Statistical shape model for probabilistic studies of the lumbar spine, A

Abstract

Introduction: Computational modeling of the spine has become a promising option for evaluating the performance of new spinal implants and procedures before they are used in patients. Most models in the literature only represent a single subject and neglect normal variation that exists between specimens. However, using a probabilistic simulation (select input variables from a normal distribution and determine how they affect outputs) of virtual patients, whose geometries are representative of actual patients, may lead to viable options for pre-clinical evaluation of devices and procedures. One of the major challenges to overcome when applying probabilistic modeling techniques to biologic systems is to capture normal shape variation between subjects. Methods: Vertebral body geometries from 8 normal CT scans were used to develop a statistical shape model (SSM) of the lumbar spine. The SSM model is comprised of eigenvalues and eigenvectors calculated with a principle component analysis. Eigenvectors, also called modes, represent how shape varies in the geometry and eigenvalues represent how important each mode is to the overall shape of the geometry. Any specimen can be represented by P= P_mean+Sum_(j=1,m)[b_j*c_j] where bj are scalar coefficients and cj are the eigenvectors. Virtual specimens can be created by randomly sampling the normal curve for each b coefficient. A finite element model, shown in figure 1, was developed containing eight ligaments (non-linear springs), an intervertebral disc (hyperelastic annulus, fluid cavity for nucleus), and linear elastic cartilage (2mm thick). A compression load of 800 N and 7.5 Nm of axial rotation was applied to the model and it was solved using Abaqus. The model was validated using experimental range of motion data. For the purpose of probabilistic analysis, tens to hundreds of model runs are desired. To facilitate the generation of these models, a procedure was developed to incorporate geometry from the SSM, automatically place ligaments and generate cartilage. Results: The first mode shape was a scaling mode, the second was associated with shape and angulation of the facet joints and the third produced variations in transverse processes. Higher modes were not visually obvious. Models created from virtual geometries demonstrated noticeable shape variation but they mated quantitatively similar to models generated from CT scans (naturals). Qualitatively, differences between virtual specimens and natural specimens were not statistically different for either area or average pressure. For manual and automatic cartilage, contact area was observed in the same general location and contact pressure was similar, 2.43 MPa compared to 2.22 MPa. Discussion: Shape variation in the lumbar spine was characterized using a statistical shape model. Models created with virtual specimens demonstrated facet contact similar to models generated with natural specimens. Cartilage generation that was automated for a probabilistic study resulted in quality meshes that fit flush into the facet geometry. With the success of models developed using virtual specimens, the same methods can be applied to the entire lumbar spine. Next steps for creating a probabilistic model are to automate the alignment of vertebral bones and implementation of probabilistic computations using a Monte Carlo method.