Computer simulation of cardiovascular diseases [0 ECTS]

Cardiovascular diseases represent the most dangerous health problem in the Western world with a
heavy impact on the life expectancy of healthy subjects, on the life’s quality of the patient and on use
of health resources. Nowadays, a detailed comprehension of local haemodynamic change, of the effects
of vascular walls modification on the flow pattern, of the gradual adaptation of the global system as a
result of surgery, is possible with the use of sophisticated computer simulations and could be extremely
useful in the preliminary phase of the preparation of therapeutic and/or surgical treatment.
This seminar intends to provide some fundamental concepts of modeling the circulation, covering: the
meaning, the importance and the stages of Computational Fluid Dynamics (CFD); the introduction of
equations (Navier-Stokes equations) and initial/value problems relevant to the description of dynamics
of interest, focusing on the prescription of boundary conditions.
The treatment of boundary conditions still represents a critical issue. The main reason is that typically
the data, needed for the correct statement of the mathematical problem, are not available (defective
problem). In order to fill this gap and to obtain a well-posed problem, the seminar will describe
different strategies for defective problems. Last, it will introduce geometrical multiscale models, that
can be regarded as methods for computing correct boundary conditions and reducing possible spurious
effects caused by the presence of artificial boundaries.
The seminar includes also a practical lesson, implementing the main theoretical aspects in FreeFem++.