Research

Check out my research highlights.

Research Statement

From bifurcation to bench and bedside

My research focus is on problems of applied nonlinear dynamics at the interface with clinical research. I develop computational models of neurological diseases in which massive changes in the energy state of neurons play a major role, e.g., in migraine, stroke, and epilepsy. The aim is not only to better understand these diseases but also to identify new opportunities how to translate this research into therapeutical methods that intervene.

In particular, I study cortical spreading depression (SD), a massive but transient perturbation of ion and water homoeostasis in the brain. SD causes neurological symptoms during migraine called aura. During acute stroke, it can also cause infarct expansion, i.e., loss of tissue at risk of infarction surrounding the infarct core. From a biomathematical perspective, SD is an emergent state. It exhibits spatio-temporal correlated large-amplitude fluctuations into states of free energy starvation. The spontaneous recovery (in episodic manifestations) is critically slowed down as the system is close to a nonequilibrium phase transitions (bifurcation) in the brain.

My vision is to design stimulation protocols for medical devices that (i) achieve fewer attacks, (ii) abort attacks in early phases, and (iii) lessen the severity of pain in migraine.

To achieve these three goals, we will design therapeutic intervention strategies using electrical and magnetic stimulation in a control engineering paradigm that (i) prevent nucleation of SD by lowering cortical susceptibility, (ii) shorten the transient decay time (minutes up to 1h) of large-amplitude fluctuations, in the event of SD occurrence, and (iii) speed up the recovery from the aftermath of SD or even completely suppress this abnormal and long-lasting (hours to days) pain state (i.e., central sensitization).

Methods: To this end, I will use a variety methods and follow a dedicated collaborative approach. I investigate molecular mechanisms using computational models for a mechanistic validation of hypotheses from systems medicine, e.g., how disruptions of channel functions in migraine regulate neuronal excitability in a Hodgkin-Huxley model with time-dependent ion concentrations. Mechanosensitivity in channel gating has to be integrated as well as cell swelling in these models. On the next level, models of neuronal subpopulations with specific synaptic receptor distribution will be investigated in the future. On the whole organ level—where most of my work has been done so far—macroscopic pattern formation in SD and neural circuits are investigated, e.g., the migraine-generator network. Finally, sensory and cognitive processing can be perturbed in the prodromal phase. Subtle symptoms often lead to false interpretations of triggers. In the aura phase visual hallucinations occur. Once all levels are integrated, this will allow me to explore risks and therapeutic potential of neuromodulation.

Computational models will help me to tightly integrate experimental and clinical data across diverse scales, from (A) molecular pathways (B) to single cells, (C) to neuronal subpopulations with specific synaptic receptor distribution, (D) to structured tissues (E) to neural circuits and networks, in particular including the migraine-generator network in the brainstem, (F) to mental dysfunctions.