computer methods and programs in biomedicine 87 ( 2 0 0 7 ) 21–27 journal homepage: www.intl.elsevierhealth.com/journals/cmpb A tracer metric numerical model for predicting tortuosity factors in three-dimensional porous tissue scaffolds B. Starly a , E. Yildirim b , W. Sun b,* a School of Industrial Engineering, University of Oklahoma, Norman, OK 73019, USA b Department of Mechanical Engineering and Mechanics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA article info Article history: Received 3 December 2006 Received in revised form 15 April 2007 Accepted 16 April 2007 Keywords: Three-dimensional tortuosity Porous media Tracer analysis Tissue engineering abstract One of the critical functions of a tissue-engineered construct is to be able to provide ade- quate nutrient and oxygen supply into the interior of the construct. An insufficient supply will lead to slower cellular proliferation rates and eventual apoptosis. The supply of the nutrients is largely governed by the transport properties of the construct which in turn is dependent on the porosity, tortuosity and surface chemistry of the tissue construct. The design and fabrication of scaffolds with tailored properties is thus a crucial step in the growth of tissue within their host environment. This paper discusses the development of a numerical characterization technique to measure the three-dimensional tortuosity fac- tors for any given interconnected porous design. Tortuosity factors are obtained in the three orthogonal principal directions for several candidate unit cell architectures. The proposed numerical technique has been validated with models of known tortuosity. The developed technique will provide a basis for the study of transport properties of the designed scaffold and its effect on cellular function and response through the development of dynamic culture bioreactors. © 2007 Elsevier Ireland Ltd. All rights reserved. 1. Introduction and background Tissue-engineered scaffolds can potentially provide clinical therapies in wound healing and tissue regeneration appli- cations [1,2]. These scaffolds provide a three-dimensional framework upon which transplanted and/or encapsulated cells can adhere, grow and differentiate to provide the intended tissue function. The classical strategy for in vitro tissue engineering involves either of the two following methods—the direct seeding of cells on the scaffolds [3,4] or by the encapsulation of cells within hydrogels [5,6]. The scaffolds containing living cells are subjected to and maintained under conditions that support appropriate tissue growth through the use of dynamic culture vessels and bioreactors. To facil- itate the growth of tissue into the interior of the scaffold, a ∗ Corresponding author. Tel.: +1 215 895 5810. E-mail address: sunwei@drexel.edu (W. Sun). highly porous and a well interconnected network is built into the scaffold model. The porous architecture allows for the movement of nutrients and essential signaling molecules by maintaining flow through the scaffold. A manmade tissue substitute must not only serve as a structural support for cells but also provide a nutritional path- way for the transfer of nutrients and molecules to regions where the new formation of tissue is desired [7]. Cells require access to nutrient molecules such as oxygen, glucose and amino acids combined with the need for the efficient removal of metabolite byproducts for proper cell survival and prolifera- tion. The consumption of nutrients by the cells must be locally balanced by the delivery of fresh nutrients into the scaffold from the medium. This rate of consumption of nutrients is largely governed by the cell type, nutrient requirements and 0169-2607/$ – see front matter © 2007 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.cmpb.2007.04.003