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Anisotropically weighted MRI
1Physical Sciences Laboratory, Center for Technology, National Institutes of Health, Bethesda, Maryland, USA.
Abstract:
The intensity of an isotropically weighted MR image is proportional to a rotationally invariant measure of bulk diffusion, Trace(D) (where D is the effective diffusion tensor). Such images can be acquired from as few as two diffusion-weighted images (DWIs). Analogously, the intensity of an anisotropically weighted MR image is proportional to a rotationally invariant measure of diffusion anisotropy derived from D, such as the variance of the principal diffusivities of D. By using linear algebra, we show that to produce an anisotropically weighted MR image requires acquiring at least seven DWIs, which is also the minimum number of DWIs sufficient to estimate the entire diffusion tensor, as well as the T2-weighted amplitude image, A(b = 0), in each voxel. A general mathematical framework for constructing isotropically weighted and anisotropically weighted MR images is also provided.
Insights
Generating isotropically weighted MR images requires only two diffusion-weighted images (DWIs). However, creating anisotropically weighted images, which reveal diffusion anisotropy, needs at least seven DWIs for comprehensive tensor and amplitude estimation.
Area of Science:
- Magnetic Resonance Imaging (MRI)
- Diffusion Tensor Imaging (DTI)
- Biomedical Engineering
Background:
- Isotropically weighted MR images reflect bulk diffusion (Trace(D)) and can be acquired using minimal diffusion-weighted images (DWIs).
- Anisotropically weighted MR images quantify diffusion anisotropy, a more complex measure derived from the diffusion tensor (D).
Purpose of the Study:
- To establish the minimum number of DWIs required for anisotropically weighted MR imaging.
- To present a general mathematical framework for constructing both isotropically and anisotropically weighted MR images.
Main Methods:
- Utilizing linear algebra to analyze the relationship between DWI acquisition and image weighting.
- Deriving the minimum DWI requirements for estimating the full diffusion tensor and T2-weighted amplitude image.
Main Results:
- Isotropic weighting requires a minimum of two DWIs.
- Anisotropic weighting necessitates a minimum of seven DWIs, which is also sufficient for full diffusion tensor and T2-weighted amplitude estimation.
- A general mathematical framework for weighted MR image construction was developed.
Conclusions:
- The number of DWIs critically impacts the type of diffusion information obtainable in MR imaging.
- Seven DWIs are the minimum requirement for comprehensive diffusion tensor imaging, enabling both isotropic and anisotropic image contrasts.
- The provided framework facilitates the creation of advanced diffusion-weighted MR contrasts.