• signal processsing
• epidemiological research
• sleep research

In the last decades, impressive technological advances have brought research in biosciences to a new interdisciplinary and translational dimension, in which computation has emerged as fundamental partner in scientific investigation. In this context, mathematical tools typically inherent to engineering can indeed magnify the investigation potentials of the sector specialists, allowing to efficiently exploit the stifling deluge of data and information, and finding simultaneous applications in a heterogeneous range of different fields.
A clear example is provided in sleep research by the advent of high-density electroencephalographic (EEG) systems. Simultaneously recording signals from hundreds of electrodes (up to 257) distributed over the scalp highly increase the spatial resolution of the investigation but make standard analysis methods, based on visual inspection and manual scoring that have been traditionally used both in clinics and research, totally inadequate. Moreover, such techniques, in combination with novel analytical approaches, revealed previously unknown features of the sleep EEG activity, such as the local, experience-dependent regulation of particular oscillations, including so-called slow waves and spindles. These and other properties of the EEG signal that can be studied only through the development of adequate automated tools. Importantly, REM sleep, a state associated with rapid eye movements (REMs) and a “tonically activated” EEG similar to that of wakefulness, poses further methodological challenges that have limited its analysis until now. In fact, REM sleep is not a homogeneous phase but it is episodically interrupted by phasic components, including REMs, muscle twitches and micro-arousals that can generate artefactual potentials corrupting the corresponding EEG signals. This great richness of signals and features, whose functional role and reciprocal relation is still under debate, brings about the strong need of optimized and validated automated procedures, allowing to efficiently manage and decode this large amount of data.
In response to the listed requirements, a multi-functional software was developed in the Matlab environment that allows automatic analysis of REM sleep high-density EEG data. The tool includes different functionalities that have been developed and validated against the visual scoring of a board certified electrophysiologist and sleep specialist, with optimal results. The first stage of the procedure allows to detect the occurrence of each elementary rapid eye movement and provides a complete characterization of ocular activity in terms of time density, aggregation tendency and directional properties (movements are in fact classified according their main direction). REMs represent a peculiar aspect of REM sleep whose physiological origin is still unclear and whose occurrence pattern has been correlated to learning processes and various psychiatric disorders. This functionality represents hence an important investigation tool both in basic REM sleep research and in clinical practice.
REMs represent also one of the main sources of contamination that affect the study of cerebral activity during REM sleep. For this reason, the global procedure considers also an ocular artifact removal stage that integrates the information provided by the REMs detection algorithm to activate a correction scheme based on adaptive filtering. The capacity of the correction algorithm in reconstructing the true EEG signals was objectively evaluated by artificially simulating the propagation of ocular potentials, showing how the proposed artifact removal procedure reaches greatly improved performance with respect to standard methods based on adaptive filters only.
Finally, the toolbox includes an EEG activation detection algorithm that precisely identifies abrupt and relative shifts in the EEG instantaneous frequency, potentially reflecting cortical desynchronization events. Growing experimental evidence has in fact suggested that the electrophysiological features of both sleep and wake can appear in an extremely local manner independently from the global vigilance state of the brain. In order to potentially detect also localized activations, the algorithm is intended to work independently channel by channel, automatically adapting to the different features of signals, without strong a priori assumptions about the frequencies involved in the activation, but always detecting frequency increases relative to the current background. Since standard clinical criteria assume that EEG activation must be accompanied by a simultaneous increase in EMG activity for the identification of a micro-arousal, also an EMG activation detection procedure was herein developed, in order to compare the properties of micro-arousals and the detected localized EEG activations. After the development, the different stages of the REM sleep toolbox listed above were applied to various sets of overnight high-density recordings, in order to characterize the REM electrophysiological features, to gain further insight into their functional meaning. Mathematical details of the algorithms are described in the first section.
Toolbox functionalities are based on several signal processing techniques that go thought Fourier and wavelet transform, adaptive filtering to non linear instantaneous energy estimators, and allowed to automatically extract significant information from a great amount of data.
However, mathematical tools, and in particular dynamical models, can also be used to integrate the available data and current knowledge in order to predict the system future states. In epidemiological research, this model-based approach is an often used and valuable tool.. Herein, we provide an example of a further evolution of this approach, in which we apply optimal control to a realistically parameterized age-structured model for the Varicella-Zoster-Virus transmission to investigate whether feasible varicella immunizations paths that are optimal in controlling both varicella and zoster exist. In fact, herpes zoster is a disease arising from reactivation of the Varicella-Zoster-Virus (VZV), causing varicella in children. As reactivation occurs when cell-mediated immunity (CMI) declines, and there is evidence that re-exposure to VZV boosts CMI, mass varicella immunization might increase the zoster burden, at least for some decades. Fear of this natural zoster boom is the main reason for the paralysis of varicella immunization in Europe. We analyze the optimality system numerically focusing on the role of the cost functional, of the relative zoster-varicella cost, and of the planning horizon length. We show that optimal programs will mostly be unfeasible for public health due to their complex temporal profiles. This complexity is the consequence of the intrinsically antagonistic nature of varicella immunization programs when aimed to control both varicella and zoster. However we show that gradually increasing – thereby feasible - vaccination schedules, can perform largely better than routine programs with constant vaccine uptake. Finally we show the optimal profiles of feasible programs targeting mitigation of the post-immunization natural zoster boom with priority.