Convolutions are a classical hallmark of most mammalian brains. Brain surface morphology is often associated with intelligence and closely correlated with neurological dysfunction. Yet, we know surprisingly little about the underlying mechanisms of cortical folding. Here we identify the role of the key anatomic players during the folding process: cortical thickness, stiffness, and growth. To establish estimates for the critical time, pressure, and the wavelength at the onset of folding, we derive an analytical model using the Föppl–von Kármán theory. Analytical modeling provides a quick first insight into the critical conditions at the onset of folding, yet it fails to predict the evolution of complex instability patterns in the post-critical regime. To predict realistic surface morphologies, we establish a computational model using the continuum theory of finite growth. Computational modeling not only confirms our analytical estimates, but is also capable of predicting the formation of complex surface morphologies with asymmetric patterns and secondary folds. Taken together, our analytical and computational models explain why larger mammalian brains tend to be more convoluted than smaller brains. Both models provide mechanistic interpretations of the classical malformations of lissencephaly and polymicrogyria. Understanding the process of cortical folding in the mammalian brain has direct implications on the diagnostics of neurological disorders including severe retardation, epilepsy, schizophrenia, and autism.

卷积是大多数哺乳动物大脑的典型特征。脑表面形态往往与智力相关，并与神经功能障碍密切相关。然而，令人惊讶的是，我们对皮质折叠的潜在机制知之甚少。在这里，我们确定了折叠过程中关键解剖参与者的作用：皮质厚度、硬度和生长。为了估计折叠开始时的临界时间、压力和波长，我们使用 Föppl-von Kármán 理论推导了一个分析模型。分析模型提供了对折叠开始时的临界条件的快速初步了解，但它无法预测后临界状态中复杂不稳定模式的演变。为了预测真实的表面形态，我们使用有限生长的连续介质理论建立了计算模型。计算模型不仅证实了我们的分析估计，而且还能够预测具有不对称图案和二次褶皱的复杂表面形态的形成。总而言之，我们的分析和计算模型解释了为什么较大的哺乳动物大脑往往比较小的大脑更复杂。两种模型都提供了无脑畸形和多小脑回经典畸形的机制解释。了解哺乳动物大脑中皮质折叠的过程对神经系统疾病的诊断有直接影响，包括严重发育迟缓、癫痫、精神分裂症和自闭症。