Journal of Biomechanics 38 (2005) 543–549 3-D computational modeling of media flow through scaffolds in a perfusion bioreactor Blaise Porter a , Roger Zauel b , Harlan Stockman c , Robert Guldberg a , David Fyhrie b, * a Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 315 Ferst Dr. NW, Atlanta, GA 30332, USA b Henry Ford Hospital, Bone and Joint Center, Department of Orthopaedic Surgery, 2799 West Grand, Boulevard, Detroit, MI 48202, USA c Sandia National Laboratories, Geochemistry Department 6118, Albuquerque, NM 87185-0750, USA Accepted 2 April 2004 Abstract Media perfusion bioreactor systems have been developed to improve mass transport throughout three-dimensional (3-D) tissue- engineered constructs cultured in vitro. In addition to enhancing the exchange of nutrients and wastes, these systems simultaneously deliver flow-mediated shear stresses to cells seeded within the constructs. Local shear stresses are a function of media flow rate and dynamic viscosity, bioreactor configuration, and porous scaffold microarchitecture. We have used the Lattice–Boltzmann method to simulate the flow conditions within perfused cell-seeded cylindrical scaffolds. Microcomputed tomography imaging was used to define the scaffold microarchitecture for the simulations, which produce a 3-D fluid velocity field throughout the scaffold porosity. Shear stresses were estimated at various media flow rates by multiplying the symmetric part of the gradient of the velocity field by the dynamic viscosity of the cell culture media. The shear stress algorithm was validated by modeling flow between infinite parallel plates and comparing the calculated shear stress distribution to the analytical solution. Relating the simulation results to perfusion experiments, an average surface shear stress of 5  10 5 Pa was found to correspond to increased cell proliferation, while higher shear stresses were associated with upregulation of bone marker genes. This modeling approach can be used to compare results obtained for different perfusion bioreactor systems or different scaffold microarchitectures and may allow specific shear stresses to be determined that optimize the amount, type, or distribution of in vitro tissue growth. r 2004 Elsevier Ltd. All rights reserved. Keywords: Fluid shear stress; Bioreactor; Scaffold; Micro CT; Imaging; Computational fluid dynamics 1. Introduction Static culture of cell-seeded 3-D scaffolds typically produces thin tissue growth localized to the construct periphery (Ishaug et al., 1997). The observed hetero- geneity in matrix synthesis is believed to be a result of inadequate distribution of nutrients and removal of waste products within the constructs (Freed et al., 1993; Pazzano et al., 2000). Improving in vitro mass transport is therefore a critical challenge in producing thick cellular constructs. Many groups have developed bioreactors that perfuse cell-seeded constructs and have demonstrated beneficial effects of perfusion on cell function and tissue growth (Glowacki et al., 1998; Goldstein et al., 2001; Bancroft et al., 2002; Cartmell et al., 2003). While flow rate is the independent variable typically reported in these studies, the same flow rate through two scaffolds with different pore sizes, porosity or pore anisotropy can impart vastly different shear stresses on the cells within the constructs. In addition to enhancing chemotransport, parallel plate flow systems apply flow-mediated shear stresses, to which bone cells are highly responsive. Shear stresses in the range of 0.5–1.5Pa (5-15dynes/cm 2 ) affect osteo- blast proliferation as well as production of alkaline phosphatase, nitric oxide (NO) and prostaglandin (PGE 2 ), indicating that shear stress is an important regulator of cell function (Reich and Frangos, 1991; Hillsley and Frangos, 1997; Smalt et al., 1997; Klein- Nulend et al., 1998; McAllister et al., 2000; Jiang et al., 2002). These short-term 2-D flow experiments suggest that flow-induced shear stresses may also modulate the ARTICLE IN PRESS *Corresponding author. Tel.: +1-313-916-3591; fax: +1-313-916- 8064. E-mail address: fyhrie@bjc.hfh.edu (D.P. Fyhrie). 0021-9290/$-see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2004.04.011