Published on November 14, 2007
Biomedical Imaging 2: Biomedical Imaging 2 Class 6 – Magnetic Resonance Imaging (MRI) Functional MRI (fMRI): Magnetic Resonance Angiography (MRA), Diffusion-weighted MRI (DWI) 02/28/07 MRI Physics: MRI Physics Magnetic Resonance in a Nutshell: Magnetic Resonance in a Nutshell Hydrogen Nuclei (Protons) Axis of Angular Momentum (Spin), Magnetic Moment Magnetic Resonance in a Nutshell: Magnetic Resonance in a Nutshell Magnetic Resonance in a Nutshell: Magnetic Resonance in a Nutshell Irradiating with a (radio frequency) field of frequency f0, causes spins to precess coherently, or in phase ↓ ROTATING REFERENCE FRAME Primary (Static) Magnetic Field: Primary (Static) Magnetic Field N S magnetic field lines By staying in the interior region of the field, we can ignore edge effects. Typical Magnetic Resonance Imager: Typical Magnetic Resonance Imager http://www.radiologyinfo.org/en/photocat/photos_pc.cfm?Image=si-symphony.jpg&pg=bodymr&bhcp=1 (Radiological Society of North America, Inc.) Generating the Primary Magnetic Field: Generating the Primary Magnetic Field http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html (Georgia State University) Gradient coils 1: Gradient coils 1 z-gradient: Anti-Helmholtz coils Gradient coils 2: Gradient coils 2 Gradients perpendicular to z Alignment of 1H Nuclei in a Magnetic Field: Alignment of 1H Nuclei in a Magnetic Field Protons must orient themselves such that the z-components of their magnetic moments lie in one of the two permissible directions What about direction of m? What is the precession frequency? Orientational Distribution of 1H Nuclei: Orientational Distribution of 1H Nuclei What fraction of nuclei are in the “up” state and what fraction are “down”? Protons must orient themselves such that the z-components of their magnetic moments lie in one of the two permissible directions The orientation with mz aligned with B0 has lower potential energy, and is favored (North pole of nuclear magnet facing South pole of external field). The fractional population of the favored state increases with increasing |B0|, and increases with decreasing (absolute) temperature T. Transitions Between Spin States (Orientations) I: Transitions Between Spin States (Orientations) I QM result: energy difference between the “up” and “down” states of mz is ΔE0 = h|B0| As always, frequency of radiation whose quanta (photons) have precisely that amount of energy is f0 = ΔE0/h So, f0 = |B0| Different nuclei have different values of . (Units of are MHz/T.) 1H: = 42.58; 2H: = 6.53; 3H: = 45.41 13C: = 10.71 31P: = 17.25 23Na: = 11.27 39K: = 1.99 19F: = 40.08 Transitions Between Spin States II: Transitions Between Spin States II The frequency f0 that corresponds to the energy difference between the spin states is called the Larmor frequency. The Larmor frequency f0 is the (apparent) precession frequency for m about the magnetic field direction. (In QM, the azimuthal part of the proton’s wave function precesses at frequency f0, but this is not experimentally observable.) Three important processes occur: Transitions Between Spin States III: Transitions Between Spin States III The number of 1H nuclei in the low-energy “up” state is slightly greater than the number in the high-energy “down” state. Irradiation at the Larmor frequency promotes the small excess of low-energy nuclei into the high-energy state. When the nuclei return to the low-energy state, they emit radiation at the Larmor frequency. The radiation emitted by the relaxing nuclei is the NMR signal that is measured and later used to construct MR images. Saturation: Saturation Suppose the average time required for an excited nucleus to return to the ground state is long (low relaxation rate, long excited-state lifetime) If the external radiation is intense or is kept on for a long time, ground-state nuclei may be promoted to the excited state faster than they can return to the ground state. Eventually, an exact 50/50 distribution of nuclei in the ground and excited states is reached At this point the system is saturated. No NMR signal is produced, because the rates of “up”→“down” and “down”→“up” transitions are equal. Relaxation I: Relaxation I What are spin-lattice relaxation and spin-spin relaxation? What do time constants T1 and T2 mean? “Lattice” means the material (i.e., tissue) the 1H nuclei are embedded in 1H nuclei are not the only things around that have magnetic moments Other species of nuclei Electrons A 1H magnetic moment can couple (i.e., exchange energy) with these other moments Spin-Lattice Relaxation I: Spin-Lattice Relaxation I Spin-lattice interactions occur whenever a physical process causes the magnetic field at a 1H nucleus to fluctuate Spin-lattice interactions cause the perturbed distribution of magnetic moments (i.e., tipped bulk magnetization) to return to equilibrium more rapidly Types of spin-lattice interaction Magnetic dipole-dipole interactions Electric quadrupole interactions Chemical shift anisotropy interactions Scalar-coupling interactions Spin-rotation interactions What is the T1 time constant associated with these processes? Spin-Lattice Relaxation II: Spin-Lattice Relaxation II What is the T1 time constant associated with spin-lattice interactions? Spin-Lattice Relaxation III: Spin-Lattice Relaxation III What is the T1 time constant associated with spin-lattice interactions? Spin-Lattice Relaxation IV: Spin-Lattice Relaxation IV What is the T1 time constant associated with spin-lattice interactions? x׳ y׳ z׳ B0 The z component of M, Mz, grows back into its equlibrium value, exponentially: Mz = |M|(1 - e-t/T1) Mz M Relaxation II: Relaxation II What are spin-lattice relaxation and spin-spin relaxation? What do time constants T1 and T2 mean? A 1H magnetic moment can couple (i.e., exchange energy with) the magnetic moments of other 1H nuclei in its vicinity These are called “spin-spin coupling” Spin-spin interactions occur when the magnetic field at a given 1H nucleus fluctuates Therefore, should the rates of these interaction depend on temperature? If so, do they increase or decrease with increasing temperature? Spin-Spin Relaxation I: Spin-Spin Relaxation I What is the T2 time constant associated with spin-spin interactions? x׳ y׳ z׳ B0 M Mz Mtr If there were no spin-spin coupling, the transverse component of M, Mtr, would decay to 0 at the same rate as Mz returns to its original orientation What are the effects of spin-spin coupling? Spin-Spin Relaxation II: Spin-Spin Relaxation II W hat are the effects of spin-spin coupling? Because the magnetic fields at individual 1H nuclei are not exactly B0, their Larmor frequencies are not exactly f0. x׳ y׳ z׳ B0 Mz But the frequency of the rotating reference frame is exactly f0. So in this frame M appears to separate into many magnetization vectors the precess about z׳. Some of them (f < f0) precess counterclockwise (viewed from above), others (f > f0) precess clockwise. Spin-Spin Relaxation III: Spin-Spin Relaxation III W hat are the effects of spin-spin coupling? Within a short time, M is completely de-phased. It is spread out over the entire cone defined by cosθ = Mz/|M| x׳ y׳ z׳ B0 Mz When M is completely de-phased, Mtr is 0, even though Mz has not yet grown back completely: Mtr = 0, Mz < |M| Mtr decreases exponentially, with time constant T2: Mtr = Mtr0 e-t/T2 This also shows why T2 can not be >T1. It must be the case that T2 T1. In practice, usually T2 << T1. Relaxation III: Relaxation III In this example, T1 = 0.5 s In this example, T2 = 0.2 s Contrast: Contrast Intrinsic : Relaxation times T1, T2, proton density, chemical shift, flow Extrinsic: TR, TE, flip angle Contrast in T1: Contrast in T2: T1-weighting: T1-weighting Short TR: Maximizes T1 contrast due to different degrees of saturation Short TE: Minimizes T2 influence, maximizes signal T2 weighting: T2 weighting Long TR: Reduces saturation and minimizes influence of different T1 Long TE: Maximizes T2 contrast Relatively poor SNR Spin density weighting: Spin density weighting Long TR: Minimizes effects of different degrees of saturation (T1 contrast) Maximizes signal Short TE: Minimizes T2 contrast Maximizes signal Effect of B0 Field Heterogeneity: Effect of B0 Field Heterogeneity What is the common element in spin-spin and spin-lattice interactions? They require fluctuations in the strength of the magnetic field in the immediate environment of a 1H nucleus If the static B0 field itself is not perfectly uniform, its spatial heterogeneity accelerates the de-phasing of the bulk magnetization vector The net, or apparent, decay rate of the transverse magnetization is 1/T2* 1/T2 + |B0|. T2* (“tee-two-star”) has a spin-spin coupling contribution and a field inhomogeneity contribution T2* < T2 always, and typically T2* << T2 MRI contrast mechanisms: MRI contrast mechanisms MR Imaging Principles: MR Imaging Principles Free induction decay (FID): Free induction decay (FID) Basic MRI measurement: Homogeneous static magnetic field (B0) RF pulse generator Antenna (coil) for sending and receiving Free induction decay (FID) signal Free: No external RF field during detection Exponential decay at rate T2* due to spin-spin relaxation (dephasing) and local field inhomogeneities Spin echo: Spin echo Inversion pulse after time t phase recovery at 2t Corrects for dephasing due to static B inhomogeneities 180 degree spin flip Spin echo sequence: Spin echo sequence Multiple p pulses create “Carr-Purcell-Meiboom-Gill (CPMG)” sequence Decays with time constant T2 Gradient fields in MRI 1: Gradient fields in MRI 1 Strength of Bz component varies linearly in space Gradient fields in MRI 2: Gradient fields in MRI 2 Larmor frequency varies linearly in space: 1st Dimension (z): Slice selection: 1st Dimension (z): Slice selection Slice position: z0 ~ f0 Slice thickness: Slice profile: profile ~ FT (pulse shape) d (Frequency f0 bandwidth B, pulse length T) Slice selection cont.: Slice selection cont. Pulse sequence (PS) for slice selection (TR = repetition time, TE = echo time) Frequency encoding: Frequency encoding The NMR signal from each x-position contains a specific center frequency The over-all NMR signal is the sum of signals along x FT recovers signal contribution at each frequency, i.e. x-location Resulting spectrum is a projection Frequency spectrum Frequency encoding cont.: Frequency encoding cont. Pulse sequence: two gradients for x and z 3rd Dimension (y): 3rd Dimension (y) How to achieve y-localization? Frequency encoding will always produce iso-lines of resonance frequencies Solution: Reconstruction from projections Phase encoding Phase encoding: Phase encoding Pulse sequence: TP 2D FT pulse sequence (spin warp): 2D FT pulse sequence (spin warp) Most commonly employed pulse sequence A Closer Look at the Phase-Encoding Gradient: A Closer Look at the Phase-Encoding Gradient A Closer Look at the Phase-Encoding Gradient: A Closer Look at the Phase-Encoding Gradient A Closer Look at the Phase-Encoding Gradient: A Closer Look at the Phase-Encoding Gradient A Closer Look at the Phase-Encoding Gradient: A Closer Look at the Phase-Encoding Gradient A Closer Look at the Phase-Encoding Gradient: A Closer Look at the Phase-Encoding Gradient k-space map: k-space map The 2D array of NMR signals obtained from repeated pulse sequences is referred to as the k-space map. kx (Frequency encoding) FT ky (Phase encoding) FT K-space From Structure to Function: From Structure to Function MRI vs. fMRI: MRI vs. fMRI fMRI investigation of hemodynamics: fMRI investigation of hemodynamics Magnetic Resonance Angiography (MRA): Magnetic Resonance Angiography (MRA) Arterial Spin Labeling (Perfusion MRI): Arterial Spin Labeling (Perfusion MRI) HOW? Basic Idea #1: Time-of-Flight (TOF): Basic Idea #1: Time-of-Flight (TOF) Basic Idea #2: Phase Contrast: Basic Idea #2: Phase Contrast Bipolar Field Gradients Bipolar Gradient Effects: Bipolar Gradient Effects First gradient Second gradient Examples of Phase-Contrast MRA: Examples of Phase-Contrast MRA fMRI vs. Nuclear Imaging (PET): fMRI vs. Nuclear Imaging (PET) Diffusion-weighted MRI (DWI): Diffusion-weighted MRI (DWI) Stronger bipolar gradients → lower tissue velocities detectable Blood flow velocities: ~(0.1 – 10) cm-s-1 Water diffusion velocity: ~200 μm-s-1 Using the same basic strategy as phase-contrast MRA, can image “apparent diffusion coefficient” (ADC) Useful for diagnosing and staging conditions that significantly alter the mobility of water e.g., cerebrovascular accident (“stroke,” apoplexy) Examples of Diffusion-weighted images: Examples of Diffusion-weighted images Examples of Diffusion-weighted images: Examples of Diffusion-weighted images
Magnetic Resonance Imaging - MRI Asma’a Al-Ekrish BDS Demonstrator ( OMF Radiology ) King Saud University College of Dentistry.
Contrast Mechanism and Pulse Sequences Allen W. Song Brain Imaging and Analysis Center Duke University.
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Biomedical Imaging 2 Class 6 – Magnetic Resonance Imaging (MRI) Functional MRI (fMRI): Magnetic Resonance Angiography (MRA), Diffusion-weighted MRI (DWI)