条形码区分神经元tau蛋白病的形态
Barcodes distinguish morphology of neuronal tauopathy
摘要：
已知神经元的几何形状对其功能很重要。因此，神经元通常按其形态分类。最近的两种方法，持久同源性和拓扑形态描述符，分配一个形态描述符称为条形码的神经元配备了一个给定的功能，如从神经元的根的欧几里得距离。这些条形码可以转换为称为持久性图像的矩阵，然后可以在各组之间进行平均。当定义函数为从根到拓扑的路径长度时，拓扑形态描述子和持久同调是等价的。我们进一步表明，持久性图像所产生的路径长度的程序提供了一个可解释的神经元形态的摘要。我们引入{拓扑形态函数}，一类类似于Sholl函数的函数，可以从相关的拓扑形态描述符中恢复。为了证明这种拓扑方法，我们将健康的皮质和海马小鼠神经元与受进行性tau蛋白病影响的神经元进行比较。我们发现健康神经元的形态和那些在症状后年龄的tau蛋白病有显着差异。我们使用持久性图像得出结论，患病组倾向于具有较短分支的神经元以及远离胞体的较少分支。
英文摘要：
The geometry of neurons is known to be important for their functions. Hence, neurons are often classified by their morphology. Two recent methods, persistent homology and the topological morphology descriptor, assign a morphology descriptor called a barcode to a neuron equipped with a given function, such as the Euclidean distance from the root of the neuron. These barcodes can be converted into matrices called persistence images, which can then be averaged across groups. We show that when the defining function is the path length from the root, both the topological morphology descriptor and persistent homology are equivalent. We further show that persistence images arising from the path length procedure provide an interpretable summary of neuronal morphology. We introduce {topological morphology functions}, a class of functions similar to Sholl functions, that can be recovered from the associated topological morphology descriptor. To demonstrate this topological approach, we compare healthy cortical and hippocampal mouse neurons to those affected by progressive tauopathy. We find a significant difference in the morphology of healthy neurons and those with a tauopathy at a postsymptomatic age. We use persistence images to conclude that the diseased group tends to have neurons with shorter branches as well as fewer branches far from the soma.
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