Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by decomposing it into patterns and therefore reducing the stability analysis into the tractable problem of a finite set of delay-coupled differential equations. We analyze delay-structured networks of phase oscillators and we find that, depending on the heterogeneity of the delays, the oscillators group in phase-shifted, anti-phase, steady, and non-stationary clusters, and analytically compute their stability boundaries. These results find direct application in the study of brain oscillations.

This paper presents a framework for creating neural field models from electrophysiological data. The Wilson and Cowan or Amari style neural field equations are used to form a parametric model, where the parameters are estimated from data. To illustrate the estimation framework, data is generated using the neural field equations incorporating modeled sensors enabling a comparison between the estimated and true parameters. To facilitate state and parameter estimation, we introduce a method to reduce the continuum neural field model using a basis function decomposition to form a finite-dimensional state-space model. Spatial frequency analysis methods are introduced that systematically specify the basis function configuration required to capture the dominant characteristics of the neural field. The estimation procedure consists of a two-stage iterative algorithm incorporating the unscented Rauch-Tung-Striebel smoother for state estimation and a least squares algorithm for parameter estimation. The results show that it is theoretically possible to reconstruct the neural field and estimate intracortical connectivity structure and synaptic dynamics with the proposed framework.

This research introduces a new method for functional brain imaging via a process of model inversion. By estimating parameters of a computational model, we are able to track effective connectivity and mean membrane potential dynamics that cannot be directly measured using electrophysiological measurements alone. The ability to track the hidden aspects of neurophysiology will have a profound impact on the way we understand and treat epilepsy. For example, under the assumption the model captures the key features of the cortical circuits of interest, the framework will provide insights into seizure initiation and termination on a patient-specific basis. It will enable investigation into the effect a particular drug has on specific neural populations and connectivity structures using minimally invasive measurements. The method is based on approximating brain networks using an interconnected neural population model. The neural population model is based on a neural mass model that describes the functional activity of the brain, capturing the mesoscopic biophysics and anatomical structure. The model is made subject-specific by estimating the strength of intra-cortical connections within a region and inter-cortical connections between regions using a novel Kalman filtering method. We demonstrate through simulation how the framework can be used to track the mechanisms involved in seizure initiation and termination.

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Tools that provide personalized risk prediction of outcomes after surgical procedures help patients make preference-based decisions among the available treatment options. However, it is unclear which modeling approach provides the most accurate risk estimation. We constructed and compared several parametric and nonparametric models for predicting prosthesis survivorship after knee replacement surgery for osteoarthritis. We used 430,455 patient-procedure episodes between April 2003 and September 2015 from the National Joint Registry for England, Wales, Northern Ireland, and the Isle of Man. The flexible parametric survival and random survival forest models most accurately captured the observed probability of remaining event-free. The concordance index for the flexible parametric model was the highest (0.705, 95% confidence interval (CI): 0.702, 0.707) for total knee replacement and was 0.639 (95% CI: 0.634, 0.643) for unicondylar knee replacement and 0.589 (95% CI: 0.586, 0.592) for patellofemoral replacement. The observed-to-predicted ratios for both the flexible parametric and the random survival forest approaches indicated that models tended to underestimate the risks for most risk groups. Our results show that the flexible parametric model has a better overall performance compared with other tested parametric methods and has better discrimination compared with the random survival forest approach.