Lumbar spine stenosis (LSS) is a narrowing of the spinal canal that results in pressure on the spinal nerves. This orthopedic disorder can cause severe pain and dysfunction. LSS is a common disabling problem amongst elderly people. In this paper, we developed a finite element model (FEM) to study the forces and the von Mises stress acting on the spine when people bend down. An artificial lumbar spine (L3) was generated from CT data by using the FEM, which is a powerful tool to study biomechanics. The proposed model is able to predict the effect of forces which apply to the lumbar spine. In addition, FEM allows us to investigate the tests into the lumbar spine instead of applying the tests to the real spine in humans. The proposed model is highly accurate and provides precise information about the lumbar spine (L3). We investigate the behavior of humans in daily life which effects to the lumbar spine in a normal person and a patient with LSS. The computational results revealed high displacement levels around the spinal canal and lower displacement levels in the spinal body when bending down. The total displacement of the axial load in a normal person was higher when compared with patients with LSS. Higher degree bends resulted in a lower total displacement when compared with lower degree bends, while the von Mises stress decreased as the bending degree increased.

As the population is aging, the incidence of orthopedic problems among elderly people such as osteoporosis, osteonecrosis, primary and secondary bone tumors, scoliosis, low bone density, osteoarthritis, Paget’s disease, and gout is increasing. These orthopedic disorders can cause severe pain and dysfunction, particularly when affecting the spine. The spine or backbone is an important part of the human body because it supports the body structure and connects the nervous system. The spine is composed of the cervical, thoracic, lumbar, sacrum, and coccyx. The lumbar spine consists of five spinal columns (L1-L5) and supports most of the upper part of the body while also protecting the spinal cord and nerves from injury. Lumbar spinal stenosis (LSS) is a common disease found in the elderly population all around the world [

Finite element simulation models (FEM) are now increasingly used to explore the biomechanical properties of the spine and to guide surgical interventions [

This study aimed to develop a FEM to compare the effect of the total displacement and von Mises stress in a normal person and in a patient with LSS while bending down using an artificial lumbar spine by using a lumbar vertebra model reconstructed from a computed tomography (CT) scan.

A two-dimensional and three-dimensional model of the third lumbar (L3) vertebra was constructed using the CT data of a human lumbar spine. The CT data were taken from a healthy person and a patient with LSS. The complete geometry of a healthy lumbar spine is illustrated in

The lumbar spine was assumed to consist of von Mises elastoplastic material. According to the principles of continuum mechanics, the displacement, stress fields, and stress equilibrium in the lumbar spine can be defined using the following equations;

where

The parameters used during the numerical simulation are shown in

Parameters | Lumbar spine (L3) | Units |
---|---|---|

Young‘s modulus ( |
12000 | PA |

Poisson’s ratio ( |
0.3 | – |

Density ( |
2000 | Kg/ |

The effect of forces applied on the human lumbar spine was simulated based on an average woman’s weight of 58.58 Kg. The forces on the human body when a person bends down at 30-degrees (

(I)

(II)

(III)

The FEM was used to find the numerical solution of the boundary value by multiplying

From symmetry of

Substituting

The divergence theorem was then applied as follows

The surface fraction boundary condition was explained by the equation

which is equivalent to

From

Since

we arranged

The third equation was substituted in the system

We then assumed that

Hence, the variational statement for the boundary value problem was finally stated as follows:

Find

where

In order to find the numerical solution of this variational boundary value problem, we imposed this problem in an

where

which represented a system of 2

Finally, this problem was solved using the quasi-Newton method. The computational analysis was performed using the COMSOL multiphysics (COMSOL Inc., MA, USA).

The effects of the total displacement and von Mises stress on a patient with a normal lumbar spine and a patient with LSS while bending down are illustrated in

The total displacement was then compared using the cross-section line of the domain of the lumbar spine, as shown in

A mathematical model of the lumbar spine has been developed to study the total displacement and von Mises stress between a normal person and a patient with LSS by using the finite element method. Numerical simulations were carried out to evaluate the effect of the forces on the lumbar spine when people bend down. The results showed that high displacement levels occurred around the spinal canal, while a lower displacement was observed around the periphery of the human spine. The total displacement of the axial load in a normal person was higher when compared with a patient with LSS. Higher degree bends resulted in a lower total displacement when compared with lower degree bends, while the von Mises stress decreased as the bending degree increased.

The authors are thankful to the reviewers. This research was supported by the Basic Research Fund of Khon Kaen University. Moreover, this research was also financially supported by Mahasarakham University. The authors also would like to thank the Department of Civil Engineering, Faculty of Engineering, Khon Kaen University for providing the COMSOL Multiphysics package.