The role of energy dissipation of polymeric scaffolds in the mechanobiological modulation of chondrogenic expression

Mechanical stimulation has been proposed to induce chondrogenesis in cell-seeded scaffolds. However, the effects of mechanical stimuli on engineered cartilage may vary substantially between different scaffolds. This advocates for the need to identify an overarching mechanobiological variable. We hypothesize that energy dissipation of scaffolds subjected to dynamic loading may be used as a mechanobiology variable. The energy dissipation would furnish a general criterion to adjust the mechanical stimulation favoring chondrogenesis in scaffold. Epiphyseal chondro-progenitor cells were then subject to unconfined compression 2 h per day during four days in different scaffolds, which differ only by the level of dissipation they generated while keeping the same loading conditions. Scaffolds with higher dissipation levels upregulated the mRNA of chondrogenic markers. In contrast lower dissipation of scaffolds was associated with downregulation of chondrogenic markers. These results showed that energy dissipation could be considered as a mechanobiology variable in cartilage. This study also indicated that scaffolds with energy dissipation level close to the one of cartilage favors chondrogenic expression when dynamical loading is present.

A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage

A new and efficient method for numerical solution of the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. Development of the method is based on a composite Gauss-Legendre quadrature approximation of the continuous spectrum relaxation function that leads to an exponential series representation. The separability property of the exponential terms in the series is exploited to develop a numerical scheme that can be reduced to an update rule requiring retention of the strain history at only the previous time step. The cost of the resulting temporal discretization scheme is O(N) for N time steps. Application and calibration of the method is illustrated in the context of a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. Accuracy of the numerical method is demonstrated by comparison to a theoretical Laplace transform solution for a range of viscoelastic relaxation times that are representative of articular cartilage.