Table 1.
Descriptive data of porcine cervical spine segments (C2-C6).
Fig 1.
Experimental set up of the spinal specimen positioned in the impact rig (left) and digital representation as a specimen specific model with virtual registered markers (right). Markers secured to the anterior aspect of the specimen and the cranial and caudal pots were used for the registration process during model creation. The markers of the cranial pot and the clusters secured to the C3, C4 and C5 vertebrae were used as tracking markers in the optimisation.
Fig 2.
Joint and coincident 6 DOF viscoelastic bushing element locations.
Only axial (Fy—left) and anteroposterior (Fx—right) viscoelastic elements were optimised, the parameters of the remaining four degrees of freedom remained at their initialised values.
Fig 3.
Optimisation pipeline used to estimate specimen specific model viscoelastic joint parameters.
Literature values [9] (k1 and b1) were used to initialise the 6 DoF viscoelastic bushing elements of the specimen-specific models (SSM). A total of 16 optimised stiffness (kopt) and damping (bopt) for axial and shear degrees of freedom were estimated.
Fig 4.
Axial loads measured at the cranial load cell during the experiments.
The initial 5 ms (segmented vertical line) of the load traces were used to drive the forward dynamics simulations by applying them to the centre of mass of the C2 segments of the models.
Fig 5.
Parameter values identified by the optimisation procedure.
Axial stiffness (top left), shear stiffness (top right), axial damping (bottom left) and shear damping (bottom right). Values are shown for each of the cervical spine joints identified by the two red coloured vertebrae on the horizontal axis and for each of the five specimens identified by the legends.
Table 2.
Axial stiffness (k) and damping (b) parameter values identified for each specimen specific model of the spinal specimens (S1-S5).
Table 3.
Shear stiffness (k) and damping (b) parameter values identified for each specimen specific model of the spinal specimens (S1-S5).
Table 4.
Root mean square errors (RMSEopt–Column 2) across the 15 tracking markers between measure and simulated kinematics during the optimisation procedure.
Fig 6.
Results of the 1000 sample Monte Carlo sensitivity analysis for the five specimen-specific models.
Results are presented in order of their effect on the ΔRMSE (largest to smallest). The axonometric view (central column) shows the response of the five models as the interpolated 3rd degree polynomial surfaces between the six possible parameter combinations. Left and right columns show the projection of each axis of the parameter variation against the ΔRMSE on their respective sides for S1 as an example of the response.
Fig 7.
Forward dynamic results of theoretical injurious sporting scenario.
Comparison of internal joint loads (Row 2) and resulting joint displacements (Row 3) calculated from the three versions of the musculoskeletal model and across three loading conditions (Row 1). Only joint loads are displayed for the Rugby Model (RM) as the kinematic constraints do not allow for joint translation which is displayed for Impact Specific (IS) and Quasi-Static (QS) versions of the model.