Cancellous Bone Young’s Modulus Variation Within the Vertebral Body of a Ligamentous Lumbar Spine—Application of Bone Adaptive Remodeling Concepts

Abstract

Bone remodeling theory based on strain energy density (SED) as the feedback control variable was used in conjunction with the finite element method to analyze the shape of the vertebral bodies within the ligamentous motion segment. The remodeling theory was once again applied to the altered two motion segments model to predict the Young’s modulus distribution of the cancellous bone within the vertebral bodies. A three-dimensional finite element model of the two motion segments ligamentous lumbar spine (L3-5) was developed. Bone remodeling response (external as well as internal) of the motion segments to a uniaxial compressive load of 424.7 N was studied. The external shape of the converged model matched the normal shape of a vertebral body. The internal remodeling resulted in regional cancellous bone Young’s moduli (or bone density) distributions similar to those reported in the literature; posterocentral regions of the vertebrae were predicted to have greater values of the elastic modulus than that of the outer regions. The results of the present study suggest that vertebral body assumes an adequate/optimum structure in terms of both its shape and its elastic moduli distribution within the cancellous region in response to the applied load. Extensions of the present model and its clinically relevant applications are discussed.