The human neck is vulnerable. In car accidents, inertia farces of the head can load or deform the tissues of the neck beyond tolerabie limits, resulting in injury. Most neck injuries are minor injuries (whiplash), but they may lead to long-lasting complaints. Severe neck injuries are disabling or fa tal. Knowledge of the mechanisms through which loads cause injuries to the neck (injury mechanisms) is incomplete, especially for minor injuries, for which usually no clearly identifiable damage in the neck can be found. Mathematica! modeHing wil! aid to understand neck injury mechanisms better. The objective of this research is to develop a detailed three-dimensional mathematica! model descrihing the dynamic behaviour of the human head and neck in accident situations without head contact. It was chosen to proceed from a relatively simple model, for gaining insight into head-neck dynamics, towards a more complex model, which includes sufficient details to assess the loads and deformations of the tissues of the neck. This thesis presents these models.

The anatomy, biomechanics and injury mechanisms of the human neck ( or cervical spine) were reviewed. Emphasis was on the mechanica! characteristics ofthe cervical spine and its tissues, which were compiled from the literature and used to construct the models. It appeared that suflident data were available to create a model, even though the characteristics are incomplete, especially for dynamic loading.

First, a relatively simple model with few anatomical details was developed. This global head-neck model camprises a rigid head and rigid vertebrae, connected through three-dimensional nonlinear viscoelastic elements for the intervertebral joints. These joints describe the lumped mechanica! behaviour of the intervertebral disc, ligaments and facet joints. Joint characteristics were derived from the behaviour of motion segmentsof the lower and upper cervical spine. Because these in vitro characteristics result in a too flexible model, the characteristics can be scaled to incorporate the stiffening effect of muscle tensioning on the neck, and to allow for calibration of the model response to impacts. The model was calibrated to match the response of human volunteers to frontal impacts and a reasonable agreement could be obtained. The linear and angular accelerations of the head and the neck rotation agreed satisfactorily, but head rotation was too large. This was ascribed to the too large rotation of the head relative to the neck due to the absence of active muscle behaviour. A parametrie study was performed using a fractional factorial design to quantify the effect of parameter changes on the model response.

Second, detailed segment models of the upper and lower cervical spine were developed as an intermediate step. These models camprise rigid bodies for the vertebrae, three-dimensionallinear viscoelastic elements for the intervertebrai disc, nonlinear viseoelastic line elements for the ligaments, and frictionless contact interactions between almast rigid bodies for the facet joints. Models of lower cervical motion segments C3- C4 and C5-C6 were in good agreement with experiments for smal] loads (20 N, 1.8 Nm) and showed a similar response to large loads (500 N, 20 Nm) as the intervertebral joints of the global model. Their eentres of rotation agreed favourably with experiments. The upper cervical spine model CO-Cl-C2 showed smaller displacements than experiments for smallloads (1.5 Nm) and larger displacements than the joints of the global model for larger loads (500 N, 15 Nm). The eentres of rotation compared well with experiments. Parametrie studies were performed with the C3-C4 and CO-Cl-C2 models.

Finally, the detailed head-neck model was formed by joining the segment models and adding muscle elements. This model camprises a rigid head and rigid vertebrae, linear viscoelastic discs, frictionless facet joints, nonlinear viscoelastic ligaments and contractile Hili-type muscles. Human volunteer responses were used to validate the model. In the lateral impact, the model agreed excellently with the volunteers for the linear and angular accelerations of the head, the trajectories of the occipital condyles and centre of gravity of the head, and the lateral head rotation. Axial head rotation was too large as were the lateral rotations of the lowest intervertebral joints. In the frontal impact, the linear and angular head accelerations agreed reasonably with the volunteer responses, but head and neck rotation were too large. Rotation of the head relative to the neck, however, was accurately reflected due to muscle tensioning. The trajectories also reflected that the model was too flexible. This was mainly attributed to the incapability of the muscle elements to curve around the vertebrae:​ their straight lines of action became unrealistic for large neck rotations, such that the musdes failed to effectively constrain the head-neck motion and stiffen the joints. Further, the lowest joints appeared too flexible compared with the in vivo ranges of motion. Qualitatively, most joint rotations were described accurately, as reflected by their eentres of rotation resembling those found for human volunteers performing slow flexion-extension movements. Tissue loads were compared with (tentative) failure limits and also showed that the deformations were too large for the frontal impact, while they were tolerabie for the lateral impact. A parametrie study was performed to estimate the effect of parameter changes on the model response.

Main conclusions are:​ active muscle behaviour is essential to accurately describe the human head-neck response to impacts;​ the global model is a computationally efficient model and, therefore, especially suited for car safety impravement and dummy neck development;​ the detailed model is suitable for studying neck injury mechanisms and neck in jury criteria, since it reveals the loads and deformations óf individual tissues of the neck. Recommendations are given for additional experiments, model enhancements, and further validation.