Introduction to NMR Spectroscopy and Imaging Lecture 10 Basics of Magnetic Resonance Imaging (Spring Term, 2011) Department of Chemistry National Sun Yat-sen.

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Introduction to NMR Spectroscopy and Imaging Lecture 10 Basics of Magnetic Resonance Imaging (Spring Term, 2011) Department of Chemistry National Sun Yat-sen University 核磁共振光譜與影像導論

Chapter 10 Basics of Magnetic Resonance Imaging Basic principle of MRI Back projection Fourier imaging Image contrast Fast 3D Imaging Functional MRI (fMRI)

Sources of Materials for this Chapter

Micro-imaging Animal imaging Whole-body (human) imaging ( MRI) Scanner = (MRI) Imager = MRI machine = MRI =NMR spectrometer with microimaging function

Golay Maxwell (Anti-Helmholtz)

Back Projection

Reconstruction

Broad band and narrow band pulses (Selective) (Nonselective)

Gaussian Half Gaussian EBURP2 Q5 (Gaussian cascade) Q3 (Gaussian cascade) There are many other selective pulses available. Customer designed pulse shapes can be synthesized on spectrometers at will. Other selective pulses (pulse shaping)

With a selective pulse of a definite excitation width of Δν, only a slice of thickness Z is excited (transverse magnetization generated)

Brute force back projection

Problems A sample contains water at two locations, x = 0 cm and x = 2.0 cm. A one- dimensional magnetic field gradient of 1 G/cm is applied along the x-axis during the acquisition of an FID. What frequencies (relative to the isocenter frequency) are contained in the Fourier transformed spectrum? An NMR spectrum is recorded from a sample containing two water locations. The frequency encoding gradient is 1 G/cm along the y-axis. The spectrum contains frequencies of +1000 Hz and -500 Hz relative to the isocenter frequency. What are the locations of the water? You want to excite spins in an xy-plane located at z = -5.0 cm. The resonance frequency at the isocenter is 63.85 MHz and your slice selection gradient is 1 G/cm. Describe in detail the RF pulse which should be used. A sample contains water at two locations, y = 1.0 cm and y = -2.0 cm. A one- dimensional magnetic field gradient is applied along the y-axis during the acquisition of an FID. The frequency encoding gradient is 1 G/cm. What frequencies (relative to the isocenter frequency) are contained in the Fourier transformed spectrum? An NMR spectrum is recorded from a sample containing two water locations. The frequency encoding gradient is 0.5 G/cm along the z-axis. The spectrum contains frequencies of -1000 Hz and +500 Hz relative to the isocenter frequency. What are the locations of the water? You want to excite spins in an xy-plane located at z = -2.0 cm. The resonance frequency at the isocenter is 63.85 MHz and your slice selection gradient is 2 G/cm. Describe in detail the RF pulse which should be used.

Single voxel image FT2 = FT1

Two-voxel image FT2 Zero-filling FT1

Field Of View (FOV) and Image Resolution

Resolution

Brute force back projection T

FT in n-dimension space Image = Spatial FT of original FIDs

Brute force back projection T k-space: (t, θ)

Te t k-space: (t, G x )

Signal in k-space:M(G x,t) = t GxGx Stack representation Contour representation

t GxGx

t θ k-space: (t, θ)

What does re-grid mean? Original signal: M(Δθ, Δt), M(Δθ,2 Δt), M(Δθ,3 Δt),…M(Δθ, (np/2)*Δt), M(2Δθ, Δt), M(2Δθ,2 Δt), M(2Δθ,3 Δt),…M(2Δθ, np*Δt), …… M(nv*Δθ, Δt), M(nv*Δθ,2 Δt), M(nv*Δθ,3 Δt),…M(nv*Δθ, np*Δt), Regrided signal: M(ΔtcosΔθ, ΔtsinΔθ), M(ΔtcosΔθ, 2ΔtsinΔθ,…, M(ΔtcosΔθ,( np/2)*ΔtsinΔθ M(2ΔtcosΔθ, ΔtsinΔθ), M(2ΔtcosΔθ, 2ΔtsinΔθ,…, M(2ΔtcosΔθ,( np/2)*ΔtsinΔθ …… M(nv*ΔtcosΔθ, ΔtsinΔθ), M(nv*ΔtcosΔθ, 2ΔtsinΔθ,…,M(nv*ΔtcosΔθ,( np/2)*ΔtsinΔθ Just coordinate transformation!

Re-griding y x

3D image of neck

Breathing lung

Beating heart

μMRI applications Single Cell Gene Expression Materials

Diffusion coefficient images of isolated Aplysia neurons acquired at 8.5 T. The cells are visible as a dark region with low diffusion coefficient within the brighter circle of the capillary tube containing artificial sea water. There is a strong contrast in these images between the nuclear region and the perikaryon, indicating that water molecules in these regions have strongly differing diffusion coefficients. A variety of irregular nuclear morphologies are apparent from the shapes of the bright regions present within the cell bodies J.S. Schoeniger, N. Aiken, E. Hsu, S.J. Blackband, J. Magn.Reson. Ser. B 103 (1994) 261.

“Smooth” CD surface in the nano-eye Not MRI mimage!

Some microimages made in this lab Unknown flower Sesame seed Fuel cell God-fish bone Onion epidermis

Weighted images Density image is the most basic Relaxation weighting Diffusion weighting Chemical shift weighting Temperature/pressure weighting Multi-quantum relaxation weighting Biochemical/physical weighting Psychological weighting

Question: what is the purpose of each of the white gradient fields?

Answer: restores the initial alignment of transverse magnetization because the slice- selection gradient field dephase the transeverse magnetization. Answer: shifts the echo (during acquisition) so that the first point is not the echo peak when phase-encoding gradient field is zero.

Spin Echo Imaging

Spin Echo Multiple Slice Imaging (SEMS) d1 can be short because each next scan is on a different slice.

Spin Echo Multiple Slice Imaging (SEMS) Tss Tpe Tef=atTec Maximum slices per TR:

TE (ms) TE (ms) 20 40 60 80 TR (ms) 250 500 750 1000 2000 Spin echo images

Inversion-recovery imaging

Inversion-recovery imaging: slice selection

Inversion-recovery imaging

TR (s) 1 2 TI(ms) 50 100 250 500 750 Inversion-recovery images

One additional gradient is applied between the 90o and 180o pulses. This gradient is along the same direction as the frequency encoding gradient. It dephases the spins so that they will rephase by the center of the echo. This gradient in effect prepares the signal to be at the edge of k-space by the start of the acquisition of the echo.

2

Gradient recalled echo images (TE=5 ms) Θ(o) 15 30 45 60 90 TR (ms) 25 50 100 200

Spin-Echo S = k r (1-exp(-TR/T1)) exp(-TE/T2) Inversion Recovery (180-90) S = k r (1-2exp(-TI/T1)+exp(-TR/T1)) Inversion Recovery (180-90-180) S = k r (1-2exp(-TI/T1)+exp(-TR/T1)) exp(-TE/T2) Gradient Recalled Echo S = k r (1-exp(-TR/T1)) Sinq exp(-TE/T2*) / (1 -Cosq exp(-TR/T1))

Multiple Slice Imaging with Other Sequences Obviously, inversion-recovery, gradient recalled echo sequences can also be performed in multi-slice acquisition mode. Maximum slices per TR for gradient echo sequence: Maximum slices per TR for inversion-recovery sequence:

Chemical shift imaging (CSI)

WeightingTR ValueTE Value T1T1 < = T 1 < < T 2 T2T2 > > T 1 > = T 2  > > T 1 < < T 2

Tissue T 1 (s) T 2 (ms) ** CSF0.8 - 20110 - 200070-230 White0.76 - 1.0861-10070-90 Gray1.09 - 2.1561 - 10985 - 125 Meninges0.5 - 2.250 - 1655 - 44 Muscle0.95 - 1.8220 - 6745 - 90 Adipose0.2 - 0.7553 - 9450 - 100 *Based on  =111 for 12mM aqueous NiCl 2

Activations (red–white color scale) and deactivations (blue–green color scale) in a group of 11 healthy elderly subjects during visual word encoding and retrieval (p 0.01, uncorrected). The Talairach coordinates of axial slices are indicated on the left-hand bottom of each image.

Concepts in Magnetic Resonance Part A, Vol. 16A(1) 35–49 (2003) Concepts in Magnetic Resonance Part A, Vol. 16A(1) 5–15 (2003)

Magnetic Resonance Microimaging (μMRI) The principle is basically the same as that of ordinary MRI. Sample size is in mm or smaller but resolution might be 10 times higher or more. Higher gradients are needed. Being at fast developing stage, with promise of single-spin imaging. A few challenges need to be addressed.

Microcoil is used (OD= 470 μm) Human hair (75 μm)

For μNMR microcoil array and surface coils Surface coils Coil arrays 100 μm Human hair

Concepts in Magnetic Resonance, Vol. 13, 128, 2001. Concepts in Magnetic Resonance, Vol. 13, 190, 2001.

0.2 mm I.D. NMR microcoil (Full of de- ionized water) Copper wire 5.5 mm Top 1.625 mm 4.4 mm 1.4 mm 5.5 mm Side 2.45 mm 0.35 mm 0.625 mm The Gradient set holder Micro-Coil Gradient System

Other magnetic resonance imaging techniques Magnetic force imaging Quantum imaging (single-spin imaging) Ferromagnetic resonance force imaging

Would MRI do these? Yes! We will make it!

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