An Integrated Finite-Element Approach to Mechanics, Transport and Biosynthesis in Tissue Engineering

Abstract

A finite-element approach was formulated, aimed at enabling an integrated study of mechanical and biochemical factors that control the functional development of tissue engineered constructs. A nonlinear biphasic displacement-velocity-pressure description was combined with adjective and diffusive solute transport, uptake and biosynthesis. To illustrate the approach we focused on the synthesis and transport of macromolecules under influence of fluid flow induced by cyclic compression. In order to produce net transport the effect of dispersion was investigated. An abstract representation of biosynthesis was employed, three cases were distinguished: Synthesis dependent on a limited small solute, synthesis dependent on a limited large solute and synthesis independent of solute transport. Results show that a dispersion model can account for augmented solute transport by cyclic compression and indicate the different sensitivity to loading that can be expected depending on the size of the limiting solute.

Computational Study of Culture Conditions and Nutrient Supply in Cartilage Tissue Engineering

“…Glucose on the other hand is present in sufficient quantities in the construct for both mixed and static cases ( Figure 7). It has been shown previously that fluid velocities within the construct induced by cyclic compression are too low to influence the transport of small solutes significantly (53,56). Therefore, as a first approximation only the effect of the presence of the loading platen was investigated in the present study.…”

“…As a first approximation the confined perfusion case was considered to be a one-dimensional problem, which is justified for low flow rates. A computational method was used that has been described previously (53). Briefly, a biphasic finite element formulation was used to derive the time varying displacement and fluid velocity field, which were subsequently used to solve the convection diffusion equations for the different solutes.…”

Mathematical modelling of fibre-enhanced perfusion inside a tissue-engineering bioreactor

“…Lasseux et al, 2004). Some models have been developed that integrate mechanical and chemical factors that control the functional development of tissue engineered constructs (Sengers et al, 2004;Lemon et al, 2006). However, these models do not account for coupling between the externally driven flow and the construct domains.…”

Modeling the coupled mechanics, transport, and growth processes in collagen tissues.

“…For this case, the deformation of the fiber is solved with Finite-Elements, using piece-wise linear elements and minimizing the residual given eq. Sengers (2004) The reason for this instability is that as the edge is pushed inwards, the solid fraction decreases, leading to an exponential reduction of the permeability and an increased fluid pressure gradient to force the fluid out through this region. This" clogging" becomes unstable as the solid must undergo further deformation to balance the pressure gradient.…”