Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) measures microvascular perfusion by capturing the temporal changes of an MRI contrast agent in a target tissue, and it provides valuable information for the diagnosis and prognosis of a wide range of tumors. Quantitative DCE-MRI analysis commonly relies on the nonlinear least square (NLLS) fitting of a pharmacokinetic (PK) model to concentration curves. However, the voxel-wise application of such nonlinear curve fitting is highly time-consuming. The arterial input function (AIF) needs to be utilized in quantitative DCE-MRI analysis. and in practice, a population-based arterial AIF is often used in PK modeling. The contribution of intravascular dispersion to the measured signal enhancement is assumed to be negligible. The MR dispersion imaging (MRDI) model was recently proposed to account for intravascular dispersion, enabling more accurate PK modeling. However, the complexity of the MRDI hinders its practical usability and makes quantitative PK modeling even more time-consuming. In this paper, we propose fast MR dispersion imaging (fMRDI) to effectively represent the intravascular dispersion and highly accelerated PK parameter estimation. We also propose a deep learning-based, two-stage framework to accelerate PK parameter estimation. We used a deep neural network (NN) to estimate PK parameters directly from enhancement curves. The estimation from NN was further refined using several steps of NLLS, which is significantly faster than performing NLLS from random initializations. A data synthesis module is proposed to generate synthetic training data for the NN. Two data-processing modules were introduced to improve the model's stability against noise and variations. Experiments on our in-house clinical prostate MRI dataset demonstrated that our method significantly reduces the processing time, produces a better distinction between normal and clinically significant prostate cancer (csPCa) lesions, and is more robust against noise than conventional DCE-MRI analysis methods.

Diffusion models have achieved impressive performance on various image generation tasks, including image super-resolution. Despite their impressive performance, diffusion models suffer from high computational costs due to the large number of denoising steps. In this paper, we proposed a novel accelerated diffusion model, termed Partial Diffusion Models (PDMs), for magnetic resonance imaging (MRI) super-resolution. We observed that the latents of diffusing a pair of low- and high-resolution images gradually converge and become indistinguishable after a certain noise level. This inspires us to use certain low-resolution latent to approximate corresponding high-resolution latent. With the approximation, we can skip part of the diffusion and denoising steps, reducing the computation in training and inference. To mitigate the approximation error, we further introduced 'latent alignment' that gradually interpolates and approaches the high-resolution latents from the low-resolution latents. Partial diffusion models, in conjunction with latent alignment, essentially establish a new trajectory where the latents, unlike those in original diffusion models, gradually transition from low-resolution to high-resolution images. Experiments on three MRI datasets demonstrate that partial diffusion models achieve competetive super-resolution quality with significantly fewer denoising steps than original diffusion models. In addition, they can be incorporated with recent accelerated diffusion models to further enhance the efficiency.