Section: Application Domains

Blood flow modeling

Participants : Bertrand Maury, Astrid Decoene.

Modeling and numerical simulation of blood flow in arteries and veins may become an important tool for medical applications, as for instance in the prediction of cardiovascular disease. Analyzing the pressure waves and estimating the wall compliance of arteries is fundamental, as these exhibit strong inter- and intra-subject variability. Currently, non-invasive pressure measurements involve excessive errors; intensive direct estimation is thus not applicable in practice. Physiologists therefore hope to be able to predict the time and space evolution of the pressure in the arterial network from a small amount of flow data measured at a few points.

Several numerical models have been developed in order to simulate blood flow in arteries and veins. They mainly consist of one to three-dimensional systems of partial differential equations, depending on the level of complexity one desires to achieve. Coupling the various models is also an issue. These numerical models allow us to compute the transversal section area, as well as the velocity or flow at different points in space, leading to a rather complete description of the arterial flow (velocity, pressure, section). But for these models to be adapted to each patient, certain numerical and physical parameters must be fitted, such as the compliance of walls and the viscosity of the blood. These parameters are difficult to estimate experimentally and may be related to measurements which involve a non-negligible error. Furthermore, their optimal value is linked to the particular modeling framework and therefore can differ from the value given by their physical definition.

Mixed models appear to be an appropriate framework for taking into account the specific nature of each patient and quantifying uncertainty in the numerical model. Flow data are available as it is possible to non-invasively measure the mean velocity in and diameter of an artery.

We aim to introduce statistical mixed models to the framework for the classical one-dimensional blood flow model.