Quantifying the centre of rotation pattern in a multi-body model of the lumbar spine

Understanding the kinematics of the spine provides paramount knowledge for many aspects of the clinical analysis of back pain. More specifically, visualisation of the instantaneous centre of rotation (ICR) enables clinicians to quantify joint laxity in the segments, avoiding a dependence on more inconclusive measurements based on the range of motion and excessive translations, which vary in every individual. Alternatively, it provides motion preserving designers with an insight into where a physiological ICR of a motion preserving prosthesis can be situated in order to restore proper load distribution across the passive and active elements of the lumbar region. Prior to the use of an unconstrained dynamic musculoskeletal model system, based on multi-body models capable of transient analysis, to estimate segmental loads, the model must be kinematically evaluated for all possible sensitivity due to ligament properties and the initial locus of intervertebral disc (IVD). A previously calibrated osseoligamentous model of lumbar spine was used to evaluate the changes in ICR under variation of the ligament stiffness and initial locus of IVD, when subjected to pure moments from 0 to 15 Nm. The ICR was quantified based on the closed solution of unit quaternion that improves accuracy and prevents coordinate singularities, which is often observed in Euler-based methods and least squares principles. The calculation of the ICR during flexion/extension revealed complexity and intrinsic nonlinearity between flexion and extension. This study revealed that, to accommodate a good agreement between in vitro data and the multi-body model predictions, in flexion more laxity is required than in extension. The results showed that the ICR location is concentrated in the posterior region of the disc, in agreement with previous experimental studies. However, the current multi-body model demonstrates a sensitivity to the initial definition of the ICR, which should be recognised as a limitation of the method. Nevertheless, the current simulations suggest that, due to the constantly evolving path of the ICR across the IVD during flexion-extension, a movable ICR is a necessary condition in multi-body modelling of the spine, in the context of whole body simulation, to accurately capture segmental kinematics and kinetics.