The Helical Compliance Vector: Utility for Quantifying Spinal Mechanics

Abstract

Background

This study introduces the helical compliance vector (HCV), a novel measuring parameter that quantifies the orientation and magnitude of joint compliance (inverse of stiffness) by integrating kinetic and kinematic data within the helical axis framework. The HCV provides high temporal and spatial resolution, enabling detailed analysis of compliance and stiffness throughout motion, surpassing the limitations of traditional static or end-range metrics, which often fail to capture transient variations in stiffness and multiplanar interactions that occur during movement.

Methods

Eight cadaveric lumbar segments (L4–L5) were tested under pure moment loading (up to 7 Nm) in lateral bending, flexion/extension, axial rotation, and a multiplanar (Kemp's) test.

Results

The findings revealed distinct moment-specific compliance trends, with the highest compliance during low-moment flexion and the lowest during axial rotation. The Kemp's test demonstrated the HCV's ability to capture complex coupled motions, combining lateral bending and axial rotation motion. Across all loading scenarios, compliance decreased significantly near the end range of motion, illustrating its evolution throughout motion.

Conclusion

By simultaneously characterizing the magnitude and directionality of compliance, the HCV framework offers a comprehensive, high-resolution approach to understanding joint mechanics. This method establishes a foundation for investigating multiplanar joint behaviors and can be extended to in vivo applications using advanced imaging and musculoskeletal modeling technologies.