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1Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN 55455, USA, 2Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA, 3Department of Radiology, University of Minnesota, Minneapolis, MN 55455, USA, 4Department of Neurology, University of Minnesota, Minneapolis, MN 55455, USA |
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| Modeling & Analysis Abstract |
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| Intoduction FreeSurfer (FS) [1], a popular software package for cortical surface flattening, explicitly minimizes metric distortion of the flattened surface. In contrast, LSCM [3] and CirclePack (CP) [2] are quasi-conformal flattening methods that preserve angles locally; however, spherical maps generated by these methods can be normalized by a Moebius transformation that minimizes metric distortion among the auomorphism group. All three methods can flatten user-defined patches as well as an entire cortical surface. Methods Topologically-correct triangulated surfaces of the left hemisphere were extracted from two high-resolution T1 MRI brain volumes (MNI, PENN) that had been parcellated by an expert neuroanatomist; parcellation of the extracted cortical sheet was guided by the volume parcellation using in-house software (ParcelMan [4]). For each brain, the left hemispheral cortex (equivalent to a topological sphere) and four lobar cortical patches (equivalent to topological discs) were flattened using FS, LSCM, and CP to create the corresponding spherical or planar maps. Measurements of angular and metric distortion of the flattened surfaces [3], which are invariant under the similarity transformations were used to describe the quality of resulting maps. Results and Conclusions Measurements of angular and metric distortion for the three methods, two brains, and five surfaces (the left hemispheral cortex and four lobar patches) are presented in Table 1, and frequency histograms of angular and metric distortion for the MNI left hemispheral cortex are illustrated in Figure 1. For the lobar patches FS clearly outperforms both conformal methods with regard to the preservation of metric information; however, for the MNI left hemispheral cortex FS and LSCM produce similar results for mean metric distortion: 31.72% and 36.07%, respectively. For all five surfaces LSCM is superior to the other methods with regard to the preservation of angular information, and CP and LSCM perform similarly with regard to metric distortion. Thus, by preserving angular (shape) information and adequately preserving metric information, LSCM may offer advantages to methods such as FS, which preserve only metric information, for flattening hemispheral cortical surfaces. References 1. Fischl B., et al., Neuroimage 9:195-207, 1999. 2. Hurdal M.K., et al., LNCompSci, 1679:279-286, 1999. 3. Ju L.L., et al., NeuroImage 19:S864, 2003. 4. Rehm K., et al., HBM2004, submitted. Acknowledgements This work is supported in part by NIH grant MH57180 and NSF grant DMS101339.
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