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From optimal control problems to brain stimulation

Friday, 29th November 2019

Location: Technische Universität Berlin
HBS building, Room HBS 005
Straße des 17. Juni 135, 10623 Berlin

Guests are welcome!

Programme

Friday, 29th November 2019

 

Programme
15:00
Sparse Solutions in Optimal Control of Partial Differential Equations
Eduardo Casas, University of Cantabria, Santander (Spain) 

15:50
Coffee Break
16:10
Transcranial stimulation targeting memory-relevant sleep oscillations: 
A potential therapeutic approach in aging and mild cognitive impairment?
Julia Ladenbauer, Kognitive Neurologie, Universitätsmedizin Greifswald

16:35
Applications of optimal control to the dynamics of a whole brain network
Teresa Chouzouris,  Neuronale Informationsverarbeitung, Technische Universität Berlin

17:00
Informal get-together ("Stammtisch")

Abstracts

Sparse Solutions in Optimal Control of Partial Differential Equations

Eduardo Casas,University of Cantabria, Santander (Spain) 

In this talk, we discuss some mathematical questions related to the optimal control of reaction-diffusion equations. First, we discuss the correct formulation of an optimal control problem so that it has at least one solution. This can be achieved by imposing bounds on the control or including a Tikhonov regularization term in the cost functional. In a second step, we motivate and show the necessary conditions for optimality. We explain how these conditions provide information on the structure of the optimal control. In particular, introducing a convenient term in the cost functional, the necessary conditions imply that optimal controls exhibit a sparse structure. We analyze several possible formulations of the control problem leading to optimal controls with different sparse structures. Finally, we show some numerical computations for sparse optimal control of the Fitz-Hugh Nagumo system. 

 

Transcranial stimulation targeting memory-relevant sleep oscillations: 
A potential therapeutic approach in aging and mild cognitive impairment?

Julia Ladenbauer, Kognitive Neurologie, Universitätsmedizin Greifswald

Memory-relevant sleep oscillations, in particular cortical slow oscillations (SO) and thalamo-cortical spindle activity, decrease during aging, which is accompanied by a decline in declarative memory consolidation. These changes are profoundly accelerated in Alzheimer's dementia and its precursor mild cognitive impairment (MCI).
We investigated the potential of slow oscillatory transcranial direct current stimulation, applied during a daytime nap and nighttime sleep in a brain-state-dependent manner, to modulate these activity patterns and sleep-related memory consolidation in healthy elderly and MCI patients.
We consistently found positive immediate effects on SO as well as fast spindle activity. Stimulation further enhanced the functional coupling between SO and spindle activity, a mechanistic component considered crucial for the transfer of memories from hippocampus to cortical long-term storage networks. Regarding memory performance, we observed that stimulation during a daytime nap significantly improved visual recognition performance, while stimulation during nighttime sleep unexpectedly resulted in a negative memory effect.
An explanation for this discrepancy and the relation to other relevant studies will be discussed.
Our findings indicate a well-tolerated therapeutic approach for disordered sleep physiology and memory deficits and advance our understanding of offline memory consolidation.

 

Applications of optimal control to the dynamics of a whole brain network

Teresa Chouzouris,  Neuronale Informationsverarbeitung, Technische Universität Berlin

Modulating and controlling neuronal activity is becoming increasingly important in clinical settings for the treatment of neurological disorders. In this study, we use a model-based approach to investigate the impact of external stimulation on the global dynamics of the brain. We implement a network model simulating spatiotemporal activity in the brain and using methods from nonlinear control theory, we optimize the stimulation effects. The network's structural connectivity is constructed using Diffusion Tensor Imaging (DTI) data from the Human Connectome Project (HCP) divided into 94 cortical and subcortical regions according to the Automated Anatomical Labelling (AAL2) atlas, each region corresponding to a node in the network. The node dynamics are defined by the phenomenological FitzHugh-Nagumo model, simulating the neuronal activity of each brain region. After systematically exploring the network's state space for varying parameters, we add external control to the nodes either synchronizing their dynamics or inducing transitions between the network states. Defining a minimization problem for the above system, we analyse the external stimuli that optimize the input energy and the deviation from the target state. We tune the number of controlled brain regions via applying sparse optimal control. This way, we transition to targeted, local stimulation.

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