One possible alternative is the use of computational fluid dynamics,64,65 selleckchem Dasatinib but these simulations are computationally intensive and can end up being as time consuming as the actual testing. To avoid these problems it has been suggested that approximations to model the fluid flow can be done based on the Darcy law (Eqn. 1, where u represents the volume-averaged velocity and it is proportional to K, the permeability tensor divided by the viscosity, ��, and to the pressure gradient, p) that describes fluid flow through a porous medium and this can be a simpler approach to understanding what actually goes on inside the constructs and the perfusion chamber.66 Table 1. Selected perfusion systems corresponding flow rates and scaffolds used with them and respective pore sizes Equation 1: general form of the Darcy law.
Another very important parameter that is closely related with the flow rate (��) is the shear stress. The shear stress on a point y at a distance from the surface is given by Equation 2, where �� is the viscosity and the velocity of the fluid on the surface.67 Equation 2: shear stress in fluids. In vivo, bone cells are subjected to shear stresses that range from 8 to 30 dyn/cm2 and in vitro has been shown that values from 2 to 10 dyn/cm2 are sufficient to stimulate osteoblasts.59,68 In the three dimensional constructs used under flow perfusion the values of shear stress to which cells are subjected are represented on Table 2. It can be seen that in these cases, the shear stress is very low, barely reaching 1 dyn/cm2, which is lower than the values that have been shown to stimulate osteoblasts.
As seen in Equation 2, the viscosity also influences the shear stress. This has also been studied by the supplementation of culture medium with different concentrations of dextran (0%, 3% and 6%). The increase of the concentration of dextran leads to an increase in viscosity. It was seen that the increasing concentration led to an increase in shear stress from 0.1 to 0.3 dyn/cm2 and that it also improved distribution and amount of mineralized matrix.23 Varying viscosity might be another alternative to study the effect of shear stress without altering scaffold architecture. Table 2. Selected perfusion systems and respective shear stresses Bearing in mind the importance of this parameter, it is necessary to try and optimize it as it might have a great influence on the osteoblastic behavior.
Still, it is a difficult Drug_discovery parameter to alter as it is influenced by characteristics such as pore size and flow rate and, although it can be easily estimated in some cases, there are situations where it is not possible to obtain accurate values and this is mainly due to the scaffold��s architecture. The commonly used fluid flow model assumes that the scaffolds present a cylindrical pore geometry which is not precise in cases where fibrous meshes are used, for example, but the approximation can be made nonetheless.