Osechinskiy Sergey, Kruggel Frithjof
Department of Biomedical Engineering, University of California, Irvine, CA 92697, USA.
Annu Int Conf IEEE Eng Med Biol Soc. 2010;2010:4278-83. doi: 10.1109/IEMBS.2010.5626179.
The topologically correct and geometrically accurate reconstruction of the cerebral cortex from magnetic resonance (MR) images is an important step in quantitative analysis of the human brain structure, e.g. in cortical thickness measurement studies. Limited resolution of MR images, noise, intensity inhomogeneities, and partial volume effects can all contribute to geometrical inaccuracies and topological errors in the model of cortical surfaces. For example, unresolved touching banks of gray matter (GM) in narrow sulci pose a particular challenge for an automated algorithm, requiring specific steps for the recovery of separating boundaries. We present a method for the automated reconstruction of the cortical compartment from MR images. The method is based on several partial differential equation (PDE) modelling stages. First, a potential field is computed in an electrostatic model with GM posing as an insulating dielectric layer surrounding a charged conductive white matter (WM) object. Second, geodesic distances from WM along the streamlines of the potential field are computed in a Eulerian framework PDE. Third, a digital skeleton surface separating GM sulcal banks is derived by finding shocks in the distance field. At the last stage, a geometric deformable model based on the level set PDE is used to reconstruct the outer cortical surface by advection along the gradient of the distance or potential field. The rule preserving the digital topology, and the skeleton of the distance field resolving fused adjacent banks in sulci, constrain the deformable model evolution. In addition, the deformable model may use the distance field as a constraint on thickness of the reconstructed cortical layer.
从磁共振（MR）图像中对大脑皮层进行拓扑正确且几何精确的重建，是人类脑结构定量分析中的重要一步，例如在皮层厚度测量研究中。MR图像的有限分辨率、噪声、强度不均匀性以及部分容积效应，都可能导致皮层表面模型出现几何不准确和拓扑错误。例如，狭窄脑沟中未分辨出的灰质（GM）相邻区域对自动算法构成了特殊挑战，需要特定步骤来恢复分隔边界。我们提出了一种从MR图像自动重建皮层区域的方法。该方法基于几个偏微分方程（PDE）建模阶段。首先，在一个静电模型中计算势场，其中GM被视为围绕带电导电白质（WM）物体的绝缘介质层。其次，在欧拉框架PDE中沿着势场的流线计算从WM出发的测地距离。第三，通过在距离场中找到激波来推导分隔GM脑沟区域的数字骨架表面。在最后阶段，基于水平集PDE的几何可变形模型用于通过沿着距离或势场的梯度进行平流来重建皮层外表面。保持数字拓扑的规则以及解决脑沟中融合相邻区域的距离场骨架，约束了可变形模型的演化。此外，可变形模型可以将距离场用作对重建皮层层厚度的约束。
