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Systems and Signals Tools for Estimation and Analysis of Mathematical Models in Endocrinology and Neurology

Final Report Summary - SYSTEAM (Systems and Signals Tools for Estimation and Analysis of Mathematical Models in Endocrinology and Neurology)

The goal of SysTEAM was to bridge the gap between systems biology, on one hand, and medical signal processing and control engineering, on the other. As planned, the main focus areas of the project activities have been endocrinology, neurology, and closed-loop anesthesia. Much effort has been also dedicated to research on signal processing for medical imaging, the latter being a tool commonly used in medicine that presents a rich source of quantifiable information.

In the area of endocrinology, significant progress has been made on the mathematical modeling and analysis of pulsatile feedback, as well as design of parameter and state estimation algorithms for release-hormone pulses. The development of an innovative pulse-modulated model for pulsatile hormone secretion and the development of system identification algorithms operating on hormone concentration data are two highlights in the endocrine part of the project. The proposed mathematical model is the first one possessing hybrid dynamics, and capturing, in complete agreement with biological evidence, both the episodic secretion of the release hormone and the continuous metabolism of the hormones with longer half-life time. None of the closed-loop models of endocrine regulation has been previously estimated and validated on actual biological data. Interestingly, the mathematical model in question constitutes a class of hybrid systems with intrinsic frequency and amplitude pulse-modulated feedback that has not been studied before in the theory of dynamical systems.

Identification of the human oculomotor system from eye-tracking data for the characterization of the muscular function has been a main topic addressed with respect to neurology. The nonlinear oculomotor dynamics are shown to be closely approximated by Wiener models, which in turn can be accurately estimated from properly designed visual stimuli presented to the test person. A method for systematic design of such stimuli is an important contribution of the project. It has been also demonstrated that Volterra-Laguerre models, in combination with sparse estimation of the model coefficients, are instrumental in obtaining parsimonious and robust models of the human smooth pursuit system. Such models are experimentally demonstrated to produce a reliable separation of Parkinsonian patients from healthy age-matched controls and are investigated in clinical experiments as a means of staging of the disease.

Deep Brain Stimulation (DBS) was another prioritized neurological topic of SysTEAM. Here a multiphysics model of a DBS electrode, surrounding brain tissue, and stimulation target has been developed. This has been a joint effort with European industrial partners. State-of-the-art electrodes and novel electrodes for field steering have been implemented and included in the model. Optimization-based methods for individualized stimuli design have been shown to be effective in maximizing the target coverage and minimizing the electric field spill.

Closed-loop anesthesia has been targeted in the subproject devoted to model-based drug delivery. Minimally parameterized Wiener models for the neuromuscular blockade and depth of anesthesia have been proposed. A suite of batch and recursive identification algorithms have been devised for their estimation and validated against clinical data from a European partner. A formal approach to the design of closed-loop drug delivery controllers from a patient safety perspective has been developed. Keeping a pre-set distance to bifurcation is shown to be instrumental in preventing the interchanging under- and over-dosing events due to closed-loop nonlinear oscillations.

Several signal processing algorithms have been developed to improve MR images, reduce artifacts, mitigate noise, and obtain quantitative tissue information. A wide range of problems posed by radiologists have been treated, typically the goal has been to estimate different physical quantities from a set of collected images. The performance of the proposed algorithms has been evaluated using both simulation and in-vivo data, as well as comparisons to previous approaches. Using new and improved estimation methods enables better tissue characterization and diagnosis.