# Breast MRI

MRI of the breast is increasingly used to monitor high-risk patients. Tracking tumors in different states is useful for obtaining important clinical information. Computational models of the deformation of the breast in different positions are being developed. Malcolm et al. investigated the use of partial least squares regression (PLSR) to predict breast deformation from the prone to the supine positions [185]. Meshes of prone breast images are fitted to data segmented from T1WI. Because of unavailability of supine MRI data in their database, the associated supine geometrics are generated using finite element models (FEM) mechanics simulation. PLSR trains a statistical model of deformation using the population of associated prone and supine models from these FEM simulation results. It is clear that the PLSR approach has the potential to be a reliable alternative to FEM because the volume averaged geometric and relative errors between the PLSR predicted supine models and the associated FEM solutions were 1.9 ± 0.7 mm and 12 ± 7%, respectively. In addition, the PLSR predictions were five orders of magnitude faster than the FEM solution.

Breast density is an important risk factor for developing breast cancer. Khalvati et al. developed multi-atlas-based breast MRI segmentation [152]. To have a diverse atlas, the training images with the manual segmentation for the whole breast were first clustered based on the similarity of the corresponding phase congruency maps (PCMs). The phase congruency of an image at location *x (PC(x))* can be calculated as follows:

i

where E(*x*) is the local energy of the image, T is a threshold to suppress the effect of noise on the local energy of the image at that location, *A _{n}* presents the amplitude of the nth Fourier component, and e is set to a small number to avoid division by

0. Afterward, group-wise registration is performed on the original images in each class based on the distance map of the corresponding PCMs to create the mean image and the corresponding mean label. For segmentation of a target image, it is first determined which class a target image belongs to. To generate the segmentation results, the target image and centroid of the class are aligned in order by a nonrigid registration. The segmentation results for the entire volume were compared with the ground truth results to evaluate the performance of this algorithm, and an average Dice similarity coefficient (DSC) of 0.93 was achieved.

Wu et al. proposed a fully automated segmentation of fibroglandular tissue and estimation of volumetric density using an atlas-aided fuzzy C-means (FCM-Atlas) method. Firstly, an initial voxel-wise likelihood map of fibroglandular tissue is produced by applying FCM clustering to the intensity space of each 2D MR slice. To achieve enhanced segmentation, a prior learned fibroglandular tissue likelihood atlas is incorporated to refine the initial FCM likelihood map. An updated likelihood map *u* _{;}^{r}* can be calculated as follows:

where *u*-* is the FCM-generated likelihood map, *W* represents the warping transformation that deforms the standard atlas to the shape of the specific breast being processed, and A is an overall fibroglandular likelihood atlas. The absolute volume of the fibroglandular tissue (|FGT|) and the amount of the |FGT| relative to the whole breast volume (FGT%) of this proposed method were compared with that of manual segmentation obtained by two experienced breast radiologists. The automated segmentation achieved a correlation of *r =* 0.92 for FGT% and *r =* 0.93 for |FGT|, which were not significantly different from the manual segmentation. In addition, it was also clear that the segmentation performance was stable both with respect to selecting different cases and to varying the number of cases needed to construct the prior probability atlas by the additional robustness analysis^{3}.

Segmentation of pectoral muscles is important for volumetric breast density estimation and for pharmacokinetic analysis of dynamic contrast enhancement. Gubern-Merida et al. developed two atlas-based pectoral muscle segmentation methods in breast MRI [111]. One method is based on a probabilistic model and the other method is a multi-atlas registration-based approach. The probabilities of the atlas are first mapped by registration process composed of two stages. The first stage is a translation transform and the second stage is a nonrigid transform based on B-splines registration. Subsequently, two atlas-based segmentation methods are performed. In the probabilistic atlas-based segmentation, method 1, a probabilistic atlas is used in a Bayesian framework and is created by computing the frequency with which each location is labeled as pectoral muscle. The probabilistic atlas, the tissue models, and the target are supplied to the Bayesian framework as a prior probability *P(X),* conditional probability *P(YX*), and a set of intensity values *Y, *respectively. The Bayesian framework estimates the segmentation X that maximizes

*P(X)P(YX)* and also includes a Markov random field regularization. Multi-atlas segmentation, method 2, approaches consist of two steps after mapping all the atlases onto the target space. First, the deformed anatomic images are compared with the target to select the most similar atlases. The selection is based on the normalized cross correlation similarity measure, and a ratio is calculated as follows:

where *M* is the mapping between the target and an atlas, *j* is the deformed atlas with maximum similarity, and *T* is target volume. The selected deformed atlas labels are fused to yield a single final segmentation of the patient or target image. The probabilistic and the multi-atlas segmentation frameworks were evaluated in a leave-one-out experiment. The multi-atlas approach performed slightly better, with an average DSC of 0.74, while, with the much faster probabilistic method, a DSC of 0.72 resulted. The authors stated that both atlas-based segmentation methods have high reliability because of their DSC values being higher than the computed interobserver variability.