Original ArticleA finite element study and mathematical modeling of lumbar pedicle screw along with various design parameters
Introduction
In today's world, the use of pedicle screw fixation in the field of spinal surgery [1] for the treatment of traumatic disorder, degenerative, thoracolumbar fractures, orthopedical and oncological diseases [2] plays an important role in biomechanical engineering and has gained worldwide acceptance. They are also used for osteoporotic patients [3] (i.e loss of bone tissue in human body). Surgical implementation of pedicle screw increases the bone quality and strength of the diseased functional spinal units (FSU). The primary stability of the pedicle screw depends on the constrained and unconstrained [4] type of screw and rod system, augmentation of the screw [5], insertion torque, pull out strength, stiffness and strain energy [6], anatomical locations of the screw, implant and thread diameter, implant pitch, bone density. Complications and failures occur due to displacement of the screw, the inclusion of various level changes in the arthrodesis, refurbishment of postoperative sagittal and coronal alignment [7] and balance problem of the implant with the bone. The angular fixation of pedicle screw with the bone decreases the pullout stiffness and the minimum sagittal angle [8] and large and longer diameter of the screw increases the pullout and vertebral fixation strength [9]. Cement augmentation of the screw with the bone [10] plays a vital role in the fixation of the pedicle screw.
Finite element (FE) analysis of screw bone connection is performed taking into consideration of the contact connections and various loading tests like flexion, extension, lateral bending and axial rotation [11] where the screws are fused into the lumbar spine model and it has been observed that pull out strength shows excellent results [12]. Pedicle screws are designed by optimizing the pilot hole size for non-self-taping screws, thread design of screw [13] and based on finite element analysis results it has been observed that von Mises stress gives remarkable benefaction to fatigue life cycle [14] bone-implant model. Changes in the implant length and diameter [15] affect maximum deflection, peak stress in screw, mean strain in bone and lead to accuracy in placement of the screw in bone [16] and reduce screw loosening [17]. The screw pullout strengths depend on bone density [18], insertion torque [19] and it has been noted that preoperative treatment maximizes the procurement of the pedicle screw [20] to the bone. The von Mises stress is maximum [21] at the neck of the pedicle screw and it has been noted that flexible fixation shows decrease in maximum stress in the screw and variation of range of motion is observed during flexion, extension, lateral bending, axial rotation and shear [22]. Often flexible rods are attached with pedicle screw [23]. They provide better stabilization and angled insertion of the screw, increase the strength [24] and thus reduce breakage and loosening of the screw. The diameter of the pedicle screw plays an important role [25] in the biomechanical stability of the vertebral column as larger diameter increases the pullout strength and decreases the equivalent stress [26] thus achieving the dynamic neutralization of the spine [27]. It is clear that the lumbar screw has a valuable influence on the control of spinal stability. Various dimensions like pitch length, major diameter, thread profile and the effect of altogether for different load have been studied in terms of stress and strain. Some mathematical formulations have been developed for stress and strain for different types of thread profiles of the screw from which the tendency of stress–strain variation can be premeditated easily.
Section snippets
FE modelling
Using image processing software (MIMICS) a 3D FE model of human lumbar vertebra (healthy, female, 55 years old, 60 kg weight) have been reconstructed from CT scan data. No ethical permission or consent was required, as only CT scan data was used and no patient was involved. In this study, L4 vertebra is taken for analysis purpose. Pedicle screw has been designed using solid modeling software with varying pitch length, major diameter, thread profile and geometry. The pitch varies as 1, 1.5, 2,
Stress distribution within the pedicle screws
For this study, statistical analyses have been performed. Variation of stress is shown in Fig. 4, in which horizontal axis denotes the variation of pitch length (1, 1.5, 2, 2.5, 3, 3.5, 4 mm) and vertical axis denotes von Mises stress on pedicle screw. After applying different loads of 100, 200 and 300 N bending tests have been performed for triangular and trapezoidal pitch that vary from 5.6, 6.6, 7.6 mm as shown in Fig. 4. The von Mises stress on pedicle screw for 100 N load varies from 55 to
Discussion
This study has certain limitations. Pull-out force on the screws, which has a great impact on the implant stability is not considered here. The rods which are always attached with the screws in the clinical situation were also not contemplated in the FE model. In the present work, mechanical behavioral studies were performed using finite element analysis. Loads of various magnitudes (100, 200, 300N are applied to the apex of the pedicle screw. The design factors considered for the design of the
Conclusion
This whole investigation and exploration based on the FE model for the lumbar pedicle screw contributes to some concluding points-
- (1)
According to the bending test for different loads, the stress on the screw for triangular pitch is higher than the trapezoidal pitch for each and every pitch length.
- (2)
Stress on the vertebral bone for trapezoidal screw is less than the triangular screw for every set of applied load and pitch length. The magnitude of the stress increases with increase in pitch length.
- (3)
Funding
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Declaration of competing interest
The authors declare no conflicts of interest associated with this manuscript.
Nomenclature
- Major diameter
- Pitch length
- Stress on screw
- Stress on bone
- Strain on bone
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