Amortized Bayesian inference on generative dynamical network models of epilepsy using deep neural density estimators.

Whole-brain modeling of epilepsy combines personalized anatomical data with dynamical models of abnormal activities to generate spatio-temporal seizure patterns as observed in brain imaging data. 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 algorithms are required to efficiently estimate the parameters pertaining to the hypothetical areas, ideally including the uncertainty. In this study, we introduce the simulation-based inference for the virtual epileptic patient model (SBI-VEP), enabling us to amortize the approximate posterior of the generative process from a low-dimensional representation of whole-brain epileptic patterns. The state-of-the-art deep learning algorithms for conditional density estimation are used to readily retrieve the statistical relationships between parameters and observations through a sequence of invertible transformations. We show that the SBI-VEP is able to efficiently estimate the posterior distribution of parameters linked to the extent of the epileptogenic and propagation zones from sparse intracranial electroencephalography recordings. The presented Bayesian methodology can deal with non-linear latent dynamics and parameter degeneracy, paving the way for fast and reliable inference on brain disorders from neuroimaging modalities.

Personalised virtual brain models in epilepsy.

Individuals with drug-resistant focal epilepsy are candidates for surgical treatment as a curative option. Before surgery can take place, the patient must have a presurgical evaluation to establish whether and how surgical treatment might stop their seizures without causing neurological deficits. Virtual brains are a new digital modelling technology that map the brain network of a person with epilepsy, using data derived from MRI. This technique produces a computer simulation of seizures and brain imaging signals, such as those that would be recorded with intracranial EEG. When combined with machine learning, virtual brains can be used to estimate the extent and organisation of the epileptogenic zone (ie, the brain regions related to seizure generation and the spatiotemporal dynamics during seizure onset). Virtual brains could, in the future, be used for clinical decision making, to improve precision in localisation of seizure activity, and for surgical planning, but at the moment these models have some limitations, such as low spatial resolution. As evidence accumulates in support of the predictive power of personalised virtual brain models, and as methods are tested in clinical trials, virtual brains might inform clinical practice in the near future.

Delineating epileptogenic networks using brain imaging data and personalized modeling in drug-resistant epilepsy.

Precise estimates of epileptogenic zone networks (EZNs) are crucial for planning intervention strategies to treat drug-resistant focal epilepsy. Here, we present the virtual epileptic patient (VEP), a workflow that uses personalized brain models and machine learning methods to estimate EZNs and to aid surgical strategies. The structural scaffold of the patient-specific whole-brain network model is constructed from anatomical T1 and diffusion-weighted magnetic resonance imaging. Each network node is equipped with a mathematical dynamical model to simulate seizure activity. Bayesian inference methods sample and optimize key parameters of the personalized model using functional stereoelectroencephalography recordings of patients' seizures. These key parameters together with their personalized model determine a given patient's EZN. Personalized models were further used to predict the outcome of surgical intervention using virtual surgeries. We evaluated the VEP workflow retrospectively using 53 patients with drug-resistant focal epilepsy. VEPs reproduced the clinically defined EZNs with a precision of 0.6, where the physical distance between epileptogenic regions identified by VEP and the clinically defined EZNs was small. Compared with the resected brain regions of 25 patients who underwent surgery, VEP showed lower false discovery rates in seizure-free patients (mean, 0.028) than in non-seizure-free patients (mean, 0.407). VEP is now being evaluated in an ongoing clinical trial (EPINOV) with an expected 356 prospective patients with epilepsy.

Circular-circular regression model with a spike at zero.

With reference to a real data on cataract surgery, we discuss the problem of zero-inflated circular-circular regression when both covariate and response are circular random variables and a large proportion of the responses are zeros. The regression model is proposed, and the estimation procedure for the parameters is discussed. Some relevant test procedures are also suggested. Simulation studies and real data analysis are performed to illustrate the applicability of the model.