Simulation-Based Inference for Whole-Brain Network Modeling of Epilepsy using Deep Neural Density Estimators

Abstract

Whole-brain network modeling of epilepsy is a data-driven approach that combines personalized anatomical information with dynamical models of abnormal brain activity to generate spatio-temporal seizure patterns as observed in brain imaging signals. Such a parametric simulator is equipped with a stochastic generative process, which itself provides the basis for inference and prediction of the local and global brain dynamics affected by disorders. However, the calculation of likelihood function at whole-brain scale is often intractable. Thus, likelihood-free inference algorithms are required to efficiently estimate the parameters pertaining to the hypothetical areas in the brain, ideally including the uncertainty. In this detailed study, we present simulation-based inference for the virtual epileptic patient (SBI-VEP) model, which only requires forward simulations, enabling us to amortize posterior inference on parameters from low-dimensional data features representing whole-brain epileptic patterns. We use state-of-the-art deep learning algorithms for conditional density estimation to retrieve the statistical relationships between parameters and observations through a sequence of invertible transformations. This approach enables us to readily predict seizure dynamics from new input data. We show that the SBI-VEP is able to accurately estimate the posterior distribution of parameters linked to the extent of the epileptogenic and propagation zones in the brain from the sparse observations of intracranial EEG signals. The presented Bayesian methodology can deal with non-linear latent dynamics and parameter degeneracy, paving the way for reliable prediction of neurological disorders from neuroimaging modalities, which can be crucial for planning intervention strategies.

Personalized virtual brains of Alzheimer’s Disease link dynamical biomarkers of fMRI with increased local excitability

“…The prior distribution p ( θ ) of a random event is unconditional probability of a data through beliefs before any evidence from observed data is taken into account, whereas the likelihood function p ( y | θ ) is the conditional probability of the observed data y given a certain set of parameter values θ . For many high-dimensional nonlinear models, such as the BNMs, the calculation of likelihood function becomes computationally expensive or prohibitive, hence, the likelihood approximation algorithms are required to efficiently estimate the parameters (Hashemi et al, 2022). SBI aims to perform flexible and efficient Bayesian inference for complex models when standard methodologies cannot be applied, due to analytic or computational difficulties in calculating the likelihood function (Cranmer et al, 2020).…”

“…Additionally, as a validation step we adapt a mechanistic causal inference framework for the accurate estimation of pathological trajectory by training the deep neural density estimators on model simulations, and the low-dimensional empirical evidence. This is performed by embedding the state-of-the-art deep neural density estimators in simulation-based inference methods (Cranmer et al, 2022) to learn an invertible transformation between parameters and data features from a budget of simulations (Gonçalves 2020, Hashemi et al, 2022).…”

Simulation-based inference for efficient identification of generative models in computational connectomics

“…To account for this limitation, we employed simulation-based inference (SBI, Cranmer et al, 2020 ) methods which only require simulations from the model to perform Bayesian inference. SBI has been applied previously in various fields, ranging from genomics ( Bernstein et al, 2021 ), evolutionary biology ( Ratmann et al, 2007 ; Avecilla et al, 2022 ), computational and cognitive neuroscience ( Gonçalves et al, 2020 ; Oesterle et al, 2020 ; Deistler et al, 2022b ; Groschner et al, 2022 ; Sabbagh et al, 2020 ; Hashemi et al, 2022 ), to robotics ( Marlier et al, 2021 ), global health ( de Witt et al, 2020 ) and astrophysics ( Alsing et al, 2018 ; Dax et al, 2021 ). For the wiring rule examples presented here, we used sequential neural posterior estimation (SNPE, Papamakarios and Murray, 2016 ; Lueckmann et al, 2017 ; Greenberg et al, 2019 ), which performs neural-network-based conditional density estimation to estimate the posterior distribution from simulated data.…”

Methods and considerations for estimating parameters in biophysically detailed neural models with simulation based inference

“…Another advantage is that SBI estimates a full distribution over model parameters that may account for the data and provides information about parameter interactions [14,18]. This information is not possible with optimization techniques that have historically been used in large-scale biophysical models such as COBYLA [5,19] and genetic algorithms [3,20], which estimate only a single parameter configuration that best fits While the substantial methodological advancements offered by SBI are promising, and have been applied to estimate parameters in small biophysically detailed neuron models [18,21] and in models with reduced representations of neural dynamics [22,23], there is currently little guidance on how these methods should be used with large-scale biophysical models. Guidance is particularly lacking in the context of performing inference on neural time series data, and in comparing estimates for data from different experimental conditions.…”