Proyectos

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]Materia investigada: Biomedicina, enfermedades cardiovasculares, regulación transcripcional.[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]Materia investigada: Regulación transcripcional, microbiología, metilaciones, cobre.[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]One goal is to enhance the methods being currently developed by Espı́ndola (Physics), Krause (Physiology), and Xavier (Biomedical Engineering) for reconstructing capillary networks with ultrasound. The super-resolution is needed for early detection diseases such as cognitive decline, cancer, or liver fibrosis. They perfuse lipid-encapsulated microbubbles as contrast agents and then localize the bubbles in the ultrasound images with the singular value filter. However, that method leaves a non-negligible percentage of bubbles undetected. Here we propose to complement the singular value filter for the detection and tracking of microbubbles with the sophisticated and mathematically sound Mumford-Shah method for image contour detection, which stems from the conceptually-insightful and numerically-robust perspective of the minimization of energies. In the reconstruction of the capillary network from ultrasound, it is impossible to directly distinguish the microbubbles, or even the blood vessels, in each frame separately, due to the attentuation and degradation in this imaging technique. It is essential to take into account the dynamic nature of the problem, distinguishing the slowly-varying signals emitted by the tissue from those emitted by the microbubbles, which flow rapidly, behave nonlinearly, and have a much shorter coherence length. We therefore propose to regard the collection of two-dimensional frames as a single three-dimensional image, where a moving bubble becomes a tubular neighbourhood of a filament, which the Mumford-Shah model is expected to recover. From these filaments, bubbles can be detected and tracked, and the vertical inclinations of theses filaments will yield the microbubbles velocities. From the velocity profiles it is possible to estimate the shear wall stresses (their ‘tangential elastic rigidities’) of the blood vessels, and anomalies in these stresses are commonly good indicators of the presence of specific diseases. A fortunate encounter between mathematics and mechanics led to the observation that the problem of finding the path that the propagation of a crack will follow inside a structure upon loading could be solved with the mathematical theory (the analysis of free-discontinuity problems) developed for the apparently unrelated image segmentation Mumford-Shah model. The variational fracture theory initiated by Francfort and Marigo is by now (20 years after) very well established. The second goal of this proposal is to further develop the ongoing collaboration between Song (Pharmaceutics), Siegel (Pharmaceutics), Sánchez (Numerical analysis), Calderer (Applied mathematics), and the PI on the study of the debonding of polymer gels from rigid substrates (relevant in the design of the synthetic polymers coating the metallic parts of pacemakers and other medical prostheses) from this variational fracture theory perspective. The third main goal is to apply the mathematical analysis of free-discontinuity problems to the modelling of the evolution of the cavity in the block caving technique in underground rock mining. This has been pursued by Ortega, Lecaros, and coworkers from the side of applied mathematics in academia, in collaboration with Gaete from the Geomechanics Research Department at El Teniente, research group to which Gutiérrez and the PI have joined in the last months. We propose to study the seismic activity induced by the fracture of the rock mass due to gravity, following the works in the last decade within the variational fracture theory that incorporate the inertia effects. The final aim is to optimize the injection of water jets for the aminoration of the seismic events near the operation sites. The three research lines are applications of the phase-field regularization by Ambrosio and Tortorelli of the Mumford-Shah free-discontinuity model, a different variant being required in each of the three contexts. The first stage of the implementation is of mathematical modelling and high-level numerical simulation abilities, in which the intuition and first-hand knowledge from the members of the research team that are experts in vascular function, ultrasound imaging, polymer chemistry, and mining geomechanics is translated into particular mathematical concepts and concrete computational methods. This is followed by a stage of calibration and validation, where the full interplay with experiments is required. The product of a robust and validated computational method will constitute then an advancement in the capabilities, available resources, and understanding in each of the applied disciplines.[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]Our interest in this project is to obtain two-dimensional models for a three-dimensional thin structures involving situations: • Magnetoelastic plates which are heterogeneous and whose heterogeneity occur at a small scale which depends of the thickness of the plate. Depending on energy scaling and the ratio between these two small parameters, different theories can be obtained. • Poroelastic shell containing a viscous fluid. • Quasistatic evolution problems for linearly elastoplastic shell with hardening.[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]This research project aims to answer the following question: How is people’s perception of noise related to the socioeconomic, urban, and environmental characteristics of their neighborhoods in the (post)pandemic context? This project seeks to contribute to noise and urban knowledge from an interdisciplinary approach at the intersection between geography, sociology, urban planning and acoustic engineering. It is thus articulated around four specific objectives (SO): SO1) to analyze the relationship between noise complaints and demographic, socioeconomic, urban and environmental variables in 6 municipalities of Santiago; SO2) characterize noise annoyance and strategies adopted by the inhabitants of 6 socioeconomically diverse neighborhoods with different exposure to noise; SO3) to evaluate the soundscapes of 6 neighborhoods; SO4) To propose guidelines for integrating the perception of noise in public policies related to noise and in urban planning.[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

One goal is to enhance the methods being currently developed by Espı́ndola (Physics), Krause (Physiology), and Xavier (Biomedical Engineering) for reconstructing capillary networks with ultrasound. The super-resolution is needed for early detection diseases such as cognitive decline, cancer, or liver fibrosis. They perfuse lipid-encapsulated microbubbles as contrast agents and then localize the bubbles in the ultrasound images with the singular value filter. However, that method leaves a non-negligible percentage of bubbles undetected. Here we propose to complement the singular value filter for the detection and tracking of microbubbles with the sophisticated and mathematically sound Mumford-Shah method for image contour detection, which stems from the conceptually-insightful and numerically-robust perspective of the minimization of energies. In the reconstruction of the capillary network from ultrasound, it is impossible to directly distinguish the microbubbles, or even the blood vessels, in each frame separately, due to the attentuation and degradation in this imaging technique. It is essential to take into account the dynamic nature of the problem, distinguishing the slowly-varying signals emitted by the tissue from those emitted by the microbubbles, which flow rapidly, behave nonlinearly, and have a much shorter coherence length. We therefore propose to regard the collection of two-dimensional frames as a single three-dimensional image, where a moving bubble becomes a tubular neighbourhood of a filament, which the Mumford-Shah model is expected to recover. From these filaments, bubbles can be detected and tracked, and the vertical inclinations of theses filaments will yield the microbubbles velocities. From the velocity profiles it is possible to estimate the shear wall stresses (their ‘tangential elastic rigidities’) of the blood vessels, and anomalies in these stresses are commonly good indicators of the presence of specific diseases. A fortunate encounter between mathematics and mechanics led to the observation that the problem of finding the path that the propagation of a crack will follow inside a structure upon loading could be solved with the mathematical theory (the analysis of free-discontinuity problems) developed for the apparently unrelated image segmentation Mumford-Shah model. The variational fracture theory initiated by Francfort and Marigo is by now (20 years after) very well established. The second goal of this proposal is to further develop the ongoing collaboration between Song (Pharmaceutics), Siegel (Pharmaceutics), Sánchez (Numerical analysis), Calderer (Applied mathematics), and the PI on the study of the debonding of polymer gels from rigid substrates (relevant in the design of the synthetic polymers coating the metallic parts of pacemakers and other medical prostheses) from this variational fracture theory perspective. The third main goal is to apply the mathematical analysis of free-discontinuity problems to the modelling of the evolution of the cavity in the block caving technique in underground rock mining. This has been pursued by Ortega, Lecaros, and coworkers from the side of applied mathematics in academia, in collaboration with Gaete from the Geomechanics Research Department at El Teniente, research group to which Gutiérrez and the PI have joined in the last months. We propose to study the seismic activity induced by the fracture of the rock mass due to gravity, following the works in the last decade within the variational fracture theory that incorporate the inertia effects. The final aim is to optimize the injection of water jets for the aminoration of the seismic events near the operation sites. The three research lines are applications of the phase-field regularization by Ambrosio and Tortorelli of the Mumford-Shah free-discontinuity model, a different variant being required in each of the three contexts. The first stage of the implementation is of mathematical modelling and high-level numerical simulation abilities, in which the intuition and first-hand knowledge from the members of the research team that are experts in vascular function, ultrasound imaging, polymer chemistry, and mining geomechanics is translated into particular mathematical concepts and concrete computational methods. This is followed by a stage of calibration and validation, where the full interplay with experiments is required. The product of a robust and validated computational method will constitute then an advancement in the capabilities, available resources, and understanding in each of the applied disciplines.

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]Retinal vascular diseases are major causes of vision loss in the United States and around the world. To better treat these disorders, we need to understand the signaling pathways that control the growth and integrity of retinal blood vessels. Our recent publications and preliminary data detail a novel angiogenic signaling system centered around heme, a co-factor critical for oxygen transport, metabolism, and gene transcription. We found that heme promotes angiogenic growth in the retina by regulating tip/stalk selection, and that reduced heme production or import leads to reduced retinal vascularization and tissue hypoxia, similar to other retinal vasculopathies including retinopathy of prematurity, choroidal neovascularization, and the rare but important exudative vitreoretinopathies. Furthermore, we found that VEGF suppresses, while Norrin-bCatenin promotes, the expression of the obligate endothelial heme importer, Flvcr2. Based on these data, we hypothesize that heme, is involved in retinal angiogenesis and retinal vasculopathies. The Specific Aims of this proposal are to (1) determine how heme intersects with Notch signaling to control angiogenic tip/stalk selection, (2) characterize the role for Flvcr2/heme in VEGF-induced angiogenic proliferation and neo-vascularization, and (3) determine whether induction of Flvcr2/heme signaling is sufficient and necessary to reverse the vascular defects and downstream vision changes observed in mouse models of exudative vitreoretinopathy. To accomplish these aims, we developed new tools to directly manipulate heme in cultured retinal endothelial cells and assess heme transport and intracellular trafficking in vitro. We also generated new conditional knock-in and knock-out alleles to manipulate endothelial heme transport in vivo. Our studies will fundamentally impact our understanding of how endothelial heme levels are controlled, and the role of heme in retinal angiogenesis and vascular disease.[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]En América Latina y el Caribe, las inequidades de género persisten en, y a través de, la educación, modelando las trayectorias de vida de niñas/os, jóvenes, mujeres y hombres de manera desigual, e impactando en el desarrollo sostenible de la región. En Chile, si bien se ha avanzado en la reducción de brechas de género en años de escolaridad, existe una fuerte segregación de género entre áreas del conocimiento en la educación superior y entre ocupaciones. Esta segregación horizontal, que genera brechas en oportunidades sociales y condiciones laborales entre hombres y mujeres, tiene sus raíces en procesos de socialización tempranos, y los sistemas educativos son fundamentales en su desarrollo y reproducción a lo largo de la vida. Sustentado en una perspectiva de género y un enfoque del curso de la vida, el presente proyecto busca desarrollar una agenda de investigación interdisciplinaria sobre segregación horizontal temprana en Chile, así como sobre sus antecedentes, moderadores y consecuencias. Para esto, se estudiarán los patrones generizados de elección de cursos electivos de enseñanza media científico-humanista, identificando diferencias entre y dentro de áreas del conocimiento, con foco en: 1) su estabilidad durante el período 2011-2022; 2) su consistencia entre establecimientos, de diversa dependencia administrativa, ubicación geográfica y composición (socio-económica, académica y de género); 3) el rol de otros significativos (padres y apoderados, docentes y pares) en estas elecciones; 4) los principales moderadores a nivel de estudiante, aula/docente y establecimiento escolar; y 5) su influencia en las transiciones a la educación superior. Lo anterior, en el contexto de un sistema escolar altamente privatizado y socio-económicamente segregado; de la desigual implementación de una reforma curricular, a partir del año 2020, destinada a ampliar y estandarizar la variedad de cursos electivos disponibles entre escuelas; y de los efectos diferenciados de la crisis sanitaria por COVID-19 en la provisión de educación, que han ampliado las brechas socioeconómicas y geográficas en resultados educativos, debido al extenso período de cierre de las escuelas y al diferencial acceso y experiencias de educación remota. Se analizará en qué medida estas características y cambios estructurales del sistema educativo interactúan con las diferencias de género en las preferencias y elecciones de los estudiantes. Mediante análisis de datos secundarios (bases de datos administrativas y de evaluaciones estandarizadas de cobertura censal); la aplicación de cuestionarios, en dos ocasiones de medición, a estudiantes de enseñanza media; y la integración de técnicas de análisis estadístico avanzadas (que incluyen análisis de datos longitudinales, modelos multinivel, análisis de clases latentes y análisis de redes sociales), el proyecto generará evidencia para comprender los mecanismos sociales a través de los cuales el género afecta las trayectorias educativas. Así, se espera contribuir al diseño de políticas públicas orientadas a reducir las brechas de género en oportunidades de aprendizaje y en las trayectorias educativas y laborales. Los resultados esperados del proyecto son: 1) publicar artículos en revistas de corriente principal, 2) diseminar resultados en circuitos nacionales e internacionales, 3) fortalecer la capacidad de investigación educacional con perspectiva de género, incorporando investigadoras jóvenes y formando a estudiantes y asistentes de investigación, 4) promover una perspectiva interdisciplinaria y un enfoque del curso de la vida para el estudio del rol del género en educación, 5) establecer una red de colaboración con investigadores internacionales, e 6) identificar relaciones causales, políticas relevantes y buenas prácticas que puedan ser transferidas. El proyecto constituye un aporte novedoso al estudio del rol del género en las trayectorias educativas en Chile. El equipo de investigadoras tiene vasta experiencia en investigación y en la aplicación de métodos cuantitativos avanzados para responder a preguntas sustantivas sobre equidad y efectividad en educación. Nuestra colaboración previa, así como nuestra formación disciplinar complementaria, darán sinergia y viabilidad al presente proyecto.[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]It is proposed to assess the feasibility of using ultrasound as a nonintrusive, in-situ, probe of plastic behavior in high-entropy alloys (HEAs). More specifically, whether it is possible to use ultrasound to reliably characterize the plasticity deformation mechanism---slip, TWIP, TRIP---of Fe80-xCo10Cr10Mnx. To this end, the speed of sound will be measured, continuously, as a function of applied stress in uniaxial tensile tests. In previous work, proposers have shown that the speed of sound as a function of stress provides a reliable tool to measure dislocation density in aluminum, copper, and stainless steel. In the latter case, it has also been shown to reliably discriminate between slip and twinning as a deformation mechanism. It is now proposed to study the possibility of extending this capability not only to new materials, HEAs, but also to a new mechanism, phase transformation. We will start with the materials whose plastic deformation is slip-dominated, since we have robust experience in this case. We shall then move to the TWIP material, where our more recent experience will be brought to bear, to end up with the unexplored, from the point of view of ultrasound, TRIP material. Samples for tensile loading will be prepared. They will be tested using a universal testing machine and ultrasound measurements of longitudinal wave velocity will be carried out in-situ. A decrease in the wave velocity as a function of applied stress will indicate a proliferation of dislocations; the dislocation density will be determined as a function of stress as will the parameters of Taylor's rule. An increase in wave velocity as a function of stress will indicate a decrease in average grain size. Modeling will be applied to determine whether this is due to twinning or phase transformation. These results will also be validated with post-mortem XRD, TEM, and metallography measurements, as well as ex-situ acoustic measurements. The success of the proposed research would have short-term and long-term benefits: In the short term it would provide a non-intrusive tool---ultrasound---to assist in the search for HEAs with pre-determined properties, as needed for specific applications. In the long-term, it would pave the way for the development of a practical, non-intrusive, tool for the evaluation of HEA pieces in service.[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

One goal is to enhance the methods being currently developed by Espı́ndola (Physics), Krause (Physiology), and Xavier (Biomedical Engineering) for reconstructing capillary networks with ultrasound. The super-resolution is needed for early detection diseases such as cognitive decline, cancer, or liver fibrosis. They perfuse lipid-encapsulated microbubbles as contrast agents and then localize the bubbles in the ultrasound images with the singular value filter. However, that method leaves a non-negligible percentage of bubbles undetected. Here we propose to complement the singular value filter for the detection and tracking of microbubbles with the sophisticated and mathematically sound Mumford-Shah method for image contour detection, which stems from the conceptually-insightful and numerically-robust perspective of the minimization of energies. In the reconstruction of the capillary network from ultrasound, it is impossible to directly distinguish the microbubbles, or even the blood vessels, in each frame separately, due to the attentuation and degradation in this imaging technique. It is essential to take into account the dynamic nature of the problem, distinguishing the slowly-varying signals emitted by the tissue from those emitted by the microbubbles, which flow rapidly, behave nonlinearly, and have a much shorter coherence length. We therefore propose to regard the collection of two-dimensional frames as a single three-dimensional image, where a moving bubble becomes a tubular neighbourhood of a filament, which the Mumford-Shah model is expected to recover. From these filaments, bubbles can be detected and tracked, and the vertical inclinations of theses filaments will yield the microbubbles velocities. From the velocity profiles it is possible to estimate the shear wall stresses (their ‘tangential elastic rigidities’) of the blood vessels, and anomalies in these stresses are commonly good indicators of the presence of specific diseases. A fortunate encounter between mathematics and mechanics led to the observation that the problem of finding the path that the propagation of a crack will follow inside a structure upon loading could be solved with the mathematical theory (the analysis of free-discontinuity problems) developed for the apparently unrelated image segmentation Mumford-Shah model. The variational fracture theory initiated by Francfort and Marigo is by now (20 years after) very well established. The second goal of this proposal is to further develop the ongoing collaboration between Song (Pharmaceutics), Siegel (Pharmaceutics), Sánchez (Numerical analysis), Calderer (Applied mathematics), and the PI on the study of the debonding of polymer gels from rigid substrates (relevant in the design of the synthetic polymers coating the metallic parts of pacemakers and other medical prostheses) from this variational fracture theory perspective. The third main goal is to apply the mathematical analysis of free-discontinuity problems to the modelling of the evolution of the cavity in the block caving technique in underground rock mining. This has been pursued by Ortega, Lecaros, and coworkers from the side of applied mathematics in academia, in collaboration with Gaete from the Geomechanics Research Department at El Teniente, research group to which Gutiérrez and the PI have joined in the last months. We propose to study the seismic activity induced by the fracture of the rock mass due to gravity, following the works in the last decade within the variational fracture theory that incorporate the inertia effects. The final aim is to optimize the injection of water jets for the aminoration of the seismic events near the operation sites. The three research lines are applications of the phase-field regularization by Ambrosio and Tortorelli of the Mumford-Shah free-discontinuity model, a different variant being required in each of the three contexts. The first stage of the implementation is of mathematical modelling and high-level numerical simulation abilities, in which the intuition and first-hand knowledge from the members of the research team that are experts in vascular function, ultrasound imaging, polymer chemistry, and mining geomechanics is translated into particular mathematical concepts and concrete computational methods. This is followed by a stage of calibration and validation, where the full interplay with experiments is required. The product of a robust and validated computational method will constitute then an advancement in the capabilities, available resources, and understanding in each of the applied disciplines.