Why decussate? Topological constraints on 3D wiring

Many vertebrate motor and sensory systems "decussate" or cross the midline to the opposite side of the body. The successful crossing of millions of axons during development requires a complex of tightly controlled regulatory processes. Because these processes have evolved in many distinct systems and organisms, it seems reasonable to presume that decussation confers a significant functional advantage - yet if this is so, the nature of this advantage is not understood. In this article, we examine constraints imposed by topology on the ways that a three-dimensional processor and environment can be wired together in a continuous, somatotopic, way. We show that as the number of wiring connections grows, decussated arrangements become overwhelmingly more robust against wiring errors than seemingly simpler same-sided wiring schemes. These results provide a predictive approach for understanding how 3D networks must be wired if they are to be robust, and therefore have implications both for future large-scale computational networks and for complex biomedical devices.