By Jin Keun Seo
This can be the 1st booklet that provides a accomplished advent to and evaluation of electro-magnetic tissue estate imaging strategies utilizing MRI, targeting Magnetic Resonance electric Impedance Tomography (MREIT), electric homes Tomography (EPT) and Quantitative Susceptibility Mapping (QSM). The distinction info from those novel imaging modalities is exclusive considering there's at present no different option to reconstruct high-resolution photographs of the electro-magnetic tissue houses together with electric conductivity, permittivity, and magnetic susceptibility. those 3 imaging modalities are in keeping with Maxwell's equations and MRI information acquisition thoughts. they're increasing MRI's skill to supply new distinction info on tissue buildings and capabilities.
To facilitate additional technical growth, the ebook presents in-depth descriptions of the main up to date examine results, together with underlying physics, mathematical theories and versions, size suggestions, computation concerns, and different hard problems.
Readership: Researchers, lecturers and graduate scholars in clinical imaging, computational arithmetic and biomedical imaging.
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Additional resources for Electro-Magnetic Tissue Properties MRI
5, the inverse DFT provides the image of m(x, y). 2. In MRI, the data acquisition time is roughly proportional to the number of phase-encoding lines due to the timeconsuming phase encoding which separates signals from diﬀerent y-positions within the image m(x, y). Hence, to accelerate the acquisition process, we can skip phase-encoding lines in the k-space. Reduction in k-space data violating the Nyquist criterion is associated with an aliasing in the image space. If we use sub-sampled kspace data by a factor of R in phase-encoding direction (y-direction), according to Poisson summation formula, the corresponding inverse Fourier transform produces a fold-over artifact.
L [water] ωL [fat] The eﬀect of χ, the chemical shift, is very small compared to B0 . For example, ωL [fat] − ωL [water] ≈ 10−6 γB0 at 3T MRI. 2 MR signal ignoring relaxation eﬀects Noting that the magnitude of the net magnetization |M⊥0 (r)| = |M ⊥ (r, t)| is independent of time t and depends on the amount January 16, 2014 16:27 9in x 6in Electro-Magnetic Tissue Properties b1693-ch02 Electro-magnetism and MRI 37 of hydrogen, the natural question is how we visualize |M⊥0 (r)| = |M ⊥ (r, t)|. 65), the magnetic ﬁeld induced by the distribution of M is expressed as BM (r, t) ≈ µ0 ∇× 4π M(r , t) × Ω r−r dr .
E = −iω0 µ0 H According to Maxwell’s equations, & ∇ × H = (σ + iω0 )E. 108) Applying the curl operation to ∇ × H = (σ + iω0 )E, we get ∇ × ∇ × H = ∇ × ((σ + iω0 )E) = ∇(σ + iω0 ) × E + (σ + iω0 )∇ × E = ∇(σ + iω0 ) × (∇ × H) − iω0 µ0 (σ + iω0 )H. 107) follows from ∇ × ∇ × H = −∇2 H − ∇∇ · H = −∇2 H. January 16, 2014 46 16:27 9in x 6in Electro-Magnetic Tissue Properties b1693-ch02 Electro-Magnetic Tissue Properties MRI The RF ﬁeld can be regarded as a stationary ﬁeld with respect to the rotating frame that is rotating at the angular frequency ω0 .