Griffin L D
Department of Neurology, UMDS, Guy's Hospital, London, U.K.
J Theor Biol. 1994 Feb 7;166(3):261-73. doi: 10.1006/jtbi.1994.1024.
The mammalian cerebral cortex is a profoundly convoluted six-layered surface. The expansion of the cortex during evolution appears to be due to an increase in the number of functional units as opposed to an increase in the complexity of the units. Geometric similarity predicts that cortical area should increase in proportion to the 2/3 power of cortical volume. Allometric analysis has shown that in fact cortical area increases as a nearly linear function of cortical volume. This can be understood by appreciating that smaller brains tend to be smooth (lissencephalic) and larger brains fissured (gyrencephalic). This process of fissuration has reached its modern terrestrial limit in the human brain where the majority of the cortical surface is hidden within folds. The thickness of the cortex (2-3 mm) is small compared to its area (2000-2500 cm2) so the application of the techniques of differential geometry (the mathematics of idealized surfaces) is justified. Geometric properties of surfaces fall into two categories: intrinsic properties (which are invariant under folding of the surface, e.g. distances measured on the surface) and extrinsic properties (pure folding). The extrinsic geometry of the cortex determines the anatomical appearance of the cortex and the shape of the white matter. The intrinsic curvature of the cortex affects the relative position of functional areas and the spread of activity within the surface itself. A cortical surface has been reconstructed from cross-sections. Analysis of this surface has shown that the cortex has significant intrinsic curvature and hence it is wrong to regard it as merely a crumpled bag. The particular geometry observed is such that the surface is peculiarly "close together". Theoretical considerations and simulations suggest that the intrinsic geometry may have a significant effect on: the necessity of non-uniform growth in models of cortical development; the location of integrative areas; and the synchronization of neuronal firing. It is suggested that intrinsic descriptions of the cortex may prove more natural than extrinsic ones.
哺乳动物的大脑皮层是一个高度卷曲的六层结构表面。在进化过程中，皮层的扩展似乎是由于功能单元数量的增加，而非单元复杂性的增加。几何相似性预测，皮层面积应与皮层体积的2/3次方成正比增加。异速生长分析表明，实际上皮层面积随皮层体积几乎呈线性增加。这可以通过认识到较小的大脑往往是光滑的（无脑回的），而较大的大脑有沟回（有脑回的）来理解。这种沟回形成过程在人类大脑中达到了现代陆地生物的极限，其中大部分皮层表面隐藏在褶皱之中。与皮层面积（2000 - 2500平方厘米）相比，皮层厚度（2 - 3毫米）较小，因此应用微分几何技术（理想化表面的数学）是合理的。表面的几何特性分为两类：内在特性（在表面折叠下不变，例如在表面上测量的距离）和外在特性（纯粹的折叠）。皮层的外在几何决定了皮层的解剖外观和白质的形状。皮层的内在曲率影响功能区域的相对位置以及表面自身内活动的传播。已从横截面重建了皮层表面。对该表面的分析表明，皮层具有显著的内在曲率，因此将其仅仅视为一个皱巴巴的袋子是错误的。观察到的特定几何形状使得表面特别“紧密相连”。理论思考和模拟表明内在几何可能对以下方面有显著影响：皮层发育模型中不均匀生长的必要性；整合区域的位置；以及神经元放电的同步性。有人提出，对皮层的内在描述可能比外在描述更自然。
