Modeling Inter-Lamellar Interactions in Angle-Ply Nanofibrous Biologic Laminates for Annulus Fibrosus Tissue Engineering

Function of the annulus fibrosus (AF) of the intervertebral disc is predicated on a high degree of structural organization over multiple length scales. Recently, we have employed aligned electrospun scaffolds to engineer nanofibrous biologic laminates that replicate the form and function of the AF [1]. Further, we determined that interlamellar shearing — a direct consequence of the +/−30° angle-ply architecture — plays an important role in reinforcing the tensile response of these materials (Fig. 1). Although we have utilized fiber-reinforced continuum models to characterize the evolving mechanics of single-lamellar AF constructs with in vitro culture [2, 3], these models are not capable of capturing the interlamellar interactions observed in bi-lamellar constructs. Indeed, continuum models of the native AF typically do not account for the organization of fiber populations into discrete, alternating planes of alignment, and so these models, too, do not account for inter-lamellar shearing interactions [4–6]. Therefore, in the present work we propose a novel constitutive model for the reinforcing role of interlamellar shearing during uniaxial extension of angle-ply biologic laminates and employ this model to evaluate the functional evolution of bilayers for AF tissue engineering.