Role of mechanical representativity in multiaxial and transverse mechanics of human annulus fibrosus: A microstructure-based biphasic finite element study.

The annulus fibrosus (AF) of the intervertebral disc is composed of a hierarchically organized network of micro-sized oriented collagen fibers (OCF) and nano-sized elastic fibers (NEF) embedded within a fluid-saturated matrix. Interlamellar (ILM) zones provide cohesion between adjacent AF lamellae (LM) and the OCF network. This complex microstructure varies depending on the disc region, thereby affecting both multiaxial and transverse AF mechanics. Accurately replicating experimental observations in numerical models requires ensuring that the specimen is representative in terms of geometry, dimensions, intrinsic architecture, and boundary conditions. Variations in specimen configurations, measurement zones, and boundary conditions in mechanical tests - whether experimental or numerical - can significantly influence the observed behavior and impact result accuracy. In this study, we investigate the role of mechanical representativity using a microstructure-based, biphasic finite element model. The properties of the AF elementary constituents are determined through a multi-step identification process informed by experimental stretching data from the literature: first, multi-lamellar axial stretching identifies matrix properties; second, multi-lamellar radial stretching isolates NEF properties; and finally, single-lamellar tests along the OCF direction determine OCF properties. The model predictions are verified against a broad spectrum of monotonic experiments from the literature, including uniaxial tension and compression, biaxial tension, and shear across different disc regions, with a thorough analysis of test conditions. Our analysis highlights the significant impact of preload and strain measurement zone selection on shear and biaxial stretching outcomes. The model further explores the poorly understood interplay between strain rate, fiber orientation, and fluid flow during circumferential stretching, revealing mechanisms that lead to either radial transverse swelling or shrinkage. Additionally, we analyze the influence of mechanical representativity - particularly the alternation between LM and ILM - on numerical predictions, shedding light on an aspect rarely addressed in other ILM-inclusive numerical models. STATEMENT OF SIGNIFICANCE: The mechanical representativity of numerically reproduced specimens and testing conditions is a key factor in ensuring the predictive accuracy of computational models based on experimental mechanical data, particularly for materials with complex microstructures. This study presents a microstructure-based biphasic computational model that incorporates the hierarchical organization of the collagen network to replicate the regional, anisotropic, and multiaxial behavior of the human annulus fibrosus. The model demonstrates the significant influence of specimen representativity and testing conditions - such as specimen dimensions, strain measurement zones, and preload - on multiaxial response predictions. Additionally, it attributes the complex and poorly understood radial auxetic response observed experimentally during circumferential stretching to fluid-microstructure interactions, while examining the interconnected effects of loading rate and lamellar-interlamellar representation.