An Investigation of Cardan Rotation Sequences on Lumbar Spine Lifting Kinematics

Abstract

Euler angles are commonly used for kinematic descriptions due to their ability to translate to clinical contexts and the conciseness of using three rotation angles. A challenge with using Euler angles is their dependency on Euler sequence selection. Many studies do not use the same Euler sequence, leading to difficulty comparing across studies. Though sequence selection recommendations have been made, there are disagreements among researchers on these recommendations. The goal of this study is to assess the effect of Cardan sequence selection on lumbar spine motions restricted to a single plane and motions across multiple planes. Cardan sequences are a subset of Euler sequences using all three orthogonal directions. This goal was investigated through collecting the lumbar spine kinematics of 22 human participants performing cyclic lifting tasks in two positions and three directions. Four spine angles were calculated: trunk flexion, lumbar flexion, lumbar lateral rotation, and lumbar axial rotation. It was hypothesized that motion restricted to a single plane would be best represented by sequences where the first rotation matches the plane of motion. Through two lifting tasks restricted to the sagittal plane, this study found sequences other than YXZ and ZXY could describe the four calculated spine angles. It was also hypothesized that motions occurring across multiple planes would be best represented by the sequence with the planes of motion ordered by the magnitude of range of motion, from largest to smallest. This is supported by investigation of four asymmetric lifting tasks where sequences XYZ and XZY were found to give the best representation of the motions performed. In these asymmetric lifting tasks, motion about X was the greatest, and the magnitudes of motion about Y and Z were very similar. When assessing the robustness of Cardan sequences for description of lumbar spine angles across single and multiple-plane lifting motions, we would recommend XYZ or XZY as the sequence of choice.