(170g) Using a Particle Method to Investigate Mass Transfer in Biological Porous Media

An effective and inherently parallelizable numerical method for the simulation of microfluidic flows
 in complicated geometries is the Lattice Boltzmann Method (LBM). For the case of scalar transport,
 thermal LBM models have been developed, initially for a narrow range of temperatures (Alexander
 et al. Phys. Rev. E, 47, 2249-2252, 1993). Issues that arose with numerical instabilities in the multi-
speed model developed by Alexander et al. were solved by combining the energy equation with the
 momentum equation (Shan, Phys. Rev. E, 55, 2780-2788, 1997). Later on, He et al., (J. Comp.
 Phys., 146, 282-300, 1998) introduced a separate internal energy distribution function to calculate
 the temperature field. This thermal LBM model was used by Palmer and Rector (J. Comp. Phys.,
 161, 1-20, 2000) and Tang et al. (Int. J. Modern Phys. B, 17, 183-187, 2003) on two dimensional
 flows, and the latter suggested further investigation of the thermal boundary conditions for more
 accurate results. The above models used the conventional Eulerian frame of reference.

Our work presents a Lagrangian approach to simulate convective scalar transfer. High performance 
computing in conjunction with a house hybrid MPI/Open MP parallelized scheme is employed in
 order to take advantage of the inherent LBM parallelizability.  Macroscopic mass transfer is
 modeled using the Lagrangian scalar tracking (LST) method (Papavassiliou, Int. J. Heat Mass
 Transfer, 45(17), 3571-3583, 2002) in conjunction with the LBM algorithm. In LST, the motion of
 scalar markers is used to synthesize the scalar profile. The trajectories of these markers are
composed by a convection part (obtained using the velocity field from the LBM simulations) and a
 diffusion part (i.e., Brownian motion obtained from a mesoscopic Monte-Carlo approach). This
 method is resourceful in terms of computational efficiency, in that it can be used to simulate various
 thermal boundary conditions and Schmidt number fluids with a single flow field resulting from an LBM 
simulation. 

The presentation will include the description of the numerical methodology and the validation
 of the method for known cases of flow in porous media. We will also show results from the application of
 this numerical technique in the case of flow through porous scaffolds, which are used in flow
 perfusion bioreactors for the growth of bone tissue. Due to their degradation characteristics and
 mechanical properties, biodegradable synthetic polymer scaffolds, such as Poly-L-lactic acid
 (PLLA) which is used in this study, seeded with osteoblastic cells have emerged as potential
 replacement therapies for damaged or lost bone tissue. The goal of this work is to optimize the 3D
 scaffold structure by understanding the fundamental behavior of the flow inside the porous scaffold
 and the fundamental behavior of mass transfer of nutrients to the cells. The 3D microarchitecture of
 the scaffolds is characterized using microtomographic (micro CT) analysis with a 10 micro meter
 resolution.  Laminar flows of osteogenic media through the cell-seeded cylindrical scaffolds in a flow
perfusion bio-reactor are modeled via LBM simulations. Velocity field and internal stress distribution fields,
 and parametric nutrient transport study results are presented as a part of this work.  Additionally,
 effects on the bone tissue regeneration of varying the internal scaffold geometry as well as that of
 the pressure force driving the flow through the scaffold are explored.