Numerical analysis of extracellular fluid flow and chemical species transport around and within porous bioactive glass.

Modeling of the physical phenomena present at the biomaterial-tissue interface provides a valuable tool for examining the underlying mechanisms which influence the overall behavior of the implant-host system. Based on histological data from a previous implantation study (E. Schepers, M. De Clercq, P. Ducheyne, and R. Kempeneers, "Bioactive glass particulate materials as a filler for bone lesions," J. Oral Rehab.; 18, 439-452, 1991, Ref. 1) which documented the differentiation of mesenchymal cells to cells expressing the osteoblastic phenotype in porous bioactive glass, a finite element momentum and mass transport model was constructed. In this analysis, the extracellular compositional variations and fluid flow conditions around and within porous bioactive glass granules were determined. Numerical simulations demonstrated that the interstitial fluid flow around these granules (300-360 microns) is viscosity dominated (low Reynolds number flow) and that the fluid inside the granules remains stagnant. This velocity field results in shear stresses proportional to the velocity gradient at the granule-fluid interface outside the particles and no shear stresses inside the particles. A parametric study on the effect of interstitial fluid flow on chemical species (Na+, Ca+2, HPO(4)-2) transport outside the granules revealed three domains. At low velocities (0-0.1 micron/s), the transport of species is diffusion controlled. At intermediate velocities (1.0-10 microns/s), diffusion and convection contribute to the species transport. The concentration of chemical species is nearly uniform at high velocities (100-800 microns/s). For all three cases, the transport of chemical species within the granules is diffusion controlled. The differences in transport mechanisms and interstitial fluid flow conditions lead to variations in concentrations, reaction rates, and shear stresses between the inside and the outside of the glass granules. These differences may influence cellular migration, attachment, differentiation, and the overall response to these bioactive materials.