Department of CISE, University of Florida, Gainesville, FL 32611-6120, USA.
Neuroimage. 2012 Apr 15;60(3):1778-87. doi: 10.1016/j.neuroimage.2012.01.095. Epub 2012 Jan 28.
Brain atlas construction has attracted significant attention lately in the neuroimaging community due to its application to the characterization of neuroanatomical shape abnormalities associated with various neurodegenerative diseases or neuropsychiatric disorders. Existing shape atlas construction techniques usually focus on the analysis of a single anatomical structure in which the important inter-structural information is lost. This paper proposes a novel technique for constructing a neuroanatomical shape complex atlas based on an information geometry framework. A shape complex is a collection of neighboring shapes - for example, the thalamus, amygdala and the hippocampus circuit - which may exhibit changes in shape across multiple structures during the progression of a disease. In this paper, we represent the boundaries of the entire shape complex using the zero level set of a distance transform function S(x). We then re-derive the relationship between the stationary state wave function ψ(x) of the Schrödinger equation [formula in text] and the eikonal equation [formula in text] satisfied by any distance function. This leads to a one-to-one map (up to scale) between ψ(x) and S(x) via an explicit relationship. We further exploit this relationship by mapping ψ(x) to a unit hypersphere whose Riemannian structure is fully known, thus effectively turn ψ(x) into the square-root of a probability density function. This allows us to make comparisons - using elegant, closed-form analytic expressions - between shape complexes represented as square-root densities. A shape complex atlas is constructed by computing the Karcher mean ψ¯(x) in the space of square-root densities and then inversely mapping it back to the space of distance transforms in order to realize the atlas shape. We demonstrate the shape complex atlas computation technique via a set of experiments on a population of brain MRI scans including controls and epilepsy patients with either right anterior medial temporal or left anterior medial temporal lobectomies.
脑图谱构建最近在神经影像学领域引起了广泛关注，因为它可用于对与各种神经退行性疾病或神经精神障碍相关的神经解剖形状异常进行特征描述。现有的形状图谱构建技术通常侧重于分析单个解剖结构，在这种情况下，重要的结构间信息会丢失。本文提出了一种基于信息几何框架的神经解剖形状复杂图谱构建新方法。形状复合物是一组相邻的形状 - 例如，丘脑、杏仁核和海马回 - 在疾病进展过程中，这些形状可能会在多个结构中发生形状变化。在本文中，我们使用距离变换函数 S(x)的零水平集来表示整个形状复合物的边界。然后，我们重新推导出薛定谔方程[公式在文本中]的定态波函数 ψ(x)与 eikonal 方程[公式在文本中]之间的关系，该方程由任何距离函数满足。这导致通过显式关系在 ψ(x)和 S(x)之间建立一一映射（在比例上）。我们通过将 ψ(x)映射到其黎曼结构完全已知的单位超球体，进一步利用这种关系，从而有效地将 ψ(x)转换为概率密度函数的平方根。这允许我们使用优雅的闭式解析表达式来进行形状复合物之间的比较，这些形状复合物表示为平方根密度。通过计算平方根密度空间中的 Karcher 均值 ψ¯(x)并将其反向映射回距离变换空间，即可构建形状复合物图谱。我们通过对一组包括对照和右前内侧颞叶或左前内侧颞叶切除术的癫痫患者的脑 MRI 扫描的人群进行的一系列实验，演示了形状复合物图谱计算技术。
