On the modeling of the intervertebral joint in multibody models for the spine

Abstract

The need to develop feasible computational musculoskeletal models of the spine has led to the development of several multibody models. Central features in these works are models for the ligaments, muscles, and intervertebral joint. The purpose of the present paper is to show how experimental measurements of joint stiffnesses can be properly incorporated using a bushing element. The required refinements to existing bushing force functions in musculoskeletal software platforms are discussed and further implemented using a SpineBushing element specific to the intervertebral joint. Four simple lumbar spine models are then used to illustrate the accompanying improvements. Electronic supplemental material for this article includes a complementary review of formulations of stiffness matrices for the intervertebral joint.

Implementation of physiological functional spinal units in a rigid-body model of the thoracolumbar spine

“…For rigid-body models, only a few nonlinear stiffness expressions were proposed previously and these were either only for one single FSU (Malakoutian et al, 2016;Weisse et al, 2012), for explicitly modelled ligaments (Liu et al, 2019;Liu et al, 2018) or had not been assessed comprehensively (Cholewicki et al, 1996). Whereas for the lumbar spine, some stiffness formulations are available (with being mainly linear formulations) (Christophy et al, 2012;Meng et al, 2015), for the thoracic spine, the stiffness formulations are even more limited. For instance, all thoracic FSUs in (Ignasiak et al, 2016) share similar linear stiffness properties, thereby ignoring physiologic differences across different spinal levels (Liu et al, 2018).…”

Incorporating Six Degree-of-Freedom Intervertebral Joint Stiffness in a Lumbar Spine Musculoskeletal Model—Method and Performance in Flexed Postures

“…In general, multibody musculoskeletal models continue to assume uncoupled motion [41], likely because of the lack of a general method to determine reasonable intervertebral translations. Importantly, incorrect translations generate large errors, thus requiring large residual forces in order to solve [40]. The current study demonstrates a method that will prevent this problem and allow intervertebral translations in future models of the spine.…”

“…Importantly, coupled and uncoupled stiffness produced different A-P translation patterns, and coupled stiffness matched translations measured in vivo [12] better than uncoupled stiffness, demonstrating the fundamental importance of coupling on intervertebral translations. A few prior studies have implemented translational DOF in musculoskeletal models along with coupled intervertebral joint stiffness represented by a 6 Â 6 stiffness matrix, but have examined only neutral spine postures [5,[37][38][39] or have utilized residual force actuators to offset the forces produced by the joint stiffness [40]. In general, multibody musculoskeletal models continue to assume uncoupled motion [41], likely because of the lack of a general method to determine reasonable intervertebral translations.…”

Musculoskeletal modelling of the human cervical spine for the investigation of injury mechanisms during axial impacts

“…The anterior-posterior (x-axis) and medio-lateral (z-axis) axes were defined parallel to the superior surface of the caudal vertebrae with the superior-inferior (y-axis) axis normal to this plane (Fig 2). Six degree of freedom viscoelastic bushing elements comprised of a linear spring and damper in parallel (Kelvin-Voight model) were defined through the OpenSim 3.3 Matlab API to be coincident with the joint frames origins to overcome dynamic errors [43]. Reference values from the literature [9] were used to initialise all degrees of freedom of the four bushing elements.…”