Dynamic multi-phase imaging of the abdomen using single shot echo-planar imaging (ss-EPI) is limited by respiratory motion artifact. While the use of respiratory triggering or breath-holding acquisitions can improve image quality^1,2, only a limited number acquisitions can be performed during a single breath-hold. Therefore, reliable and efficient methods for motion correction of abdominal organs in free-breathing acquisitions are highly desirable. Previous work has demonstrated the utility of using the Extended Kalman Filter for real-time image-based motion correction in spiral-navigated acquisitions³. Here we present an initial feasibly study for applying the EKF framework for real-time estimation of abdominal motion using each EPI frame as its own navigator (i.e. self-navigated).

EKF Framework: The Extended Kalman Filter provides a principled approach for image-based tracking of objects in MRI data in real-time³. The EKF itself provides recursive state estimates in nonlinear dynamic systems perturbed by Gaussian noise. The basic dynamic state-space model of the EKF, as implemented here can be written as a set of system equations of the form:$$\mathbf{x}_k = \mathbf{A}\mathbf{x}_{k-1}+\mathbf{w};P(\mathbf{w})\sim N(0,\mathbf{Q})$$

$$\mathbf{y}_k = h(\mathbf{y}_{k-1})+\mathbf{v};P(\mathbf{v})\sim N(0,\mathbf{R}),$$where $$$\mathbf{x}_k$$$ is the (unobserved) state of the dynamic system at time-step k and $$$\mathbf{y}_k$$$ are the (observed) measurements. We let $$$ \mathbf{x}_k=\left[\mathbf{t}_x,\mathbf{t}_y,\mathbf{t}_z,\mathbf{\theta}_x,\mathbf{\theta}_y,\mathbf{\theta}_z\right]^T$$$ represent the six rigid-body motion parameters in x-y-z space, and $$$\mathbf{y}_k$$$ a N_v-dimensional vector of voxel intensities for the 2D slice acquired at time k. For image-based tracking, the measurement model $$$h(·)$$$ describes a 2D interpolation into a fixed reference image $$$\mathbf{y}_{ref}$$$ (corresponding slice of the first volume) at the locations specified by $$$\mathbf{x}_k$$$.

Filter Settings: The dynamics are modeled using a simple random walk, with $$$\mathbf{A}$$$ as the identity matrix. In addition, as there is very little rotation of abdominal organs during free breathing, we constrain the motion estimates to include translations only by setting $$$\mathbf{Q}=\left[1,1,1,1\times10^{-10},1\times10^{-10},1\times10^{-10}\right]^T$$$. Local image tracking within regions-of-interest (ROIs) is achieved by setting the diagonal elements of $$$R^{-1}$$$ to zero for voxels outside the ROI.

Image Acquisition: The study was approved by the local Institutional Review Board (UCSD IRB) and all volunteers gave written informed consent. Coronal ss-EPI data were acquired on a 3T GE DISCOVERY MR750 scanner with the following parameters: TR/TE (ms)= 3000/58; FOV = 440 mm; matrix = 128x128; number of slices = 32; slice thickness = 6mm, phase FOV = 0.75, number of frames = 21.

The results of EKF tracking of the kidney is shown in Figure 1. As illustrated, the EKF algorithm successfully tracked the translational motion of the kidney during normal respiratory cycles. Retrospective correction of time series data using real-time EKF motion estimates significantly reduced the variation in voxel intensities within the tracked ROI. The EKF algorithm provides a principled approach for real-time motion tracking by using each measurement frame along with a dynamic model to update the predicted pose of the tracked object. This study demonstrates the feasibility of using the EKF for robust slice-by-slice rigid-body motion tracking of the abdomen in free-breathing ss-EPI data.