November 13, 2009

My Vision and Scientific Achievements

My current and proposed research focuses on challenging problems at the interface of neurology and applied nonlinear science, as a branch of physics. My vision is to design control methods that prevent progressive recruitment of cortical tissue into dysfunctional states occurring during migraine and stroke and transfer results from bench to bedside.

My work has significantly contributed to our understanding of migraine as a dynamical disease. In theoretical studies, I have predicted the generic nature of the nonlinear reaction-diffusion process in migraine, that is, its bifurcation structure. In experimental and clinical studies, I have provided solid evidence for this prediction.

The reaction-diffusion process is known in the medical literature under the name spreading depression or SD. It is a slowly traveling wave that invades human cortex at a pace of about 3 mm/min. It was long believed that SD can invade a whole cortical hemisphere in a full-scale migraine attack, except for the frontal lobe. So roughly speaking 50% of one hemisphere. My work showed that the invaded regions are much more confined (~5%) and, surprisingly, these regions are not predetermined by heterogeneities in the cellular composition of the cortex (cytoarchitectural borders), but determined by 3 factors: the ignition of SD, anatomical landmarks, and emerging universal patterns.

I firstly predicted that cortical perturbations that ignite SD all collapse into the same characteristic shape of a particle-like wave independent of the initial perturbation size. The collapse happens on a comparably fast time scale after which the emerged particle-like SD wave regularly propagates for a longer but again transient time. Eventually it vanishes having covered about 5% of one cortical hemisphere. In the language of nonlinear dynamics, the identified mechanism is called a ghost of a saddle-node bifurcation, a metaphor describing a bottleneck configuration in state space that sucks in all sufficiently largely perturbed cortical states and, while recovery is slowed down, a pattern with universal space and time scales emerges.

I mimicked experimentally in retinal SD the characteristics of this pattern formation process. My next prediction was that the path of such a SD wave depends on cortical folding, which is partly individual and provided therefore a key criteria in confirming the theory by clinical data. Using functional magnetic resonance imaging we establish a map between visual cortex and the visual field in a migraine patient who suffered from typical visual field defects during migraine. We showed that his moving visual field defects matched SD propagation in the patient's cortex precisely the way the model predicted. We obtained a spatial resolution unmatched by direct SD measurements.

I believe, and my colleagues share this view, that the proposed bifurcation structure will open up novel therapeutic approaches targeting migraines by changing the bottleneck passage time. Therefore, I studied in the last three years in detail control methods, in particular time-delayed feedback control (chaos control). Several studies both related to SD propagation but also others considering for example semiconductor systems and coupled excitable elements in networks resulted from this work.

In 2006, the first data of SD in humans during the acute phase of stroke was presented and the hypothesis formulated that SD worsens stroke outcome (recently called 'killer waves' in Nature Medicine). I began to investigated the emergence of re-entrant SD patterns that cycle around the infarct core. The infarct tissue provides an anatomical block for SD similar to the functional block I investigated ten years earlier in spiral SD waves. My particular interest was in an unifying picture that explains transitions form SD patterns related to migraine to those of stroke, because over the last 6 years we collected a data base of 200 migraine patients with persistent visual field defects (> 1 year) but without evidence from noninvasive imaging of migrainous infarction. In a recent study, we proposed a unifying mathematical framework of reaction-diffusion systems with augmented transmission capabilities to study the emergence and transitions between these observed clinical data.

I had the privilege to do all this in collaboration with very distinct colleagues and friends.

1 comment:

  1. I believe, and my colleagues share this view, that the proposed bifurcation structure will open up novel therapeutic approaches targeting migraines by changing the bottleneck passage time.