An Innovative Mathematical Model of the Spine: Predicting Cobb and Intervertebral Angles Using the 3D Position of the Spinous Processes Measured by Vertebral Metrics

Abstract

Back pain is regularly associated with biomechanical changes in the spine. The traditional methods to assess spine biomechanics use ionising radiation. Vertebral Metrics (VM) is a non-invasive instrument developed by the authors in previous research that assesses the spinous processes’ position. However, the spine model used by VM is not accurate. To overcome it, the present paper proposes a pioneering and simple articulated model of the spine built through the data collected by VM. The model is based on the spring–mass system and uses the Levenberg–Marquardt algorithm to find the arrangement of vertebral bodies. It represents the spine as rigid geometric transformations from one vertebra to the other when the extremity vertebrae are stationary. The validation process used the Bland–Altman method to compare the Cobb and the intervertebral angles computed by the model with the radiographic exams of eight patients diagnosed with Ankylosing Spondylitis. The results suggest that the model is valid; however, previous clinical information would improve outcomes by customising the lower and upper vertebrae positions, since the study revealed that the C6 rotation slightly influences the computed angles. Applying VM with the new model could make a difference in preventing, monitoring, and early diagnosing spinal disorders.