Micro finite element analysis of vertebrae using zero-thickness cohesive elements represents post-failure fracture patterns

Bone tissue failure consists of damage, defined as a loss of material integrity or stiffness, and fracture, describing the separation of the material. Bone tissue damage plays a role in regulating bone turnover. Bone fracture can lead to loss of mobility, pain and the need for stabilization procedures. Micro finite element (μFE) modeling has been used as a non-destructive tool to investigate stiffness, strength, post-yield behavior, damage and fracture in bone. Previous studies have utilized elastic-plastic mechanics and continuum damage mechanics (with or without element deletion) to model damage or a fracture mechanics approach with an existing crack to model fracture. This work combines continuum damage mechanics with cohesive zone modeling to simulate damage initiation, crack formation, and fracture propagation in rodent vertebrae. Voxel-based μFE models were generated from micro computed tomography (μCT) images of the 2nd Lumbar (L2) vertebrae in five rat spinal motion segments (L1-L3). A μCT compatible loading device was used to apply axial compressive loading to failure under a sequential loading/imaging protocol. Displacement boundary conditions for the μFE models were derived from a surface-based registration algorithm using the loaded and unloaded μCT scans. Zero-thickness cohesive elements were inserted in a region of interest representing ¼ of each full model. Damage was modeled within the cohesive elements as a smooth decrease in stiffness and combined with a continuum damage model to represent a decrease of stiffness due to material failure. At the onset of fracture, the fully degraded cohesive elements were deleted allowing adjacent surfaces to separate. Damage site locations (vertebral body or posterior elements) and patterns of fracture (crack formation leading to separation or compaction) in the μFE models matched those in the post-failure μCT images. The proposed approach, while computationally expensive, enables modeling of post-failure behavior of vertebral bone, allowing the identification of damage initiation sites, fracture propagation and contact between failed trabeculae.