Nguyên lý tạo ảnh trong MRI (NMR dx rad imaging physics course) phần 2

Stewart, PhD, DABMP 2 Take Aways: Five Things You should be able to Explain after the NMR Lectures ¬ The magnetic characteristics of the nucleus and the magnetic properties of matter ¬

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Nuclear Magnetic Resonance – Chapter 14

Brent K Stewart, PhD, DABMP Professor, Radiology and Medical Education Director, Diagnostic Physics

a copy of this lecture may be found at:

http://courses.washington.edu/radxphys/PhysicsCourse04-05.html

Take Aways: Five Things You should be able

to Explain after the NMR Lectures

¬ The magnetic characteristics of the nucleus and the magnetic properties of matter

¬ How the NMR signal is generated and detected

¬ T1 and T2 relaxation: how they arise and how they are measured

¬ Pulse sequence methods used and pulse sequence timing (e.g., TR and TE) and inherent NMR parameters (e.g., T1 and T2) give rise to tissue contrast

¬ How a 1D gradient can be used to provide an echo and allow for quick imaging with shallow flip angle sequences

Soft Tissue Transparency and First NMR Image

c.f Mokovski, A Medical Imaging Systems, p 3.

2003 Nobel Prize for Medicine - MRI

¬ Laterbur and Mansfield (2003, medicine):

discoveries concerning magnetic resonance imaging (MRI)

¬ Rabi (1944, physics):

nuclear magnetic resonance (NMR) methodology

¬ Bloch and Purcell (1952, physics): NMR precision measurements

¬ Ernst (1991, chemistry):

high-resolution NMR spectroscopy

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Nuclear Magnetic Resonance

¬ NMR the study of the magnetic properties of the nucleus

¬ Magnetic field associated with nuclear spin/chg distr.

¬ Not an imaging technique – provides spectroscopic data

¬ Magnetic Resonance Imaging – magnetic gradients and

mathematical reconstruction algorithms produce the

N-dimensional image from NMR free-induction decay data

¬ High contrast sensitivity to soft tissue differences

¬ Does not use ionizing radiation (radio waves)

¬ Important to understand the underlying principles of

NMR in order to transfer this knowledge to MRI

NMR T1 for Tumor and Normal Tissue

c.f Mansfield, et al NMR Imaging in Biomedicine, 1982, p 22.

c.f http://www.gg.caltech.edu/~dhl/

Image Contrast – What does it depend on?

¬ Radiation needs to interact with the body’s tissues in

some differential manner to provide contrast

¬ X-ray/CT: differences in e-density (e-/cm3= ρ · -/g)

¬ Ultrasound: differences in acoustic impedance (Z = ρ·c)

¬ Nuclear Medicine: differences in tracer concentration (ρ)

¬ MRI: many intrinsic and extrinsic factors affect contrast

¬ intrinsic: ρH,T1, T2, flow, perfusion, diffusion,

¬ extrinsic: TR, TE, TI, flip angle,

c.f Bushberg, et al The Essential Physics

Magnetism and the Magnetic Properties of Matter

¬ Mag field generated by moving charges (e-or quarks)

¬ Most materials do not exhibit overt magnetic properties

¬ Exception: permanent magnet

¬ Magnetic susceptibility – extent to which a material becomes magnetized when placed in a magnetic field

¬ Three categories of magnetic susceptibility

¬ Diamagnetic –opposing applied field

¬Ca, H2O, most organic materials (C and H)

¬ Paramagnetic –enhancing field, no self-magnetism

¬O2, deoxyhemoglobin and Gd-based contrast agents

¬ Ferromagnetic –‘superparamagnetic’, greatly enhancing field

¬Exhibits self-magnetism: Fe, Co and Ni

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¬ Magnetic fields arise from magnetic dipoles (N/S)

¬ N –side the origin of magnetic field lines (arbitrary)

¬ Attraction (N-S) and repulsion (N-N & S-S)

¬ Magnetic field strength (flux density): B

¬ Measured in tesla (T) and gauss (G): 1 T = 10,000 G

¬ Earth magnetic field ~ 1/20,000 T or 0.5 G

¬ Magnetic fields arise from

¬ Permanent magnets

¬ Current through a wire or solenoid (current amplitude sets B

magnitude)

c.f Bushberg, et al The Essential Physics of Medical Imaging, 2 nd ed., p 374 and 377.

Magnetic Characteristics of the Nucleus

¬ Magnetic properties of nuclei determined by the spin and charge

distribution (quarks) of the nucleons (p+and n)

¬ Magnetic moment (µ) describes the nuclear B field magnitude

¬ Pairing of p+-p+or n-n causes µto cancel out

¬ So if P (total p+) and N (total n) is even no/little µ

¬ If N even and P odd or P even and N odd resultant µ(NMR eff.)

Nuclear Magnetic Characteristics of the Elements

¬ Biologically relevant elements that are candidates for NMR/MRI

¬ Magnitude of µ

¬ Physiologic concentration

¬ Isotopic abundance

¬ Relative sensitivity

¬ 1H (p+) provide 104-106times the signal from 23Na or 31P c.f Bushberg, et al The Essential Physics of Medical

Imaging, 2 nd ed., p 376.

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¬ Spinning p+considered ‘classically’ as a bar magnet

¬ Thermal energy randomizes direction of µ no net magnetization

¬ Application of an external magnetic field (B0) two energy states

¬ Lower energy µparallel w/ B0and higher energy µanti-parallelw/ B0

¬ Number of excess µ@ 1.0T and 310 K 3 ppm (very small effect)

¬ For typical voxel in MRI: 1021p+ 3x1015more µin lower state

of Medical Imaging, 2 nd ed., p 377.

c.f http://www.hull.ac.uk/mri

Larmor Frequency

¬ ‘Classically’ a torque on µby B0causes precession

¬ Precession occurs at an angular frequency (rotations/sec or radians/sec)*

¬ Larmor equation: ω0(radians/sec)= γ·B0; f0(rotations/sec or Hz)= ( )·B0

¬ = gyromagnetic ratio (MHz/T) unique to each element

¬ Choice of freq the resonance phen to be ‘tuned’ to a specific element

¬ For 1H @ 1.5T = 64 MHz (Channel 3)

c.f Bushberg, et al The Essential Physics of Medical Imaging, 2 nd ed., p 379.

* Note: 360° = 2π radians,

1 radian = 57.3°

c.f Hendee, et al Medical Imaging Physics,

4 th ed., p 357.

Larmor Frequency & US VHF Broadcast Spectrum

c.f http://www.rentcom.com/wpapers/

telex/telex3.html

1.5 T = 64 MHz

of Medical Imaging, 2 nd ed., p.18.

3.0 T = 128 MHz

¬ At equilibrium, no B field ⊥B0 (all along z-axis)

¬ Random distribution of µin x-y plane averages out: Bxy= 0

¬ Small µzadd up to measurable

M0(equilibrium magnetization)

¬ Absorbed radiofrequency EM radiation low-E to high-E

¬ High-E nuclei lose energy to environment: return to equilibrium state and Mz (longitudinal magnetization)

M0 c.f Bushberg, et al The Essential Physics

c.f http://www.hull.ac.uk/mri /lectures/gpl_page.html

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Raphex 2000 Diagnostic Questions

¬ D42 Which of the following elements would not be of

interest in an MRI image?

¬ D53 For hydrogen imaging in a 1.0 T MRI unit, the

frequency of the RF signal is about:

¬ A 400 kHz

¬ B 4 MHz

¬ E 4 GHz

Geometric Orientation

¬ Two frames of reference used

¬ Laboratory frame–stationary

reference from observer’s

POV

¬ Rotating frame–angular

frequency equal to the Larmor

precessional frequency

¬ Both frames are useful in

explaining various interactions

¬ Mxy: transverse magnetization,

⊥B0(at equilibrium = 0)

¬ When RF applied, Mztipped

into the x-y (transverse) plane

of Medical Imaging, 2 nd ed., pp 380-381.

Rotating Frame

Rotating Frame Lab Frame

Resonance and Excitation

¬ Return to equilibrium results in RF emission from µ with

¬ Amplitude proportional the number of excited nuclei (spin ρ)

¬ Rate depends on the characteristics of the sample (T1 and T2)

¬ Excitation, detection & analysis the basics for NMR/MRI

¬ Resonance occurs when applied RF magnetic field (B1)

is precisely matched in frequency to that of the nuclei

¬ Absorption of RF energy promotes low-E µ high-E µ

¬ Amplitude and duration of RF pulse determines the number of nuclei that undergo the energy transition (θ)

¬ Continued RF application induces a return to equilibrium

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RF Pulse Angle Tip:

0°

90°

180°

Higher energy state

Changing Reference Frames

¬ Why is MRI so hard to learn?

¬ Changing reference frames

¬ Classical versus Quantum Mechanical explanation

¬ Lab and rotating frames

¬ Changing scales

¬ Macroscopic

¬ Intermediate (spin isochromats)

¬ Microscopic/QM

¬ Start with a voxel of 1 mm x 1 mm

x 10 mm as a starting point and then split up later into smaller and smaller pieces

¬ B1field component rotating at Larmor f0(off-freq little effect)

¬ Rotating reference frame: B1stationary in x-y plane

¬ B1applied torque to Mz rotation: θ= γ ·B1·

¬ Flip angle (θ) describes the rotation through which the longitudinal

magnetization (Mz) is displaced to generate transverse

magnetization (Mxy)

¬ Common angles: 90°(π/2 radians: π/2 pulse) and 180°(πradians)

Lab Frame Rotating Frame

¬ Time required 10-100 µsec

¬ 90°pulse largest Mxy (signal) generated

¬ For flip angle (θ)< 90°

¬ smaller Mxycomponent generated and less signal

¬ less time necessary to displace Mz

¬ greater amount of Mxy(signal) per excitation time

¬ Low flip angle (θ)very important in rapid MRI scanning

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Free Induction Decay: T2 and T2*Relaxation

¬ 90° pulse produces phase coherence of nuclei

¬ As Mxyrotates at f0the receiver coil (lab frame) through

magnetic induction (dB/dt) produces a damped

sinusoidal electronic signal: free induction decay (FID)

¬ Decay of the FID envelope due to loss of phase coherence of the individual spins due to intrinsic micro magnetic field variations in the sample: spin-spin interaction T2 decay constant

¬ Mxy(t) = M0e-(t/T2): decay of Mxyafter 90° pulse

¬ T2: time required for Mxyto to 37% (1/e) peak level

¬ T2 relaxation relatively unaffected by B0

¬ T2 decay mechanisms det by the molecular structure of the sample

¬ Mobile molecules (e.g., CSF) exhibit a long T2 as rapid molecular

motion reduces intrinsic B inhomogeneities

¬ Large, stationary structures have short T2

¬ B0inhomogeneities and susceptibility agents (e.g., contrast

materials) cause more rapid dephasing T2* decay

c.f http://www.hull.ac.uk/mri

Return to Equilibrium: T1 Relaxation

¬ Loss of Mxyphase coherence (T2 & T2* decay) occurs relatively quickly

¬ Return of Mzto M0 (equilibrium) takes longer

¬ Excited spins release energy

to local environment (‘lattice’):

spin-lattice relaxation T1 decay constant

¬ Mz(t) = M0[1-e-(t/T1)]: recovery of

Mzafter 90°pulse

¬ T1: time required for Mzto to 63%: (1-e-1) M0

¬ After t = 5 T1 Mz(t) ≅M0

of Medical Imaging, 2 nd ed., p 387. c.f http://www.hull.ac.uk/mri/lectures/gpl_page.html

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¬ Method to determine T1: use

various ∆t between 90°pulses

and estimate by curve fitting

¬ Dissipation of absorbed energy

into the lattice (T1) varies

substantially for various tissue

structures and pathologies

(prev Damadian table)

¬ Energy transfer most efficient

when the precessional

frequency of the excited nuclei

overlaps with the vibrational

frequencies of the lattice

¬ Large slow-moving molecules low vibrational freq (very small overlap with f0: longest T1)

¬ Moderately sized molecules (e.g., lipids, proteins and fat) and viscous fluids low & intermed

freq (great overlap: short T1)

¬ Small molecules low, intermediate and high freq (small overlap with f0: long T1)

¬ T1: Soft tissue [0.1,1] and aqueous substances [1,4]

¬ T1 relaxation as B0

¬ Contrast agents: spin-lattice sink

Comparison of T1 and T2

¬ T1 > T2 > T2* (T2 4-10X

shorter than T1)

¬ Small molecules: long T1 and

long T2 (e.g., water, CSF)

¬ Intermediate molecules: short

T1 and short T2 (most tissues)

¬ Large/bound molecules: long

T1 and short T2

¬ The differences in T1 and T2,

as well as spin density (ρ)

provide much to MRI contrast

and exploited for the diagnosis

of pathologic conditions

T1 and T2 versus B Field Strength

c.f Mansfield, et al NMR Imaging in Biomedicine, 1982, p 23

1.5 T = 64 MHz

3.0 T = 128 MHz

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¬ D56 In MRI, pure water will have a T1 and a

T2.

¬ A long, long

¬ B long, short

¬ C short, long

¬ D short, short

¬ D55 In MRI contrast is created by all of the following

except:

¬ A Administration of a contrast agent.

¬ B Differences in atomic number

¬ C Differences in hydrogen content.

¬ D Differences in T1 time of tissues.

¬ E Differences in T2 time of tissues.

¬ D52 In biological tissue, relaxation times are ordered:

¬ A T1 < T2 < T2*

¬ B T1 < T2* < T2

¬ C T2* < T2 < T1

¬ D T2 < T2* < T1

¬ E T2 < T1 < T2*

¬ D46 The T2 relaxation time of a tissue is about 60 msec

on an MRI system with a 0.5 Tesla magnet On a 1.5 Tesla MRI system, one might expect the T2 relaxation time to:

¬ A Decrease significantly.

¬ B Decrease slightly.

¬ C Increase significantly.

¬ D Increase slightly.

¬ E Remain the same.

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Pulse Sequences

¬ Tailoring pulse sequence

emphasizes the image contrast

dependent on ρ, T1 and T2

contrast weightedimages

¬ Timing, order, polarity, pulse

shaping, and repetition

frequency of RF pulses and

gradient (later) application

¬ Three major pulse sequences

¬ Spin echo

¬ Inversion recovery

¬ Gradient recalled echo

c.f http://www.indianembassy.org/dydemo/page3.htm

Spin Echo (SE) - Echo Time (TE)

¬ Initial 90°pulse (t = 0) maximal Mxyand phase coherence

¬ FID exponentially decays via T2* relaxation

¬ At t = TE/2 a 180°pulse is applied induces spin rephasing

¬ Spin inversion: spins rotate in the opposite direction, undoing all the T2* dephasingthrough ∆t= TE/2 at t = TE (∆t= 2·TE/2)

¬ An FID waveform echo (“spin echo”) produced at t = TE

Spin Echo (SE) - Echo Time (TE)

¬ Maximum echo amplitude depends on T2 and not T2*

¬ FID envelope decay still dependent on T2*

¬ SE formation separates RF excitation and signal acquisition events

¬ FID echo envelope centered at TE sampled and digitized with ADC

¬ Multiple echos generated by successive 180°pulses allow

determination of sample T2 -exponential curve fitting: Mxy(t) ∝e-t/T2

SE - Repetition Time (TR) & Partial Saturation

¬ Standard SE pulse sequences use a series of 90°pulses separated

by ∆t = TR (repetition time, msec): [300,3000]

¬ This ∆t allows recovery of Mzthrough T1 relaxation processes

¬ After the 2nd90°pulse, a steady-state Mzproduces the same FID amplitude from subsequent 90°pulses: partial saturation

¬ Degree of partial saturationdependent on T1 relaxation and TR

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