We have recently submitted an article on the growth of engineered tissue constructs (Continuum theory of fibrous tissue damage mechanics using bond kinetics: application to cartilage tissue engineering, RJ Nims, KM Durney, AD Cigan, A Duss?aux, CT Hung, GA Ateshian, 2015, submitted to Royal Interface Focus).

The model describes the growth of engineered cartilage due both to proteoglycan-induced swelling (Donnan-equilibrium model) and the collagen fibers (exponential-power law fiber distribution deposited in a daily-multigenerational fashion).

Based on our hypothesis of growth and later confirmed experimentally the collagen fiber model incorporates damage whereby collagen fibers deposited in early generations will become damaged and "fail" as the tissue grows and swells (under the influence of proteoglycan deposition) while collagen deposited in later generations will be recruited. The damage is modeled based on the Simo criteria (Simo, 1987) and according to a log-normal cumulative distribution function.

The values of ksi (fiber modulus) and damage mu and sigma (mean and standard deviation of the log-normal CDF) were fit with a MATLAB wrapper function to fit both the swelling response (J) and material elasticity (Czzzz) of experimental constructs. The model was validated to constructs treated with chondroitinase to alter the swelling pressure of the construct during the growth.
Model features available in FEBio version 2.4.0.