Phase transitions in a simple model of focal stroke imitate recovery and suggest neurorehabilitation strategies

A stroke is a brain insult that can take offline (often permanently) extended regions of the brain. As a consequence, cognitive tasks or representations implemented by the affected circuitry lose their computational substrate (they become orphan). The brain must adapt to attempt retaining such functions. The existing clinical literature offers a complex picture, often with conflicting observations, about how the brain gets reorganized after stroke. It also does little use of the few mathematical works on the topic. Can a minimal mathematical model of cortical plasticity shed light on this complex phenomenology? Here we explore such minimal model, and find a specific phenomenology: a lasting perilesional reorganization for small injuries, and a temporary contralesional reorganization for large injuries that is not always reverted to ipsilesional. We furthermore show the mechanisms behind these dynamics in our model: a second order phase transition with a critical point, as well as a delayed engagement of perilesional reorganization in large injuries. These dynamics emerge out of a fairly minimal modeling of plasticity, and they reproduce the story put together from clinical observations. We further explore neurorehabilitation strategies, and argue that increased tissue susceptibility (a property that diverges at critical points) can be crucial to manipulate plasticity in beneficial ways.