Modeling and manufacturing of an artificial intervertebral disc.

Stoia, Dan Ioan ; Toth-Tascau, Mirela

1. INTRODUCTION

Degenerative disc disease represents one of the multiple causes of the low back pain (Eijkelkamp, 2002). In treating these diseases, non-surgical treatments are initially prescribed (Metfessel et al., 2005). When surgical intervention is necessary, spinal fusion or Artificial Intervertebral Disc (AID) implantation are performed. The long-term benefits of artificial disc implantation are still unknown, thus, total disc replacement with AID is considered investigational (Regence, 2009).

The development of AID is based on: anatomical knowledge, biomechanical studies, appropriate geometrical models, biomaterials and manufacturing technologies.

Intervertebral Disc (ID) tissue is a cartilaginous structure connecting the vertebral bodies and allowing movement of the spine (Schroeder et al., 2006). The ID is composed of a gelatinous structure called nucleus pulposus surrounded by a fibrous-resistant structure called annulus fibrosus. The disc is subjected to a combination of elastic, viscous and osmotic stresses (Schroeder et al., 2006).

There are some theoretical and experimental studies on ID biomechanics which propose several models and perform comparisons between them (Schroeder et al., 2006).

In order to develop an appropriate geometrical model, the geometrical parameters of an ID can be obtained from the anthropometrical data or acquired by medical imaging investigations (X-ray, CT scan, NMR, etc).

Artificial intervertebral discs are synthetic replacements for damaged ID in the cervical or lumbar regions of the spine (Regence, 2009). AID may be broadly divided into parts that replace the nucleus only (partial replacement) and devices that replace the whole ID (total replacement) (Bradford et al., 2009), (Regence, 2009) (Metfessel et al., 2005), (Eijkelkamp, 2002).

2. ANALITICAL APPROACH

The lower lumbar level (L5-S1 ID) supports the entire weight of the upper body. This static gravity force is distributed on the structure of the disc as a total pressure Pd (figure 1). Due to the geometry of the ID we can admit that this pressure is a sum of two pressures: the pressure on the nucleus pulposus Pn and the pressure on the annulus fibrosus [P.sub.i] (equation 1).

[P.sub.d] = [P.sub.i] + [P.sub.n] (1)

The surface of nucleus pulposus was approximated as half surface of an ellipsoid with the dimensions a, b and c, while the surface of annulus fibrosus was approximated as an elliptic ring shape with the dimensions [a.sub.1] and [b.sub.1].

The anthropometric dimensions of the disc were measured on a computer tomography image. The values are representative for the subject x only, and are presented in the table 1. Here, h represent the total high of the disc; a and b are the equatorial radii (along the x and y axes) and c is the polar radius (along the z-axis); [a.sub.1] and [b.sub.1] are the major and minor semi-axes.

The surface of annulus fibrosus ([A.sub.i]) was calculated by subtracting two surfaces: one of the ellipses which circumscribe the annulus and the other one which circumscribe the nucleus (equation 1). The surface of nucleus pulposus ([A.sub.n]) was calculated using the approximate equation 2, where p = 1.6075 represents the constant of Knud Thomsen (Michon, 2008). The side surface of the analytical calculated ID was calculated using equation 3.

[A.sub.i] = [pi] x [a.sub.1] x [b.sub.1] - [pi] x a x b = 3673.8 [mm.sup.2] (2)

[A.sub.n] [congruent to] 4[pi]/2 ([a.sup.p] x [b.sup.p] + [a.sup.p] x [c.sup.p] + [b.sup.p] x [c.sup.p]/3).sup.1/p] = 952,44 [mm.sup.2] (3)

The total surface of the ID is obtained as a sum of [A.sub.i] and [A.sub.n] (equation 4):

[A.sub.t] = [A.sub.i] + [A.sub.n] = 4626,24[mm.sup.2] (4)

In order to validate the analytical approximation used in the surface calculus, a 3D model of the ID, having the same dimensions, was realized. The model consists of two parts: one is the annulus and the other is the nucleus (figure 2). Using a measurement tool, the area of each one was determined.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

Comparing the measurements with the analytical calculations the differences are less than 3 [mm.sup.2] for the annulus and less than 1 [mm.sup.2] in the case of nucleus. This reduced (0.08% and 0.1% respectively) errors prove the validity of the analytical calculus.

The calculated side area, together with the values of the forces acting at this level (invasively measured by Nachemson (Panjabi & White, 2000) can be used in order to determinate the surface pressure acting on the disc.

3. INTERVERTEBRAL DISC MANUFACTURING

The progress in manufacturing technologies, including rapid prototyping, allows new opportunities to execute the AID components.

Using the rapid prototyping machine LD Modeller 3D Systems, and taking into account the analytical considerations, an intervertebral artificial disc was manufactured. The 3D model used for manufacturing was the same one used for the surface calculation.

The prototyping machine uses the additive method of lamination in order to successively grow the part. Some of the main parameters used in manufacturing process are presented in table 2.

Like any other prototyping process, the lamination uses 3D sliced files which contain information about the model in layer format (Cooper, 2001).

The result of the prototyping process is a plastic disc, having the custom dimensions presented in table 1. During the post-processing stage all the non-solidified peels were removed from the part's contour, resulting the finite piece (figure 3). The disc has valid shapes and dimensions, is stiff and easy to further machining.

The disadvantage of the artificial disc is induced by the fabrication process. The lamination uses a plastic sheet which is not biocompatible and therefore the product cannot be implanted. Anyway, it can be used together with the analytical data in mechanical testing, in order to reveal the portative loading capacity. When the construction accomplishes the strength and stiffness requirements, another process can be used in order to manufacture biocompatible spinal discs.

In spinal constructions, the customization of the mechanical elements plays an important role in reducing the intra-operatory time. The present protocol is dedicated to the customization of the spinal artificial disc (figure 4). Using the three main elements of the protocol (the value of the disc side surface, the manufactured artificial disc, and the loading data), realistic mechanical tests can be performed.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

4. CONCLUSIONS

In order to manufacture an AID, the geometry and the surface area of the natural ID must be well known. In this study, the upper surface of the natural ID was analytical approximated. The conceptual design, followed by the surface measurements confirms the validity of the approximation. In order to validate the conceptual design, the virtual 3D model was prototyped, and an AID physical model was obtained. The AID physical model is not manufactured by biocompatible materials.

This study will be used as a starting point in design, manufacturing and testing of an AID, which represents a future work.

The protocol can be adapted to any intervertebral disc, taking into consideration the load changes and disc size. An improved model will consist of two rigid plates and an elastomeric core interposed between them. Thus, based on the proposed protocol, other customized ID will be designed and manufactured using biocompatible materials.

5. REFERENCES

Bradford, D.S.; Berven, S.H. & Hu, S. (2009). Intervertebral Disc Replacement. A Role in the Management of Chronic Low pain Caused by Degenerative Disc Disease, Available from: http://www.spineuniverse.com/ Accessed on: 2009-05-03

Cooper, K.G. (2001). Rapid Prototyping Technology: Selection and Application, CRC Press, ISBN 978-0824702618, USA

Eijkelkamp, M.F. (2002). On the development of an artificial intervertebral disc, Available from: http://irs.ub.rug.nl/ppn/242148816 Accessed on: 2009-05-03

Metfessel, B.; Marr, T.J.; Dick, J.; Olson, J. & Polly, D. (2005). Technology Assessment Report: Lumbar Artificial Intervertebral Discs, Available from: http://www.icsi.org--Institute for Clinical Systems Improvement Accessed on: 2009-05-03

Michon, G.P. (2008). Final Answers, Available from: http://home.att.net/~numericana/answer/ellipsoid.html Accessed on: 2009-05-03

Panjabi, M.M. & White, A.A. (2000). Biomechanics in the Musculoskeletal System, Churchill Livingstone, ISBN 0-443-06585-3, Philadelphia

Schroeder, Y.; Wilson, W.; Huyghe, J. & Baaijens, F.P.T. (2006). Osmoviscoelastic finite element model of the intervertebral disc. European Spine Journal, Vol. 15, Suppl. 3, August 2006, pp. 361-371, ISSN 1432-0932

*** (2009) http://blue.regence.com/--The Regence Group Surgery Section--Artificial Intervertebral Disc, Accessed on: 2009-05-03

Tab. 1. Anthropometric dimensions of L5-S1 ID for subject x

a[mm] [a.sub.1][mm] b[mm] [b.sub.1][mm] c[mm] h[mm]

20 50 9 27 9 18

Tab. 2. Lamination process parameters

Building technique Sheet lamination
Sheet thickness [mm] 0.15
Number of layers 120
Material sheet type Polyethylene
Post--processing type Removing peel supports