Current students


ITALIA MATTEOCycle: XXXVI

Section: Systems and Control
Advisor: DERCOLE FABIO
Tutor: GARATTI SIMONE

Major Research topic:
Modeling, Analysis, and Control of Complex Dynamical Diseases: from in-silico models towards in-vivo applications.

Abstract:
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Human diseases are often associated with complex dynamical characteristics.
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This phenomenon suggests various directions for research, including collecting data over long times, developing biologically-based mathematical models, analyzing these models, and developing therapies.
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On the one hand, complex diseases are caused by a combination of multiple genetic, environmental, and lifestyle factors, most of which have not yet been understood. On the other hand, dynamical disease refers to illnesses associated with striking changes in the dynamics of some bodily functions.
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The vast majority of severe diseases fall into these categories, several genetic alterations and many typically adult on-set diseases, e.g., genetic diseases, nervous system diseases, heart diseases, refractive errors, kidney diseases, autoimmune diseases, and many more. 
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Most complex diseases show important dynamical characteristics, such as feedbacks, emergent behaviours, and evolutionary adaptations. Additionally, most dynamical diseases give rise to typical complex nonlinear phenomena, e.g., self-sustained oscillations (periodic or even chaotic), wave propagation, clusters synchronization, and bifurcations. Therefore, complexity and dynamism are often two complementary sides of the same coin in a severe disease framework.
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Understanding the evolution of a complex dynamical disease and how to treat it optimally are important open questions that could benefit from contributions of mathematics, physics, engineering, and control theory in particular. Indeed, a large literature successfully proposes mathematical models for the physiological systems and analyses the properties of these models using systems theory, nonlinear dynamics concepts and engineering techniques. However, there are still many open questions and research to be addressed in this promising field, especially in the applications to (personalized) medicine hoping to achieve patients 'cure, or, at least, some improvements to patients' advantage.
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The large increases in data collected by individuals combined with improvements in effective data analysis methods and ever-increasing computational power available in current portable facilitate the development and perfecting of these approaches. All these advances will require close interdisciplinary collaborations between basic scientists, physicians, doctors, and engineers.
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Thus, the Ph.D. Thesis is a multidisciplinary project at the interface between (biologic) systems theory, biostatistics, computational (biologic) algorithms, and medicine. The activities include the development of mathematical complex dynamical models, theoretical and numerical analysis exploiting implementations in computer programs, and real applications to biomedical problems.
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More specifically, genetic and nervous systems diseases are going to be investigated in collaboration with excellent and sector-leader research centres/laboratories that make available experimental data to calibrate and validate the models with two focuses: for genetic diseases, a worldwide well known (family of) diseases, cancer, and, for the nervous systems a less famous illness (but unfortunately the same with a very high global incidence, i.e., 4-15%) called Restless Legs Syndrome (RLS).
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For the first, the major investigation's objective is understanding the interplay between the evolution of cancer resistance to chemotherapeutic treatments and the treatment optimal control that exploits instead of suffering the highly complex, dynamic, and adaptive cancer typical behaviour. The research of the optimal chemotherapy protocol is faced with a multiscale evolutionary hybrid model that couples continuous partial differential equations - to describe the concentration of the main energetic substrates (oxygen, glucose, and lactate) in the tumour environment - to an agent-based formulation to assign to each tumour cell its own individual characteristics to account for cellular heterogeneity. Moreover, the model could be combined with adaptive therapies, cell metabolic network, angiogenesis, radiotherapy, metastasis, and immunotherapy.
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In contrast to cancer, RLS is a recently discovered disease that has not already received enough attention, and pretty much everything has yet to be discovered. In agreement with the International RLS Study Group, the minimal criteria accepted for the diagnosis of RLS are: (1) an urge to move the legs, usually accompanied or caused by uncomfortable and unpleasant sensations in the legs; (2) the urge to move or unpleasant sensations begin or worsen during periods of rest or inactivity such as lying or sitting; (3) the urge to move or unpleasant sensations are partially or totally relieved by movement, such as walking or stretching; (4) the urge to move or unpleasant sensations are worse in the evening or night than during the day or only occur in the evening or night.
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The close but not perfect synchronization between leg movements (LM) within the bilateral pairs and their correlated durations, as for the association between periodic leg movements during sleep (PLMS) and arousals, seem to indicate that both events are regulated by a complex mechanism including them and other sleep events, such as heart rate and blood pressure, involving several and potentially different generators interacting with each other in a more complex way than in a simple unidirectional causal-effect mechanism. Both the observation of PLMS in patients with complete transverse cervical spinal lesions and the recently reported pharmacological dissociation of cortical arousals from PLMS suggest the existence of different generators for each phenomenon, possibly located in different areas of the central nervous system. The rules that govern a synchronization between different generators during sleep are still unclear. Indeed, it is an unanswered question whether two different synchronized spinal generators, one controlling each leg, or only one single pacemaker is present. For the first time, the research investigates the hypothesis that only one (resulting) peacemaker causes the PLMS. An RLS human model does not already exist, opening up various general modelling techniques and potentially significant improvements for patients' cure.
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