A Mathematical Model for Post-Implant Collagen Remodeling in an Autologous Engineered Pulmonary Arterial Conduit.

A mathematical model of the long term in vivo remodeling in post-implanted pulmonary artery (PA) conduits was developed from . experimental results from two extant ovine in vivo studies. Results in both studies indicated that the in vivo conduits remained dimensionally stable up to 80 weeks, so that the conduits maintained a constant in vivo stress and deformation state. In contrast, continued remodeling of the constituent collagen fiber network as evidenced by an increase in effective tissue uniaxial tangent modulus, which then stabilized by one year post-implant. A meso-structural constitute model was then applied to extant planar biaxial mechanical data and revealed an initial pronounced increase in effective collagen fiber modulus, paralleled by a simultaneous shift towards longer, more uniformly length-distributed collagen fibers. A time-evolving structural mixture based mathematical model specialized for this unique form of tissue remodeling was developed, with a focus on time-evolving collagen fiber stiffness as the driver for tissue-level remodeling. The model was able to fully reproduce 1) the observed tissue level increases in stiffness by time evolving simultaneous increases in collagen fiber modulus and lengths, 2) maintenance of the constant collagen fiber angular dispersion, and 3) stabilization of the remodeling processes at one year. Interestingly, the remodeling model indicated that the basis for tissue homeostasis was maintenance of the collagen fiber ensemble stress for all orientations, and not individual collagen fiber stresses.