Data Assimilation in Cardiovascular Fluid–Structure Interaction Problems: An Introduction

Numerical methods for incompressible fluid dynamics have recently received a strong impulse from the applications to the cardiovascular system. In particular, fluid–structure interaction methods have been extensively investigated in view of an accurate and possibly fast simulation of blood flow in arteries and veins. This has been strongly motivated by the progressive interest in using numerical tools not only for understanding the general physiology and pathology of the vascular system. The opportunity offered by medical images properly preprocessed and elaborated to simulate blood flow in real patients highlighted the potential impact of scientific computing on the clinical practice. Therefore, in silico experiments are currently extensively used in bioengineering for completing (and sometimes driving) more traditional in vivo and in vitro investigations. Parallel to the development of numerical models, the need for quantitative analysis for diagnostic purposes has strongly stimulated the design of new methods and instruments for measurements and imaging. Thanks to these developments, a huge amount of data is nowadays available. Data Assimilation is the accurate merging of measures (including images) and numerical simulations for a mathematically sound integration of different sources of information. The outcome of this process includes both the patient-specific measures and the general principles underlying the development of mathematical models. In this way, simulations are adapted to the availability of individual data and are therefore supposed to be more reliable; measures are correspondingly filtered by the mathematical models assumed to describe the underlying phenomena, resulting in a (hopefully) significant reduction of the noise.