Biomechanical modeling of metal screw loadings on the human vertebra

Abstract

During spinal fusion surgery, angled screw insertion can provide a more favorable stress distribution reducing failure events (screw breakage and loosening). Finite element (FE) analysis can be employed for identifying the optimal insertion path, preventing stress concentrations, and ensuring a lower failure incidence. In this work, a patient-specific FE model of L4 vertebra, virtually implanted with two pedicle screws, was obtained from diagnostic images and numerically investigated. Linearly elastic, inhomogeneous, and isotropic material properties were assigned to bone based on density distributions reconstructed from the medical images. The mechanical response of the screws-vertebra system was analyzed through a progressive damage procedure, considering a stress-based criterion. Different screws insertion angles were simulated, as well as physiological loading conditions. In each loading case, screw orientation influences the fracture mechanism (i.e., brittle or ductile one), as well as the fracture pattern and load. Besides, stresses in trabecular bone and pedicle screws are significantly affected by the screw configuration. The caudomedial trajectory indicates the most safe case, significantly reducing the stress concentrations in both trabecular bone and screws. Our findings aim to furnish a useful indication to surgeons regarding the screws insertion angle, further reducing the failure risk and improving the clinical outcome of the fixation procedure.

GraphicAbstract

A patient-specific image-based FE modeling strategy of implanted human vertebra is developed and used to investigate the effect of pedicle screw insertion angles on the stress distribution in the human vertebra to find the safest screw insertion trajectory that minimizes stress concentrations reducing the onset of loosening phenomena and/or screw breakage. A caudomedial trajectory significantly reduces the stress concentrations in both trabecular bone and screws, resulting in the least critical case, thus safer from a clinical perspective.

Appendix A

To derive the density-based E values for the cortical shell of the vertebra, a customized equation (Eq. (5)) has been adopted and derived as follows. Five values of $\rho _{app}$ and the corresponding E values have been defined. These pairs have been chosen through a preliminary analysis aiming to obtain for the cortical shell a heterogeneous E distribution with values of Youngs modulus in line with the literature (i.e., ranging from 12 to 14 GPa). Then, these pairs have been fitted through a fitting procedure. Among the several fitting relations, a power relationship, that can be expressed in a general form as

$$\begin{aligned} y=a \times x^{b}+c \end{aligned}$$

(A1)

has been chosen due to its ability to fit well data with a coefficient of determination R$^2$ equal to 0.91. In Table 5, the $\rho _{app}$-E values used to derive the Eq. (5) have been reported. The fitting procedure furnished the following coefficients for the power relation expressed by Eq. (A1): $a=-892.5$, $b=-2.491$ and $c=14360$.

Table 5 The pairs $\rho _{app}$-E that have been used to derive the density-elasticity relationship for the cortical bone

1.1 Appendix B

In Tables 6 and 7 the p values of the Shapiro-Wilk test and Levene’s test have been reported for the two tested variables, i.e. $\sigma _{\max }$ and $\sigma _\mathrm{{VM}}$.

Table 6 Shapiro-Wilk and Levene’s tests results for screws insertion angles comparison. The variable tested is $\sigma _{\max }$

Table 7 Shapiro-Wilk and Levene’s tests results for screws insertion angles comparison. The variable tested is $\sigma _{\text {VM}}$