Diffusion tensor imaging (DTI) is a widely used imaging technique for mapping living human braintissue's microstructure and structural connectivity. Recently, deep learning methods have been proposed to rapidlyest...Diffusion tensor imaging (DTI) is a widely used imaging technique for mapping living human braintissue's microstructure and structural connectivity. Recently, deep learning methods have been proposed to rapidlyestimate diffusion tensors (DTs) using only a small quantity of diffusion-weighted (DW) images. However, thesemethods typically use the DW images obtained with fixed q-space sampling schemes as the training data, limitingthe application scenarios of such methods. To address this issue, we develop a new deep neural network calledq-space-coordinate-guided diffusion tensor imaging (QCG-DTI), which can efficiently and correctly estimate DTsunder flexible q-space sampling schemes. First, we propose a q-space-coordinate-embedded feature consistencystrategy to ensure the correspondence between q-space-coordinates and their respective DW images. Second, aq-space-coordinate fusion (QCF) module is introduced which eficiently embeds q-space-coordinates into multiscalefeatures of the corresponding DW images by linearly adjusting the feature maps along the channel dimension,thus eliminating the dependence on fixed diffusion sampling schemes. Finally, a multiscale feature residual dense(MRD) module is proposed which enhances the network's feature extraction and image reconstruction capabilitiesby using dual-branch convolutions with different kernel sizes to extract features at diferent scales. Compared tostate-of-the-art methods that rely on a fixed sampling scheme, the proposed network can obtain high-quality diffusiontensors and derived parameters even using DW images acquired with flexible q-space sampling schemes. Comparedto state-of-the-art deep learning methods, QCG-DTI reduces the mean absolute error by approximately 15% onfractional anisotropy and around 25% on mean diffusivity.展开更多
We consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solution...We consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is studied with sufficiently large viscosity of fluid. Finally, we show a continuous dependence result on the initial data which directly yields the weak-strong uniqueness of solutions.展开更多
基金Project supported by the National Natural Science Foundation of China(No.62062023)。
文摘Diffusion tensor imaging (DTI) is a widely used imaging technique for mapping living human braintissue's microstructure and structural connectivity. Recently, deep learning methods have been proposed to rapidlyestimate diffusion tensors (DTs) using only a small quantity of diffusion-weighted (DW) images. However, thesemethods typically use the DW images obtained with fixed q-space sampling schemes as the training data, limitingthe application scenarios of such methods. To address this issue, we develop a new deep neural network calledq-space-coordinate-guided diffusion tensor imaging (QCG-DTI), which can efficiently and correctly estimate DTsunder flexible q-space sampling schemes. First, we propose a q-space-coordinate-embedded feature consistencystrategy to ensure the correspondence between q-space-coordinates and their respective DW images. Second, aq-space-coordinate fusion (QCF) module is introduced which eficiently embeds q-space-coordinates into multiscalefeatures of the corresponding DW images by linearly adjusting the feature maps along the channel dimension,thus eliminating the dependence on fixed diffusion sampling schemes. Finally, a multiscale feature residual dense(MRD) module is proposed which enhances the network's feature extraction and image reconstruction capabilitiesby using dual-branch convolutions with different kernel sizes to extract features at diferent scales. Compared tostate-of-the-art methods that rely on a fixed sampling scheme, the proposed network can obtain high-quality diffusiontensors and derived parameters even using DW images acquired with flexible q-space sampling schemes. Comparedto state-of-the-art deep learning methods, QCG-DTI reduces the mean absolute error by approximately 15% onfractional anisotropy and around 25% on mean diffusivity.
基金supported by National Basic Research Program of China(973 Program)(Grant No.2011CB808002)National Natural Science Foundation of China(Grant Nos.11071086,11371152,11401439 and 11128102)+3 种基金the Natural Science Foundation of Guangdong Province(Grant No.S2012010010408)the Foundation for Distinguished Young Talents in Higher Education of Guangdong(Grant No.2014KQNCX162)the University Special Research Foundation for Ph.D Program(Grant No.20104407110002)the Science Foundation for Young Teachers of Wuyi University(Grant No.2014zk06)
文摘We consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is studied with sufficiently large viscosity of fluid. Finally, we show a continuous dependence result on the initial data which directly yields the weak-strong uniqueness of solutions.
