FINITE ELEMENT ANALYSIS IMPROVES SPINAL IMPLANT DESIGN

Surgical implant with model of vertebrae in background.

Finite element analysis (FEA) has enabled the Biomechanics Laboratory of the University of Texas Medical Branch to minimize the principal tensile stresses of a spinal hook implant, thereby reducing the possibility of failure due to stress corrosion. Such a failure could be dangerous to the patient, especially if the spinal hook were to penetrate the neural canal. FEA not only optimized design, according to Dr. Allan Tencer, Director of the Galveston, Texas laboratory, but also dramatically reduced the prototype steps, yielding a time savings of five-to-one.

The field of orthopedic medicine has been using FEA for hips and knees, but its application to the spine is new. It provided a revolutionary tool for Dr. Tencer's laboratory. "Without FEA, it would have been very difficult to get good estimates of the implant's design. We would have ended up doing some hand calculations of its strange shape. Besides, it would have entailed building a lot of different prototypes - varying geometries, testing them mechanically for failure, then trying over again."

The laboratory uses the Algor Supersap full stress/dynamic modeling and analysis package on an IBM AT with an EGA monitor. The IBM AT can handle large finite element problems, integrating analysis with graphics, modeling and meshing. "With Algor," Dr. Tencer says, "you can run through about five different configurations in a day. Without it, it probably would have taken a day or two to build and test a prototype which, incidentally, would not have given the insight that FEA provides."

A company under contract with the laboratory is fabricating the prototype, which the laboratory will soon examine on a testing machine. The spinal hook, four millimeters deep and four millimeters wide, is to attach under a ring of bone through which the spinal cord passes. Holding the hook is an assembly that resides in a surgically created cavity in the spinal musculature. The assembly has rods connecting it to other assemblies placed on the spine. The sizes of the rods vary, from 3/16 inch to 1/4 inch in diameter and from as long as 2/3 the spine's length to one two-inch segment. The composition of the hook and assembly is of a surgical grade stainless steel alloy. Because of the body's corrosive environment, Dr. Tencer explains, its important to have similar material. The body will ultimately break it down in about six months to one year, depending on how much activity the patient is allowed.

Dr. Tencer, an assistant professor of surgery with a Ph.D. in engineering, describes the vertebra as having a complex structural geometry. The front part, where the disks connect to the spine, is cylindrical. Connected to the back of the spine is the ring through which the spinal cord passes. There are projections in three directions from that cylinder, which connect to other tissues, muscles, and ligaments. In seeking the optimal design of the spinal hook, Dr. Tencer could modify three dimensions: its width, the depth of penetration into the spinal canal, and the inner radius of the hook as it goes around the bone.

In order to model the irregular and porous vertebra, the laboratory embedded it in resin, then cut it with a diamond saw into thin sections of about 100 microns, making a set of essentially 2-D planes with finite thickness. X-rays were taken of these slices to distinguish between mineralized bone and any other tissue present. From there, Dr. Tencer used a personal computer based CAD program, VersaCAD, whose data files can be read by Supersap, and a digitizing tablet to create a set of 2-D plane sections. Algor's Layergen was used to connect the flat plane sections together.

For an additional source of verification, the laboratory used holographic laser interferometry to measure the surface deformation on the vertebra at the loading sight of the hook. This technique, Dr. Tencer explains, served to accurately measure very small deformations in the direction of the applied load. "It is similar to using a strain gage, although that gives a very localized output. Here, you can measure the deformation from a set of fringes which appear on the object. The fringes are an actual measure of how much the surface has deformed. Although we cannot see inside the object, which FEA modeling enables us to do, the interferometry lets us verify some parts of the model by comparing the deformations."

Dr. Tencer and stress contour plot.

With the data collected, Dr. Tencer input it into Algor's SuperDraw, a full-featured graphics program providing CAD tools to create models on the screen, using a combination of lines, arcs, circles, and an element library that includes brick, plate/shell, truss, beam, membrane, and pipe. SuperDraw also has symbol capability with automatic scaling. "Submodels" can be stored for placement in other models or placement in different positions in the same model. The Algor program also computes section properties, such as moments of inertia.

To analyze the model, Dr. Tencer created a mesh with Algor's MSHGEN. He entered keynodes, which are the points in space that accurately define the model's outline, then divided it into polygons, called keynode regions. For each region, Dr. Tencer specified the model's density in two directions. Along with specifying the mesh density, he defined edge curvatures and pressures. Adjacent regions were automatically checked for compatible curvatures and mesh densities. Throughout the definition process, the mesh was displayed on-screen with TDraw, enabling Dr. Tencer to modify the mesh as he built it.

Dr. Tencer used Algor's brick element for modeling because it allowed experimentation with the material properties. He also used the plate element for some of the spinal hook design. Dr. Tencer used Layergen to create a 3-D mesh, generating a brick element model from layers of 2-D meshes formed from MSHGEN. The layers did not need to be in the same plane, nor have the same topology, though consistent numbering rules had to be followed. Dr. Tencer specified the number of layers he wanted from each file and how far apart the layers should be. Boundary conditions, material properties, and applied pressure data were all retained from the original MSHGEN files.

With the mesh defined, he put on forces at points in the model. "We had a clear idea where we wanted to load stresses on the spinal hook. We were really identifying point loads," he explains. "Incidentally, some of the meshes got pretty complicated and the only way we could identify the nodes was to use Algor's zoom feature and node numbering to look at the mesh in the area we wanted to and determine where we wanted to apply the load." The model simulated the stresses Dr. Tencer applied - 1100 Newton's (247 pounds), which was an upper-range pullout load that is put on the spine.

To create a stress output file from the processed model, Dr. Tencer used POST, which was able to combine multiple load cases after the model was processed. With TDraw, he superimposed the deflected model onto the original, shown in a different color, and saw the deficiency in the spinal hook design. He iterated changes in its width, inner radius and penetration depth into the spinal canal until he reached a design that minimized the principal tensile stresses. Dr. Tencer points out that all this was accomplished on-screen, without having to build a prototype for any iteration.

The biomechanics laboratory's success with the spinal hook implant has led it to undertake other FEA applications in biomechanics. As Dr. Tencer relates, "We are using FEA to study a sea coral material as a bone substitute. We want to study the intricate structure and the effects of making the implants in mixed materials. That's very difficult to determine experimentally, but FEA helps. We are also applying FEA to study arthritis. When the surface of any joint in the body becomes degraded, the friction increases. As arthritis progresses, there is a mechanical change. We can't account for the reason for the change, but we can actually measure the pressure between the bones as they contact each other. Someday, this should contribute significantly to the etiology of arthritis."

The advantages of using Algor's Supersap full stress/dynamic modeling and analysis package, Dr. Tencer concludes, are that it provides analysis that would not have been practical by any other means; that it dramatically reduces the prototype cycle; and that it integrates analysis with graphics; modeling and meshing.

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