| Data | Autorul si titlu comunicarii | Abstract |
| Joi, 29 Martie, 2018, ora 11 |
Petru Mironescu Funcţionale nelocale în procesarea imaginilor | Schematic, o imagine restaurata plecand de la imaginea f este o noua imagine, u, mai neteda decat f, obtinuta din f printr-un procedeu (filtru), daca se poate automatizat. Un filtru popular este ROF (Rudin-Osher-Fatemi). Matematic, imaginea restaurata u este solutia problemei $$ {\rm min}\left\{u\in BV(\Omega);\int_{\Omega}\left|Du\right|+ \lambda\int_{\Omega}\left|u-f\right|^2\right\} $$ Voi discuta cateva proprietati tipice ale acestui filtru, si avatarurile sale nelocale, in care variatia totala $ \int_{\Omega}\left|Du\right| $ este aproximata cu diverse functionale. |
| Marti, 9 iulie 2019, ora 10.00 |
1. Phase-field modeling of prostate cancer growth and treatments Guillermo Lorenzo Computational Mechanics \& Advanced Materials Group Department of Civil Engineering and Architecture University of Pavia, Italy2. Optimal control for a prostate tumor growth model Gabriela MarinoschiInstitute of Mathematical Statistics and Applied Mathematics “Gheorghe Mihoc-Caius Iacob” |
1. Phase-field modeling of prostate cancer growth and treatments Prostate cancer is a major health problem among aging men worldwide. Nowadays, most cases are detected and treated at an early stage, when the tumor is still localized within the prostate. However, the limited individualization of the clinical management of this disease has led to significant overtreatment, which may cause adverse side-effects and reduce the patient’s quality of life. Moreover, current diagnostic methods may underestimate tumor aggressiveness, which may hence survive the prescribed treatment and compromise the patient’s life expectancy. Mathematical oncology is a new trend that can contribute to overcome these issues. This approach relies on the use of mathematical models and computer simulations to predict clinical outcomes and design optimal treatments on a patient-specific basis. In this context, I will present mathematical models to describe the evolution of organ-confined prostatic tumors based on key mechanisms and I will show relevant simulations both in experimental setups and organ-scale, patient-specific scenarios. As the development of this disease can be interpreted as an evolving interface problem between healthy and tumoral tissue, these models are based on the phase-field method to account for the coupled dynamics of both tissues. Isogeometric analysis permits to accurately and efficiently address the nonlinearity of the models, the complex anatomy of the prostate, and the intricate tumoral morphologies. The mathematical models and isogeometric methods presented herein provide a patient-specific computational framework to forecast prostate cancer evolution at organ scale, investigate the mechanisms of prostatic tumor growth, and explore optimal strategy. 2. Optimal control for a prostate tumor growth model We present a phase-field type model consisting of three equations, one accounting for the healthy to tumoral cell transition described by an order parameter, coupled with the equation for the variation of the nutrient. The third equation expresses the evolution of the prostate-specific antigen (PSA) influenced by the order parameter and nutrient concentration. The purpose is to control this system via the nutrient source and a treatment scheme such that to meet some objectives, especially |