Quantification of brain morphology has become an important cornerstone in understanding brain structure. Measures of cortical morphology such as thickness and surface area are frequently used to compare groups of subjects or characterise longitudinal changes. However, such measures are often treated as independent from each other. A recently described scaling law, derived from a statistical physics model of cortical folding, demonstrates that there is a tight covariance between three commonly used cortical morphology measures: cortical thickness, total surface area, and exposed surface area. We show that assuming the independence of cortical morphology measures can hide features and potentially lead to misinterpretations. Using the scaling law, we account for the covariance between cortical morphology measures and derive novel independent measures of cortical morphology. By applying these new measures, we show that new information can be gained; in our example we show that distinct morphological alterations underlie healthy ageing compared to temporal lobe epilepsy, even on the coarse level of a whole hemisphere. We thus provide a conceptual framework for characterising cortical morphology in a statistically valid and interpretable manner, based on theoretical reasoning about the shape of the cortex.

中文翻译：

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人脑形态的独立成分

大脑形态的量化已成为理解大脑结构的重要基石。皮质形态的测量，如厚度和表面积，经常用于比较受试者组或表征纵向变化。然而，这些措施通常被视为相互独立。最近描述的缩放定律源自皮质折叠的统计物理模型，表明三种常用的皮质形态测量之间存在紧密的协方差：皮质厚度、总表面积和暴露表面积。我们表明，假设皮质形态测量的独立性可以隐藏特征并可能导致误解。使用标度律，我们解释了皮层形态测量之间的协方差，并推导出新的皮层形态独立测量。通过应用这些新措施，我们表明可以获得新信息；在我们的示例中，我们表明，与颞叶癫痫相比，即使在整个半球的粗糙水平上，健康衰老的基础上也存在明显的形态学改变。因此，我们基于对皮层形状的理论推理，提供了一个概念框架，用于以统计上有效和可解释的方式表征皮层形态。