Stable and efficient retrospective 4D-MRI using non-uniformly distributed quasi-random numbers.

The purpose of this work is the development of a robust and reliable three-dimensional (3D) Cartesian imaging technique for fast and flexible retrospective 4D abdominal MRI during free breathing. To this end, a non-uniform quasi random (NU-QR) reordering of the phase encoding (k(y)-k(z)) lines was incorporated into 3D Cartesian acquisition. The proposed sampling scheme allocates more phase encoding points near the k-space origin while reducing the sampling density in the outer part of the k-space. Respiratory self-gating in combination with SPIRiT-reconstruction is used for the reconstruction of abdominal data sets in different respiratory phases (4D-MRI). Six volunteers and three patients were examined at 1.5 T during free breathing. Additionally, data sets with conventional two-dimensional (2D) linear and 2D quasi random phase encoding order were acquired for the volunteers for comparison. A quantitative evaluation of image quality versus scan times (from 70 s to 626 s) for the given sampling schemes was obtained by calculating the normalized mutual information (NMI) for all volunteers. Motion estimation was accomplished by calculating the maximum derivative of a signal intensity profile of a transition (e.g. tumor or diaphragm). The 2D non-uniform quasi-random distribution of phase encoding lines in Cartesian 3D MRI yields more efficient undersampling patterns for parallel imaging compared to conventional uniform quasi-random and linear sampling. Median NMI values of NU-QR sampling are the highest for all scan times. Therefore, within the same scan time 4D imaging could be performed with improved image quality. The proposed method allows for the reconstruction of motion artifact reduced 4D data sets with isotropic spatial resolution of 2.1 x 2.1 x 2.1 mm(3) in a short scan time, e.g. 10 respiratory phases in only 3 min. Cranio-caudal tumor displacements between 23 and 46 mm could be observed. NU-QR sampling enables for stable 4D-MRI with high temporal and spatial resolution within short scan time for visualization of organ or tumor motion during free breathing. Further studies, e.g. the application of the method for radiotherapy planning are needed to investigate the clinical applicability and diagnostic value of the approach.