Detection of microbubble trajectories on M-mode images using Kalman filtering

Ultrasound contrast agents (UCA) are widely used for the diagnosis of cardiovascular diseases. They typically consist of shell encapsulated microbubbles which, when injected in blood, increase the blood/tissue ratio in ultrasound medical images. Characterizing the behavior of microbubbles hit by US energy, it is important to optimize their performance in clinical applications. In this paper, the movement of microbubbles pushed away from US probes by the radiation force is considered. A simple experimental set-up is used to obtain M-mode images in which each microbubble describes a trace of variable brightness position and slope. A Kalman filter model allows an iterative estimation of the instantaneous values of variables such as the bubble position, velocity and acceleration, in a discrete time process. The model constrains the solution of the estimation by two control parameters: the variance of acceleration and the maneuverability, characterizing the bubble inertia. The accuracy of the method has been evaluated on artificial images reporting different phenomena: trace crossing, intensity variation, sudden interruption and different background noise levels. In most cases, the traces have been detected with a mean error lower than one pixel