Reducing motion artifacts in 4D MR images using principal component analysis (PCA) combined with linear polynomial fitting model

We have previously developed a retrospective 4D‐MRI technique using body area as the respiratory surrogate, but generally, the reconstructed 4D MR images suffer from severe or mild artifacts mainly caused by irregular motion during image acquisition. Those image artifacts may potentially affect the accuracy of tumor target delineation or the shape representation of surrounding nontarget tissues and organs. So the purpose of this study is to propose an approach employing principal component analysis (PCA), combined with a linear polynomial fitting model, to remodel the displacement vector fields (DVFs) obtained from deformable image registration (DIR), with the main goal of reducing the motion artifacts in 4D MR images. Seven patients with hepatocellular carcinoma (2/7) or liver metastases (5/7) in the liver, as well as a patient with non‐small cell lung cancer (NSCLC), were enrolled in an IRB‐approved prospective study. Both CT and MR simulations were performed for each patient for treatment planning. Multiple‐slice, multiple‐phase, cine‐MRI images were acquired in the axial plane for 4D‐MRI reconstruction. Single‐slice 2D cine‐MR images were acquired across the center of the tumor in axial, coronal, and sagittal planes. For a 4D MR image dataset, the DVFs in three orthogonal direction (inferior–superior (SI), anterior–posterior (AP), and medial–lateral (ML)) relative to a specific reference phase were calculated using an in‐house DIR algorithm. The DVFs were preprocessed in three temporal and spatial dimensions using a polynomial fitting model, with the goal of correcting the potential registration errors introduced by three‐dimensional DIR. Then PCA was used to decompose each fitted DVF into a linear combination of three principal motion bases whose spanned subspaces combined with their projections had been validated to be sufficient to represent the regular respiratory motion. By wrapping the reference MR image using the remodeled DVFs, ‘synthetic’ MR images with reduced motion artifacts were generated at selected phase. Tumor motion trajectories derived from cine‐MRI, 4D CT, original 4D MRI, and ‘synthetic’ 4D MRI were analyzed in the SI, AP, and ML directions, respectively. Their correlation coefficient (CC) and difference (D) in motion amplitude were calculated for comparison. Of all the patients, the means and standard deviations (SDs) of CC comparing ‘synthetic’ 4D MRI and cine‐MRI were 0.98±0.01,0.98±0,01, and 0.99±0.01 in SI, AP, and ML directions, respectively. The mean±SD Ds were 0.59±0.09 mm,0.29±0.10 mm, and 0.15±0.05 mm in SI, AP and ML directions, respectively. The means and SDs of CC comparing ‘synthetic’ 4D MRI and 4D CT were 0.96±0.01,0.95±0.01, and 0.95±0.01 in SI, AP, and ML directions, respectively. The mean±SD Ds were 0.76±0.20 mm,0.33±0.14 mm, and 0.19±0.07 mm in SI, AP, and ML directions, respectively. The means and SDs of CC comparing ‘synthetic’ 4D MRI and original 4D MRI were 0.98±0.01,0.98±0.01, and 0.97±0.01 in SI, AP, and ML directions, respectively. The mean±SD Ds were 0.58±0.10 mm,0.30±0.09 mm, and 0.17±0.04 mm in SI, AP, and ML directions, respectively. In this study we have proposed an approach employing PCA combined with a linear polynomial fitting model to capture the regular respiratory motion from a 4D MR image dataset. And its potential usefulness in reducing motion artifacts and improving image quality has been demonstrated by the preliminary results in oncological patients. PACS numbers: 87.57. cp, 87.57. nj, 87.61. ‐c