Lecture 13: Field gradients Homogeneous field 0 B Pulsed field gradients (Gz) B0 Gradients dephase transverse magnetization Gz = 0 units Gradients dephase transverse magnetization Gz = 1 units Gradients dephase transverse magnetization Gz = 2 units Gradients dephase transverse magnetization Gz = 4 units Pulsed field gradients (Gy) B0 Gradient echoes τττ τ z 1 φ G H GRADIENTS AND MAGNETIC RESONANCE IMAGING Lars G. Hanson Copenhagen University Hospital Hvidovre https://eprints.drcmr.dk/37/1/MRI English a4.pdf Slice selection by Gz H1 Gz a Slice selection by Gz H1 Gz slice select a b c Selective pulse: amplitude modulation Axial slice selection by Gz Sagittal slice selection by Gx Coronal slice selection by Gy Magnetization in the slice x y 1D imaging in the slice H1 Gz Gy Gx slice select read a b c Magnetization in the slice with gradient Gx Magnetization in the slice with gradient Gx Magnetization in the slice with gradient Gx 2D imaging in the slice H1 Gz TR TE encode Gy Gx slice select read a b c hgd e f Magnetization in the slice with gradient Gy Magnetization in the slice with gradient Gy Magnetization in the slice with gradient Gy Combination of gradients Gx and Gy Combination of gradients Gx and Gy Combination of gradients Gx and Gy 3D gradient echo imaging H1 TE TR Gy encode xG encode t x y τ τ Gz read b c hf ga ed High resolution in all dimensions More time consuming Regular patterns create signal Regular patterns create signal Unique shape as superposition of patterns ℜ{Ψ}ℑ{Ψ}Ψ∗Ψ x Unique shape as superposition of patterns Unique shape as superposition of patterns Unique shape as superposition of patterns Unique shape as superposition of patterns Image reconstruction • resembles diffraction methods (crystallography) • wavelength of the phase patterns generated by gradients • wavelength of the radio waves is irrelevant (but starts to interfere at high field, where it approaches the body dimensions) • Ω assumed to be identical differences must be corrected to avoid artifacts k space k k space 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 016 k space −4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 80 0−4 k space 0 0 0 0 0 0 0 0 0 0 +1 +1 +1 +1 +1 +1+1+1+1+1 10+2 −2 −2 +2 k space 11 −1 −1 −1 −1 −1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 −1+3 +3 −1 −1 −1−1 −1 −1 See Figure 15 in https://eprints.drcmr.dk/37/1/MRI English a4.pdf Figure 15: Image reconstruction. The figure shows how simple patterns (line 1) can be summed up to complex images (line 2). The reconstructed images are, in this case, created from the patterns that have