Programme for the workshop The numerical brain: forward and inverse problems in neuroscience applications
| October 21, 2024 | |
|---|---|
| 8:45 – 9:45 | Registration |
| 9:45 – 9:50 | Opening |
| 9:50 – 10:35 | Axel Hutt (Inria) |
| 10:35 – 11:00 | Coffee break |
| 11:00 – 11:45 | Jean Pascal Pfister (ETH) |
| 11:50 – 12:35 | Daniele Avitabile (VU)/Gabriel Lord (U Radboud) |
| 12:35 – 13:45 | Lunch |
| 13:35 – 14:30 | Daniela Calvetti (Case Western Reserve University) |
| 14:35 – 15:20 | Jana de Wiljes (TU Ilmenau) |
| 15:20 – 15:50 | Coffee break |
| 15:50 – 16:35 | Maria Carla Piastra (U. Twente) |
| October 22, 2024 | |
|---|---|
| 9:00 – 9:45 | Marco Iglesias (U. Nottingham) |
| 9:50 – 10:35 | Hanne Kekkonen (TU/D) |
| 10:35 – 11:00 | Coffee break |
| 11:00 – 11:45 | Laura Scarabosio (U. Radboud) |
| 11:50 – 12:35 | Daan Crommelin (CWI, UvA) |
| 12:35 – 13:45 | Lunch |
| 13:35 – 14:30 | Vincent Rivoirard (U. Paris Dauphine) |
| 14:35 – 15:20 | Marie E. Rognes (Simula) |
| 15:20 – 15:50 | Coffee break |
| 15:50 – 16:35 | Tristan van Leeuwen (CWI, UU) |
| 16:35 – 17:30 | Lightning talks |
| 18:30 – 21:00 | Dinner |
| October 23, 2024 | |
|---|---|
| 9:00 – 9:45 | Geir Nævdal (Norce) |
| 9:50 – 10:35 | Erkki Somersalo (Case Western Reserve University) |
| 10:35 – 11:00 | Federica Milinanni (KTH) |
| 11:00 – 11:45 | Giovanni Samaey (KU Leuven) |
| 11:50 – 12:35 | Frank van der Meulen (VU) |
| 12:35 – 13:45 | Closing and Lunch |
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)
Title: Learning model closures for multiscale dynamical systems
Abstract: Model closures based on data have attracted a lot of interest in recent years due to the rapid developments in machine learning methods. Multiscale dynamical systems are approximated with reduced-order models that are augmented with closures, or parameterizations, inferred from data. It has been demonstrated for a variety of systems that data-driven closures improve the finite-time predictions generated by the hybrid model (reduced-order model plus closure). The lead time at which predictions remain accurate can vary substantially between different approaches for learning the closure from data. Furthermore, capturing the correct long-timescale behavior, such as transitions between different regimes or metastable states, is nontrivial. I will discuss some recent results on these issues.
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)
Title: Statistical inference for partially observed stochastic processes via change of measure
Abstract: Stochastic processes are commonly used for modelling in neuroscience. Examples include diffusions generated as solutions to a stochastic (partial) differential equation and point proceses. Estimating parameters based on discrete-time partial observations is often a challenging task, due to intractability of the likelihood (i.e. it cannot be written down in closed form). I will show general ideas on expressing the likelihood as an expectation over a stochastic process that we can simulate from. This paves the way for using methods from Bayesian computation or stochastic expectation maximisation. The underlying principle is that the distribution of the process that is conditioned on the observations can be obtained by a change of measure of the distribution of the unconditional (forward) process. This is joint work with Moritz Schauer, Stefan Sommer, Thorben Pieper and Marc Corstanje.
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 (University of Bern, 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: Multilevel MCMC methods for Bayesian posterior sampling with high-resolution data
Abstract: Sampling Bayesian posterior distributions requires many evaluations of the likelihood, each of which involves a forward model simulation for particular parameter values and a comparison with measurement data. In recent years, multilevel techniques have been proposed to alleviate the cost of these likelihood evaluations by introducing a multilevel hierarchy, both with respect to the resolution of the forward model and with respect to the dimensionality of parameter space. The dimensionality of the data, however, is usually kept fixed. While that is appropriate in settings where measurement data is sparse, the computational cost of the likelihood evaluation is sometimes dominated by the dimensionality of the data when high-resolution data is available. In this work, I will discuss approaches to alleviate this computational cost, by including level-dependent data resolution or by the appropriate use of summary statistics. We illustrate the approaches with examples from civil engineering and cardiac electrophysiology.This talk is based on joint work with Pieter Vanmechelen, Maarten Volkaerts, Marie Cloet, Hans Dierckx and Piet Claus.
Speaker: Laura Scarabosio (Radboud University, The Netherlands)
Title: Forward and inverse shape uncertainty quantification with physics-based
models
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)
Title: Randomised partial observations in continuous filtering
Abstract: The family of Ensemble Square Root Filters (ESRFs) is widely used across various application areas due to their computational efficiency, robustness, and capability to track signals in nonlinear and high-dimensional settings. Many of these discrete filters are connected through a time limit to a deterministic version of the Ensemble Kalman Bucy Filter (EnKBF). Recently, the long-term stability and accuracy of this continuous EnKBF family were investigated under idealized conditions, assuming the underlying system was fully observed. In this study, we examine the signal processing capabilities of the respective filter under fixed, randomized and adaptively changing partial observations.
Lightning talks:
- Diksha Bhandari, Ensemble transform methods for predictive uncertainty in natural language comprehension
- Nadezhda Chaplinskaia, Towards a virtual Deep Brain Stimulation epileptic patient
- Mattia Corti, Uncertainty Quantification for Fisher-Kolmogorov Model on Graphs Applied to Patient-Specific Alzheimer’s Disease
- Caterina B. Leimer Saglio, A high-order Discontinuous Galerkin method for the numerical modelling of epileptic seizures
- Charl Linssen, Neuron and synapse models in NESTML: From specification to simulation
- Angelica Pozzi, Neurodynamics models. Mechanistic model for TMS data and thalamo-cortical modelling
- Jaco J.M. Zwanenburg, Imaging the beating brain with MRI