Engineered Alignment in Media Equivalents: Magnetic Prealignment and Mandrel Compaction

We predicted and measured the evolution of smooth muscle cell (SMC) orientation in media-equivalents (MEs) for four fabrication conditions (F−, M−, F+, M+) under Free or Mandrel compaction (F/M) with and without magnetic prealignment of the collagen fibrils in the circumferential direction (±). Mandrel compaction refers to SMC-induced compaction of the ME that is constrained by having a nonadhesive mandrel placed in the ME lumen. Predictions were made using our anisotropic biphasic theory (ABT) for tissue-equivalent mechanics. Successful prediction of trends of the SMC orientation data for all four fabrication cases was obtained: maintenance of the initial isotropic state for F−, loss of initial circumferential alignment for F+, development of circumferential alignment for M−, and enhancement of initial circumferential alignment for M+. These results suggest two mechanisms by which the presence of the mandrel leads to much greater mechanical stiffness in the circumferential direction reported for mandrel compacted MEs relative to free compacted MEs: (1) by inducing an increasing circumferential alignment of the SMC and collagen, and (2) by inducing a large stress on the SMC, resulting in secretion and accumulation of stiffening components.

A Finite Element Solution for the Anisotropic Biphasic Theory of Tissue-Equivalent Mechanics: The Effect of Contact Guidance on Isometric Cell Traction Measurement

We present a method for solving the governing equations from our anisotropic biphasic theory of tissue-equivalent mechanics (Barocas and Tranquillo, 1997) for axisymmetric problems. A mixed finite element method is used for discretization of the spatial derivatives, and the DASPK subroutine (Brown et al., 1994) is used to solve the resulting differential-algebraic equation system. The preconditioned GMRES algorithm, using a preconditioner based on an extension of Dembo’s (1994) adaptation of the Uzawa algorithm for viscous flows, provides an efficient and scaleable solution method, with the finite element method discretization being first-order accurate in space. In the cylindrical isometric cell traction assay, the chosen test problem, a cylindrical tissue equivalent is adherent at either end to fixed circular platens. As the cells exert traction on the collagen fibrils, the force required to maintain constant sample length, or load, is measured. However, radial compaction occurs during the course of the assay, so that the cell and network concentrations increase and collagen fibrils become aligned along the axis of the cylinder, leading to cell alignment along the axis. Our simulations predict that cell contact guidance leads to an increase in the load measured in the assay, but this effect is diminished by the tendency of contact guidance to inhibit radial compaction of the sample, which in turn reduces concentrations and hence the measured load.