A mathematical model of the combination of lateral tilt and rotation of the vertebra

Abstract

An important section of spinal biomechanics is the analysis of various types of movements in spinal segments, which are difficult to observe, and setting up experiments is quite complex. There are few articles devoted to this topic, and the methodological approaches outlined in these studies are so heterogeneous that they do not allow for a comparative analysis. In this situation, the abstract language of mathematics allows us to objectively answer the questions that arise. Aim of the study was to develop a mathematical model of a spinal segment to calculate the combination of rotation angles and lateral inclination of the vertebra, as well as to identify factors influencing these parameters. Material and methods. The developed mathematical model of the motion segment of the spine was used as the main tool for the study. The initial data for this model were the coordinates of the reference points of the vertebrae, which makes it possible to determine a number of parameters describing their complex structure. Using this model, the parameters of the combination of vertebral movement in the frontal and horizontal planes were calculated. Results and discussion. The developed model of the combination of movements in the spinal segment is adequate to the ideas about the nature of movements in the spinal segments. The coefficient of combination of lateral tilt and rotation of the vertebra for the cervical vertebrae is from 0.5 to 0.7, for the thoracic vertebrae from 0.3 to 0.5, and for the lumbar vertebrae from 0.0 to 0.1. Fluctuations in the value of this coefficient depend on the angle of inclination of the upper articular surfaces of the underlying vertebra. Reducing the size of the articular surfaces leads to a decrease in the magnitude of the angular movements of the vertebra, and their convergence leads to an increase in mobility in the spinal segments. A negative angle of inclination of the articular surfaces causes opposite rotation of the vertebra.

Keywords

• mathematical model
• spine
• rotation
• angular parameters
• motion modeling