Inferring interactions from time series
Neural and physiological systems contain interacting processes whose relationships change over time. We develop mathematical and statistical methods to infer these interactions from imaging, electrophysiological and autonomic recordings. Functional connectivity describes statistical dependence, while directed and effective-connectivity approaches address how the past or modelled state of one process relates to another. A central methodological task is to determine which aspects of a network can be identified from the measurements available and under the assumptions of the chosen model.
Our work includes nonlinear Granger-causality formulations, echo state network models and parsimonious descriptions of long multivariate associations. These methods investigate relationships that may be missed by simple linear or short-memory models. Graph analysis and dynamic network models provide complementary descriptions of the organisation of interactions across a system. Reproducibility studies examine the stability of directed and undirected connectomes, including how inferred networks vary with data and analysis choices.
Connecting neural models with brain–body physiology
Biophysical inverse modelling links observed activity to the parameters of a dynamical system. Physics-constrained neural networks and Bayesian inference offer approaches to estimating these parameters while incorporating knowledge of the underlying processes. The aim is to connect statistical descriptions of a signal with mechanistic models that can explain aspects of its temporal behaviour. Such models also help make the assumptions behind an inferred interaction explicit.
Brain–body research extends this perspective to cardiovascular and autonomic regulation. Joint analyses of heart-rate variability and functional imaging, together with physiologically inspired control models, investigate changing coupling, complexity, stability and responsiveness. Multisensory and behavioural measurements provide further contexts for studying neural dynamics. Across these applications, temporal structure and interactions between systems are treated as scientific objects of interest, rather than reduced to a single average measure.
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Profiles by research interest
Additional profiles by research interest (1)
Publications
2026
Neuroimage. Reports
INTRODUCTION: This study aims to identify early brain network changes in de novo Parkinson's disease (PD) using resting state-functional Magnetic Resonance Imaging (rs-fMRI), graph-theoretical analysis, and a functional brain network disruption index (k), applied here for the first time to de novo PD. MATERIALS AND METHODS: The study enrolled untreated de no…Read the full abstractCollapse abstract
INTRODUCTION: This study aims to identify early brain network changes in de novo Parkinson's disease (PD) using resting state-functional Magnetic Resonance Imaging (rs-fMRI), graph-theoretical analysis, and a functional brain network disruption index (k), applied here for the first time to de novo PD. MATERIALS AND METHODS: The study enrolled untreated de novo PD patients and age- and sex-matched healthy controls. PD patients underwent comprehensive clinical assessments (MDS-UPDRS III, H&Y, MMSE, MoCA, NMSS). MRI data were acquired on a 3T system, including 3D T1-weighted MPRAGE and rs-fMRI. rs-fMRI data were pre-processed and analysed using graph theory. RESULTS: The study included 30 de novo PD patients and 30 healthy controls. While global network metrics did not differ significantly, local metrics revealed a reduced disruption index k in de novo PD patients. The disruption index k was negatively correlated with MMSE scores and demonstrated strong discriminatory power between PD patients and healthy controls based on clustering coefficient metrics. Significant differences in hub regions were found, as some disappeared in PD patients while others emerged compared to healthy controls. CONCLUSIONS: This study provides evidence of widespread functional alterations in the local brain networks of de novo Parkinson's disease (PD) patients, suggesting early reorganization of brain connectivity. The disruption index (k) demonstrated the ability to detect early and subtle changes in functional brain networks in de novo Parkinson patients. SIGNIFICANCE: rs-fMRI can provide valuable insights into the early stages of PD pathophysiology helping to understand the complexity of PD.
2025
Journal of Neurology
OBJECTIVE: The objective of this study is to present a report from the Big Multiple Sclerosis Data (BMSD) statistics workshop (Bari – Italy, June 2023) which focused on advanced statistical approaches for real-world data (RWD) analyses in multiple sclerosis (MS). The report emphasises the application of these approaches in predicting individual treatment res…Read the full abstractCollapse abstract
OBJECTIVE: The objective of this study is to present a report from the Big Multiple Sclerosis Data (BMSD) statistics workshop (Bari – Italy, June 2023) which focused on advanced statistical approaches for real-world data (RWD) analyses in multiple sclerosis (MS). The report emphasises the application of these approaches in predicting individual treatment response, assessing comparative effectiveness and safety of therapies and their sequences, and harmonizing data for large-scale federated analyses. METHODS: The BMSD network, comprising five national registries and the international MSBase database (> 350,000 total patients), convened in June 2023 in Bari (Italy) to review methodological advances in RWD analysis. Experts discussed strengths, limitations, and regulatory implications of frequentist, Bayesian, and machine learning (ML) approaches, with case studies on treatment response modelling, comparative effectiveness, safety surveillance, and Common Data Model (CDM)-based federated learning. RESULTS: Bayesian and ML techniques, integrated with causal inference frameworks, can improve personalized predictions of treatment benefit and risk by using high-dimensional longitudinal data. Propensity score-based methods and marginal structural models remain essential for minimizing confounding in comparative analyses, but require rigorous diagnostics and sensitivity analyses. Adoption of a CDM facilitates harmonization of heterogeneous datasets, while federated learning enables privacy-preserving, multi-jurisdictional collaboration. Together, these innovations address key challenges in studying treatment sequences, rare adverse events, and underrepresented patient groups. CONCLUSIONS: This workshop report highlights how advanced statistical and computational methodologies enhance the robustness, interpretability, and regulatory relevance of MS RWD studies. By promoting the integration of complementary statistical and computational approaches within harmonized data infrastructures, the BMSD network is positioned to accelerate the translation of real-world evidence into precision medicine for MS.
2023
Brain stimulation
BACKGROUND: The autonomic response to transcutaneous auricular vagus nerve stimulation (taVNS) has been linked to the engagement of brainstem circuitry modulating autonomic outflow. However, the physiological mechanisms supporting such efferent vagal responses are not well understood, particularly in humans. HYPOTHESIS: We present a paradigm for estimating d…Read the full abstractCollapse abstract
BACKGROUND: The autonomic response to transcutaneous auricular vagus nerve stimulation (taVNS) has been linked to the engagement of brainstem circuitry modulating autonomic outflow. However, the physiological mechanisms supporting such efferent vagal responses are not well understood, particularly in humans. HYPOTHESIS: We present a paradigm for estimating directional brain-heart interactions in response to taVNS. We propose that our approach is able to identify causal links between the activity of brainstem nuclei involved in autonomic control and cardiovagal outflow. METHODS: We adopt an approach based on a recent reformulation of Granger causality that includes permutation-based, nonparametric statistics. The method is applied to ultrahigh field (7T) functional magnetic resonance imaging (fMRI) data collected on healthy subjects during taVNS. RESULTS: Our framework identified taVNS-evoked functional brainstem responses with superior sensitivity compared to prior conventional approaches, confirming causal links between taVNS stimulation and fMRI response in the nucleus tractus solitarii (NTS). Furthermore, our causal approach elucidated potential mechanisms by which information is relayed between brainstem nuclei and cardiovagal, i.e., high-frequency heart rate variability, in response to taVNS. Our findings revealed that key brainstem nuclei, known from animal models to be involved in cardiovascular control, exert a causal influence on taVNS-induced cardiovagal outflow in humans. CONCLUSION: Our causal approach allowed us to noninvasively evaluate directional interactions between fMRI BOLD signals from brainstem nuclei and cardiovagal outflow.
2021
Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences
While Granger causality (GC) has been often employed in network neuroscience, most GC applications are based on linear multivariate autoregressive (MVAR) models. However, real-life systems like biological networks exhibit notable nonlinear behaviour, hence undermining the validity of MVAR-based GC (MVAR-GC). Most nonlinear GC estimators only cater for additi…Read the full abstractCollapse abstract
While Granger causality (GC) has been often employed in network neuroscience, most GC applications are based on linear multivariate autoregressive (MVAR) models. However, real-life systems like biological networks exhibit notable nonlinear behaviour, hence undermining the validity of MVAR-based GC (MVAR-GC). Most nonlinear GC estimators only cater for additive nonlinearities or, alternatively, are based on recurrent neural networks or long short-term memory networks, which present considerable training difficulties and tailoring needs. We reformulate the GC framework in terms of echo-state networks-based models for arbitrarily complex networks, and characterize its ability to capture nonlinear causal relations in a network of noisy Duffing oscillators, showing a net advantage of echo state GC (ES-GC) in detecting nonlinear, causal links. We then explore the structure of ES-GC networks in the human brain employing functional MRI data from 1003 healthy subjects drawn from the human connectome project, demonstrating the existence of previously unknown directed within-brain interactions. In addition, we examine joint brain-heart signals in 15 subjects where we explore directed interaction between brain networks and central vagal cardiac control in order to investigate the so-called central autonomic network in a causal manner. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.
2020
NeuroImage. Clinical
Primary open angle Glaucoma (POAG) is one of the most common causes of permanent blindness in the world. Recent studies have suggested the hypothesis that POAG is also a central nervous system disorder which may result in additional (i.e., extra-ocular) involvement. The aim of this study is to assess possible structural, whole-brain connectivity alterations…Read the full abstractCollapse abstract
Primary open angle Glaucoma (POAG) is one of the most common causes of permanent blindness in the world. Recent studies have suggested the hypothesis that POAG is also a central nervous system disorder which may result in additional (i.e., extra-ocular) involvement. The aim of this study is to assess possible structural, whole-brain connectivity alterations in POAG patients. We evaluated 23 POAG patients and 15 healthy controls by combining multi-shell diffusion weighted imaging, multi-shell, multi-tissue probabilistic tractography, graph theoretical measures and a recently designed 'disruption index', which evaluates the global reorganization of brain networks. We also studied the associations between the whole-brain structural connectivity measures and indices of visual acuity including the field index (VFI) and two Optical Coherence Tomography (OCT) parameters, namely the Macula Ganglion Cell Layer (MaculaGCL) and Retinal Nerve Fiber Layer (RNFL) thicknesses. We found both global and local structural connectivity differences between POAG patients and controls, which extended well beyond the primary visual pathway and were localized in the left calcarine gyrus (clustering coefficient p = 0.036), left lateral occipital cortex (clustering coefficient p = 0.017, local efficiency p = 0.035), right lingual gyrus (clustering coefficient p = 0.009), and right paracentral lobule (clustering coefficient p = 0.009, local efficiency p = 0.018). Group-wise (clustering coefficient, p = 6.59∙10-7 and local efficiency p = 6.23·10-8) and subject-wise disruption indices (clustering coefficient, p = 0.018 and local efficiency, p = 0.01) also differed between POAG patients and controls. In addition, we found negative associations between RNFL thickness and local measures (clustering coefficient, local efficiency and strength) in the right amygdala (local efficiency p = 0.008, local strength p = 0.016), right inferior temporal gyrus (clustering coefficient p = 0.036, local efficiency p = 0.042), and right temporal pole (local strength p = 0.008). Overall, we show, in patients with POAG, a whole-brain structural reorganization that spans across a variety of brain regions involved in visual processing, motor control, and emotional/cognitive functions. We also identified a pattern of brain structural changes in relation to POAG clinical severity. Taken together, our findings support the hypothesis that the reduction in visual acuity from POAG can be driven by a combination of local (i.e., in the eye) and more extended (i.e., brain) effects.
Additional publications (2)
2019
Entropy
High-frequency neuroelectric signals like electroencephalography (EEG) or magnetoencephalography (MEG) provide a unique opportunity to infer causal relationships between local activity of brain areas. While causal inference is commonly performed through classical Granger causality (GC) based on multivariate autoregressive models, this method may encounter im…Read the full abstractCollapse abstract
High-frequency neuroelectric signals like electroencephalography (EEG) or magnetoencephalography (MEG) provide a unique opportunity to infer causal relationships between local activity of brain areas. While causal inference is commonly performed through classical Granger causality (GC) based on multivariate autoregressive models, this method may encounter important limitations (e.g., data paucity) in the case of high dimensional data from densely connected systems like the brain. Additionally, physiological signals often present long-range dependencies which commonly require high autoregressive model orders/number of parameters. We present a generalization of autoregressive models for GC estimation based on Wiener-Volterra decompositions with Laguerre polynomials as basis functions. In this basis, the introduction of only one additional global parameter allows to capture arbitrary long dependencies without increasing model order, hence retaining model simplicity, linearity and ease of parameters estimation. We validate our method in synthetic data generated from families of complex, densely connected networks and demonstrate superior performance as compared to classical GC. Additionally, we apply our framework to studying the directed human brain connectome through MEG data from 89 subjects drawn from the Human Connectome Project (HCP) database, showing that it is able to reproduce current knowledge as well as to uncover previously unknown directed influences between cortical and limbic brain regions.
2019
Entropy
A growing number of studies are focusing on methods to estimate and analyze the functional connectome of the human brain. Graph theoretical measures are commonly employed to interpret and synthesize complex network-related information. While resting state functional MRI (rsfMRI) is often employed in this context, it is known to exhibit poor reproducibility,…Read the full abstractCollapse abstract
A growing number of studies are focusing on methods to estimate and analyze the functional connectome of the human brain. Graph theoretical measures are commonly employed to interpret and synthesize complex network-related information. While resting state functional MRI (rsfMRI) is often employed in this context, it is known to exhibit poor reproducibility, a key factor which is commonly neglected in typical cohort studies using connectomics-related measures as biomarkers. We aimed to fill this gap by analyzing and comparing the inter- and intra-subject variability of connectivity matrices, as well as graph-theoretical measures, in a large (n = 1003) database of young healthy subjects which underwent four consecutive rsfMRI sessions. We analyzed both directed (Granger Causality and Transfer Entropy) and undirected (Pearson Correlation and Partial Correlation) time-series association measures and related global and local graph-theoretical measures. While matrix weights exhibit a higher reproducibility in undirected, as opposed to directed, methods, this difference disappears when looking at global graph metrics and, in turn, exhibits strong regional dependence in local graphs metrics. Our results warrant caution in the interpretation of connectivity studies, and serve as a benchmark for future investigations by providing quantitative estimates for the inter- and intra-subject variabilities in both directed and undirected connectomic measures.