Quantitative analysis and stochastic modeling of osteophyte formation and growth process on human vertebrae based on radiographs: a follow-up study

Osteophytes are frequently observed in elderly people and most commonly appear at the anterior edge of the cervical and lumbar vertebrae body. The anterior osteophytes keep developing and will lead to neck/back pain over time. In clinical practice, the accurate measurement of the anterior osteophyte length and the understanding of the temporal progression of anterior osteophyte growth are of vital importance to clinicians for effective treatment planning. This study proposes a new measuring method using the osteophyte ratio index to quantify anterior osteophyte length based on lateral radiographs. Moreover, we develop a continuous stochastic degradation model with time-related functions to characterize the anterior osteophyte formation and growth process on cervical and lumbar vertebrae over time. Follow-up data of anterior osteophytes up to 9 years are obtained for measurement and model validation. The agreement test indicates excellent reproducibility for our measuring method. The proposed model accurately fits the osteophyte growth paths. The model predicts the mean time to onset of pain and obtained survival function of the degenerative vertebrae. This research opens the door to future quantification and mathematical modeling of the anterior osteophyte growth on human cervical and lumbar vertebrae. The measured follow-up data is shared for future studies.