Astola Laura, Florack Luc, ter Haar Romeny Bart
Eindhoven University of Technology, PO Box 513, NL-5600 MB Eindhoven, The Netherlands.
Inf Process Med Imaging. 2007;20:642-9. doi: 10.1007/978-3-540-73273-0_53.
In this paper we discuss new measures for connectivity analysis of brain white matter, using MR diffusion tensor imaging. Our approach is based on Riemannian geometry, the viability of which has been demonstrated by various researchers in foregoing work. In the Riemannian framework bundles of axons are represented by geodesics on the manifold. Here we do not discuss methods to compute these geodesics, nor do we rely on the availability of geodesics. Instead we propose local measures which are directly computable from the local DTI data, and which enable us to preselect viable or exclude uninteresting seed points for the potentially time consuming extraction of geodesics. If geodesics are available, our measures can be readily applied to these as well. We consider two types of geodesic measures. One pertains to the connectivity saliency of a geodesic, the second to its stability with respect to local spatial perturbations. For the first type of measure we consider both differential as well as integral measures for characterizing a geodesic's saliency either locally or globally. (In the latter case one needs to be in possession of the geodesic curve, in the former case a single tangent vector suffices.) The second type of measure is intrinsically local, and turns out to be related to a well known tensor in Riemannian geometry.
在本文中，我们讨论了利用磁共振扩散张量成像对脑白质进行连通性分析的新方法。我们的方法基于黎曼几何，其可行性已在前人的研究中得到了不同研究者的证明。在黎曼框架下，轴突束由流形上的测地线表示。在这里，我们不讨论计算这些测地线的方法，也不依赖于测地线的可用性。相反，我们提出了一些局部测量方法，这些方法可以直接从局部扩散张量成像数据中计算得出，并且能够让我们预先选择可行的种子点或排除无趣的种子点，以便进行可能耗时的测地线提取。如果有测地线可用，我们的测量方法也可以很容易地应用于这些测地线。我们考虑两种类型的测地线测量方法。一种涉及测地线的连通显著性，另一种涉及它相对于局部空间扰动的稳定性。对于第一种测量方法，我们既考虑用于局部或全局表征测地线显著性的微分测量方法，也考虑积分测量方法。（在后一种情况下，需要拥有测地线曲线，在前一种情况下，一个单一的切向量就足够了。）第二种测量方法本质上是局部的，并且结果表明它与黎曼几何中一个著名的张量有关。
