- Tuesday, July 9, 2019:
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, Italy)
Abstract: 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 treatment strategies.
- Tuesday, July 9, 2019:
Optimal control for a prostate tumor growth model – Gabriela Marinoschi (ISMMA)
Abstract: 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 the decrease of the tumor.
- Tuesday, February 19, 2019:
BEM-CGM algorithms for inverse boundary value problems in 2D steady-state anisotropic heat conduction – Liviu Marin (University of Bucharest and ISMMA)
Abstract: We investigate the numerical reconstruction of the missing thermal boundary conditions on an inaccessible part of the boundary in the case of steady-state heat conduction in anisotropic solids from the knowledge of over-prescribed noisy data on the remaining accessible boundary. This inverse boundary value problem is approached by employing a variational formulation which transforms it into an equivalent control problem. Four such approaches are presented and both a parameter-dependent and a parameter independent gradient based algorithms are obtained in each case. The numerical implementation is realized for the 2D case by employing the boundary element method (BEM) and assuming that the available boundary data are either exact or noisy. For perturbed Cauchy data the numerical solution is stabilized/regularised by stopping the iterative procedure according to Morozov’s discrepancy principle.
- Thursday, March 29, 2018:
Rolul inegalitatilor de tip Hardy în teoria spatiilor de functii – Petru Mironescu (University Claude Bernard Lyon, France)
Abstract: În prima parte, voi ilustra rolul fundamental al inegalităților lui Hardy în teoria spațiilor de funcții prin două exemple de bază: calculul funcțional în spațiile Sobolev și teoria spațiilor Sobolev cu ponderi. În partea a doua, voi prezenta aplicații ale acestor teorii la studiul funcțiilor Sobolev unimodulare.
- Thursday, October 19, 2017:
An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology – Cecilia Cavaterra (University of Milan, Italy)
Abstract: We considered an inverse boundary value problem for the monodomain equation, which describes the evolution of the electric potential in the heart tissue. The goal is the determination of a small inhomogeneity inside the domain occupied by the heart from observations of the potential on the boundary. Such a problem is related to the detection of myocardial ischemic regions, characterized by severely reduced blood perfusion and consequent lack of electric conductivity. Both theoretical analysis and numerical reconstruction techniques are developed.