Title : A Novel and Stable Approach to Anatomical Structure Morphing for Enhanced Intraoperative 3 D Visualization

The usage of three dimensional models in planning and navigating computer assisted surgeries is now well established. These models provide intuitive visualization to the surgeons contributing to significant better surgical outcomes. Models obtained from specifically acquired CT scans have the disadvantage that they induce high radiation dose to the patient. In this paper we propose a novel and stable method to construct a patient-specific model that provides an appropriate intraoperative 3D visualization without the need for a pre or intra-operative imaging. Patient specific data consists of digitized landmarks and surface points that are obtained intra-operatively. The 3D model is reconstructed by fitting a statistical deformable model to the minimal sparse digitized data. The statistical model is constructed using Principal Component Analysis from training objects. Our morphing scheme efficiently and accurately computes a Mahalanobis distance weighted least square fit of the deformable model to the 3D data model by solving a linear equation system. Relaxing the Mahalanobis distance term as additional points are incorporated enables our method to handle small and large set of digitized points efficiently. Our novel incorporation of M-estimator based weighting of the digitized points enables us to effectively reject outliers and compute stable models. Normalization of the input model data and the digitized points makes our method size invariant and hence applicable directly to any anatomical shape. The method also allows incorporation of non-spatial data such as patient height and weight. The predominant applications are hip and knee surgeries. Expanded five paragraph summary: Advances in imaging technology and computing power has made computer assisted three dimensional visualization in the operating room a reality. Surgeons now can pick from a wide range of imaging methodology ranging from CT, MRI, PET etc, depending on their requirement. While these visualization techniques greatly enhance the quality of the surgical outcome they have a common drawback. The constant question is the amount of radiation dose injected into the patient. Our goal is to provide an alternative smarter option to the surgeons by generating 3D visualization without conventional imaging techniques. The concepts of principal component analysis (PCA) based statistical shape model building and anatomical shape morphing could be combined together to form a powerful tool to perform shape prediction. A 3D statistical model is constructed from a training set of anatomical shapes. Patient specific data consists of digitized landmarks and bone surface points that are acquired intra-operatively. The patient specific 3D model is reconstructed by fitting the statistical deformable model to the sparse set of digitized points. Fleute et al [1] fit the morphed model surface to sparse intra-operative data via jointly optimizing morphing and pose. Chan et al [2] optimize morphing and pose separately using an iterative closest point (ICP) method. Our initial research on morphing was based on iteratively removal of shape information coded by digitized points from the PCA model presented at SPIE-04 [3]. The extrapolated surface is computed as the most probable surface in the shape space given the data. To seamlessly handle both a small and large set of digitized points and for providing real time interactivity we reformulated the problem as a linear equation system with additional terms to compute a Mahalanobis distance weighted least square fit of the model to the 3D data [4]. We solve for the shape parameters that minimize the residual errors between the reconstructed model and the cloud of random points. Relaxing the Mahalanobis distance term as additional points are digitized greatly enhanced the convergence behaviour of our technique [5]. This novel method operates directly in the PCA shape space incorporating the full set of possible variations. The novelty is that the computation is real time as shape parameters are determined by solving a single linear system of equations. Handling of outliers is a very crucial requirement especially in the surgical scenario. Instead of a using rigid threshold using a box-filter to reject the outliers we decided for a smarter and robust M-estimator based weighting mechanism that creates an inverted valley function. This helps us to effectively reject outliers and compute stable models. The scale of the object plays a crucial role in both modeling and morphing. To achieve shape invariance we normalized the input model data and the digitized points. In this paper we demonstrate proof of principle of our method using the proximal femur structure. We have tested our method on a larger database of 30 objects. CT scans of the model building population were segmented and a sequence of correspondence establishing methods was employed to compute the optimal PCA model. A series of experiments was carried out to evaluate the new method with regards to robustness to outliers and to study the effect of normalization. Three anatomical landmarks, the femoral notch and the upper and the lower trochanter are used as the first set of digitized points. This is used to initially register the model to the patient anatomy. The remaining points are added uniformly across the spherical parameterization so that they occupy different locations on the bone surface. Our experiments verified that the M-estimator based weighting function was very successful in robustly eliminating outliers and also enabling stable predictions (Fig 1). Our normalization schemes also make our method size invariant and readily applicable to any kind of anatomy. Rectangular or box filters are quite easy to incorporate for outlier rejection, but they do not smartly handle the outliers and are quite rigid. Outlier resistance based on Gaussian function seems to be an option but they don’t fall off sharply enough. The novel usage of M-estimators based weighting enables for a smart estimation mechanism that is robust to outliers. Direct incorporation of the M-estimator into the function definition makes the minimization problem nonlinear and not easy to solve. Hence we incorporated the M-estimating weight function into the fitting function. This gives us all the advantages of the M-estimator and also we don’t lose the linearity of the problem. Normalization of the shapes prior to modeling and normalizing the digitized data makes our method size invariant and robust. Our experiments on this proximal femur data show that our method can robustly reject outliers. Our method has the advantage in that it is fast, highly interactive and needs only a small number of points to be digitized intra-operatively. The method also allows incorporation of nonspatial data such as patient height and weight. The predominant applications are surgeries such as total knee arthroplasty and total hip surgery. Supplemental information: Fig 1: Figure showing a screen shot of our method. As can be seen the outliers are robustly eliminated and a stable prediction is realized. References 1. Fleute, M. , Lavallee, S. : Building a Complete Surface Model from Sparse Data Using Statistical Shape Models, MICCAI (1998) 879-887 2. Chan, C.S. , Edwards, P.J., Hawkes, D.J.,: Integration of ultrasound-based registration with statistical shape models for computer-assisted orthopaedic surgery, SPIE, Medical Imaging (2003) 414-424 3. Kumar, T.R. , Nolte, L.P., Styner, M.A.,: Bone morphing with statistical shape models for enhanced visualization, SPIE Medical Imaging (2004). 4. Kumar, T.R. , Joshi, S.C. , Styner, M.A., : Bone model morphing for enhanced surgical visualization, IEEE ISBI : From Nano to Macro ISBI (2004). 5. Kumar T.R. , Nolte L.P., and Styner, M.A.: A Novel Approach to Anatomical Structure Morphing for Intraoperative Visualization MICCAI 2004.