The clinical analysis of magnetic resonance (MR) can be accelerated through the undersampling in the k-space (Fourier domain). Deep learning techniques have been recently received considerable interest for accelerating MR imaging (MRI). In this paper, a deep learning method for accelerating MRI is presented, which is able to reconstruct undersampled MR images obtained by reducing the k-space data in the direction of the phase encoding. In particular, we focus on the reconstruction of MR images related to patients affected by multiple sclerosis (MS) and we propose a new multimodal deep learning architecture that is able to accelerate the MRI up to 8 times, while providing a high quality of the reconstructed image, especially in the area of the brain lesions. Experiments have been performed on T2W and FLAIR images, both providing useful information for MS MRI, and have shown that the proposed multimodal network is able to achieve a higher reconstruction accuracy with respect to existing methods, while effectively reducing the execution time of the clinical analysis.