Introduction

The design geometry of a surgical screw directly affects its safety and efficacy. A surgical screw must be strong enough to reliably provide its fastening function and also to withstand the forces of insertion and tightening. While some standards exist for screw geometry [1], a functionally required deviation from standard designs raises questions about safety. In particular, there are many needs for low-profile screws, because the reduced height of the screw head offers several benefits. For instance, a low-profile head protrudes less from a fracture fixation plate, thereby minimizing irritation of overlying tissue. However, the low-profile head may necessitate a drive interface (e.g. hex socket) that is pushed into the screw shank, potentially creating a new critical section for strength. Surgical screw strength has been studied in some detail, though generally with reference to standard screw designs [2]. Thus, there is a need to better understand the effect on strength of designing a low-profile screw head upon an otherwise standardized screw geometry.

A screw that is oversized compared with the hole into which it is inserted generates volumetric interference, and this interference increases the torque required to insert the screw. Such interference may be a functional design specification, intended to stabilize the screw by compacting the bone that the screw thread pushes aside during insertion. This design tactic has been studied to assess its effect on screw pull-out strength [3]. Excessive interference may cause fracture of the bone, or it could result in screw failure if the insertion resistance is too great. Hence, there is need to study the effect that a designed screw-to-bone interference may have on the insertion torque of a surgical screw.

This study consisted of two parts, both aimed at optimizing the design of a low-profile surgical screw. The first part examined the relationship between volumetric interference and screw insertion torque, using CAD analysis and empirical testing. The second part examined the screw\”s mechanical strength in a parametric simulation. The approach and results are discussed as constituting both design verification and validation.

Methods

Screw-to-bone interference

The first objective was to determine the contribution that volumetric interference makes to the total torque required to insert a screw. It was hypothesized that the total work done inserting a screw consists of two parts: 1) a portion to drive the standard thread form through the tapped hole, and 2) a portion to push aside bone as the screw geometry interferes with untapped bone. It was further hypothesized that the work due to interference is proportional to the interference volume. Thus, the work-volume relation was modeled as dW=kdV, with k being an unknown material constant. Substituting the work-torque relationship (dW=Tdθ) led to a relation between insertion torque, the material constant, and the angular rate of volumetric interference: T=kdV/dθ. Hence, it was hypothesized that the torque contribution arising from volumetric interference is proportional to the volume\”s angular rate.

The latter quantity, dV/dθ, was examined using 3D CAD models in Pro/Engineer. A screw model with both a standard thread form and head height was assembled into a model representing a tapped hole. The screw was advanced (\”threaded\”) into the hole until interference started (at the point where the thread runout commenced). Then, the screw was further advanced at rotational increments until it was fully inserted. At every increment, the volumetric interference was determined using the software\”s interference search and calculation function. The resulting data set of V vs. θ was numerically differentiated to provide a data set of dV/dθ vs. θ.

The insertion torque was examined in an empirical test that mimicked the CAD study. High density (40 pcf) rigid polyurethane foam simulated a bone bed. Such rigid foam is commonly used as a surrogate for bone in certain tests [4] because it provides comparable but more uniform properties. The screw was first assembled into a pre-tapped hole to a controlled depth. The initial depth left a short insertion distance over which there was no volumetric interference. Then, the screw was driven into the hole at a constant speed until it was fully inserted, while the driving torque and rotation angle were continuously recorded. The data set was divided into portions before and after the start of interference. The \”before\” portion was extrapolated forward to represent the continued torsional load required without interference volume. In the \”after\” portion, the extrapolated values were subtracted from the total measured torque, leaving the remainder to represent the portion of torsional load attributable to the volumetric interference.

The data from the CAD and empirical studies were then combined at common points of the independent variable θ (insertion angle). Linear regression analysis was applied to assess the hypothesized proportionate relationship.

Screw strength

The second objective evaluated the strength of a low-profile screw design. The design maintained the same, standard thread form of the legacy design. However, its low-profile head necessitated extending the hex drive socket into the screw\”s shank. This in turn raised a question about how close the hex socket could be placed to the screw thread without initiating a stress concentration that was not present in the legacy design.

The question was addressed using a parametric evaluation of a simple axisymmetric finite element model of the geometry in question. The critical screw geometry was simplified to the drive socket, the screw shank, and a short threaded portion. The socket was represented as a conically tipped hole. The shank had the actual diameter. The threaded portion was simplified to a constant diameter that transitioned into the shank via a small fillet radius. The constant diameter of the threaded portion was represented by its pitch diameter. In the parametric study, the proximity between the tip of the socket and the start of the thread was varied, and the maximum stress, occurring in the fillet radius, was recorded. The model was loaded with axial and torsional load values obtained from screw testing reported in the literature [5]. The finite element model was created and analyzed using ANSYS.

Results

Screw-to-bone interference

In the CAD study, the results reflected the complex geometry of the interfering screw and hole. The volumetric interference initially rose at a rapid rate; this stage showed the interference generated over the thread runout. Then, the interference increased at a constant rate. This stage started once the screw\”s shank fully interfered with the tapped hole, after which point, the rate was constant because the screw shank had a constant diameter. Finally, the interference increased at a much greater rate near the final insertion point; this stage represented interference as the screw head penetrated the bone bed.

The results of the empirical testing, and the evaluation after combining the empirical results with the CAD results, are forthcoming and will be discussed at the conference.

Screw strength

The parametric analysis was conducted at nine different levels. The levels ranged from a very close proximity (between the fillet and the socket) that was intuitively unsafe, to a proximity that appeared unlikely to cause a new stress concentration. The analysis results were verified using an independent stress calculation that took data from a relevant stress concentration graph.

The results were examined in a plot of maximum von Mises stress vs. the socket-to-fillet distance (an axially oriented dimension). There was an inverse relationship between the variables. The stress rapidly approached very high values for the smallest distance values, and it approached an apparent asymptotic minimum as the distance increased. Transforming the independent variable to its reciprocal yielded a nearly linear relationship (r2 = 0.99). The resulting linear model was used in determining a sampling plan for an empirical test. Statistical planning software showed that a seven-level test with three samples per level should yield a test with an alpha level of 0.02 and a power of 0.95. Test samples, for a test yet to be conducted, were designed using the same distance values that were assessed in the analysis.

Discussion

Both arms of this study were useful in optimizing the screw design. The functional requirements for the screw necessitated a low-profile head design. This in turn altered the drive interface in a way that would weaken the screw, unless the thread start were moved further down the screw and the shank diameter increased. However, both of these changes would lead to increased screw-to-bone interference and insertion torque, and hence material stress. The parametric strength analysis provided a design curve whereby the screw\”s geometry could be chosen to avoid the introduction of a new stress concentration. Hence, that part of the study was a design verification: It demonstrated that the design could meet the functional requirements for strength. Simultaneously, there was little available information by which to assess the effect of changes in screw-to-bone interference. Since the design changes would necessarily increase the interference, which in turn would increase the insertion torque by an unknown amount, our understanding of a key user requirement, namely a reasonable insertion torque, would be diminished. Elucidating the relation between volumetric interference and insertion torque contributed to a better understanding of the user interface. In this sense, the study provided a design validation: It helped to assure that the design requirement (adequate strength) met a user need (reasonable insertion torque). Since both design verification and design validation must be performed and documented to satisfy FDA regulations, the combined studies partially fulfilled the regulations and likewise helped to assure a safe, effective product.

The simplified geometry used in the finite element model was intended to serve for the purposes of a pilot study. Rather than providing specific results that could be compared with failure stresses, the study aimed to include only the most pertinent geometric details and to simulate the effect of changes in one particular dimension. The results provided a design curve that aided in planning an empirical test which will provide definitive results. A more elaborate 3D FE model of the screw may have provided more accurate stress results. However, since empirical tests are ultimately required, the combined approach of simple modeling followed by analysis-enabled-testing was chosen as the efficient project path.

The rigid foam material used in the interference testing does not exactly represent typical bone into which the screws are inserted. Therefore, the material constant determined cannot be used to directly predict screw insertion torque. Nevertheless, rigid foam has precedence in its usefulness as a surrogate for bone. In the present case, it served in identifying the proportional relationship between insertion torque and the angular rate of volumetric interference. Understanding this proportional relationship, it is hence possible to assess the expected insertion torque of a potential screw design based solely on its angular rate of volumetric interference, which can be easily measured using CAD software. Further work would be required to assess whether actual bone provides a similar proportional relationship, but the broad precedence for rigid foam as a bone testing substitute suggests that a fundamental difference is not likely, in spite of acknowledged property value differences.

References

[1] ISO 5835: \”Implants for Surgery – Metal Bone Screws with Hexagonal Drive Connection, Spherical Undersurface of Head, Asymmetrical Thread – Dimensions,\” International Organization for Standardization, Geneva, 1991.

[2] Hughes, A. N., and Jordan, B. A., 1974, \”Some Mechanical Properties of Surgical Bone Screws of French Manufacture (Stainless Steel) and Uk Manufacture (Titanium Alloy),\” Engineering in Medicine, 3(2), pp. 3-5.

[3] Hee, H. T., Khan, M. S., Goh, J. C., and Wong, H. K., 2006, \”Insertion Torque Profile During Pedicle Screw Insertion of the Thoracic Spine with and without Violation of the Pedicle Wall: Comparison between Cylindrical and Conical Designs,\” Spine, 31(22), pp. E840-6.

[4] Chapman, J. R., Harrington, R. M., Lee, K. M., Anderson, P. A., Tencer, A. F., and Kowalski, D., 1996, \”Factors Affecting the Pullout Strength of Cancellous Bone Screws,\” Transactions of the ASME. Journal of Biomechanical Engineering, 118(3), pp. 391-8.

[5] Nunamaker, D. M., and Perren, S. M., 1976, \”Force Measurements in Screw Fixation,\” Journal of Biomechanics, 9(11), pp. 669-675.