Spine Model for Vibration Analysis - Computational Biomechanics of the Musculoskeletal System - page 178

T12

L1

L2

Annulus and fibers

L3

L4

L5

Ligaments

S1

FIgure 15.2 The finite element model of the T12-Pelvis spine segment in lateral view and back view.

were modeled using three-dimensional cable elements. The interosseous sacroiliac ligament was
also modeled using three-dimensional cable elements and embedded in the imaginary cartilage
between the sacroiliac joint-like fibers. Because the ilium was fixed in the model, which might
provide high stability for the sacroiliac joint, the other ligaments relevant to the sacroiliac joint
were neglected (Guo and Teo 2005).
For modeling, the procedures, methods, and material properties were based on the literature
(Goel, Park, and Kong 1994; Kim et al, 1991; Sharma, Langrana, and Rodriguez 1995, 1998). The
nonlinear stress-strain behaviors of the ligaments were also obtained from the literature (Sharma,
Langrana, and Rodriguez 1995). The nucleus pulposus has a high Poisson's ratio and low Young's
modulus (incompressible, like water). More details about modeling of the human spine have been
given elsewhere (Guo et al. 2005; Guo and Teo 2005). The material properties and element types of
all the spinal components are shown in Table 15.1. The three-dimensional sliding surface-contact
conditions of the facet contact articulation surfaces were built, supporting large deformation and
making it suitable for simulating facet articulation (Guo, Zhang, and Zhang 2011). For all the analy-
ses, the translation degrees of freedom of the inferior surfaces were fixed.
In modal analyses, the upper body mass of the human body is an important factor for the
frequency characteristics of FE models. In this study, the distributed mass of 40 kg was assigned
to the T12-Pelvis FE model, as well as the L1-L5 and L1-S1 finite element models. Eighty percent
of upper body weight was assigned to the top vertebra of the model and the other mass was evenly
assigned to the vertebrae of the L1-S1 segments. The vertical line of the lumped mass was assigned
1.0 cm anterior to the center of the L3-L4 motion segment, which assumes a normal sedentary
posture (Guo et al. 2008).
For FE models with one segment and two segments, only a lumped mass of 40 kg was imposed
on the top of the superior vertebra. Besides consideration of the distribution of upper body weight,
mass changes of the upper body were also studied, from 30 kg to 60 kg in some special studies, for
the assumption of thin or fat people during the modal analysis.
All modeling and simulations were carried out in the commercially available finite element anal-
ysis software ANSYS. After the modal analyses, the natural frequencies and vibration modes of the
FE models were extracted, which could be used for further special analyses.