Biomech Model Mechanobiol (2009) 8:499–507 DOI 10.1007/s10237-009-0153-6 ORIGINAL PAPER Darcian permeability constant as indicator for shear stresses in regular scaffold systems for tissue engineering Petra Vossenberg · G. A. Higuera · G. van Straten · C. A. van Blitterswijk · A. J. B. van Boxtel Received: 16 December 2008 / Accepted: 24 March 2009 / Published online: 10 April 2009 © Springer-Verlag 2009 Abstract The shear stresses in printed scaffold systems for tissue engineering depend on the flow properties and void volume in the scaffold. In this work, computational fluid dynamics (CFD) is used to simulate flow fields within porous scaffolds used for cell growth. From these models the shear stresses acting on the scaffold fibres are calculated. The results led to the conclusion that the Darcian (k 1 ) per- meability constant is a good predictor for the shear stresses in scaffold systems for tissue engineering. This permeabil- ity constant is easy to calculate from the distance between and thickness of the fibres used in a 3D printed scaffold. As a consequence computational effort and specialists for CFD can be circumvented by using this permeability constant to predict the shear stresses. If the permeability constant is below a critical value, cell growth within the specific scaffold design may cause a significant increase in shear stress. Such a design should therefore be avoided when the shear stress experienced by the cells should remain in the same order of magnitude. Keywords Shear stress · Printed scaffolds · Computational fluid dynamics · Permeability constants P. Vossenberg · G. van Straten · A. J. B. van Boxtel Systems and Control Group, Wageningen University, P.O. Box 17, 6700 AA Wageningen, The Netherlands P. Vossenberg · G. A. Higuera · C. A. van Blitterswijk Department of Tissue Regeneration, Institute for Biomedical Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands P. Vossenberg (B ) Food and Bioprocess Engineering Group, P.O. Box 8129, 6700 EV Wageningen, The Netherlands e-mail: petra.vossenberg@wur.nl 1 Introduction Tissue engineering applies the principles of biology and engi- neering to the development of functional substitutes for damaged tissue such as skin, cartilage or bone (Langer and Vacanti 1993). The core materials used in tissue engineering are different types of cells, for example fibroblasts, chondro- cytes or mesenchymal stem cells (MSCs). To establish a tissue culture, expansion and differentiation of cells is needed. This expansion and differentiation should preferably occur in a physiological environment which is closer to the cells’ native environment. To achieve this, bio- reactor systems may be used. One way to culture cells in vitro is in a perfusion bioreactor housing a three-dimensional (3D) scaffold. Other options include two-dimensional (2D) poly- styrene tissue culture flasks, spinner flasks, where the cells are usually grown on microcarriers, and hollow-fibre reac- tors, where the cells are attached to the outside of the fibres (Pörtner et al. 2005). In a perfusion system, the cells may be attached to printed scaffolds (see Fig. 1 as an example), which can be fabri- cated using 3D printing technology consisting of fibres of the copolymers polyethylene oxide terephtalate (PEOT) and polybutylene terephtalate (PBT) with polyethylene glycol (PEG) starting blocks (Moroni et al. 2006). Many other types of scaffold are nowadays available with varying architec- tures, composite materials and surface chemistries. Scaffolds provide a large surface area that facilitates the attachment, survival, migration, proliferation and differentiation of cells (Muschler et al. 2004). Furthermore, the scaffold contains void spaces to allow mass transport to take place through con- vection and diffusion (Karande et al. 2004). The advantage of printed scaffolds is that they have a formally designed regular structure, which is reproducible. This offers the potential for greater control and a better prediction of the fluid flow within 123