prof. Veneziani's seminar at SISSA

[Emanuele Tuillier Illingworth]

SEMINAR ANNOUNCEMENT

Title:
/Emergent challenges in bringing Cardiovascular Mathematics to the 
Bedside: //
//Data Assimilation, Uncertainty Quantification, Cost reduction, 
Patient-specific modelling/

Speaker:
/Alessandro Veneziani//
//Dept. of Mathematics and Computer Science//
//Emory University, Atlanta (GA) USA/

Abstract:
/Mathematical and numerical modelling of cardiovascular problems has 
experienced a terrific progress in the last years, evolving into a 
unique tool for patient-specific analysis. However, the extensive 
introduction of numerical procedures as a part of an established 
clinical routine and more in general of a consolidated support to the 
decision making process of physicians still requires some steps both in 
terms of methods and infrastructures (to bring computational tools to 
the operating room or to the bedside). //
//
//The quality of the numerical results needs to be carefully assessed 
and certified. An important research line - quite established in other 
fields - is the integration of numerical simulations and measurements in 
what is usually called Data Assimilation. A rigorous merging of 
available data (images, measures) and mathematical models is expected to 
reduce the uncertainty intrinsic in mathematical models featuring 
parameters that would require a patient-specific quantification; and to 
improve the overall quality of information provided by measures. 
However, computational costs of assimilation procedures - and in 
particular variational approaches - may be quite high, as typically we 
need to solve inverse problems, dual and possibly backward-in-time 
equations. For this reason, appropriate model reduction techniques are 
required, to fit assimilation procedures within the timelines and the 
size of patient cohorts usually needed by medical doctors. In this talk, 
we will consider some applications of variational data assimilation in 
vascular and cardiac problems and associated model reduction techniques 
currently investigated to bring  numerical simulations into the clinical 
routine. //
//
//For solving incompressible flows in network of pipes we will address 
hierarchical modeling (HiMod) of the solution of partial differential 
equations in domains featuring a prevalent mainstream, like arteries. 
The HiMod approach consists of approximating the main direction of each 
vessel with finite elements, coupled with spectral approximation of the 
transverse dynamics. The rationale is that a few modes are enough to a 
reliable approximation of secondary motion. In addition, modal 
adaptivity allows to tune the local accuracy of the model. This results 
in a "psychologically" 1D modeling to be compared with classical 
approaches based on the Euler equations.//
//
//Finally, we will address some more advanced applications of 
geometrical processing for (a) investigating patient-specific 
bioresorbable stents; (b) supporting decision making of neurosurgeons in 
deploying flow diverters for cerebral aneurysms./


Venue: SISSA, Friday 19 December at 11 in lecture room 133