Structural connectivity in the brain is typically studied by reducing its observation to a single spatial resolution. However, the brain possesses a rich architecture organized over multiple scales linked to one another. We explored the multiscale organization of human connectomes using datasets of healthy subjects reconstructed at five different resolutions. We found that the structure of the human brain remains self-similar when the resolution of observation is progressively decreased by hierarchical coarse-graining of the anatomical regions. Strikingly, a geometric network model, where distances are not Euclidean, predicts the multiscale properties of connectomes, including self-similarity. The model relies on the application of a geometric renormalization protocol which decreases the resolution by coarse-graining and averaging over short similarity distances. Our results suggest that simple organizing principles underlie the multiscale architecture of human structural brain networks, where the same connectivity law dictates short- and long-range connections between different brain regions over many resolutions. The implications are varied and can be substantial for fundamental debates, such as whether the brain is working near a critical point, as well as for applications including advanced tools to simplify the digital reconstruction and simulation of the brain.

大脑中的结构连接性通常是通过将其观察力降低到单个空间分辨率来研究的。但是，大脑拥有一个丰富的结构，该结构以相互关联的多个尺度组织。我们使用以五种不同分辨率重建的健康受试者的数据集探索了人类连接组的多尺度组织。我们发现，当观察的分辨率通过解剖区域的分层粗粒度逐渐降低时，人脑的结构保持自相似。引人注目的是，距离不是欧几里得的几何网络模型可以预测连接体的多尺度特性，包括自相似性。该模型依赖于几何重归一化协议的应用，该协议通过在短相似距离上进行粗粒度化和平均来降低分辨率。我们的结果表明，简单的组织原则是人类结构性大脑网络的多尺度体系结构的基础，其中相同的连通性定律规定了许多分辨率下不同大脑区域之间的短距离和长距离连接。其含义是多种多样的，对于基本的辩论（例如，大脑是否在临界点附近工作）以及包括简化了大脑的数字重建和模拟的高级工具在内的应用程序，可能具有重大意义。相同的连通性定律规定了许多分辨率下不同大脑区域之间的近距离和远距离连接。其含义是多种多样的，对于基本的辩论（例如，大脑是否在临界点附近工作）以及包括简化了大脑的数字重建和模拟的高级工具在内的应用程序，可能具有重大意义。相同的连通性定律规定了许多分辨率下不同大脑区域之间的近距离和远距离连接。其含义是多种多样的，对于基本的辩论（例如，大脑是否在临界点附近工作）以及包括简化了大脑的数字重建和模拟的高级工具在内的应用程序，可能具有重大意义。