Cardiac MRI commonly uses prior information about the location of the heart to assist acquisition and reconstruction. For example, a region of interest (ROI) containing the heart is typically used for localized shimming or dynamic shimming to optimize the magnetic field homogeneity over the heart [1-3]. Additionally, heart localization is a common first step for many post-processing algorithms such as automatic left ventricular segmentation [4-5] and automatic scan-plane prescription [6]. Many of these applications require the user to manually place an ROI over the heart prior to scanning. In this work, we propose an algorithm that automatically fits a 3D ellipsoidal ROI over the heart using a fast multi-slice scout scan. This automatic ROI placement simplifies workflow, and the ellipsoidal shape can be sliced to yield elliptical ROIs for dynamic shimming along arbitrary oblique scan planes or to facilitate post-processing applications.

Eight subjects (four volunteers, four patients) were scanned on a 1.5 T GE scanner using the RTHawk Research platform (HeartVista, Inc., Los Altos, CA) to acquire cardiac-triggered free-breathing multi-slice GRE images at 10 sagittal locations with 3-cm slice spacing and 32-cm field of view (FOV). A time series of images was obtained by imaging each slice location continuously for two heartbeats using a five-interleaf spiral readout. The slice location was advanced every two heartbeats until all 10 slices were acquired, yielding a total scan duration of 20 heartbeats. For each slice, sliding-window reconstruction was used to generate images at 40 time frames spanning two heartbeats. The pulse sequence and acquisition scheme are shown in Fig. 1.

Each set of sagittal images was reformatted into a T x (S N_x N_y) matrix $$$X$$$, where T is the number of temporal frames, S is the number of slices, and N_x and N_y are the image dimensions (Fig. 2a-2b). In this work, T = 40, S = 10, N_x = N_y = 142. The matrix $$$X$$$ was normalized by subtracting the temporal mean from each column, effectively removing the average intensity from each pixel in the dataset. The singular value decomposition $$$X = UΣV^T$$$ was computed, where columns of $$$U$$$ ($$$u_i$$$) are left singular vectors of size T describing the temporal variability of $$$X$$$, and columns of $$$V$$$ ($$$v_i$$$) are right singular vectors of size (S N_x N_y). The magnitude of $$$v_i$$$ represents a spatial “motion map” for each of the (S N_x N_y) pixels, where the magnitude of each pixel in $$$v_i$$$ indicates the degree to which the temporal waveform $$$u_i$$$ describes the temporal variability of that pixel.

A single $$$v_i$$$ was automatically selected as a cardiac motion map using knowledge that the corresponding $$$u_i$$$ should exhibit high periodicity due to the two-RR triggering per slice (e.g., Fig. 2b). A 3D ellipsoid that optimally covered the high-intensity regions of the motion map was computed by solving the following convex optimization problem:

$$minimize:\sum_j y_j\|Ax_j-b\|_2$$

$$subject\,\,to:-\log\det A\leq V_{max}$$

where the 3x3 matrix $$$A$$$ and 3x1 vector $$$b$$$ are variables that parametrize an ellipsoid {$$$x \mid \, \|Ax-b\|_2 \leq 1$$$}, $$$y_j$$$ is the magnitude of pixel j in the motion map, $$$x_j$$$ is a 3x1 position vector containing the coordinates of pixel j, and $$$V_{max}$$$ is a parameter specifying the maximum volume of the ellipsoid. This optimization problem is a variant of a minimum volume covering ellipsoid problem, and it was solved in Python using CVXPY [7].

Figure 3a shows an automatically selected left singular vector from a subject scan, which exhibits a two-cycle periodicity that is correlated with the two-heartbeat triggering used to acquire each slice. Reformatted slices from the corresponding right singular vector are shown in Fig. 3b. Bright regions, which correspond to areas of high correlation with the left singular vector, are located predominantly over the heart. Cross-sections of the resulting ellipsoidal ROI are shown on each slice of the motion map (Fig. 3b) and on diastolic frames from each slice (Fig. 3c). Figure 4 shows one slice from eight different subject scans, with cross-sections of the resulting ellipsoidal ROI shown in yellow.We presented a 3D heart localization algorithm to automatically determine the placement and orientation of an ellipsoidal ROI for optimal heart coverage. The proposed technique uses dynamic images acquired from a rapid, cardiac-triggered multi-slice scan. The algorithm was demonstrated on datasets from eight subject scans, which yielded good ROI placement over the heart with the ellipsoidal orientation conforming to the overall shape of the heart. Future work will investigate automatic scan-plane prescription using the resulting ellipsoidal long axis.