5 Parameter sensitivity analysis on the mode shapes and resonance frequencies in an analytical vibration model of the lumbar spine

J.H. van Dieën Spinal segments with altered stiffness causing spinal deformations and low-back pain might be identifiable by comparing stiffness values between adjacent levels, since positive or negative outliers might indicate a clinically relevant condition. The stiffness matrix of a structure can be obtained by parameter estimation techniques such as model updating, which requires the construction of an analytical model, resembling the “real” structure, based on material properties and geometrical information. For the lumbar spine, these data can be obtained from quantitative computed tomography (qCT) images. However, building subject-specific models is a time consuming procedure, while it is unknown what level of accuracy is needed to obtain a reliable estimate of the stiffness matrix. Therefore, a simple vibration model of the lumbar spine was built based on lumped mass and stiffness to examine the sensitivity of the modal parameters to changes in geometry and mass properties. Input data were obtained from qCTimages of six lumbar goat spines. Subsequently, by changing the input parameters, the normalized relative sensitivities (NRS) of the first three mode shapes and corresponding eigenfrequencies to these input parameters were determined. The NRS of the mode shapes was highest for vertebral height, followed by stiffness, except in mode 2 where mass was more important than stiffness. Also, the eigenfrequencies were most sensitive to changes in vertebral height, followed by stiffness, although mass was more influential in mode 1. Changes in inertia and the location of the centre of mass had less influence on the mode shapes and eigenfrequencies. In conclusion, the most important parameters for successful model updating of the stiffness matrix are vertebral height and mass.