Ghost of a Saddle-node Bifurcation

At the 17th “Dynamical Neuroscience” symposium hosted by the U.S. National Institutes of Health (NIH), migraine was presented as a dynamic disease. The discussion revolved around ghosts, saddles, and knots.

The title “Ghost of a Saddle-Node Bifurcation” has clearly caught your attention. It comes from the vocabulary of nonlinear dynamics, better known as chaos theory, a branch of theoretical physics. But this blog post is actually about migraines, as will be the case in so many of my future posts. From time to time, I’ll also discuss other neurological diseases. And always from the perspective of physics.

Theoretical physics and clinical neurology, two seemingly independent fields, converge in the concept of dynamic diseases. This is a term that was deliberately developed over 30 years ago as a counterpoint to that of genetic diseases. While the latter proceeds from the individual parts to the overall system (bottom-up), the former aims to move from the whole to the parts (top-down).

The language of chaos theory differs significantly from that of genetics. In the former, for example, “ghosts” of a saddle-knot bifurcation appear.

Both approaches—that is, the description of a disease at the level of genetics and that at the level of nonlinear dynamics—constantly complement each other. They are even interdependent if one wishes to fully exploit the possibilities of modern medical technology. But of course, not every genetic disease is also a dynamic disease, and vice versa.

What is a dynamic disease?

So what is a dynamic disease? In a groundbreaking 1977 paper, Michael C. Mackey and Leon Glass defined it as diseases whose temporal course follows certain rhythms. These rhythms can be described mathematically using nonlinear dynamics, and within the framework of so-called branching theory, transitions between rhythms can be classified. In short, dynamic diseases are diseases that can be defined with mathematical precision. Behind this lies the hope that this mathematical understanding will also open up novel therapeutic approaches.

The 17th meeting was held under the theme “Dynamic Diseases”

Two weeks ago in Chicago, at a symposium organized by the U.S. National Institutes of Health (NIH), I presented my new work, in which I, together with clinical colleagues, provide experimental evidence and support it with theoretical models to demonstrate that migraine is such a dynamic disease. To do this, I had to expand the concept to include not only temporal aspects of the disease but also spatial ones. In particular, the spatial patterns of pathological neuronal hyperexcitability during a migraine attack. These patterns form in the cerebral cortex in a characteristic manner.

The bottleneck is a transient trap

From bifurcation to bench to bedside – Translational research

According to these new findings, the cause of migraine—from a top-down perspective—is a bottleneck situation. In the language of bifurcation theory, this bottleneck situation stems from the spirit of a saddle-node bifurcation. Of course, the spirit is a metaphor, specifically for a bifurcation that is in the process of resolving. Fortunately, one does not need to understand the background of this metaphor in detail. Put simply, this “spirit” forces a neural overexcitation—which normally subsides quickly—into a characteristic waveform and causes it to persist in this form for a while before it subsides again. This delay is symbolized by the passage through a bottleneck. If this passage takes too long, it can result in neural disturbances (called an aura) and the headaches typical of migraines.

The real challenge lies in bridging the gap from theory through the laboratory to clinical application. Novel therapeutic approaches can either accelerate the passage through the bottleneck or widen the bottleneck. These approaches can be bottom-up, i.e., pharmacological, in which case findings from genetic studies on migraine are helpful. Or they can be top-down, e.g., using EEG feedback and transcranial or visual stimulation.

The translation of these findings from theoretical physics into clinical applications will be the focus of my research in the coming years.