I- Development and analysis of signal processing and AI-based methods for neurophysiological signal processing and monitoring
In sports, neurophysiological signals, such as heart rate variability, ECG and EEG signals, are increasingly monitored to assess the athlete’s training load objectively, avoid over-training and injury, and monitor his mental health and well-being. Recently, novel signals from mobile and wearable sensors continuously monitor the athletes’ training. These signals provide a real-time assessment and feedback, which can help fatigue detection during training and, hence, help athletes and coaches in adapting and responding accordingly by a personalized training program. However, these signals are not directly interpretable and are often subject to movement artifacts. Therefore, the development of such personalized training programs requires a good understanding of the signals and the extraction of reliable indicators that link the signals to higher-level variables, such as the athlete’s physical and mental health.
In BOOST, we investigate both the standard neurophysiological signals and the signals from wearable devices to analyses and enhance the athletes’ performance. Advanced signal processing and machine learning techniques are developed for signals’ preprocessing, analyzing the relevant correlations, and defining new indicators. New signal/AI tools will be developed, and new solutions to analyses and enhance the athletes’ performance will be analyzed.
I.1. Mathematical analysis of the Semi-classical method and its extension
In BOOST, we explore various signal processing and AI approaches to respond to the challenges mentioned above. In particular, we are interested in a quantum-inspired method for signal processing based on the semi-classical Schrödinger operator’s spectral analysis. This method provides an accurate and insightful characterization of neurophysiological signals with a pulse-shaped nature. This method, called semi-classical signal analysis (SCSA), decomposes the signal into a set of functions given by the squared eigenfunctions of the Schrödinger operator associated with its negative eigenvalues. Thus, unlike traditional signal decomposition tools, the SCSA expresses the signal through a set of signal’s signal-dependent functions, i.e, these functions are not fixed and known in advance but are computed by solving the spectral problem of the Schrödinger operator whose potential is the signal to be analyzed. Accordingly, these eigenfunctions capture more details on the signal and its morphological variations, an interesting property when the signal is recorded continuously.
The SCSA has been successfully implemented in various applications for signal representation, denoising, post-processing, and feature extraction. For instance, it has been used for arterial blood pressure waveform analysis, for magnetic resonance spectroscopy (MRS) denoising, for MRS water suppression, and for MRS lipid suppression. It has also been employed for feature extraction in epileptic seizure detection and the characterization of PPG signals and blood pressure signals for non-invasive estimation of central pressure and arterial stiffness, respectively. Additionally, the SCSA has been extended to the 2D case for image representation and denoising, which offers a powerful alternative for image processing.
I. 2 Non-intrusive signal monitoring for sport performance analysis and enhancement
BOOST aims to explore brain and cardiovascular signals to understand signals’ variability during exercise and to define effective training programs that would enhance the athletes’ performance, avoid overtraining and prevent injury and stress. The investigations will be conducted on readily available signals such as EEG, ECG, blood pressure, PPG… but also on less easily measurable signals, where we propose to develop virtual sensors to non-intrusively measure non accessible variables such as heart rate variability and arterial stiffness.
Examples of projects include:
- Arterial stiffness estimation and assessment
- Stress evaluation and assessment from brain and physiological signal
II- Modeling of bio-informed systems
BOOST will develop novel mathematical models to describe systems that involve the human and to use physiological signals to calibrate the models and infer the unknown states. This modeling task will help define prior information about the status or performance of the patient or the athlete. It will contribute to build reliable bio-informed feedback systems which can be used for monitoring the athletes’ health and physiological status and to improve their performance or provide personalized training programs. The models will provide a tool for testing, simulating and predicting systems responses to various situations and thus will help in an efficient design of the decision making strategies.Bio-informed systems usually exhibit complex dynamics and singularities, with multi-scale behaviors,non-linearities, discontinuities, delays and noise. Conventional ODE and PDE models sometimes fail at capturing these types of phenomena which may require the introduction of non-local operators such as fractional operator or integral operator, or stochastic components. BOOST will focus on developing mathematical models to respond to specific needs related to the studied applications. We will particularly focus on linear and nonlinear dynamical systems in both finite and infinite dimensions.The development of new models will require to adapt existing analysis tools to their specificity. For instance, dedicated tools for stability or robustness analysis may be required.
II. 1 Cortico-cardiovascular modeling for stress monitoring
monitoring the mental and physical health of an athlete is crucial for their well-being as well as for their performance. In parallel to the signal/AI analysis that will be performed on simultaneous recording of brain and physiological signals, BOOST will also work on modeling the cortico-cardiovascular interactions to understand the factors that play a role in the stress. This is a challenging topic that requires good understanding of both the neurological and cardiovascular behaviors in response to the stress and the underlying complexity. BOOST will focus on modeling the brain-heart interaction using both model-based approaches and model-free methods with the objective of extracting pertinent indicators of the mental and physical health of the athlete. We will focus on designing simple indicators which can be continuously and non-invasively measured and monitored.
II.2. Modeling of human neuromechanical control
Understanding the mechanisms of human neuromechanical control is critical to many applications such as the design of efficient control strategies for exoskeletons to assist frail individuals or teach users to learn new motor tasks. While good models of learned, anticipatory (open-loop) control have been developed previously, including in a stochastic context,25,26 its interdependence with re-active (closed-loop) control still has to be properly understood.27 BOOST will focus on developing mathematical models of the complex interplay between open-loop and closed-loop control in the human neuromechanical system. The combination of open- and closed-loop control in the human system leads to challenging mathematical problems due to their nonlinear, nondeterministic, and multidimensional nature. Those models will make testable predictions about the extent to which the brain should rely on open-loop control or closed-loop control depending on the task at hand, and disambiguate the (delayed) neural feedback from the (energetically costly) muscles contraction both determining the response to perturbations. They will predict not only average motor behavior but also its variability across repetitions and its response to unknown perturbations imposed by the environment.
II.3 Design of estimation methods and algorithms
Estimation of dynamical systems is an important topic in several fields. It may take different forms depending on the field of study even if the meaning is the same and refers to getting the value of an unknown or several unknown parameters or variables. Estimation appears naturally in mathematical modeling of dynamical systems, where often the model needs to be calibrated, that is the model’s parameters are found to best match the data. In addition, the estimation can appear in a control problem, where control design depends on state variables which are not directly accessible to measurements and in that case estimation of the state is required to the control to be able to function well and reach its objectives. Estimation can also be useful in sensing problems, where the objective is to measure quantities that are not directly accessible either because of the non availability of hard sensors or because of economical or physical constraints.
In that case, using some available measurements and a mathematical model of the system linking the unknown to the available measurements can provide good sensing of the unknown variable. The latter is often referred to as virtual sensor. Estimation can take different forms depending on the objective but also on the nature of equations that are involved in modeling the system. The estimation approach can also have different mathematical and computational properties, which can be different for each problem. BOOST will work on developing estimation methods and algorithms for various classes of dynamical systems. We will focus on observer design which are well-known in control theory for state estimation of dynamical systems ruled by ordinary differential equations. We will extend the concept to other systems’classes
Learning observers
Asymptotic and non-asymptotic estimators
Inverse approaches
III- Develop optimal control methods and algorithms to improve human-exoskeleton in interaction
