Parametric Sensitivity Analysis of the Most Recent Computational Models of Rabbit Cardiac Pacemaking

The cellular basis of cardiac pacemaking activity, and specifically the quantitative contributions of particular mechanisms, is still debated. Reliable computational models of sinoatrial nodal (SAN) cells may provide mechanistic insights, but competing models are built from different data sets and with different underlying assumptions. To understand quantitative differences between alternative models, we performed thorough parameter sensitivity analyses of the SAN models of Maltsev & Lakatta (2009) and Severi et al (2012). Model parameters were randomized to generate a population of cell models with different properties, simulations performed with each set of random parameters generated 14 quantitative outputs that characterized cellular activity, and regression methods were used to analyze the population behavior. Clear differences between the two models were observed at every step of the analysis. Specifically: (1) SR Ca2+ pump activity had a greater effect on SAN cell cycle length (CL) in the Maltsev model; (2) conversely, parameters describing the funny current (If) had a greater effect on CL in the Severi model; (3) changes in rapid delayed rectifier conductance (GKr) had opposite effects on action potential amplitude in the two models; (4) within the population, a greater percentage of model cells failed to exhibit action potentials in the Maltsev model (27%) compared with the Severi model (7%), implying greater robustness in the latter; (5) confirming this initial impression, bifurcation analyses indicated that smaller relative changes in GKr or Na+-K+ pump activity led to failed action potentials in the Maltsev model. Overall, the results suggest experimental tests that can distinguish between models and alternative hypotheses, and the analysis offers strategies for developing anti-arrhythmic pharmaceuticals by predicting their effect on the pacemaking activity.

Numerical and semi-analytical models of sliding masses: application to the 1783 Scilla tsunamigenic landslide

The Scilla rock avalanche occurred on 6 February 1783 along the coast of the Calabria region (southern Italy), close to the Messina Strait. It was triggered by a mainshock of the Terremoto delle Calabrie seismic sequence, and it induced a tsunami wave responsible for more than 1500 casualties along the neighboring Marina Grande beach. The main goal of this work is the application of semi-analtycal and numerical models to simulate this event. The first one is a MATLAB code expressly created for this work that solves the equations of motion for sliding particles on a two-dimensional surface through a fourth-order Runge-Kutta method. The second one is a code developed by the Tsunami Research Team of the Department of Physics and Astronomy (DIFA) of the Bologna University that describes a slide as a chain of blocks able to interact while sliding down over a slope and adopts a Lagrangian point of view. A wide description of landslide phenomena and in particular of landslides induced by earthquakes and with tsunamigenic potential is proposed in the first part of the work. Subsequently, the physical and mathematical background is presented; in particular, a detailed study on derivatives discratization is provided. Later on, a description of the dynamics of a point-mass sliding on a surface is proposed together with several applications of numerical and analytical models over ideal topographies. In the last part, the dynamics of points sliding on a surface and interacting with each other is proposed. Similarly, different application on an ideal topography are shown. Finally, the applications on the 1783 Scilla event are shown and discussed.

Action-based dynamical models of the Fornax dwarf spheroidal galaxy

Il lavoro presentato in questa Tesi si basa sul calcolo di modelli dinamici per Galassie Sferoidali Nane studiando il problema mediante l'utilizzo di funzioni di distribuzione. Si è trattato un tipo di funzioni di distribuzione, "Action-Based distribution functions", le quali sono funzioni delle sole variabili azione. Fornax è stata descritta con un'appropriata funzione di distribuzione e il problema della costruzione di modelli dinamici è stato affrontato assumendo sia un alone di materia oscura con distribuzione di densità costante nelle regioni interne sia un alone con cuspide. Per semplicità è stata assunta simmetria sferica e non è stato calcolato esplicitamente il potenziale gravitazionale della componente stellare (le stelle sono traccianti in un potenziale gravitazionale fissato). Tramite un diretto confronto con alcune osservabili, quali il profilo di densità stellare proiettata e il profilo di dispersione di velocità lungo la linea di vista, sono stati trovati alcuni modelli rappresentativi della dinamica di Fornax. Modelli calcolati tramite funzioni di distribuzione basati su azioni permettono di determinare in maniera autoconsistente profili di anisotropia. Tutti i modelli calcolati sono caratterizzati dal possedere un profilo di anisotropia con forte anisotropia tangenziale. Sono state poi comparate le stime di materia oscura di questi modelli con i più comuni e usati stimatori di massa in letteratura. E stato inoltre stimato il rapporto tra la massa totale del sistema (componente stellare e materia oscura) e la componente stellare di Fornax, entro 1600 pc ed entro i 3 kpc. Come esplorazione preliminare, in questo lavoro abbiamo anche presentato anche alcuni esempi di modelli sferici a due componenti in cui il campo gravitazionale è determinato dall'autogravità delle stelle e da un potenziale esterno che rappresenta l'alone di materia oscura.

Analytic models of self-gravitating rotating gaseous tori with central black hole

In this thesis project, I present stationary models of rotating fluids with toroidal distributions that can be used to represent the active galactic nuclei (AGN) central obscurers, i.e. molecular tori (Combes et al., 2019), as well as geometrically thick accretion discs, like ADAF discs (Narayan and Yi, 1995) or Polish doughnuts (Abramowicz, 2005). In particular, I study stationary rotating systems with a more general baroclinic distribution (with a vertical gradient of the angular velocity), which are often more realistic and less studied, due to their complexity, than the barotropic ones (with cylindrical rotation), which are easier to construct. In the thesis, I compute analytically the main intrinsic and projected properties of the power-law tori based on the potential-density pairs of Ciotti and Bertin (2005). I study the density distribution and the resulting gravitational potential for different values of α, in the range 2 < α < 5. For the same models, I compute the surface density of the systems when seen face-on and edge-on. I then apply the stationary Euler equations to obtain rotational velocity and temperature distributions of the self-gravitating models in the absence of an external gravitational potential. In the thesis I also consider the power-law tori with the presence of a central black hole in addition to the gas self-gravity, and solving analytically the stationary Euler equations, I compute how the properties of the system are modified by the black hole and how they vary as a function of the black hole mass. Finally, applying the Solberg-Høiland criterion, I show that these baroclinic stationary models are linearly stable in the absence of the black hole. In the presence of the black hole I derive the analytical condition for stability, which depends on α and on the black hole mass. I also study the stability of the tori in the hypothesis that they are weakly magnetized, finding that they are always unstable to this instability.

Hidden Schrödinger symmetry in FLRW and Bianchi I minisuperspace models of cosmology and black holes Schwarzschild dynamics

A broad sector of literature focuses on the relationship between fluid dynamics and gravitational systems. This thesis presents results that suggest the existence of a new kind of fluid/gravity duality not based on the holographic principle. The goal is to provide tools that allow us to systematically unearth hidden symmetries for reduced models of cosmology. The focus is on the field space of these models, i.e. the superspace. In fact, conformal isometries of the supermetric leave geodesics in the field space unaltered; this leads to symmetries of the models. An innovative aspect is the use of the Eisenhart-Duval’s lift. Using this method, systems constrained by a potential can be treated as free ones. Moreover, charges explicitly dependent on time, i.e. dynamical, can be found. A detailed analysis is carried out on three basic models of homogenous cosmology: i) flat Friedmann-Lemaître-Robertson-Walker’s isotropic universe filled with a massless scalar field; ii) Schwarzschild’s black hole mechanics and its extension to vacuum (A)dS gravity; iii) Bianchi’s anisotropic type I universe with a massless scalar field. The results show the presence of a hidden Schrödinger’s symmetry which, being intrinsic to both Navier-Stokes’ and Schrödinger’s equations, indicates a correspondence between cosmology and hydrodynamics. Furthermore, the central extension of this algebra explicitly relates two concepts. The first is the number of particles coming from the fluid picture; while the second is the ratio between the IR and UV cutoffs that weighs how much a theory has of “classical” over “quantum”. This suggests a spacetime that emerges from an underlying world which is described by quantum building blocks. These quanta statistically conspire to appear as gravitational phenomena from a macroscopic point of view.

Validation of microFE models of human metastatic vertebrae

La colonna vertebrale è uno dei principali siti per lo sviluppo delle metastasi ossee. Esse modificano le proprietà meccaniche della vertebra indebolendo la struttura e inducendo l’instabilità spinale. La medicina in silico e i modelli agli elementi finiti (FE) hanno trovato spazio nello studio del comportamento meccanico delle vertebre, permettendo una valutazione delle loro proprietà meccaniche anche in presenza di metastasi. In questo studio ho validato i campi di spostamento predetti da modelli microFE di vertebre umane, con e senza metastasi, rispetto agli spostamenti misurati mediante Digital Volume Correlation (DVC). Sono stati utilizzati 4 provini da donatore umano, ognuno composto da una vertebra sana e da una vertebra con metastasi litica. Per ogni vertebra è stato sviluppato un modello microFE omogeneo, lineare e isotropo basato su sequenze di immagini ad alta risoluzione ottenute con microCT (voxel size = 39 μm). Sono state imposte come condizioni al contorno gli spostamenti ottenuti con la DVC nelle fette prossimali e distali di ogni vertebra. I modelli microFE hanno mostrato buone capacità predittive degli spostamenti interni sia per le vertebre di controllo che per quelle metastatiche. Per range di spostamento superiori a 100 μm, il valore di R2 è risultato compreso tra 0.70 e 0.99 e il valore di RMSE% tra 1.01% e 21.88%. Dalle analisi dei campi di deformazione predetti dai modelli microFE sono state evidenziate regioni a maggior deformazione nelle vertebre metastatiche, in particolare in prossimità delle lesioni. Questi risultati sono in accordo con le misure sperimentali effettuate con la DVC. Si può assumere quindi che il modello microFE lineare omogeneo isotropo in campo elastico produca risultati attendibili sia per le vertebre sane sia per le vertebre metastatiche. La procedura di validazione implementata potrebbe essere utilizzata per approfondire lo studio delle proprietà meccaniche delle lesioni blastiche.

Computational Analysis Based on Parametric Models of Historic Masonry Vaulted Structures Strengthened by Fiber-Reinforced Composite Materials

Historic vaulted masonry structures often need strengthening interventions that can effectively improve their structural performance, especially during seismic events, and at the same time respect the existing setting and the modern conservation requirements. In this context, the use of innovative materials such as fiber-reinforced composite materials has been shown as an effective solution that can satisfy both aspects. This work aims to provide insight into the computational modeling of a full-scale masonry vault strengthened by fiber-reinforced composite materials and analyze the influence of the arrangement of the reinforcement on the efficiency of the intervention. At first, a parametric model of a cross vault focusing on a realistic representation of its micro-geometry is proposed. Then numerical modeling, simulating the pushover analyses, of several barrel vaults reinforced with different reinforcement configurations is performed. Finally, the results are collected and discussed in terms of force-displacement curves obtained for each proposed configuration.

Micro-FEM models based on micro-CT reconstructions for the in vitro characterization of the elastic properties of trabecular bone tissue.

This master’s thesis describes the research done at the Medical Technology Laboratory (LTM) of the Rizzoli Orthopedic Institute (IOR, Bologna, Italy), which focused on the characterization of the elastic properties of the trabecular bone tissue, starting from october 2012 to present. The approach uses computed microtomography to characterize the architecture of trabecular bone specimens. With the information obtained from the scanner, specimen-specific models of trabecular bone are generated for the solution with the Finite Element Method (FEM). Along with the FEM modelling, mechanical tests are performed over the same reconstructed bone portions. From the linear-elastic stage of mechanical tests presented by experimental results, it is possible to estimate the mechanical properties of the trabecular bone tissue. After a brief introduction on the biomechanics of the trabecular bone (chapter 1) and on the characterization of the mechanics of its tissue using FEM models (chapter 2), the reliability analysis of an experimental procedure is explained (chapter 3), based on the high-scalable numerical solver ParFE. In chapter 4, the sensitivity analyses on two different parameters for micro-FEM model’s reconstruction are presented. Once the reliability of the modeling strategy has been shown, a recent layout for experimental test, developed in LTM, is presented (chapter 5). Moreover, the results of the application of the new layout are discussed, with a stress on the difficulties connected to it and observed during the tests. Finally, a prototype experimental layout for the measure of deformations in trabecular bone specimens is presented (chapter 6). This procedure is based on the Digital Image Correlation method and is currently under development in LTM.

"Influence of lower-limb joint models on subject-specific musculoskeletal model predictions during gait" ( "modelli muscoloscheletrici personalizzati dell'arto inferiore: Analisi dell'effetto della modellazione dei giunti sulla predizione dei carichi agenti sul sistema scheletrico durante il cammino").

The aim of the present thesis was to investigate the influence of lower-limb joint models on musculoskeletal model predictions during gait. We started our analysis by using a baseline model, i.e., the state-of-the-art lower-limb model (spherical joint at the hip and hinge joints at the knee and ankle) created from MRI of a healthy subject in the Medical Technology Laboratory of the Rizzoli Orthopaedic Institute. We varied the models of knee and ankle joints, including: knee- and ankle joints with mean instantaneous axis of rotation, universal joint at the ankle, scaled-generic-derived planar knee, subject-specific planar knee model, subject-specific planar ankle model, spherical knee, spherical ankle. The joint model combinations corresponding to 10 musculoskeletal models were implemented into a typical inverse dynamics problem, including inverse kinematics, inverse dynamics, static optimization and joint reaction analysis algorithms solved using the OpenSim software to calculate joint angles, joint moments, muscle forces and activations, joint reaction forces during 5 walking trials. The predicted muscle activations were qualitatively compared to experimental EMG, to evaluate the accuracy of model predictions. Planar joint at the knee, universal joint at the ankle and spherical joints at the knee and at the ankle produced appreciable variations in model predictions during gait trials. The planar knee joint model reduced the discrepancy between the predicted activation of the Rectus Femoris and the EMG (with respect to the baseline model), and the reduced peak knee reaction force was considered more accurate. The use of the universal joint, with the introduction of the subtalar joint, worsened the muscle activation agreement with the EMG, and increased ankle and knee reaction forces were predicted. The spherical joints, in particular at the knee, worsened the muscle activation agreement with the EMG. A substantial increase of joint reaction forces at all joints was predicted despite of the good agreement in joint kinematics with those of the baseline model. The introduction of the universal joint had a negative effect on the model predictions. The cause of this discrepancy is likely to be found in the definition of the subtalar joint and thus, in the particular subject’s anthropometry, used to create the model and define the joint pose. We concluded that the implementation of complex joint models do not have marked effects on the joint reaction forces during gait. Computed results were similar in magnitude and in pattern to those reported in literature. Nonetheless, the introduction of planar joint model at the knee had positive effect upon the predictions, while the use of spherical joint at the knee and/or at the ankle is absolutely unadvisable, because it predicted unrealistic joint reaction forces.

Deep learning models for the automatic analysis of volleyball plays

Collecting and analysing data is an important element in any field of human activity and research. Even in sports, collecting and analyzing statistical data is attracting a growing interest. Some exemplar use cases are: improvement of technical/tactical aspects for team coaches, definition of game strategies based on the opposite team play or evaluation of the performance of players. Other advantages are related to taking more precise and impartial judgment in referee decisions: a wrong decision can change the outcomes of important matches. Finally, it can be useful to provide better representations and graphic effects that make the game more engaging for the audience during the match. Nowadays it is possible to delegate this type of task to automatic software systems that can use cameras or even hardware sensors to collect images or data and process them. One of the most efficient methods to collect data is to process the video images of the sporting event through mixed techniques concerning machine learning applied to computer vision. As in other domains in which computer vision can be applied, the main tasks in sports are related to object detection, player tracking, and to the pose estimation of athletes. The goal of the present thesis is to apply different models of CNNs to analyze volleyball matches. Starting from video frames of a volleyball match, we reproduce a bird's eye view of the playing court where all the players are projected, reporting also for each player the type of action she/he is performing.

Development of iodine and air chemistry models for the simulation of plasma in Helicon Plasma Thrusters

The aim of this work is to analyse the chemistry models of low pressure Helicon discharges fed with iodine and air. In particular the focus of this research is to understand the plasma dynamics in order to predict propulsive performances of iodine and air-breathing Helicon Plasma Thrusters. The two systems have been simulated and analysed with the use of global models, i.e. a 0 dimensional tool to solve the set of governing equations by assuming that all quantities are volume averaged. Furthermore, some strategies have been implemented to improve the accuracy of this approach. A verification have been accomplished on the global models for both iodine and air, comparing results against simulations taken from literature. Moreover, the iodine global model has been validated against the experimental measurements of REGULUS, an helicon plasma thruster developed by the Italian company T4i, with a good agreement. From the analysis of iodine model, it has been found a significantly higher density for atomic positive ions with respect to molecular ions. Negative ions, instead, have shown to have negligible effect on the propulsive results. Also, the influence of reactions between heavy particles has been analysed with the global model. Results have demonstrated that, in the iodine case, chemistry is almost entirely affected by electronic collisions. For what concerns air-breathing results, it has been investigated the effects of the orbital height on propulsive performances. In particular, the global model has shown that at lower height, the values of thrust and specific impulse are lower due a change in atmosphere concentration. Finally, the iodine chemistry model has been introduced in the fluid code 3D-VIRTUS in order to preliminary assess the plasma properties of a Helicon discharge chamber for electric propulsion.