Development of Clinical Decision Support Systems based on Mathematical Models of Physiological Systems

In the last years of research, I focused my studies on different physiological problems. Together with my supervisors, I developed/improved different mathematical models in order to create valid tools useful for a better understanding of important clinical issues. The aim of all this work is to develop tools for learning and understanding cardiac and cerebrovascular physiology as well as pathology, generating research questions and developing clinical decision support systems useful for intensive care unit patients. I. ICP-model Designed for Medical Education We developed a comprehensive cerebral blood flow and intracranial pressure model to simulate and study the complex interactions in cerebrovascular dynamics caused by multiple simultaneous alterations, including normal and abnormal functional states of auto-regulation of the brain. Individual published equations (derived from prior animal and human studies) were implemented into a comprehensive simulation program. Included in the normal physiological modelling was: intracranial pressure, cerebral blood flow, blood pressure, and carbon dioxide (CO2) partial pressure. We also added external and pathological perturbations, such as head up position and intracranial haemorrhage. The model performed clinically realistically given inputs of published traumatized patients, and cases encountered by clinicians. The pulsatile nature of the output graphics was easy for clinicians to interpret. The manoeuvres simulated include changes of basic physiological inputs (e.g. blood pressure, central venous pressure, CO2 tension, head up position, and respiratory effects on vascular pressures) as well as pathological inputs (e.g. acute intracranial bleeding, and obstruction of cerebrospinal outflow). Based on the results, we believe the model would be useful to teach complex relationships of brain haemodynamics and study clinical research questions such as the optimal head-up position, the effects of intracranial haemorrhage on cerebral haemodynamics, as well as the best CO2 concentration to reach the optimal compromise between intracranial pressure and perfusion. We believe this model would be useful for both beginners and advanced learners. It could be used by practicing clinicians to model individual patients (entering the effects of needed clinical manipulations, and then running the model to test for optimal combinations of therapeutic manoeuvres). II. A Heterogeneous Cerebrovascular Mathematical Model Cerebrovascular pathologies are extremely complex, due to the multitude of factors acting simultaneously on cerebral haemodynamics. In this work, the mathematical model of cerebral haemodynamics and intracranial pressure dynamics, described in the point I, is extended to account for heterogeneity in cerebral blood flow. The model includes the Circle of Willis, six regional districts independently regulated by autoregulation and CO2 reactivity, distal cortical anastomoses, venous circulation, the cerebrospinal fluid circulation, and the intracranial pressure-volume relationship. Results agree with data in the literature and highlight the existence of a monotonic relationship between transient hyperemic response and the autoregulation gain. During unilateral internal carotid artery stenosis, local blood flow regulation is progressively lost in the ipsilateral territory with the presence of a steal phenomenon, while the anterior communicating artery plays the major role to redistribute the available blood flow. Conversely, distal collateral circulation plays a major role during unilateral occlusion of the middle cerebral artery. In conclusion, the model is able to reproduce several different pathological conditions characterized by heterogeneity in cerebrovascular haemodynamics and can not only explain generalized results in terms of physiological mechanisms involved, but also, by individualizing parameters, may represent a valuable tool to help with difficult clinical decisions. III. Effect of Cushing Response on Systemic Arterial Pressure. During cerebral hypoxic conditions, the sympathetic system causes an increase in arterial pressure (Cushing response), creating a link between the cerebral and the systemic circulation. This work investigates the complex relationships among cerebrovascular dynamics, intracranial pressure, Cushing response, and short-term systemic regulation, during plateau waves, by means of an original mathematical model. The model incorporates the pulsating heart, the pulmonary circulation and the systemic circulation, with an accurate description of the cerebral circulation and the intracranial pressure dynamics (same model as in the first paragraph). Various regulatory mechanisms are included: cerebral autoregulation, local blood flow control by oxygen (O2) and/or CO2 changes, sympathetic and vagal regulation of cardiovascular parameters by several reflex mechanisms (chemoreceptors, lung-stretch receptors, baroreceptors). The Cushing response has been described assuming a dramatic increase in sympathetic activity to vessels during a fall in brain O2 delivery. With this assumption, the model is able to simulate the cardiovascular effects experimentally observed when intracranial pressure is artificially elevated and maintained at constant level (arterial pressure increase and bradicardia). According to the model, these effects arise from the interaction between the Cushing response and the baroreflex response (secondary to arterial pressure increase). Then, patients with severe head injury have been simulated by reducing intracranial compliance and cerebrospinal fluid reabsorption. With these changes, oscillations with plateau waves developed. In these conditions, model results indicate that the Cushing response may have both positive effects, reducing the duration of the plateau phase via an increase in cerebral perfusion pressure, and negative effects, increasing the intracranial pressure plateau level, with a risk of greater compression of the cerebral vessels. This model may be of value to assist clinicians in finding the balance between clinical benefits of the Cushing response and its shortcomings. IV. Comprehensive Cardiopulmonary Simulation Model for the Analysis of Hypercapnic Respiratory Failure We developed a new comprehensive cardiopulmonary model that takes into account the mutual interactions between the cardiovascular and the respiratory systems along with their short-term regulatory mechanisms. The model includes the heart, systemic and pulmonary circulations, lung mechanics, gas exchange and transport equations, and cardio-ventilatory control. Results show good agreement with published patient data in case of normoxic and hyperoxic hypercapnia simulations. In particular, simulations predict a moderate increase in mean systemic arterial pressure and heart rate, with almost no change in cardiac output, paralleled by a relevant increase in minute ventilation, tidal volume and respiratory rate. The model can represent a valid tool for clinical practice and medical research, providing an alternative way to experience-based clinical decisions. In conclusion, models are not only capable of summarizing current knowledge, but also identifying missing knowledge. In the former case they can serve as training aids for teaching the operation of complex systems, especially if the model can be used to demonstrate the outcome of experiments. In the latter case they generate experiments to be performed to gather the missing data.

Mathematical models of cognitive processes

The research activity carried out during the PhD course was focused on the development of mathematical models of some cognitive processes and their validation by means of data present in literature, with a double aim: i) to achieve a better interpretation and explanation of the great amount of data obtained on these processes from different methodologies (electrophysiological recordings on animals, neuropsychological, psychophysical and neuroimaging studies in humans), ii) to exploit model predictions and results to guide future research and experiments. In particular, the research activity has been focused on two different projects: 1) the first one concerns the development of neural oscillators networks, in order to investigate the mechanisms of synchronization of the neural oscillatory activity during cognitive processes, such as object recognition, memory, language, attention; 2) the second one concerns the mathematical modelling of multisensory integration processes (e.g. visual-acoustic), which occur in several cortical and subcortical regions (in particular in a subcortical structure named Superior Colliculus (SC)), and which are fundamental for orienting motor and attentive responses to external world stimuli. This activity has been realized in collaboration with the Center for Studies and Researches in Cognitive Neuroscience of the University of Bologna (in Cesena) and the Department of Neurobiology and Anatomy of the Wake Forest University School of Medicine (NC, USA). PART 1. Objects representation in a number of cognitive functions, like perception and recognition, foresees distribute processes in different cortical areas. One of the main neurophysiological question concerns how the correlation between these disparate areas is realized, in order to succeed in grouping together the characteristics of the same object (binding problem) and in maintaining segregated the properties belonging to different objects simultaneously present (segmentation problem). Different theories have been proposed to address these questions (Barlow, 1972). One of the most influential theory is the so called “assembly coding”, postulated by Singer (2003), according to which 1) an object is well described by a few fundamental properties, processing in different and distributed cortical areas; 2) the recognition of the object would be realized by means of the simultaneously activation of the cortical areas representing its different features; 3) groups of properties belonging to different objects would be kept separated in the time domain. In Chapter 1.1 and in Chapter 1.2 we present two neural network models for object recognition, based on the “assembly coding” hypothesis. These models are networks of Wilson-Cowan oscillators which exploit: i) two high-level “Gestalt Rules” (the similarity and previous knowledge rules), to realize the functional link between elements of different cortical areas representing properties of the same object (binding problem); 2) the synchronization of the neural oscillatory activity in the γ-band (30-100Hz), to segregate in time the representations of different objects simultaneously present (segmentation problem). These models are able to recognize and reconstruct multiple simultaneous external objects, even in difficult case (some wrong or lacking features, shared features, superimposed noise). In Chapter 1.3 the previous models are extended to realize a semantic memory, in which sensory-motor representations of objects are linked with words. To this aim, the network, previously developed, devoted to the representation of objects as a collection of sensory-motor features, is reciprocally linked with a second network devoted to the representation of words (lexical network) Synapses linking the two networks are trained via a time-dependent Hebbian rule, during a training period in which individual objects are presented together with the corresponding words. Simulation results demonstrate that, during the retrieval phase, the network can deal with the simultaneous presence of objects (from sensory-motor inputs) and words (from linguistic inputs), can correctly associate objects with words and segment objects even in the presence of incomplete information. Moreover, the network can realize some semantic links among words representing objects with some shared features. These results support the idea that semantic memory can be described as an integrated process, whose content is retrieved by the co-activation of different multimodal regions. In perspective, extended versions of this model may be used to test conceptual theories, and to provide a quantitative assessment of existing data (for instance concerning patients with neural deficits). PART 2. The ability of the brain to integrate information from different sensory channels is fundamental to perception of the external world (Stein et al, 1993). It is well documented that a number of extraprimary areas have neurons capable of such a task; one of the best known of these is the superior colliculus (SC). This midbrain structure receives auditory, visual and somatosensory inputs from different subcortical and cortical areas, and is involved in the control of orientation to external events (Wallace et al, 1993). SC neurons respond to each of these sensory inputs separately, but is also capable of integrating them (Stein et al, 1993) so that the response to the combined multisensory stimuli is greater than that to the individual component stimuli (enhancement). This enhancement is proportionately greater if the modality-specific paired stimuli are weaker (the principle of inverse effectiveness). Several studies have shown that the capability of SC neurons to engage in multisensory integration requires inputs from cortex; primarily the anterior ectosylvian sulcus (AES), but also the rostral lateral suprasylvian sulcus (rLS). If these cortical inputs are deactivated the response of SC neurons to cross-modal stimulation is no different from that evoked by the most effective of its individual component stimuli (Jiang et al 2001). This phenomenon can be better understood through mathematical models. The use of mathematical models and neural networks can place the mass of data that has been accumulated about this phenomenon and its underlying circuitry into a coherent theoretical structure. In Chapter 2.1 a simple neural network model of this structure is presented; this model is able to reproduce a large number of SC behaviours like multisensory enhancement, multisensory and unisensory depression, inverse effectiveness. In Chapter 2.2 this model was improved by incorporating more neurophysiological knowledge about the neural circuitry underlying SC multisensory integration, in order to suggest possible physiological mechanisms through which it is effected. This endeavour was realized in collaboration with Professor B.E. Stein and Doctor B. Rowland during the 6 months-period spent at the Department of Neurobiology and Anatomy of the Wake Forest University School of Medicine (NC, USA), within the Marco Polo Project. The model includes four distinct unisensory areas that are devoted to a topological representation of external stimuli. Two of them represent subregions of the AES (i.e., FAES, an auditory area, and AEV, a visual area) and send descending inputs to the ipsilateral SC; the other two represent subcortical areas (one auditory and one visual) projecting ascending inputs to the same SC. Different competitive mechanisms, realized by means of population of interneurons, are used in the model to reproduce the different behaviour of SC neurons in conditions of cortical activation and deactivation. The model, with a single set of parameters, is able to mimic the behaviour of SC multisensory neurons in response to very different stimulus conditions (multisensory enhancement, inverse effectiveness, within- and cross-modal suppression of spatially disparate stimuli), with cortex functional and cortex deactivated, and with a particular type of membrane receptors (NMDA receptors) active or inhibited. All these results agree with the data reported in Jiang et al. (2001) and in Binns and Salt (1996). The model suggests that non-linearities in neural responses and synaptic (excitatory and inhibitory) connections can explain the fundamental aspects of multisensory integration, and provides a biologically plausible hypothesis about the underlying circuitry.

Models for the Study of Cortical Activity During Cognitive ans Motor Tasks

This thesis is mainly devoted to show how EEG data and related phenomena can be reproduced and analyzed using mathematical models of neural masses (NMM). The aim is to describe some of these phenomena, to show in which ways the design of the models architecture is influenced by such phenomena, point out the difficulties of tuning the dozens of parameters of the models in order to reproduce the activity recorded with EEG systems during different kinds of experiments, and suggest some strategies to cope with these problems. In particular the chapters are organized as follows: chapter I gives a brief overview of the aims and issues addressed in the thesis; in chapter II the main characteristics of the cortical column, of the EEG signal and of the neural mass models will be presented, in order to show the relationships that hold between these entities; chapter III describes a study in which a NMM from the literature has been used to assess brain connectivity changes in tetraplegic patients; in chapter IV a modified version of the NMM is presented, which has been developed to overcomes some of the previous version’s intrinsic limitations; chapter V describes a study in which the new NMM has been used to reproduce the electrical activity evoked in the cortex by the transcranial magnetic stimulation (TMS); chapter VI presents some preliminary results obtained in the simulation of the neural rhythms associated with memory recall; finally, some general conclusions are drawn in chapter VII.

Mathematical Optimization Applied to Thermal and Electrical Energy Systems

This Thesis aims at building and discussing mathematical models applications focused on Energy problems, both on the thermal and electrical side. The objective is to show how mathematical programming techniques developed within Operational Research can give useful answers in the Energy Sector, how they can provide tools to support decision making processes of Companies operating in the Energy production and distribution and how they can be successfully used to make simulations and sensitivity analyses to better understand the state of the art and convenience of a particular technology by comparing it with the available alternatives. The first part discusses the fundamental mathematical background followed by a comprehensive literature review about mathematical modelling in the Energy Sector. The second part presents mathematical models for the District Heating strategic network design and incremental network design. The objective is the selection of an optimal set of new users to be connected to an existing thermal network, maximizing revenues, minimizing infrastructure and operational costs and taking into account the main technical requirements of the real world application. Results on real and randomly generated benchmark networks are discussed with particular attention to instances characterized by big networks dimensions. The third part is devoted to the development of linear programming models for optimal battery operation in off-grid solar power schemes, with consideration of battery degradation. The key contribution of this work is the inclusion of battery degradation costs in the optimisation models. As available data on relating degradation costs to the nature of charge/discharge cycles are limited, we concentrate on investigating the sensitivity of operational patterns to the degradation cost structure. The objective is to investigate the combination of battery costs and performance at which such systems become economic. We also investigate how the system design should change when battery degradation is taken into account.

Design of wireless sensor networks for fluid dynamic applications

In fluid dynamics research, pressure measurements are of great importance to define the flow field acting on aerodynamic surfaces. In fact the experimental approach is fundamental to avoid the complexity of the mathematical models for predicting the fluid phenomena. It’s important to note that, using in-situ sensor to monitor pressure on large domains with highly unsteady flows, several problems are encountered working with the classical techniques due to the transducer cost, the intrusiveness, the time response and the operating range. An interesting approach for satisfying the previously reported sensor requirements is to implement a sensor network capable of acquiring pressure data on aerodynamic surface using a wireless communication system able to collect the pressure data with the lowest environmental–invasion level possible. In this thesis a wireless sensor network for fluid fields pressure has been designed, built and tested. To develop the system, a capacitive pressure sensor, based on polymeric membrane, and read out circuitry, based on microcontroller, have been designed, built and tested. The wireless communication has been performed using the Zensys Z-WAVE platform, and network and data management have been implemented. Finally, the full embedded system with antenna has been created. As a proof of concept, the monitoring of pressure on the top of the mainsail in a sailboat has been chosen as working example.

Sviluppo di modelli motore e veicolo per l'analisi di strategie di controllo in applicazioni Software e Hardware In the Loop

This work describes the development of a simulation tool which allows the simulation of the Internal Combustion Engine (ICE), the transmission and the vehicle dynamics. It is a control oriented simulation tool, designed in order to perform both off-line (Software In the Loop) and on-line (Hardware In the Loop) simulation. In the first case the simulation tool can be used in order to optimize Engine Control Unit strategies (as far as regard, for example, the fuel consumption or the performance of the engine), while in the second case it can be used in order to test the control system. In recent years the use of HIL simulations has proved to be very useful in developing and testing of control systems. Hardware In the Loop simulation is a technology where the actual vehicles, engines or other components are replaced by a real time simulation, based on a mathematical model and running in a real time processor. The processor reads ECU (Engine Control Unit) output signals which would normally feed the actuators and, by using mathematical models, provides the signals which would be produced by the actual sensors. The simulation tool, fully designed within Simulink, includes the possibility to simulate the only engine, the transmission and vehicle dynamics and the engine along with the vehicle and transmission dynamics, allowing in this case to evaluate the performance and the operating conditions of the Internal Combustion Engine, once it is installed on a given vehicle. Furthermore the simulation tool includes different level of complexity, since it is possible to use, for example, either a zero-dimensional or a one-dimensional model of the intake system (in this case only for off-line application, because of the higher computational effort). Given these preliminary remarks, an important goal of this work is the development of a simulation environment that can be easily adapted to different engine types (single- or multi-cylinder, four-stroke or two-stroke, diesel or gasoline) and transmission architecture without reprogramming. Also, the same simulation tool can be rapidly configured both for off-line and real-time application. The Matlab-Simulink environment has been adopted to achieve such objectives, since its graphical programming interface allows building flexible and reconfigurable models, and real-time simulation is possible with standard, off-the-shelf software and hardware platforms (such as dSPACE systems).

Development of synthetic molecular circuits for the control of cell systems

Synthetic biology is a young field of applicative research aiming to design and build up artificial biological devices, useful for human applications. How synthetic biology emerged in past years and how the development of the Registry of Standard Biological Parts aimed to introduce one practical starting solution to apply the basics of engineering to molecular biology is presented in chapter 1 in the thesis The same chapter recalls how biological parts can make up a genetic program, the molecular cloning tecnique useful for this purpose, and an overview of the mathematical modeling adopted to describe gene circuit behavior. Although the design of gene circuits has become feasible the increasing complexity of gene networks asks for a rational approach to design gene circuits. A bottom-up approach was proposed, suggesting that the behavior of a complicated system can be predicted from the features of its parts. The option to use modular parts in large-scale networks will be facilitated by a detailed and shared characterization of their functional properties. Such a prediction, requires well-characterized mathematical models of the parts and of how they behave when assembled together. In chapter 2, the feasibility of the bottom-up approach in the design of a synthetic program in Escherichia coli bacterial cells is described. The rational design of gene networks is however far from being established. The synthetic biology approach can used the mathematical formalism to identify biological information not assessable with experimental measurements. In this context, chapter 3 describes the design of a synthetic sensor for identifying molecules of interest inside eukaryotic cells. The Registry of Standard parts collects standard and modular biological parts. To spread the use of BioBricks the iGEM competition was started. The ICM Laboratory, where Francesca Ceroni completed her Ph.D, partecipated with teams of students and Chapter 4 summarizes the projects developed.

Neutrino velocity measurement with the OPERA experiment in the CNGS beam

In the thesis is presented the measurement of the neutrino velocity with the OPERA experiment in the CNGS beam, a muon neutrino beam produced at CERN. The OPERA detector observes muon neutrinos 730 km away from the source. Previous measurements of the neutrino velocity have been performed by other experiments. Since the OPERA experiment aims the direct observation of muon neutrinos oscillations into tau neutrinos, a higher energy beam is employed. This characteristic together with the higher number of interactions in the detector allows for a measurement with a much smaller statistical uncertainty. Moreover, a much more sophisticated timing system (composed by cesium clocks and GPS receivers operating in “common view mode”), and a Fast Waveform Digitizer (installed at CERN and able to measure the internal time structure of the proton pulses used for the CNGS beam), allows for a new measurement with a smaller systematic error. Theoretical models on Lorentz violating effects can be investigated by neutrino velocity measurements with terrestrial beams. The analysis has been carried out with blind method in order to guarantee the internal consistency and the goodness of each calibration measurement. The performed measurement is the most precise one done with a terrestrial neutrino beam, the statistical accuracy achieved by the OPERA measurement is about 10 ns and the systematic error is about 20 ns.

Computational Modeling of Cardiac Excitation-Contraction Coupling in Physiological and Pathological Conditions

The cardiomyocyte is a complex biological system where many mechanisms interact non-linearly to regulate the coupling between electrical excitation and mechanical contraction. For this reason, the development of mathematical models is fundamental in the field of cardiac electrophysiology, where the use of computational tools has become complementary to the classical experimentation. My doctoral research has been focusing on the development of such models for investigating the regulation of ventricular excitation-contraction coupling at the single cell level. In particular, the following researches are presented in this thesis: 1) Study of the unexpected deleterious effect of a Na channel blocker on a long QT syndrome type 3 patient. Experimental results were used to tune a Na current model that recapitulates the effect of the mutation and the treatment, in order to investigate how these influence the human action potential. Our research suggested that the analysis of the clinical phenotype is not sufficient for recommending drugs to patients carrying mutations with undefined electrophysiological properties. 2) Development of a model of L-type Ca channel inactivation in rabbit myocytes to faithfully reproduce the relative roles of voltage- and Ca-dependent inactivation. The model was applied to the analysis of Ca current inactivation kinetics during normal and abnormal repolarization, and predicts arrhythmogenic activity when inhibiting Ca-dependent inactivation, which is the predominant mechanism in physiological conditions. 3) Analysis of the arrhythmogenic consequences of the crosstalk between β-adrenergic and Ca-calmodulin dependent protein kinase signaling pathways. The descriptions of the two regulatory mechanisms, both enhanced in heart failure, were integrated into a novel murine action potential model to investigate how they concur to the development of cardiac arrhythmias. These studies show how mathematical modeling is suitable to provide new insights into the mechanisms underlying cardiac excitation-contraction coupling and arrhythmogenesis.

CT perfusion image processing: analysis of liver tumors

Perfusion CT imaging of the liver has potential to improve evaluation of tumour angiogenesis. Quantitative parameters can be obtained applying mathematical models to Time Attenuation Curve (TAC). However, there are still some difficulties for an accurate quantification of perfusion parameters due, for example, to algorithms employed, to mathematical model, to patient’s weight and cardiac output and to the acquisition system. In this thesis, new parameters and alternative methodologies about liver perfusion CT are presented in order to investigate the cause of variability of this technique. Firstly analysis were made to assess the variability related to the mathematical model used to compute arterial Blood Flow (BFa) values. Results were obtained implementing algorithms based on “ maximum slope method” and “Dual input one compartment model” . Statistical analysis on simulated data demonstrated that the two methods are not interchangeable. Anyway slope method is always applicable in clinical context. Then variability related to TAC processing in the application of slope method is analyzed. Results compared with manual selection allow to identify the best automatic algorithm to compute BFa. The consistency of a Standardized Perfusion Index (SPV) was evaluated and a simplified calibration procedure was proposed. At the end the quantitative value of perfusion map was analyzed. ROI approach and map approach provide related values of BFa and this means that pixel by pixel algorithm give reliable quantitative results. Also in pixel by pixel approach slope method give better results. In conclusion the development of new automatic algorithms for a consistent computation of BFa and the analysis and definition of simplified technique to compute SPV parameter, represent an improvement in the field of liver perfusion CT analysis.

Spatio-temporal models of the functional architecture of the visual cortex

In this work I tried to explore many aspects of cognitive visual science, each one based on different academic fields, proposing mathematical models capable to reproduce both neuro-physiological and phenomenological results that were described in the recent literature. The structure of my thesis is mainly composed of three chapters, corresponding to the three main areas of research on which I focused my work. The results of each work put the basis for the following, and their ensemble form an homogeneous and large-scale survey on the spatio-temporal properties of the architecture of the visual cortex of mammals.

Closed-loop investigation of the dynamical properties of cardiomyocyte electrophysiology by means of Dynamic clamp and Mathematical modelling

The research field of my PhD concerns mathematical modeling and numerical simulation, applied to the cardiac electrophysiology analysis at a single cell level. This is possible thanks to the development of mathematical descriptions of single cellular components, ionic channels, pumps, exchangers and subcellular compartments. Due to the difficulties of vivo experiments on human cells, most of the measurements are acquired in vitro using animal models (e.g. guinea pig, dog, rabbit). Moreover, to study the cardiac action potential and all its features, it is necessary to acquire more specific knowledge about single ionic currents that contribute to the cardiac activity. Electrophysiological models of the heart have become very accurate in recent years giving rise to extremely complicated systems of differential equations. Although describing the behavior of cardiac cells quite well, the models are computationally demanding for numerical simulations and are very difficult to analyze from a mathematical (dynamical-systems) viewpoint. Simplified mathematical models that capture the underlying dynamics to a certain extent are therefore frequently used. The results presented in this thesis have confirmed that a close integration of computational modeling and experimental recordings in real myocytes, as performed by dynamic clamp, is a useful tool in enhancing our understanding of various components of normal cardiac electrophysiology, but also arrhythmogenic mechanisms in a pathological condition, especially when fully integrated with experimental data.

Multi-phase electric drives for mobility

Multi-phase electrical drives are potential candidates for the employment in innovative electric vehicle powertrains, in response to the request for high efficiency and reliability of this type of application. In addition to the multi-phase technology, in the last decades also, multilevel technology has been developed. These two technologies are somewhat complementary since both allow increasing the power rating of the system without increasing the current and voltage ratings of the single power switches of the inverter. In this thesis, some different topics concerning the inverter, the motor and the fault diagnosis of an electric vehicle powertrain are addressed. In particular, the attention is focused on multi-phase and multilevel technologies and their potential advantages with respect to traditional technologies. First of all, the mathematical models of two multi-phase machines, a five-phase induction machine and an asymmetrical six-phase permanent magnet synchronous machines are developed using the Vector Space Decomposition approach. Then, a new modulation technique for multi-phase multilevel T-type inverters, which solves the voltage balancing problem of the DC-link capacitors, ensuring flexible management of the capacitor voltages, is developed. The technique is based on the proper selection of the zero-sequence component of the modulating signals. Subsequently, a diagnostic technique for detecting the state of health of the rotor magnets in a six-phase permanent magnet synchronous machine is established. The technique is based on analysing the electromotive force induced in the stator windings by the rotor magnets. Furthermore, an innovative algorithm able to extend the linear modulation region for five-phase inverters, taking advantage of the multiple degrees of freedom available in multi-phase systems is presented. Finally, the mathematical model of an eighteen-phase squirrel cage induction motor is defined. This activity aims to develop a motor drive able to change the number of poles of the machine during the machine operation.

Modelling, simulation and control of rotary-wing aircraft in multi-agent scenario

The topic of this thesis is the design and the implementation of mathematical models and control system algorithms for rotary-wing unmanned aerial vehicles to be used in cooperative scenarios. The use of rotorcrafts has many attractive advantages, since these vehicles have the capability to take-off and land vertically, to hover and to move backward and laterally. Rotary-wing aircraft missions require precise control characteristics due to their unstable and heavy coupling aspects. As a matter of fact, flight test is the most accurate way to evaluate flying qualities and to test control systems. However, it may be very expensive and/or not feasible in case of early stage design and prototyping. A good compromise is made by a preliminary assessment performed by means of simulations and a reduced flight testing campaign. Consequently, having an analytical framework represents an important stage for simulations and control algorithm design. In this work mathematical models for various helicopter configurations are implemented. Different flight control techniques for helicopters are presented with theoretical background and tested via simulations and experimental flight tests on a small-scale unmanned helicopter. The same platform is used also in a cooperative scenario with a rover. Control strategies, algorithms and their implementation to perform missions are presented for two main scenarios. One of the main contributions of this thesis is to propose a suitable control system made by a classical PID baseline controller augmented with L1 adaptive contribution. In addition a complete analytical framework and the study of the dynamics and the stability of a synch-rotor are provided. At last, the implementation of cooperative control strategies for two main scenarios that include a small-scale unmanned helicopter and a rover.

Data surveillance for infectious diseases: models, complex networks and machine learning

In this thesis, we investigate the role of applied physics in epidemiological surveillance through the application of mathematical models, network science and machine learning. The spread of a communicable disease depends on many biological, social, and health factors. The large masses of data available make it possible, on the one hand, to monitor the evolution and spread of pathogenic organisms; on the other hand, to study the behavior of people, their opinions and habits. Presented here are three lines of research in which an attempt was made to solve real epidemiological problems through data analysis and the use of statistical and mathematical models. In Chapter 1, we applied language-inspired Deep Learning models to transform influenza protein sequences into vectors encoding their information content. We then attempted to reconstruct the antigenic properties of different viral strains using regression models and to identify the mutations responsible for vaccine escape. In Chapter 2, we constructed a compartmental model to describe the spread of a bacterium within a hospital ward. The model was informed and validated on time series of clinical measurements, and a sensitivity analysis was used to assess the impact of different control measures. Finally (Chapter 3) we reconstructed the network of retweets among COVID-19 themed Twitter users in the early months of the SARS-CoV-2 pandemic. By means of community detection algorithms and centrality measures, we characterized users’ attention shifts in the network, showing that scientific communities, initially the most retweeted, lost influence over time to national political communities. In the Conclusion, we highlighted the importance of the work done in light of the main contemporary challenges for epidemiological surveillance. In particular, we present reflections on the importance of nowcasting and forecasting, the relationship between data and scientific research, and the need to unite the different scales of epidemiological surveillance.