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- ItemModal decomposition and flow analysis of Aorta’s MRI-Acquired blood flow(2024) Kantor Nagel, Nicolás; Cádiz Cádiz, Rodrigo Fernando; Brevis Vergara, Wernher; Pontificia Universidad Católica de Chile. Escuela de IngenieríaThis study utilizes Proper Orthogonal Decomposition (POD) and Bessel functions to analyze arterial blood flow from MRI data. By decomposing velocity fields into Bessel functions, we efficiently captured the majority of kinetic energy with a low-order model, demonstrating that dominant POD modes align closely with specific Bessel functions across various arterial geometries. We analyzed spatial and temporal dynamics by examining POD modes and their temporal evolution through singular value decomposition (SVD) and Fourier transforms. Results show that lower POD modes capture significant kinetic energy and exhibit consistent patterns across geometries, while higher modes reveal complex, turbulent features. Notably, higher POD modes correspond to higher temporal frequencies, supporting theoretical predictions from Womersley’s flow equations and simulations. The phantom data displayed increased turbulence with higher-order modes contributing more to the kinetic energy, highlighting the impact of geometric sharpness on flow dynamics. In summary, this approach integrates spatial and temporal analyses to provide a robust framework for interpreting 4D flow MRI data, improving our understanding of arterial dynamics and offering potential for enhanced diagnostic capabilities by simplifying flow reconstruction and emphasizing key flow characteristics.
- ItemA Numerical framework to address the inverse problem of estimating Lamé parameters using HDG Runge-Kutta methods(2024) Cortés Castillo, Pablo; Sánchez Uribe, Manuel; Pontificia Universidad Católica de Chile. Escuela de IngenieríaIn engineering, the problem of characterizing the immediate subsoil of the earth’s crust is a subject of extensive research. A common approach for solving this problem is to induce elastic waves from the surface to the underground. So, when the propagating media is not homogeneous, we expect collisions of these waves with inclusions, represented by changes in the Lame parameters ´ (λ, µ) that uniquely determine the composition of the isotropic solid. An inverse problem arises from measuring the elastic waves that propagate back to the surface and compare with some direct model predictions. To address this problem, we rst deliver an accurate numerical characterization of the time-dependent elastic waves by solving the elastodynamics PDE using an HDG nite elements spatial discretization with weak symmetry. We also present several time-marching schemes with different orders of convergence and properties and prove optimal error estimates for every scheme, generating a wide variety of fully-discrete direct solvers. Furthermore, we provide suitable treatment for numerical artifacts, such as the locking phenomenon, and review relevant techniques to perform computational domain truncation, such as PMLs, including a damping term. Finally, we consider the inverse problem of minimizing a mis-t L2 loss between boundary measurements of the ground truth and the forward model numerical solution. We propose a rst-order algorithm that iteratively delivers descent directions by characterizing Frechet derivatives of the loss function in a discrete fashion. ´Moreover, we present a full adjoint analysis of the continuous PDE-restricted optimization problem; this provides a continuous characterization of the second-order information of the Loss function when L2 regularization is included.
- ItemSequías y la distribución del empleo e ingreso agrícola en Chile: Explorando impactos diferenciados por género y categoría ocupacional(2024) Moraga Ortiz, Camila; Pérez Silva, Rodrigo Alberto; Pontificia Universidad Católica de Chile. Facultad de Agronomía y Sistemas NaturalesLas sequías tienen impactos profundos y desiguales en las sociedades y economías, exacerbando las desigualdades estructurales, particularmente en el sector agrícola, y afectando de manera desproporcionada a las poblaciones más vulnerables. Este estudio examina cómo las sequías, representadas mediante los decretos de escasez hídrica, afectan de manera diferencial el empleo e ingreso agrícola en Chile según diferentes categorías ocupacionales, tanto para mujeres como hombres. Utilizando datos de la Encuesta CASEN (2000–2017) y un modelo de diferencias en diferencias (Dif-in-Dif), se identificaron patrones significativos de impacto: las comunas tratadas muestran un aumento en el empleo agrícola tras las sequías, con beneficios notables para las mujeres empleadoras, quienes, a diferencia de los hombres, se ven relegadas a la pequeña agricultura como consecuencia de las sequías. De manera similar, y aunque los resultados no evidencian cambios importantes en los ingresos entre grupos, las mujeres que trabajan como cuenta propia y empleadas, pero no como empleadoras, observan un aumento relativo en sus ingresos. En conjunto, estos resultados sugieren que, debido a las sequías, la desigualdad de ingresos se reduce entre las mujeres, pero la brecha de género aumenta tanto en términos de categoría ocupacional, con más hombres como empleadores, como en ingresos. Estos hallazgos destacan la necesidad de transformar las estructuras que perpetúan desigualdades y de fortalecer políticas públicas inclusivas, integrando un enfoque diferencial e interseccional. Dicho enfoque es esencial para promover un desarrollo rural más resiliente y equitativo frente al cambio climático.
- ItemColorectal cancer in Chile: process discovery and enhancement using process mining and simulation(2024) Álvarez Abusleme, Tomás Joaquín; Vera Andreo, Jorge Rafael; Pontificia Universidad Católica de Chile. Escuela de IngenieríaColorectal cancer (CRC) is a significant health issue globally, with particular prevalence in Chile. This thesis is structured into two distinct phases: the first aims to discover and analyze the CRC care process within the Southern Metropolitan Public Healthcare System (SMPHS) of Chile, while the second focuses on delivering a feasible improvement strategy for CRC care in this region. The discovery phase utilized Process Mining, an innovative approach enabling quick identification of common pathways and performance indicators within a system. This study utilized real-world data from the SMPHS to swiftly analyze and evaluate the CRC care process. Spanning from 2017 to 2023, the dataset encompassed 2048 and 2524 patient cases. Through collaboration with the Management and Networks Department of the SMPHS, key dynamics and challenges in diagnosis and treatment were uncovered and are detailed in this study. The improvement phase presents a microsimulation model designed to simulate the implementation of a CRC screening strategy. This strategy involves conducting random fecal immunochemical tests for the population aged between 50 and 75. Positive test results lead to a colonoscopy procedure, aimed at promoting early detection of CRC. All demographic and medical data used in the model was obtained from respected sources to ensure the validity of the model. The results suggest that as population adherence rates to the screening program increase, there is a consistent reduction in late-stage cancer cases; however, overall costs also rise.
- ItemUndistorted mri B0 field map estimation using an augmented space(2024) Bravo Kunz, Belen; Irarrázaval Mena, Pablo; Pontificia Universidad Católica de Chile. Escuela de IngenieríaThis thesis presents a method to calculate the magnetic field inhomogeneity map (fieldmap) of an object within a magnetic resonance (MR) scanner. The fieldmap is essential for several MR applications, including correcting off-resonance artifacts, generating quantitative susceptibility maps (QSM), separating water and fat signals, and improving the quality of Magnetic Resonance Spectroscopic Imaging (MRSI). Accurate fieldmap estimation is critical to ensure the effectiveness of these applications. Existing methods for fieldmap calculation assume that the entire MR signal is acquired at a single time point, the echo time, an approximation that breaks down for sequences with long readouts or non-Cartesian trajectories. To overcome this limitation, the off-resonance signal equation was reformulated without this approximation and propose a solution using a signal model in an augmented space. Applying the method to fast imaging sequences such as EPI and Spiral imaging, simulation results demonstrate a 30% improvement in normalized root mean square error for artifact correction accuracy compared to the classic fieldmap calculation method, while real scanner data demonstrate an 11% improvement. We successfully tested the method in simulations and real data, confirming its effectiveness and potential for broader MR imaging applications.