various factors affect the volume of BM harvested, and their influence can be estimated by observing the flow in the cancellous bone. Recent computational fluid dynamics (CFD) analyses of BM with 3-D reconstruction of the cancellous bone have profiled flow velocity or wall shear stress (WSS) and have shown that some parts on the surface of the cancellous bone have higher WSS and that this high WSS may tear cells from the surface of the bone. CFD analysis may therefore help determining a method for efficient stem cell harvest. However, it is difficult to validate CFD using BM structure because of its porosity. To improve the accuracy of WSS and flow pattern calculations, blood characteristics should be incorporated as key factors and the effects of non-Newtonian flow and viscosity on the flow patterns evaluated. Therefore, the purpose of this study was to evaluate CFD analyses of BM in the cancellous bone based on flow where viscosity depended on the shear rate.
BM from porcine ilium bones was extracted, and the viscosities of samples, with or without anti-clotting medications, were measured at various shear rates. 3-D reconstruction of the cancellous bone was performed using micro-CT after removing BM and fat from the bone. The resolution of the reconstruction was 11.7 μm per pixel, which was sufficient to reconstruct the porous structure. The size of the bone sample was 2.5 × 2.5 × 3.5 mm. The number of mesh was approximately 4.3 million.
CFD analyses were performed using 3-D reconstruction and viscosity profile at three pressure differences (5, 7, and 10 kPa). Constant pressure was applied in the outlet.
The viscosity of BM could be divided into three shear rate ranges. The first corresponded with a shear rate over 100 1/s, where the viscosity was constant at less than 0.01 Pa·s. Transient curves were observed for shear rates 0.01–100 1/s. At lower shear rates, the viscosity was again constant, at over 105 Pa·s. These changes were higher than the changes in blood viscosity based on the shear rate.
The CFD analyses showed that the results depended on the inlet pressure. When the pressure difference was 10 kPa, the viscosity change almost disappeared, and the velocity profile was similar to that of Newtonian flow. When the pressure difference was 5 or 7 kPa, changes in viscosity and completely changed flow patterns were observed. The WSS profile also changed with the velocity profile.
Therefore, pressure can be a major factor in the velocity profile of BM in the cancellous bone. Effects of non-Newtonian flow on velocity and WSS profiles were observed under an appropriate pressure difference.