Assessment of bone strength and fracture behavior of degenerative vertebrae through quantifying morphology and density distribution

Lumbar degeneration leads to changes in geometry and density distribution of vertebrae, which could further influence the mechanical property and behavior. This study aimed to quantitatively describe the variations in shape and density distribution for degenerated vertebrae by statistical models, and utilized the specific statistical shape model (SSM)/statistical appearance model (SAM) modes to assess compressive strength and fracture behavior. Highly detailed SSM and SAM were developed based on the 75 L1 vertebrae of elderly men, and their variations in shape and density distribution were quantified with principal component (PC) modes. All vertebrae were classified into mild (n = 22), moderate (n = 29), and severe (n = 24) groups according to the overall degree of degeneration. Quantitative computed tomography-based finite element analysis was used to calculate compressive strength for each L1 vertebra, and the associations between compressive strength and PC modes were evaluated by multivariable linear regression (MLR). Moreover, the distributions of equivalent plastic strain (PEEQ) for the vertebrae assigned with the first modes of SSM and SAM at mean ± 3SD were investigated. The Leave-One-Out analysis showed that our SSM and SAM had good performance, with mean absolute errors of 0.335±0.084 mm and 64.610±26.620 mg/cm³, respectively. A reasonable accuracy of bone strength prediction was achieved by using four PC modes (SSM 1, SAM 1, SAM 4, and SAM 5) to construct the MLR model. Furthermore, the PEEQ values were more sensitive to degeneration-related variations of density distribution than those of morphology. The density variations may change the deformity type (compression deformity or wedge deformity), which further affects the fracture pattern. Statistical models can identify the morphology and density variations in degenerative vertebrae, and the SSM/SAM modes could be used to assess compressive strength and fracture behavior. The above findings have implications for assisting clinicians in pathological diagnosis, fracture risk assessment, implant design, and preoperative planning.