Epilepsy is a prevalent brain disorder, characterized by sudden, abnormal brain activity, making it difficult to live with. One-third of people with epilepsy do not respond to anti-epileptic drugs. Drug-resistant epilepsy is treated with brain surgery. Successful surgical treatment relies on identifying brain regions responsible for seizure onset, known as epileptogenic zones (EZ). Despite various methods for EZ estimation, evaluating their efficacy remains challenging due to a lack of ground truth for empirical data. To address this, we generated and evaluated a cohort of 30 virtual epilepsy patients, using patient-specific anatomical and functional data from 30 real drug-resistant epilepsy patients. This personalized modeling approach, based on each patient's brain data, is called a virtual brain twin. For each virtual patient, we provided data that included anatomically parcellated brain regions, structural connectivity, reconstructed intracranial electrodes, simulated brain activity at both the brain region and electrode levels, and key parameters of the virtual brain twin. These key parameters, which include the EZ hypothesis, serve as the ground truth for simulated brain activity. For each virtual brain twin, we generated synthetic spontaneous seizures, stimulation-induced seizures and interictal activity. We systematically evaluated these simulated brain signals by quantitatively comparing them against their corresponding empirical intracranial recordings. Simulated signals based on patient-specific EZ captured spatio-temporal seizure generation and propagation. Through in-silico exploration of stimulation parameters, we also demonstrated the role of patient-specific stimulation location and amplitude in reproducing empirically stimulated seizures. The virtual epileptic cohort is openly available, and can be used to systematically evaluate methods for the estimation of EZ or source localization using ground truth EZ parameters and source signals.

Individualized anatomical information has been used as prior knowledge in Bayesian inference paradigms of whole-brain network models. However, the actual sensitivity to such personalized information in priors is still unknown. In this study, we introduce the use of fully Bayesian information criteria and leave-one-out cross-validation technique on the subject-specific information to assess different epileptogenicity hypotheses regarding the location of pathological brain areas based on a priori knowledge from dynamical system properties. The Bayesian Virtual Epileptic Patient (BVEP) model, which relies on the fusion of structural data of individuals, a generative model of epileptiform discharges, and a self-tuning Monte Carlo sampling algorithm, is used to infer the spatial map of epileptogenicity across different brain areas. Our results indicate that measuring the out-of-sample prediction accuracy of the BVEP model with informative priors enables reliable and efficient evaluation of potential hypotheses regarding the degree of epileptogenicity across different brain regions. In contrast, while using uninformative priors, the information criteria are unable to provide strong evidence about the epileptogenicity of brain areas. We also show that the fully Bayesian criteria correctly assess different hypotheses about both structural and functional components of whole-brain models that differ across individuals. The fully Bayesian information-theory based approach used in this study suggests a patient-specific strategy for epileptogenicity hypothesis testing in generative brain network models of epilepsy to improve surgical outcomes.

Surgical interventions in epileptic patients aimed at the removal of the epileptogenic zone have success rates at only 60-70%. This failure can be partly attributed to the insufficient spatial sampling by the implanted intracranial electrodes during the clinical evaluation, leading to an incomplete picture of spatio-temporal seizure organization in the regions that are not directly observed. Utilizing the partial observations of the seizure spreading through the brain network, complemented by the assumption that the epileptic seizures spread along the structural connections, we infer if and when are the unobserved regions recruited in the seizure. To this end we introduce a data-driven model of seizure recruitment and propagation across a weighted network, which we invert using the Bayesian inference framework. Using a leave-one-out cross-validation scheme on a cohort of 45 patients we demonstrate that the method can improve the predictions of the states of the unobserved regions compared to an empirical estimate that does not use the structural information, yet it is on the same level as the estimate that takes the structure into account. Furthermore, a comparison with the performed surgical resection and the surgery outcome indicates a link between the inferred excitable regions and the actual epileptogenic zone. The results emphasize the importance of the structural connectome in the large-scale spatio-temporal organization of epileptic seizures and introduce a novel way to integrate the patient-specific connectome and intracranial seizure recordings in a whole-brain computational model of seizure spread.

This paper studies the controllability of pairs of identical nonholonomic vehicles maintaining a constant distance. The study provides controllability results for the five most common types of robot vehicles: Dubins, Reeds-Shepp, differential drive, car-like and convexified Reeds-Shepp. The challenge of achieving controllability of such systems is that their admissible control domains depend on configuration variables. A theorem of controllability specifical for such systems has been obtained based on known controllability theorems. As a result, we show that pairs of the latter three types are completely controllable, i.e. can be steered between any two arbitrary configurations. The same does not hold for pairs of Dubins or Reeds-Shepp vehicles, and a description of the reachable sets in these cases is provided. Finally, as direct extension of controllability results of pairs of identical vehicles, the controllability results for two kinds of formation of n identical vehicles are presented.

This paper addresses the problem of determining time-optimal trajectories, between two specified configurations, for a nonholonomic bidirectional steered robot. It presents an original geometric reasoning that is grounded on Pontryagin's maximum principle, which provides analytical solutions of this problem in a visually clear way and allows for an effective algorithm to compute the exact optimal trajectories between two arbitrarily specified configurations. The proposed geometric reasoning is based on the analysis of the switching functions of the optimal controller and the definition of a switching vector from which it is able to determine a unit vector rotating along a unit circle of an appropriate coordinate system. It is shown that simple geometric rules are sufficient to determine all possible rotations of this unit vector, from which the time-optimal trajectories can be uniquely determined. The proposed algorithm, which is based on this geometric reasoning, is guaranteed to be complete and has a low computational cost. Moreover, the proposed geometric representation provides an interesting insight into the structure of this class of nonholonomic systems, thereby offering a model for further studies.