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.

Multiphase flow in porous media: meta-modeling techniques for sensitivity analysis and risk assessment

One of the biggest challenges that contaminant hydrogeology is facing, is how to adequately address the uncertainty associated with model predictions. Uncertainty arise from multiple sources, such as: interpretative error, calibration accuracy, parameter sensitivity and variability. This critical issue needs to be properly addressed in order to support environmental decision-making processes. In this study, we perform Global Sensitivity Analysis (GSA) on a contaminant transport model for the assessment of hydrocarbon concentration in groundwater. We provide a quantification of the environmental impact and, given the incomplete knowledge of hydrogeological parameters, we evaluate which are the most influential, requiring greater accuracy in the calibration process. Parameters are treated as random variables and a variance-based GSA is performed in a optimized numerical Monte Carlo framework. The Sobol indices are adopted as sensitivity measures and they are computed by employing meta-models to characterize the migration process, while reducing the computational cost of the analysis. The proposed methodology allows us to: extend the number of Monte Carlo iterations, identify the influence of uncertain parameters and lead to considerable saving computational time obtaining an acceptable accuracy.

Studio di Flow-Assurance e sensitivity analysis in sistemi di distribuzione di petrolio e gas naturale

Argomento del lavoro è stato lo studio di problemi legati alla Flow-Asurance. In particolare, si focalizza su due aspetti: i) una valutazione comparativa delle diverse equazioni di stato implementate nel simulatore multifase OLGA, per valutare quella che porta a risultati più conservativi; ii) l’analisi della formazione di idrati, all’interno di sistemi caratterizzati dalla presenza di gas ed acqua. Il primo argomento di studio nasce dal fatto che per garantire continuità del flusso è necessario conoscere il comportamento volumetrico del fluido all’interno delle pipelines. Per effettuare tali studi, la Flow-Assurance si basa sulle Equazioni di Stato cubiche. In particolare, sono state confrontate: -L’equazione di Soave-Redlich-Kwong; -L’equazione di Peng-Robinson; -L’equazione di Peng-Robinson modificata da Peneloux. Sono stati analizzati 4 fluidi idrocarburici (2 multifase, un olio e un gas) con diverse composizioni e diverse condizioni di fase. Le variabili considerate sono state pressione, temperatura, densità e viscosità; sono state poi valutate le perdite di carico, parametro fondamentale nello studio del trasporto di un fluido, valutando che l'equazione di Peng-Robinson è quella più adatta per caratterizzare termodinamicamente il fluido durante una fase di design, in quanto fornisce l'andamento più conservativo. Dopo aver accertato la presenza di idrati nei fluidi multifase, l’obiettivo del lavoro è stato analizzare come il sistema rispondesse all’aggiunta di inibitori chimici per uscire dalla regione termodinamica di stabilità dell’idrato. Gli inibitori utilizzati sono stati metanolo e mono-etilen-glicole in soluzione acquosa. L’analisi è stata effettuata confrontando due metodi: -Metodo analitico di Hammerschmidt; -Metodo iterativo con PVTSim. I risultati ottenuti hanno dimostrato che entrambi gli inibitori utilizzati risolvono il problema della formazione di idrato spostando la curva di stabilità al di fuori delle pressioni e temperature che si incontrano nella pipeline. Valutando le quantità da iniettare, il metodo di Hammerschmidt risulta quello più conservativo, indicando portate maggiori rispetto al PVTsim, soprattutto aggiungendo metanolo.

Keller-Segel system, chemotaxis and applications to a mathematical model for Alzheimer's disease

In questa tesi viene presentato il modello di Keller-Segel per la chemiotassi, un sistema di tipo parabolico-ellittico che appare nella descrizione di molti fenomeni in ambito biologico e medico. Viene mostrata l'esistenza globale della soluzione debole del modello, per dati iniziali sufficientemente piccoli in dimensione N>2. La scelta di dati iniziali abbastanza grandi invece può causare il blow-up della soluzione e viene mostrato sotto quali condizioni questo si verifica. Infine il modello della chemiotassi è stato applicato per descrivere una fase della malattia di Alzheimer ed è stata effettuata un'analisi di stabilità del sistema.

Modeling and simulation of a synthetic genetic circuit that implements a multicelled behavior in a growing microcolony of E. coli

Synthetic Biology is a relatively new discipline, born at the beginning of the New Millennium, that brings the typical engineering approach (abstraction, modularity and standardization) to biotechnology. These principles aim to tame the extreme complexity of the various components and aid the construction of artificial biological systems with specific functions, usually by means of synthetic genetic circuits implemented in bacteria or simple eukaryotes like yeast. The cell becomes a programmable machine and its low-level programming language is made of strings of DNA. This work was performed in collaboration with researchers of the Department of Electrical Engineering of the University of Washington in Seattle and also with a student of the Corso di Laurea Magistrale in Ingegneria Biomedica at the University of Bologna: Marilisa Cortesi. During the collaboration I contributed to a Synthetic Biology project already started in the Klavins Laboratory. In particular, I modeled and subsequently simulated a synthetic genetic circuit that was ideated for the implementation of a multicelled behavior in a growing bacterial microcolony. In the first chapter the foundations of molecular biology are introduced: structure of the nucleic acids, transcription, translation and methods to regulate gene expression. An introduction to Synthetic Biology completes the section. In the second chapter is described the synthetic genetic circuit that was conceived to make spontaneously emerge, from an isogenic microcolony of bacteria, two different groups of cells, termed leaders and followers. The circuit exploits the intrinsic stochasticity of gene expression and intercellular communication via small molecules to break the symmetry in the phenotype of the microcolony. The four modules of the circuit (coin flipper, sender, receiver and follower) and their interactions are then illustrated. In the third chapter is derived the mathematical representation of the various components of the circuit and the several simplifying assumptions are made explicit. Transcription and translation are modeled as a single step and gene expression is function of the intracellular concentration of the various transcription factors that act on the different promoters of the circuit. A list of the various parameters and a justification for their value closes the chapter. In the fourth chapter are described the main characteristics of the gro simulation environment, developed by the Self Organizing Systems Laboratory of the University of Washington. Then, a sensitivity analysis performed to pinpoint the desirable characteristics of the various genetic components is detailed. The sensitivity analysis makes use of a cost function that is based on the fraction of cells in each one of the different possible states at the end of the simulation and the wanted outcome. Thanks to a particular kind of scatter plot, the parameters are ranked. Starting from an initial condition in which all the parameters assume their nominal value, the ranking suggest which parameter to tune in order to reach the goal. Obtaining a microcolony in which almost all the cells are in the follower state and only a few in the leader state seems to be the most difficult task. A small number of leader cells struggle to produce enough signal to turn the rest of the microcolony in the follower state. It is possible to obtain a microcolony in which the majority of cells are followers by increasing as much as possible the production of signal. Reaching the goal of a microcolony that is split in half between leaders and followers is comparatively easy. The best strategy seems to be increasing slightly the production of the enzyme. To end up with a majority of leaders, instead, it is advisable to increase the basal expression of the coin flipper module. At the end of the chapter, a possible future application of the leader election circuit, the spontaneous formation of spatial patterns in a microcolony, is modeled with the finite state machine formalism. The gro simulations provide insights into the genetic components that are needed to implement the behavior. In particular, since both the examples of pattern formation rely on a local version of Leader Election, a short-range communication system is essential. Moreover, new synthetic components that allow to reliably downregulate the growth rate in specific cells without side effects need to be developed. In the appendix are listed the gro code utilized to simulate the model of the circuit, a script in the Python programming language that was used to split the simulations on a Linux cluster and the Matlab code developed to analyze the data.

Safety factors in sheet pile wall design: considerations by using traditional methods and FEM analysis

The purpose of the work is: define and calculate a factor of collapse related to traditional method to design sheet pile walls. Furthermore, we tried to find the parameters that most influence a finite element model representative of this problem. The text is structured in this way: from chapter 1 to 5, we analyzed a series of arguments which are usefull to understanding the problem, while the considerations mainly related to the purpose of the text are reported in the chapters from 6 to 10. In the first part of the document the following arguments are shown: what is a sheet pile wall, what are the codes to be followed for the design of these structures and what they say, how can be formulated a mathematical model of the soil, some fundamentals of finite element analysis, and finally, what are the traditional methods that support the design of sheet pile walls. In the chapter 6 we performed a parametric analysis, giving an answer to the second part of the purpose of the work. Comparing the results from a laboratory test for a cantilever sheet pile wall in a sandy soil, with those provided by a finite element model of the same problem, we concluded that:in modelling a sandy soil we should pay attention to the value of cohesion that we insert in the model (some programs, like Abaqus, don’t accept a null value for this parameter), friction angle and elastic modulus of the soil, they influence significantly the behavior of the system (structure-soil), others parameters, like the dilatancy angle or the Poisson’s ratio, they don’t seem influence it. The logical path that we followed in the second part of the text is reported here. We analyzed two different structures, the first is able to support an excavation of 4 m, while the second an excavation of 7 m. Both structures are first designed by using the traditional method, then these structures are implemented in a finite element program (Abaqus), and they are pushed to collapse by decreasing the friction angle of the soil. The factor of collapse is the ratio between tangents of the initial friction angle and of the friction angle at collapse. At the end, we performed a more detailed analysis of the first structure, observing that, the value of the factor of collapse is influenced by a wide range of parameters including: the value of the coefficients assumed in the traditional method and by the relative stiffness of the structure-soil system. In the majority of cases, we found that the value of the factor of collapse is between and 1.25 and 2. With some considerations, reported in the text, we can compare the values so far found, with the value of the safety factor proposed by the code (linked to the friction angle of the soil).

"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.