Estimation of the compliance of the arterial walls through Kalman

Andersson, Annica Elisabeth

Estimation of the compliance of the arterial walls through Kalman

Wednesday 20th July 2011

Formaggia, L.

Nobile, F.

Very powerful tools to model bloodow in the arteries have been developed in recent years, giving an accurate description of how important variables, like pressure, section area and velocity change during a heartbeat. However, the physical parameters that intervene can vary considerably between patients, making predictions dicult in specic cases. In order to adapt the simulation to each patient, a Kalman filter has been implemented, rst in its classical version, then generalised into an extended Kalman lter (EKF). This method uses the knowledge of how a state vector evolves in time along with in vivo measurements to lter the measurement error and the inaccuracy we insert by making a guess on the parameters. If we apply it to a state vector made up of the section area, the mean velocity and the parameter β, which is related to the compliance of the vessel wall, we arrive to an estimation of the parameter in the specific patient. The procedure, especially the EKF, attains good accuracy in most of the tested cases, and shows robustness towards measurement errors. In addition it can be applied to cases where we only have measurements on one state variable and where we only have a small frequency of measurements. Having an estimate of the parameter can help choosing the treatment in case of need. For instance it could help dimensioning the stent that has to be inserted, since it gives us the possibility to simulate the result of a local increase of stiness of the wall.