Development of a Micro-Finite Element Model of the Intervertebral Disc using Sub-modeling Techniques

INTRODUCTION The annulus fibrosus (AF) consists primarily of tightly arranged concentric lamellae of parallel type I collagen fiber bundles, elastin, proteoglycans, water and cells, interconnected by translamellar bridging networks [1,2]. Collagen fibers are oriented approximately 25° to 45° to the transverse plane of the disc and are arranged in alternating directions within each successive lamellae [3]. The primary purpose of the alternating collagen fiber angle between adjacent lamellae is to ensure the tensile recruitment of fibers in axial rotation and bending directions, and during combined motions. Understanding the interrelationships between the architecture and micro-mechanical behavior of the AF is important for developing treatment strategies for degenerative disc disease and herniation injury. Furthermore, defining the mechanical and functional properties of the AF microstructure is becoming increasingly important in the field of tissue engineering [4]. However, the mechanical behavior and interactions between lamellae at the micro level are not welldefined [2,5]. Finite element (FE) modeling has proved to be very useful in the field of biomechanics due to its noninvasiveness. In addition, FE analysis is useful in situations where it is difficult to conduct experiments, such as at the microscale. However, previous models were developed to study the macro scale, and micro model simulations are not available. Developing a micro-FE model of the AF is challenging because the three dimensional magnitude and direction of the loads in the tissue at this scale cannot be measured in-vivo. The main objective of this study is to develop a technique to derive the boundary conditions (BC) of a micro scale FE model of the AF using the sub-modeling technique.