Programme for the workshop The numerical brain: forward and inverse problems in neuroscience applications

Speaker: Francesca Cavallini (VU Amsterdam, The Netherlands)



Speaker: Daniela Calvetti (Case Western Reserve University, USA)

Title: The numerical challenges of spatially distributed brain energy metabolism models

Abstract: A common way to model cellular metabolism is to use local compartment models in which different cell types such as neurons and astrocytes interact through exchange of metabolites. Such models, while rather straightforward to implement, fail to take into account the effect of diffusion through extracellular space and possibly via astrocyte syncytium. In this talk, we discuss a novel spatially distributed brain metabolism model accounting for the effects of diffusion and tissue heterogeneity. The additional details substantially increase the computational complexity of the model. In this talks we will present the model and discuss an extension to include electrophysiology.

Speaker: Daan Crommelin (CWI, The Netherlands)



Speaker: Axel Hutt (Inria, France)

Title: Forecasting of neural activity by data assimilation and their statistics

Abstract: Data assimilation permits to compute optimal forecasts in high-dimensional systems as, e.g., in weather forecasting. Typically such forecasts are spatially distributed time series of system variables. We hypothesize that such forecasts are not optimal if the major interest does not lie in the temporal evolution of system variables but in time series composites or features. For instance, in neuroscience spectral features of neural activity are the primary functional elements. The present work proposes a data assimilation framework
for forecasts of time-frequency distributions. The framework comprises the ensemble Kalman filter and a detailed statistical ensemble verification. The performance of the framework is evaluated for a simulated FitzHugh-Nagumo model, various measurement noise levels and for in situ-, nonlocal and speed observations. We discover a resonance effect in forecast errors between forecast time and frequencies in observations.

Speaker: Marco Iglesias (University of Nottingham, UK)

Title: Ensemble Kalman Inversion for Magnetic Resonance Elastography

Abstract: Magnetic resonance elastography (MRE) is an MRI-based diagnostic technique used to measure the mechanical properties of biological tissues. MRE data is processed using an inversion algorithm to create a map of these biomechanical properties. In this presentation, I will discuss a new implementation of the ensemble Kalman inversion (EKI) framework for reconstructing tissue biomechanical properties from MRE data. This method offers significant advantages: it accurately identifies variations in material properties at disease boundaries through a level-set parameterization of abnormal/malignant tissue, calibrated within the EKI framework. Additionally, tissue property heterogeneity is modelled using Gaussian random fields, allowing for the evaluation of uncertainty in the reconstructed material properties. We illustrate the benefits of this approach with 2D and 3D experiments using synthetic MRE data of the human kidney and brain.This work is done in collaboration with Deirdre McGrath (Sir Peter Mansfield Imaging Centre, Nottingham), Susan Francis (Sir Peter Mansfield Imaging Centre, Nottingham)) and Michael Tretyakov (Mathematical Sciences, Nottingham).

Speaker: Hanne Kekkonen (TU Delft, The Netherlands)

Title: Edge preserving priors for inverse problems

Abstract: The Bayesian approach to inverse problems allows us to encode our a priori knowledge of the unknown function of interest as a probability distribution. Gaussian process priors are often used in Bayesian inverse problems due to their fast computational properties. However, the smoothness of the resulting estimates is not well suited for modelling functions with sharp changes, such as signals with quick jumps.

To address this, wavelet-based Besov priors offer a promising alternative. Smooth functions with few local irregularities can be sparsely represented in the wavelet basis, making Besov priors ideal for modeling spatially inhomogeneous signals and images. The sparsity-promoting and edge-preservation properties of Besov priors can be further enhanced by introducing a new random variable that takes values in the space of 'trees,' ensuring that the realisations exhibit jumps only on a small set.

Speaker: Tristan van Leeuwen (CWI, The Netherlands)

Title: Challenges in computational imaging of the brain.

Abstract: Several imaging modalities exist that allow one to image the brain. Well-known modalities include CT and MRI. More recently, low-frequency ultrasound has been proposed as a method that could be relatively cheap and safe. These different modalities lead to various challenges when reconstructing the data to obtain 3D images. In this talk, I will give some examples of such computational challenges and possible ways to address them.

Speaker: Frank van der Meulen (VU Amsterdam, The Netherlands)



Speaker: Federica Milinanni (KTH, Sweden)

Title: Inverse Uncertainty Quantification and Forward Uncertainty Propagation in Reaction Network Models

Abstract: Signalling pathways within neurons can be described via reaction networks. Different approaches can be used to model these biological systems: among others, ODE models describe the time evolution of concentrations of reaction compounds, while stochastic models allow us to simulate the number of molecules in the system. In both types of models, reaction rate constants are treated as model parameters. Using experimental data we perform inverse uncertainty quantification on the model parameters in the Bayesian framework, using methods from the class of Markov chain Monte Carlo methods to approximate the parameter posterior distribution. We consider both likelihood-based (SMMALA) and likelihood-free (ABC-MCMC) methods. The uncertainty in the parameters is propagated to predictions and global sensitivity analysis can be performed based on the posterior distribution. We developed an R package, uqsa, that performs many of these tasks. We describe uqsa and show uncertainty quantification results on models and data from neuroscience.

Speaker: Geir Nævdal (Norce, Norway)

Title:  Estimating perfusion using ensemble-based data assimilation

Abstract: The brain perfusion shows how the blood is taken up in different part of the brain and can provide information about how the brain is functioning. In recent works, an approach using ensemble-based data assimilation for estimating perfusion has be developed. The methodology will be presented, and the result obtained with this approach will be compared with common estimates of perfusion.

Speaker: Maria Carla Piastra (University of Twente, The Netherlands)

Title: Source reconstruction of ANT-DBS induced evoked potentials and epileptiform discharges in patients with refractory epilepsy

Abstract: Epilepsy is a chronic neurological disease that afflicts over 60 million people, worldwide. In 70% of the cases, patients can be effectively treated with antiepileptic drugs and for the remainder resective surgery can be an option. When both options are not viable or efficacious, deep brain stimulation (DBS) has emerged as an important treatment option. At present, DBS of the anterior nucleus of the thalamus (ANT) is a Class I evidence treatment for medically refractory epilepsy. However, DBS treatment effects are variable across patients, without knowledge of mechanisms or biomarkers that may account for this variation.

Can we further our understanding of DBS in patients with epilepsy by using a combination of sophisticated and personalized computer simulations and clinical data to improve the treatment?

Speaker: Vincent Rivoirard (University Paris Dauphine, France)

Title: Bayesian estimation of the neuronal functional connectivity graph by using Hawkes processes 

Abstract: Hawkes processes are a specific class of point processes modeling the probability of occurrences of an event depending on past occurrences. They are therefore naturally used when we are interested in the inference of neuronal functional connectivity graphs. We shall focus more specifically on the class of nonlinear multivariate Hawkes processes that allow to model both excitation and inhibition phenomena and parameter estimation will be performed by using the Bayesian nonparametric approach. However, since simulating posterior distributions is often out of reach in reasonable time, especially in the multivariate framework, we will more specifically use the variational Bayesian approach which provides a direct and fast computation of an approximation of the posterior distributions. The aim of this talk will be to present various algorithms based on this methodology, enabling the scaling and analysis in reasonable time of graphs containing several dozen neurons.Joint work with Déborah Sulem and Judith Rousseau.

Speaker: Jean Pascal Pfister (ETH, Switzerland)

Title: Nonlinear Bayesian filtering as a unifying principle in neuroscience

Abstract: A remarkable property of the brain is its ability to perform robust computation while being made of unreliable elements and being driven by ambiguous and noisy stimuli. In this talk, I will argue that a fundamental task that the brain needs to solve is the dynamical extraction of relevant information from a continuous stream of unreliable observations. This task can be generically formulated as a nonlinear Bayesian filtering task. I will therefore reinterpret several phenomena in neuroscience from this nonlinear filtering principle. Short-term plasticity will be seen as a nonlinear filter that estimates the presynaptic membrane potential from observed spikes. Long-term plasticity will be seen as a nonlinear filter that estimates the dynamically changing ground truth weights. Finally neuronal dynamics will be seen as a nonlinear filter that dynamically extracts features from synaptic inputs. Taken together, those results support the idea that the brain is adapted to optimally extract relevant information from unreliable observations. 

Speaker: Marie E. Rognes (Simula, Norway)

Title: Brains in motion: computational mathematics and the brain's waterscape

Abstract: TBA

Speaker: Giovanni Samaey (KU Belgium)

Title: TBA

Abstract: TBA

Speaker: Laura Scarabosio (Radboud University, The Netherlands)

Title: Forward and inverse shape uncertainty quantification with physics-based 

Abstract: We consider the task of quantifying the effect of geometric 
uncertainties on the behavior of a system whose physics is described by 
partial differential equations (PDEs). In particular, we focus on 
uncertainty in the shape of the physical domain or of an internal 
interface. We first address how such uncertainties can be modeled, and 
how to efficiently compute different realizations of the solution to the 
PDE. Then, we will address both the forward propagation of uncertainty 
and the inverse problem in a Bayesian setting. For both cases, we will 
discuss computational methods for efficient shape uncertainty 
quantification and their theoretical guarantees.

Speaker: Erkki Somersalo (Case Western Reserve University, USA)

Title: Sparse dictionary learning and brain activity mapping by M/EEG

Abstract: Magnetoencephalography (MEG) and electroencephalography (EEG)  are brain imaging modalities with excellent time resolution, while the spatial resolution, in particular for deep brain activity, is limited.  Often, it is of less interest to solve the inverse problem in detail to identify exactly the location of the source, but rather identifying an active brain region in an atlas may be sufficient. In this talk, the inverse problem is considered as a dictionary learning problem where the goal is to identify a subdictionary that best explains the data. The methodology is based on the Bayesian paradigm with statistical error analysis incorporated in the method.

Speaker: Jana de Wiljes (TU Ilmenau, Germany)