In MR guided radiation therapy planning both MR and CT images of patients are acquired and co-registered to obtain accurate soft-tissue contours and Hounsfield Units (HU) for dose calculation. Direct HU generation from MRI would eliminate the need for CT acquisition allowing the full advantages of MRI to be exploited throughout treatment. The methods for the generation of synthetic (or substitute) CT images from MRI may be broadly categorized into regression-based methods¹ and atlas-based methods² which require multiple images, are computationally intensive or both. In this work, a regression-based approach to generate substitute CT (sCT) images directly from a single MRI sequence is applied. Unlike other regression models used for HU prediction we discard MRI intensities for building the regression model and instead use class probabilities (bone, soft tissues and air) for a voxel in the random forest regression model to predict the corresponding HU. The proposed approach is intuitive as there is not a direct relationship between CT (HU) and MRI signal intensities; In our model we propose to exploit the direct relationship between class probabilities of air, bone and soft tissues and corresponding HU maps. The method is shown to be accurate, fast and efficient.

CT scans of a porcine leg phantom were used to validate the proposed method. The approach is divided into two parts: (a) an expectation maximization (EM) based clustering of the soft tissues, bone and the air classes followed by (b) random forest regression based prediction of CT intensities for every voxel from class probabilities. A 3D ultrashort echo time (PETRA) sequence (TE 0.07 ms and TR 10 ms; spacing: 0.93mm isotropic, size: 3203) of the phantom (104x72x185mm) was acquired on a 3T system (Skyra, Siemens). This was co-registered to the corresponding CT image³ (spacing: 1.17x1.17x2mm; size: 512x512x111) to build tissue specific regression models. An EM based clustering was then performed on the co-registered MRI to identify the soft tissues, dense bone and air classes. Unlike longer echo times the PETRA sequence is useful in separating the bone and the air classes. For each of the tissue classes (soft tissue, air and bone) the corresponding CT and MRI intensities were sampled from the co-registered CT/PETRA images to build tissue-specific regression models. A non-linear random forest regression model with class probabilities for every voxel was used to build tissue specific regression lines. Thus a separate random forest regression model is used for soft tissue and bone. Air identified from the EM model is directly assigned a value of -1000 HU. For validation, an EM based clustering identified the soft tissue, the bone and the air in the phantom. Tissue specific regression models of the soft tissues and the bone were generated from half of the image to predict the other half of the image. The air class, the soft tissue class and the bone tissue class were combined to generate the sCT. Use of half of the bone information during the training stage ensures that the training and the testing voxels were segregated. The substitute CT framework is illustrated in Figure 1. For comparison the same pipeline was also used to generate a sCT using a combination of two echoes (ultrashort 0.04 ms & short 4 ms, 18° flip angle) from a separate UTE (Works-in-progress) sequence.

Figure 2 shows example images used in the validation of the bone tissue class. This was repeated for the soft-tissue class and the unsupervised learning framework did not require training images. The entire synthetic CT was reconstructed in under 180 seconds. Checkerboard images of the CT and the substitute CT are presented in Figure 3 and demonstrate excellent agreement. The CT and the substitute CT were both thresholded at 500 HU to segment cortical bone. The surface distance difference map of the bone in mm is presented in Figure 4 and the mean absolute surface distance error was 1.34 mm. The mean HU error (CT number) between the actual CT and sCT was -0.01 ± 22.84 across the entire volume and 15.59 ± 180.72 excluding background air. The corresponding values obtained from the dual-echo UTE sequence were higher: a mean of 1.89 mm for the bone surface error and greater HU error differences of 1.52 ± 39.13 and 102.35 ± 332.48 for the entire volume and excluding air respectively.The single sequence (PETRA) derived sCT had a low mean absolute surface distance for the bone and a low mean HU error. It was shown to outperform an alternative dual-echo sequence, and shows promise for the automated generation of fast MRI based sCT in radiation therapy planning and PET attenuation correction.