Inferring White Matter Geometry from Di.usion Tensor MRI: Application to Connectivity Mapping
Inferring White Matter Geometry from Di.usion Tensor MRI: Application to Connectivity Mapping
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DOI：
10.1007/978-3-540-24673-2_11
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发表时间：
2004-05
期刊：
影响因子：
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通讯作者：
C. Lenglet;R. Deriche;O. Faugeras
中科院分区：
文献类型：
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作者：
C. Lenglet;R. Deriche;O. Faugeras
我们引入了一种利用扩散张量 MRI 绘制大脑白质连接图的新方法。 DT-MRI 是一种独特的非侵入性技术，能够探测和量化生物组织中水分子的各向异性扩散。我们解决了在具有潜在多个纤维方向的复杂扩散剖面区域中一致的神经纤维重建问题。我们的方法依赖于对所采集的 MRI 体积进行全局建模，作为黎曼流形，并分 4 个主要步骤进行：首先，我们通过使用 M 上的 Laplace-Beltrami 算子建立布朗运动和扩散 MRI 之间的联系。然后，我们揭示了水分子扩散特性的唯一知识如何足以推断其几何形状。扩散张量和 M 的度量之间存在直接映射。接下来，通过访问该度量，我们提出了一种新颖的水平集公式方案来近似与 M 上的径向布朗运动相关的距离函数。最后，导出了使用指数图的严格数值方案来估计 M 的测地线，将其视为水分子的扩散路径。对合成和真实扩散 MRI 数据集进行的数值实验说明了这种全局方法的潜力。
We introduce a novel approach to the cerebral white matter connectivity mapping from diffusion tensor MRI. DT-MRI is the unique non-invasive technique capable of probing and quantifying the anisotropic diffusion of water molecules in biological tissues. We address the problem of consistent neural fibers reconstruction in areas of complex diffusion profiles with potentially multiple fibers orientations. Our method relies on a global modelization of the acquired MRI volume as a Riemannian manifoldMand proceeds in 4 majors steps: First, we establish the link between Brownian motion and diffusion MRI by using the Laplace-Beltrami operator onM. We then expose how the sole knowledge of the diffusion properties of water molecules onMis sufficient to infer its geometry. There exists a direct mapping between the diffusion tensor and the metric ofM. Next, having access to that metric, we propose a novel level set formulation scheme to approximate the distance function related to a radial Brownian motion onM. Finally, a rigorous numerical scheme using the exponential map is derived to estimate the geodesics ofM, seen as the diffusion paths of water molecules. Numerical experimentations conducted on synthetic and real diffusion MRI datasets illustrate the potentialities of this global approach.