Letters to the Editor

We appreciate the author(s)’ letter to editor for the discussion and the series of interesting questions that were posed. It is an inevitable fact that a model is bounded by inputs described to it in the form of material properties, boundary conditions and constraints. These series of inputs dictate the response of the system that is modelled. Therefore, particular attention must be given to all aforementioned input properties, if a realistic result is to be obtained. As in any modelling approach, we were faced with a series of contradicting reports in the literature that affect the outcome of the model. However, we have relied on the mainstream publications that many previous authors have already cited in their studies. The first issue the authors have brought up is that the study of porcine spinal ligaments has shown that those ligaments close to the vertebrae (ALL and PLL) have no attachment sites on the bony elements. This is contrary to our own observation during multiple in vitro experiments and other studies that we have come across. A detailed description of ligament attachments has been provided by the following authors: Panjabi et al. (1982), Shirazi-Adl et al. (1986), McGill (1988) and Schmidt et al. (2007), in which the attachment sites were indicated to be on the edge of the vertebrae in the lumbar region. The authors have suggested that lumbar ligaments may have little contribution in resisting an external load during flexion/extension. In the literature, it is well accepted that every joint in the human skeletal system, including the lumbar spinal joints, is surrounded by several ligaments, by which the joint movement is primarily restrained and stabilised (Solomonow 2009). Solomonow (2009) has further described that ‘as joints go through their range of motion, the ligaments ensure that the bones associated with the joints travel in their prescribed kinematic path, to keep the articular joint surfaces in contact at all times’. Therefore, the ligaments of the lumbar spine must also have a mechanical purpose and affect joint loads during motion. Further, the authors have suggested that the apophyseal joints may have a larger contribution in limiting segmental motion in flexion/extension. Although we agree with the authors, as we included the facets in our model to address what we felt was a shortcoming of previous simulations, the contribution of the ligaments still cannot be ignored during flexion/extension motion, as we have stated in our paper. We have observed that the ligaments’ resistance to the external loads varies for each direction of applied load. In extension, we have shown that there is a complex load sharing between ligaments, facets and intervertebral disc. We commented that the facets may even play a larger role in flexion, when one considers the weight of the upper trunk in forward postures. Furthermore, to the suggestion of the authors about the lack of loadbearing characteristic of the disc during flexion, we may cite Adams et al. (1980), who have shown that the intervertebral disc can withstand more than half of the bending moment applied externally to a functional spinal unit. With respect to kinematics, Heuer et al. (2007) have also shown, under 10 Nm applied bending load, that the intervertebral disc still provides a substantial resistance to bending, even after transecting the complete set of lumbar ligaments. The authors have suggested that the ligaments’ proprioceptive role may be an important topic to explore. Indeed, we strongly agree that an optimal model would be the one that contains a full material description of ligament properties (including nonlinear viscoelasticity) to most accurately predict ligament strain, as an indication of a potential proprioceptive function. It is known that the stretch characteristics of the ligaments may be a stimuli for proprioceptive receptors to activate deep back muscles (paraspinal muscle, multifidus), as it is described by Solomonow et al. (1999). However, the goal of the current study was to develop a generic approach for a multi-body spinal model, in which the most important factors were included to allow a reasonable estimate of a load sharing between the passive elements of the lumbar spine during a simulated physiological range of motion. As Solomonow et al. (2000) have stated, viscoelasticity and creep of the spinal ligaments may influence the ligaments’ proprioceptive role, and, therefore, we agree that the viscoelasticity of the ligaments, and their response to varying strain rates, is an important aspect to be included in any future model of the lumbar spine. The current model, as described in the paper, has this potential and can accept any linear or nonlinear properties of the ligaments, once accurate data are available. The authors’ objection to the nonlinear length–tension relationship of the ligaments is regarded as an important and valid comment. We referred to the publication of Zander et al. (2004) to underline the variability of simulation results due to ligament stiffness. The current