Abstract

Coronary artery disease, which is one of the leading causes of death in the world, is caused by the build-up of atherosclerotic plaques in the vessel walls. The result is a reduction of oxygen supply to the heart, which increases the risk of myocardial infarction, stroke and unstable angina. For high-risk patients, coronary artery bypass graft (CABG) is the preferred treatment. In particular, the gold standard procedure for the surgical treatment
of the left anterior descending (LAD) coronary artery disease is the left internal mammary artery (LIMA) bypass. However, despite its excellent patency rates, LIMA bypass may fail due to restenosis. Specifically, the long-term patency of LIMA is thought to be related to the degree of stenosis in the native vessel.
In this context, we present a computational study of the fluid-dynamics in patient-specific geometries with the aim of investigating a possible relationship between coronary stenosis and LIMA graft failure. Firstly, we propose a strategy to prescribe realistic boundary conditions in absence of measured data, based on an extension of the well–known Murray’s law to provide the flow division at bifurcations in case of stenotic vessels and non-Newtonian blood rheology. With the aim of investigating the actual influence of non-Newtonian blood rheology on the hemodynamics of 3D patient-specific stenotic vessels, we also show some results regarding the comparison between Newtonian and non-Newtonian rheology. Then,
we show the results regarding numerical simulations in patients treated with grafts in which the degree of coronary stenosis is virtually varied, in order to compare the fluid-dynamics in terms of hemodynamic indices potentially involved in restenosis development. Finally, we present some preliminary results concerning fluid-structure interaction simulations in CABGs with the aim of better understanding the influence of the bypass mechanical properties on the risk of graft failure.

contatto: christian.vergara@polimi.it

Abstract

We are going to discuss many applications and generalizations of Freiman’s theorem in discrete mathematics and elsewhere. No previous knowledge is assumed.

Abstract

We are going to talk about the so called Heilbronn’s problems, some geometrical Ramsey problems and Sidon-type and sum-product problems from arithmetic combinatorics.

contact: pasquale.ciarletta@polimi.it

Abstract

In the context of Large Eddy Simulation (LES) of turbulent flows, only the more energetic scales of motions are represented while the effect of the smaller ones is modelled. For complex and unsteady flows, it is difficult to set a priori the numerical resolution corresponding to the scales that must be directly simulated. Adaptive (in the polynomial or grid sense) LES should overcome this problem allowing to locally adapt the discretization resolution to simulate a necessary amount of the turbulent scales. The present talk is focused on the polynomial degree adaptation in a discontinuous Galerkin method. The polynomial adaptivity procedure is quite established for non turbulent phenomena, and usually relies on a suitable local error estimation. In a turbulent flows this approach should lead to a convergence towards the direct numerical simulation (DNS), in contrast with the aim of a LES. In the present talk different approaches will be presented and discussed.

contact: christian.vergara@polimi.it

Abstract

In this talk I will discuss a method to prove the absence of critical points for the Helmholtz equation in 3D. The key element of the approach is the use of multiple frequencies in a fixed range, and the proof is based on the spectral analysis of the associated problem. This question is strictly connected with the Rado-Kneser-Choquet theorem, whose direct extension to the Helmholtz equation or to three dimensions is not possible.

Abstract

A growing research in recent years focused on the development of next generation bioreactors capable of generating engineered constructs that mimic at least some of the physiological functions of native organ systems. Such microphysiological systems rely on the combination of microfluidic and tissue engineering to generate a high number of identical 3D organoid models that can be used for drug and toxicological screening.
Moreover, the ultimate aim is to be able to connect multiple tissues within an organ system and from there multiple organ systems among themselves to better recapitulate the complexity and interconnection of human physiology, going from organ-on-a-chip to humans-on-a-chip. The effective development of these devices requires a solid understanding of their interconnected fluidics to predict the transport of nutrients and waste through the constructs and improve the design accordingly. In this lecture, the focus will be on a specific model of bioreactor developed at the Center for Cellular and Molecular Engineering (CCME), with multiple input/outputs, aimed at generating osteochondral constructs, i.e., a biphasic construct in which one side is cartilaginous in nature, while the other is osseous. Some of the challenges at the level of computational modelling of the system will be described, such as addressing the multi-physics nature of the problem that combines free flow in channels with hindered flow in porous media, and coupling of fluid dynamics with advection-diffusion-reaction equations that model the transport of biomolecules throughout the system and their interaction with living constructs. The same design and modelling approach is applicable to multi-chamber, interconnected system. In particular, it may be applied to human-on-chip devices. To this end, a lumped parameter approach to predict the behavior of multi-unit bioreactor systems with modest computational effort, will also be described. Furthermore, the lecture will present a comparison of the modeling outcomes with the experimental results and will introduce some of the opportunities opened by the possibility of using microphysiological systems to understand human physiology in challenging environments, such as microgravity on board the International Space Station, which is the object of a recent grant obtained by CCME. Finally, the lecture will outline some open problems where a modelling and computational approach can help guide the experimental development of microphysiological systems, such as understanding the processes of limb morphogenesis, digit patterning, and segmentation, and their translation to a regenerative approach.