Development of control-oriented models of Dual Clutch Transmission systems

A control-oriented model of a Dual Clutch Transmission was developed for real-time Hardware In the Loop (HIL) applications, to support model-based development of the DCT controller. The model is an innovative attempt to reproduce the fast dynamics of the actuation system while maintaining a step size large enough for real-time applications. The model comprehends a detailed physical description of hydraulic circuit, clutches, synchronizers and gears, and simplified vehicle and internal combustion engine sub-models. As the oil circulating in the system has a large bulk modulus, the pressure dynamics are very fast, possibly causing instability in a real-time simulation; the same challenge involves the servo valves dynamics, due to the very small masses of the moving elements. Therefore, the hydraulic circuit model has been modified and simplified without losing physical validity, in order to adapt it to the real-time simulation requirements. The results of offline simulations have been compared to on-board measurements to verify the validity of the developed model, that was then implemented in a HIL system and connected to the TCU (Transmission Control Unit). Several tests have been performed: electrical failure tests on sensors and actuators, hydraulic and mechanical failure tests on hydraulic valves, clutches and synchronizers, and application tests comprehending all the main features of the control performed by the TCU. Being based on physical laws, in every condition the model simulates a plausible reaction of the system. The first intensive use of the HIL application led to the validation of the new safety strategies implemented inside the TCU software. A test automation procedure has been developed to permit the execution of a pattern of tests without the interaction of the user; fully repeatable tests can be performed for non-regression verification, allowing the testing of new software releases in fully automatic mode.

Design, development, and analysis of hybrid metal-composite tube for industrial application

In the aerospace, automotive, printing, and sports industries, the development of hybrid Carbon Fiber Reinforced Polymer (CFRP)-metal components is becoming increasingly important. The coupling of metal with CFRP in axial symmetric components results in reduced production costs and increased mechanical properties such as bending, torsional stiffness, mass reduction, damping, and critical speed compared to the single material-built ones. In this thesis, thanks to a novel methodology involving a rubbery/viscoelastic interface layer, several hybrid aluminum-CFRP prototype tubes were produced. Besides, an innovative system for the cure of the CFRP part has been studied, analyzed, tested, and developed in the company that financed these research activities (Reglass SRL, Minerbio BO, Italy). The residual thermal stresses and strains have been investigated with numerical models based on the Finite Element Method (FEM) and compared with experimental tests. Thanks to numerical models, it was also possible to reduce residual thermal stresses by optimizing the lamination sequence of CFRP and determining the influence of the system parameters. A novel software and methodology for evaluating mechanical and damping properties of specimens and tubes made in CFRP were also developed. Moreover, to increase the component's damping properties, rubber nanofibers have been produced and interposed throughout the lamination of specimens. The promising results indicated that the nanofibrous mat could improve the material damping factor over 77% and be adopted in CFRP components with a negligible increment of weight or losing mechanical properties.

Development and characterization of deep learning techniques for neuroimaging data

Deep learning methods are extremely promising machine learning tools to analyze neuroimaging data. However, their potential use in clinical settings is limited because of the existing challenges of applying these methods to neuroimaging data. In this study, first a data leakage type caused by slice-level data split that is introduced during training and validation of a 2D CNN is surveyed and a quantitative assessment of the model’s performance overestimation is presented. Second, an interpretable, leakage-fee deep learning software written in a python language with a wide range of options has been developed to conduct both classification and regression analysis. The software was applied to the study of mild cognitive impairment (MCI) in patients with small vessel disease (SVD) using multi-parametric MRI data where the cognitive performance of 58 patients measured by five neuropsychological tests is predicted using a multi-input CNN model taking brain image and demographic data. Each of the cognitive test scores was predicted using different MRI-derived features. As MCI due to SVD has been hypothesized to be the effect of white matter damage, DTI-derived features MD and FA produced the best prediction outcome of the TMT-A score which is consistent with the existing literature. In a second study, an interpretable deep learning system aimed at 1) classifying Alzheimer disease and healthy subjects 2) examining the neural correlates of the disease that causes a cognitive decline in AD patients using CNN visualization tools and 3) highlighting the potential of interpretability techniques to capture a biased deep learning model is developed. Structural magnetic resonance imaging (MRI) data of 200 subjects was used by the proposed CNN model which was trained using a transfer learning-based approach producing a balanced accuracy of 71.6%. Brain regions in the frontal and parietal lobe showing the cerebral cortex atrophy were highlighted by the visualization tools.

Development and characterization of a distributed measurement system for the evaluation of voltage quality in electric power networks

The research activity carried out during the PhD course in Electrical Engineering belongs to the branch of electric and electronic measurements. The main subject of the present thesis is a distributed measurement system to be installed in Medium Voltage power networks, as well as the method developed to analyze data acquired by the measurement system itself and to monitor power quality. In chapter 2 the increasing interest towards power quality in electrical systems is illustrated, by reporting the international research activity inherent to the problem and the relevant standards and guidelines emitted. The aspect of the quality of voltage provided by utilities and influenced by customers in the various points of a network came out only in recent years, in particular as a consequence of the energy market liberalization. Usually, the concept of quality of the delivered energy has been associated mostly to its continuity. Hence the reliability was the main characteristic to be ensured for power systems. Nowadays, the number and duration of interruptions are the “quality indicators” commonly perceived by most customers; for this reason, a short section is dedicated also to network reliability and its regulation. In this contest it should be noted that although the measurement system developed during the research activity belongs to the field of power quality evaluation systems, the information registered in real time by its remote stations can be used to improve the system reliability too. Given the vast scenario of power quality degrading phenomena that usually can occur in distribution networks, the study has been focused on electromagnetic transients affecting line voltages. The outcome of such a study has been the design and realization of a distributed measurement system which continuously monitor the phase signals in different points of a network, detect the occurrence of transients superposed to the fundamental steady state component and register the time of occurrence of such events. The data set is finally used to locate the source of the transient disturbance propagating along the network lines. Most of the oscillatory transients affecting line voltages are due to faults occurring in any point of the distribution system and have to be seen before protection equipment intervention. An important conclusion is that the method can improve the monitored network reliability, since the knowledge of the location of a fault allows the energy manager to reduce as much as possible both the area of the network to be disconnected for protection purposes and the time spent by technical staff to recover the abnormal condition and/or the damage. The part of the thesis presenting the results of such a study and activity is structured as follows: chapter 3 deals with the propagation of electromagnetic transients in power systems by defining characteristics and causes of the phenomena and briefly reporting the theory and approaches used to study transients propagation. Then the state of the art concerning methods to detect and locate faults in distribution networks is presented. Finally the attention is paid on the particular technique adopted for the same purpose during the thesis, and the methods developed on the basis of such approach. Chapter 4 reports the configuration of the distribution networks on which the fault location method has been applied by means of simulations as well as the results obtained case by case. In this way the performance featured by the location procedure firstly in ideal then in realistic operating conditions are tested. In chapter 5 the measurement system designed to implement the transients detection and fault location method is presented. The hardware belonging to the measurement chain of every acquisition channel in remote stations is described. Then, the global measurement system is characterized by considering the non ideal aspects of each device that can concur to the final combined uncertainty on the estimated position of the fault in the network under test. Finally, such parameter is computed according to the Guide to the Expression of Uncertainty in Measurements, by means of a numeric procedure. In the last chapter a device is described that has been designed and realized during the PhD activity aiming at substituting the commercial capacitive voltage divider belonging to the conditioning block of the measurement chain. Such a study has been carried out aiming at providing an alternative to the used transducer that could feature equivalent performance and lower cost. In this way, the economical impact of the investment associated to the whole measurement system would be significantly reduced, making the method application much more feasible.

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.

Finite element models of coseismic deformation due to the 2009 L'Aquila (Italy) and 2008 Wenchuan(China) earthquakes

The topic of my Ph.D. thesis is the finite element modeling of coseismic deformation imaged by DInSAR and GPS data. I developed a method to calculate synthetic Green functions with finite element models (FEMs) and then use linear inversion methods to determine the slip distribution on the fault plane. The method is applied to the 2009 L’Aquila Earthquake (Italy) and to the 2008 Wenchuan earthquake (China). I focus on the influence of rheological features of the earth's crust by implementing seismic tomographic data and the influence of topography by implementing Digital Elevation Models (DEM) layers on the FEMs. Results for the L’Aquila earthquake highlight the non-negligible influence of the medium structure: homogeneous and heterogeneous models show discrepancies up to 20% in the fault slip distribution values. Furthermore, in the heterogeneous models a new area of slip appears above the hypocenter. Regarding the 2008 Wenchuan earthquake, the very steep topographic relief of Longmen Shan Range is implemented in my FE model. A large number of DEM layers corresponding to East China is used to achieve the complete coverage of the FE model. My objective was to explore the influence of the topography on the retrieved coseismic slip distribution. The inversion results reveals significant differences between the flat and topographic model. Thus, the flat models frequently adopted are inappropriate to represent the earth surface topographic features and especially in the case of the 2008 Wenchuan earthquake.

Design, development and first evaluation of a client/server system for managing and querying linguistic corpora

This thesis is concerned with the role played by software tools in the analysis and dissemination of linguistic corpora and their contribution to a more widespread adoption of corpora in different fields. Chapter 1 contains an overview of some of the most relevant corpus analysis tools available today, presenting their most interesting features and some of their drawbacks. Chapter 2 begins with an explanation of the reasons why none of the available tools appear to satisfy the requirements of the user community and then continues with technical overview of the current status of the new system developed as part of this work. This presentation is followed by highlights of features that make the system appealing to users and corpus builders (i.e. scholars willing to make their corpora available to the public). The chapter concludes with an indication of future directions for the projects and information on the current availability of the software. Chapter 3 describes the design of an experiment devised to evaluate the usability of the new system in comparison to another corpus tool. Usage of the tool was tested in the context of a documentation task performed on a real assignment during a translation class in a master's degree course. In chapter 4 the findings of the experiment are presented on two levels of analysis: firstly a discussion on how participants interacted with and evaluated the two corpus tools in terms of interface and interaction design, usability and perceived ease of use. Then an analysis follows of how users interacted with corpora to complete the task and what kind of queries they submitted. Finally, some general conclusions are drawn and areas for future work are outlined.

Subject-specific musculoskeletal models of the lower limbs for the prediction of skeletal loads during motion

The determination of skeletal loading conditions in vivo and their relationship to the health of bone tissues, remain an open question. Computational modeling of the musculoskeletal system is the only practicable method providing a valuable approach to muscle and joint loading analyses, although crucial shortcomings limit the translation process of computational methods into the orthopedic and neurological practice. A growing attention focused on subject-specific modeling, particularly when pathological musculoskeletal conditions need to be studied. Nevertheless, subject-specific data cannot be always collected in the research and clinical practice, and there is a lack of efficient methods and frameworks for building models and incorporating them in simulations of motion. The overall aim of the present PhD thesis was to introduce improvements to the state-of-the-art musculoskeletal modeling for the prediction of physiological muscle and joint loads during motion. A threefold goal was articulated as follows: (i) develop state-of-the art subject-specific models and analyze skeletal load predictions; (ii) analyze the sensitivity of model predictions to relevant musculotendon model parameters and kinematic uncertainties; (iii) design an efficient software framework simplifying the effort-intensive phases of subject-specific modeling pre-processing. The first goal underlined the relevance of subject-specific musculoskeletal modeling to determine physiological skeletal loads during gait, corroborating the choice of full subject-specific modeling for the analyses of pathological conditions. The second goal characterized the sensitivity of skeletal load predictions to major musculotendon parameters and kinematic uncertainties, and robust probabilistic methods were applied for methodological and clinical purposes. The last goal created an efficient software framework for subject-specific modeling and simulation, which is practical, user friendly and effort effective. Future research development aims at the implementation of more accurate models describing lower-limb joint mechanics and musculotendon paths, and the assessment of an overall scenario of the crucial model parameters affecting the skeletal load predictions through probabilistic modeling.

Activity and mechanisms of action of novel organosulfur derivatives of the HDAC inhibitor Valproic Acid in human experimental models of non-small-cell lung cancer

Non-small-cell lung cancer (NSCLC) represents the leading cause of cancer death worldwide, and 5-year survival is about 16% for patients diagnosed with advanced lung cancer and about 70-90% when the disease is diagnosed and treated at earlier stages. Treatment of NSCLC is changed in the last years with the introduction of targeted agents, such as gefitinib and erlotinib, that have dramatically changed the natural history of NSCLC patients carrying specific mutations in the EGFR gene, or crizotinib, for patients with the EML4-ALK translocation. However, such patients represent only about 15-20% of all NSCLC patients, and for the remaining individuals conventional chemotherapy represents the standard choice yet, but response rate to thise type of treatment is only about 20%. Development of new drugs and new therapeutic approaches are so needed to improve patients outcome. In this project we aimed to analyse the antitumoral activity of two compounds with the ability to inhibit histone deacethylases (ACS 2 and ACS 33), derived from Valproic Acid and conjugated with H2S, in human cancer cell lines derived from NSCLC tissues. We showed that ACS 2 represents the more promising agent. It showed strong antitumoral and pro-apoptotic activities, by inducing membrane depolarization, cytocrome-c release and caspase 3 and 9 activation. It was able to reduce the invasive capacity of cells, through inhibition of metalloproteinases expression, and to induce a reduced chromatin condensation. This last characteristic is probably responsible for the observed high synergistic activity in combination with cisplatin. In conclusion our results highlight the potential role of the ACS 2 compound as new therapeutic option for NSCLC patients, especially in combination with cisplatin. If validated in in vivo models, this compound should be worthy for phase I clinical trials.

Kinematic models of interseismic deformation from inversion of GPS and InSAR measurements to estimate fault parameters and coupling degree

We have used kinematic models in two Italian regions to reproduce surface interseismic velocities obtained from InSAR and GPS measurements. We have considered a Block modeling, BM, approach to evaluate which fault system is actively accommodating the occurring deformation in both considered areas. We have performed a study for the Umbria-Marche Apennines, obtaining that the tectonic extension observed by GPS measurements is explained by the active contribution of at least two fault systems, one of which is the Alto Tiberina fault, ATF. We have estimated also the interseismic coupling distribution for the ATF using a 3D surface and the result shows an interesting correlation between the microseismicity and the uncoupled fault portions. The second area analyzed concerns the Gargano promontory for which we have used jointly the available InSAR and GPS velocities. Firstly we have attached the two datasets to the same terrestrial reference frame and then using a simple dislocation approach, we have estimated the best fault parameters reproducing the available data, providing a solution corresponding to the Mattinata fault. Subsequently we have considered within a BM analysis both GPS and InSAR datasets in order to evaluate if the Mattinata fault may accommodate the deformation occurring in the central Adriatic due to the relative motion between the North-Adriatic and South-Adriatic plates. We obtain that the deformation occurring in that region should be accommodated by more that one fault system, that is however difficult to detect since the poor coverage of geodetic measurement offshore of the Gargano promontory. Finally we have performed also the estimate of the interseismic coupling distribution for the Mattinata fault, obtaining a shallow coupling pattern. Both of coupling distributions found using the BM approach have been tested by means of resolution checkerboard tests and they demonstrate that the coupling patterns depend on the geodetic data positions.

Development and Validation of a Model-Based Combustion Controller for Water Injection Management

This manuscript reports the overall development of a Ph.D. research project during the “Mechanics and advanced engineering sciences” course at the Department of Industrial Engineering of the University of Bologna. The project is focused on the development of a combustion control system for an innovative Spark Ignited engine layout. In details, the controller is oriented to manage a prototypal engine equipped with a Port Water Injection system. The water injection technology allows an increment of combustion efficiency due to the knock mitigation effect that permits to keep the combustion phasing closer to the optimal position with respect to the traditional layout. At the beginning of the project, the effects and the possible benefits achievable by water injection have been investigated by a focused experimental campaign. Then the data obtained by combustion analysis have been processed to design a control-oriented combustion model. The model identifies the correlation between Spark Advance, combustion phasing and injected water mass, and two different strategies are presented, both based on an analytic and semi-empirical approach and therefore compatible with a real-time application. The model has been implemented in a combustion controller that manages water injection to reach the best achievable combustion efficiency while keeping knock levels under a pre-established threshold. Three different versions of the algorithm are described in detail. This controller has been designed and pre-calibrated in a software-in-the-loop environment and later an experimental validation has been performed with a rapid control prototyping approach to highlight the performance of the system on real set-up. To further make the strategy implementable on an onboard application, an estimation algorithm of combustion phasing, necessary for the controller, has been developed during the last phase of the PhD Course, based on accelerometric signals.

Development and testing of innovative methodologies for modelling and control of normal and knocking combustion and implementation of novel rapid prototyping solutions

The thesis work deals with topics that led to the development of innovative control-oriented models and control algorithms for modern gasoline engines. Knock in boosted spark ignition engines is the widest topic discussed in this document because it remains one of the most limiting factors for maximizing combustion efficiency in this kind of engine. First chapter is thus focused on knock and a wide literature review is proposed to summarize the preliminary knowledge that even represents the background and the reference for discussed activities. Most relevant results achieved during PhD course in the field of knock modelling and control are then presented, describing every control-oriented model that led to the development of an adaptive model-based combustion control system. The complete controller has been developed in the context of the collaboration with Ferrari GT and it allowed to completely redefine the knock intensity evaluation as well as the combustion phase control. The second chapter is focused on the activity related to a prototyping Port Water Injection system that has been developed and tested on a turbocharged spark ignition engine, within the collaboration with Magneti Marelli. Such system and the effects of injected water on the combustion process were then modeled in a 1-D simulation environment (GT Power). Third chapter shows the development and validation of a control-oriented model for the real-time calculation of exhaust gas temperature that represents another important limitation to the performance increase in modern boosted engines. Indeed, modelling of exhaust gas temperature and thermocouple behavior are themes that play a key role in the optimization of combustion and catalyst efficiency.

Development and Implementation of the Plasma Focus Technology for Radiation Therapy Applications

A Plasma Focus device can confine in a small region a plasma generated during the pinch phase. When the plasma is in the pinch condition it creates an environment that produces several kinds of radiations. When the filling gas is nitrogen, a self-collimated backwardly emitted electron beam, slightly spread by the coulomb repulsion, can be considered one of the most interesting outputs. That beam can be converted into X-ray pulses able to transfer energy at an Ultra-High Dose-Rate (UH-DR), up to 1 Gy pulse-1, for clinical applications, research, or industrial purposes. The radiation fields have been studied with the PFMA-3 hosted at the University of Bologna, finding the radiation behavior at different operating conditions and working parameters for a proper tuning of this class of devices in clinical applications. The experimental outcomes have been compared with available analytical formalisms as benchmark and the scaling laws have been proposed. A set of Monte Carlo models have been built with direct and adjoint techniques for an accurate X-ray source characterization and for setting fast and reliable irradiation planning for patients. By coupling deterministic and Monte Carlo codes, a focusing lens for the charged particles has been designed for obtaining a beam suitable for applications as external radiotherapy or intra-operative radiation therapy. The radiobiological effectiveness of the UH PF DR, a FLASH source, has been evaluated by coupling different Monte Carlo codes estimating the overall level of DNA damage at the multi-cellular and tissue levels by considering the spatial variation effects as well as the radiation field characteristics. The numerical results have been correlated to the experimental outcomes. Finally, ambient dose measurements have been performed for tuning the numerical models and obtaining doses for radiation protection purposes. The PFMA-3 technology has been fully characterized toward clinical implementation and installation in a medical facility.

Incompressible limit and well-posedness of PDE models of tissue growth

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. A coupled system of equations describes the cell density and the nutrient concentration and the derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L3-version of the celebrated Aronson-Bénilan estimate, and a sharp uniform L4-bound on the pressure gradient. We further investigate the sharpness of this bound through a finite difference upwind scheme, which we prove to be stable and asymptotic preserving. Our second study is centered around porous medium equations including convective effects. We are able to extend the techniques developed for the nutrient case, hence finding the complementarity relation on the limit pressure. Moreover, we provide an estimate of the convergence rate at the incompressible limit. Finally, we study a multi-species system. In particular, we account for phenotypic heterogeneity, including a structured variable into the problem. In this case, a cross-(degenerate)-diffusion system describes the evolution of the phenotypic distributions. Adapting methods recently developed in the context of two-species systems, we prove existence of weak solutions and we pass to the incompressible limit. Furthermore, we prove new regularity results on the total pressure, which is related to the total density by a power law of state.