Importance of nonlinear and multivariable flexibility coefficients in the prediction of human cervical spine motion

The flexibility matrix currently forms the basis for multibody dynamics models of cervical spine motion. While studies have aimed to determine cervical motion segment behavior, their accuracy and utility have been limited by both experimental and analytical assumptions. Flexibility terms have been primarily represented as constants despite the spine's nonlinear stiffening response. Also, nondiagonal terms, describing coupled motions, of the matrices are often omitted. Currently, no study validates the flexibility approach for predicting vertebral motions; nor have the effects of matrix approximations and simplifications been quantified. Therefore, the purpose of this study is to quantify flexibility relationships for cervical motion segments, examine the importance of nonlinear components of the flexibility matrix, and determine the extent to which multivariable relationships may alter motion prediction. To that end, using unembalmed human cervical spine motion segments, a full battery of flexibility tests were performed for a neutral orientation and also following an axial pretorque. Primary and coupled matrix components were described using linear and piecewise nonlinear incremental constants. A third matrix approach utilized multivariable incremental relationships. Measured motions were predicted using structural flexibility methods and evaluated using RMS error between predicted and measured responses. A full set of flexibility relationships describe primary and coupled motions for C3-C4 and C5-C6. A flexibility matrix using piecewise incremental responses offers improved predictions over one using linear methods (p<0.01). However, no significant improvement is obtained using nonlinear terms represented by a multivariable functional approach (p<0.2). Based on these findings, it is suggested that a multivariable approach for flexibility is more demanding experimentally and analytically while not offering improved motion prediction.