Tissue engineering transport

Robert Langer, Polymer Systems for Controlled Release of Macromolecules, Immobilized Enzyme Medical Bioreactors, and Tissue Engineering J. J. Linderman, P. A. Mahama, K. E. Forsten, and D, A. Lauffenburger, Diffusion and Probability in Receptor Binding and Signaling Rakesh K. Jain, Transport Phenomena in Tumors... 

The development of biomechanical models derived from continuum formulations for transport of water and charged species in porous media has been carried out for various soft tissues [1-3] and implemented using finite element models (FEMs) [4-8], Such models provide quantitative views of the response of these complex structures that is especially useful in the study of orthopedic, vascular, ocular, and soft tissue substitutes developed by tissue engineering. In this paper a formulation and FEM are described that incorporate and extend these works in a very general model that identifies physical material properties and allows transient analyses of both natural and artificial soft tissue structures. 

DEVELOPMENT OF A FINITE ELEMENT APPROACH TO MECHANICS, TRANSPORT AND BIOSYNTHESIS IN TISSUE ENGINEERING... 

The proposed model consists of a biphasic mechanical description of the tissue engineered construct. The resulting fluid velocity and displacement fields are used for evaluating solute transport. Solute concentrations determine biosynthetic behavior. A finite deformation biphasic displacement-velocity-pressure (u-v-p) formulation is implemented [12, 7], Compared to the more standard u-p element the mixed treatment of the Darcy problem enables an increased accuracy for the fluid velocity field which is of primary interest here. The system to be solved increases however considerably and for multidimensional flow the use of either stabilized methods or Raviart-Thomas type elements is required [15, 10]. To model solute transport the input features of a standard convection-diffusion element for compressible flows are employed [20], For flexibility (non-linear) solute uptake is included using Strang operator splitting, decoupling the transport equations [9],... 

Closure After completing this chapter, the reader should be able to derive differential equations describing diffusion and reaction, discuss the meaning of the effectiveness factor and its relationship to the Thiele modulus, and identify the regions of mass transfer control and reaction rate control. The reader should be able to apply the Weisz-Prater and Mears criteria to identify gradients and diffusion limitations. These principles should be able to be applied to catalyst particles as well as biomaierial tissue engineering. The reader should be able to apply the overall effectiveness factor to a packed bed reactor to calculate the conversion at the exit of the reactor. The reader should be able to describe the reaction and transport steps in slurry reactors, trickle bed reactors, fluidized-besd reactors, and CVD boat reactors and to make calculations for each reactor. 

Chu, L., H.S. Wiley, and D.A. Lauffenburger, Endocytic relay as a potential means for enhancing ligand transport. Tissue Engineering, 1996, 2, 17-38. 

The inclusion of oil-soluble fillers in the continuous phase aims to produce co-polymers or to bulk and/or surface modify the polymer. When the additive does not take part in the polymerization reaction, it can be deemed as filler which can then be leached out to provide nano-porosity to the walls of PHP. Such nano-pores are important in tissue engineering and BI since such nano-pores allow the transport of small molecules (nutrients/metabolites) to and from the microorganisms. 

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