Simeon Smith and Dr. Anton Bowden, Mechanical Engineering Department
Three-dimensional computer models are commonly used to understand and analyze pathological conditions of the spine. Models of the spine are most beneficial when they match each patient’s spinal geometry. Currently, making a model for a specific patient is a long, multi-step process that must be started anew for each person. The goal of this project was to create a parametric model that can be used to instantly generate the spinal geometry of any particular patient based on the input of a few controlling parameters.
My original plan was to first gather spine geometry dimensions by making measurements on 3D spine models created from CT image sets. I was then going to perform statistical analysis to determine relationships between the dimensions so that I would know how the rest of the geometry should change as a few dimensions, or parameters, were changed. The final step was to generate a reference spine model in NX, a CAD software package, and to parameterize it by programming in the dimensions and relationships that I found.
However, I encountered two problems with this plan. First, it turned out that Dr. Bowden no longer had access to the CD image sets from which I was to create 3D models. This made it impossible to find spinal dimensions and parametric relationships. Second, there was much more work than I anticipated involved in creating the reference spine model in NX. I realized that it would involve a time-intensive process of manually defining dimensions and changeable geometry in NX using methods that I was unfamiliar with.
In order to overcome these challenges, it was necessary to change the plan and narrow the scope of the research. For defining dimensions, I decided to use published vertebral dimensions that were measured from actual spines by Panjabi et al*. Since generating a reference model to parameterize would require a great deal of time and was something I did not readily know how to do, I decided to develop a single parametric vertebra as opposed to an entire spine.
With the redefined scope of developing a single parametric vertebra from published dimensions, I began by creating workable geometry for the vertebra in NX. This was the bulk of the work involved in the project and involved a lot of trial and error. The geometry was based off of a stereolithography (STL) file of an L3 vertebra, obtained from Dr. Bowden. In NX, I created planes which intersected the STL model in places where I would need to profile the geometry. In each plane, I sketched a series of points that followed the profile of the vertebra cross section, fit a series of splines (curves) through the points to outline the profile, and defined dimensions between the endpoints of the splines. As the dimensions between the endpoints are changed, the endpoints move position and the splines are moved and scaled accordingly. This is how the geometry transforms as parameters are changed. By matching up endpoints of splines between intersecting planes, I created a 3D wireframe geometry of the vertebra (Figure 1). To complete the geometry, I defined surfaces that were bound by the intersecting splines and whose shape were a very close match to the geometry of the STL model. The geometry was created for half the vertebra and then mirrored across the center plane to generate the other half (Figure 2).
Next, I parameterized the model, using eleven of the linear and angular dimensions given by Panjabi as my independent, controlling parameters. The position of each plane and spline endpoint in the model was defined by a relationship with one of the controlling parameters, so that all of the geometry associated with a given parameter scaled accordingly as that parameter was changed. Originally, I was going to find relationships between some of these eleven parameters so that there were fewer independent parameters. However, this seems like a more accurate and realistic approach since more variation is possible in the geometry. There were some bugs to work out, but in the end I was able to define all of the geometry with sufficient relationships to make a fully parametric vertebra. Some results showing how the vertebra updates with changed parameters are in Figures 3 and 4.
Despite this project resulting in only a single parametric vertebra rather than an entire spine, I still feel it was a success for a few reasons. First, I learned a great deal because I had to problemsolve and find a new way of doing things when the original plan did not work out. I had to employ methods that I did not previously know how to do, many of which did not work the first time. Second, I had a lot of fun doing this research. Third, I feel that this project still offers a significant contribution. This is the first parametric model of a vertebra that has been created, and the methods I developed here can be applied in the same manner to the rest of the vertebrae in order to create an entire parametric spine.