Magnetic Resonance Imaging

Transcription

1 Introduction to Medical Engineering (Medical Imaging) Suetens 4 Magnetic Resonance Imaging Ho Kyung Kim Pusan National University The Nobel Prize in Medicine or Physiology in 2003 Paul C. Lauterbur the first NMR image in 1973 Peter Mansfield the math theory for fast scanning & image reconstruction in 1974 MRI Measures a magnetic property of tissue Based on the nuclear magnetic resonance (NMR) NMR studies the behavior of atomic nuclei with spin angular momentum (J) and associated magnetic moment (µ) in an external magnetic field (B) NMR (i.e., the property of spin angular momentum) can be described by the quantum electrodynamics(= the special theory of relativity + the quantum mechanics) What happens when human tissue, which contains a huge quantity of particles, is placed in an external magnetic field? 2

2 Spin = = gyromagnetic ratio(constant) Classical mechanics (i.e., the laws of Newton and Maxwell) can describe an orbital angular momentum Quantum electrodynamics can only describe a spin angular momentum (shortly, spin) with an associated magnetic moment electrons, protons, neutrons net spin is the vector sum Nucleus H H C C N N O O P S Ca No spin, no NMR sensitivity Spin 1/ /2 1 1/2 0 5/2 1/2 3/2 7/2 (MHz/T) Magnetic moment The interaction between and yields a precession motion and a potential energy = γ Solution: Transverse term: = 0!"# $ Longitudinal term: % = % 0 ) = (torque = distance force) d d = ) = (0,0,( ' ) & ' = ( ' The motion of is a precessionabout the z-axis with precession freq. & ' In a rotating reference frame, the effective perceived by is zero 4

3 Space quantization Potential energy. = = ( ' cos4 = 5( ' cos4 Minimal if Classical mechanics says that 5 % [ 5,+5] Quantum mechanics says that the outcome of a measurement of a physical variable is a "multiple of a basic amount (quantum)," so-called quantization. = :ħ( ' with : = <, <+1,,< 1,< ħ = h/2b <= spin quantum number e.g., proton (nucleus of H ) with < = 1/2. = ħ( '. = + ħ( ' Proton can occupy only two energy states! Spin-up state: % > 0 Spin-down state: % < 0 5 A proton in the state. can switch to. by absorbing an energy:.. = ħ( ' Resonance condition & GH = ( ' = & ', called the Larmor (angular) frequency Depends on molecular structure e.g., If ( ' = 1 T, the Larmorfreq. is approximately 42.6 MHz for H Radio-frequency (RF) waves suffice the typical resonance condition MRI visualizes hydrogen-containing tissues muscles, brain, kidney, CSF, edema, fat, bone marrow, etc. 6

4 Dynamic equilibrium For I J spins in a voxel, the net macroscopic magnetization vector in a voxel is given by M N K ' = "O " More the spin-up states, more net polarization in the direction of Larger, larger K ' & signal On average, the net transverse magnetization of P = 0; hence K ' = (0,0,P ' ) Longitudinal P ' cannot be measured Transvers P can be measured The net magnetization precession about the axis of : K $ = K ' γ 7 Disturbing the dynamic equilibrium Apply RF wave (EM wave with the Larmorfreq.) by sending AC current along the x and y axes Transverse component: ( = (!"# $ Longitudinal term: ( % = 0 K = K γ(+ ) In the rotating reference frame, Kprecesses about (not ) with precession freq. & = ( 8

5 Flip angle: Q = R ( ds = ( ' = & Any flip angle with an appropriate choice of ( & Halving the up-time of the RF field requires 2 ( or 4 AC power! Increase temperature in tissue The 90 pulse K = (0,P ',0) K rotates clockwise in the transverse plane in the stationary reference frame The 180 or inverse pulse K = (0,0, P ' ) K rotates about z axis; all the individual spins rotate in phase(phase coherence) Relaxation: return to dynamic equilibrium when the RF field is switched off 9 Spin-spin relaxation Causes dephasingprocess (i.e., disappearance of the transverse component of the net magnetization vector) P = P ' sinq!/v W P ' sinq = the value of transverse componentimmediately after the RF pulse X = the spin-spin relaxation time dependent considerably upon the tissue X 100 msfor fat while X 2000 msfor cerebrospinal fluid (CSF) 10

6 Spin-lattice relaxation Causes the longitudinal component of the net magnetization vector to increase from P ' cosq (the value of longitudinal componentimmediately after the RF pulse) P % = P ' cosq!/v Z +P ' (1!/V Z) X = the spin-lattice relaxation time dependent considerably upon the tissue type & proportional to X 200 msfor fat while X 3000 msfor cerebrospinal fluid (CSF) at 1.5 T for the same tissue, always X > X 11 Summary The RF pulse creates a net transverse magnetization due to energy absorption and phase coherence. After the RF pulse, two distinct relaxation phenomena ensure that the dynamic (thermal) equilibrium is reached again. 12

7 Inversion recovery (IR) For an inversion pulse, the longitudinal magnetization becomes "null" after the inversion time(ti) TI = 70% of X Proper choice of TI can suppress the signal of particular tissue type STIR (short TI inversion recovery) suppression of fatty tissue short TI FLAIR (fluid attenuated inversion recovery) suppression of fluid (e.g., CSF) long TI 13 Signal detection P in each voxel rotates clockwise at the precession freq. in the stationary reference frame and induces an AC currentin an antenna (coil) 14

8 For Q = 90 Detected signal in the stationary reference frame ] = ] +^] = P!/V W!"# $ ' Detected signal in the rotating reference frame ] = P!/V W ' If the experiment is repeated after a repetition timetr, P % TR = P ' (1!ab/V Z) After a new excitation with a 90 pulse, ] = P ' (1!ab/V Z)!/V W Tissue-dependent parameters: the amount of spins, X, X System-or operator-dependent parameters: ( ', TR, 15 Slice or volume selection Superimposing a linear magnetic field gradient along the c-axis onto the main : d = e,e,e % = 0,0, fg h in dimension of millitesla/meter f% 1000 smaller than Larmorfrequency: & c = (( ' +e % c) Thickness of the selected slice or slab (volume) c = # j h = kl j h RF pulse bandwidth BW = & = e % c Table motion is not required for the slice selection! Limitations for very thin c e % < mt/m for safety Difficulty in the realization of a very small BW Small SNR in a thin slice (due to few spins) c(fwhm) = 2 mm or 1 mm for 1.5 T or 3 T 16

9 Position encoding After a 90 pulse, the transverse component of the net magnetization stands still: P o,p, = P ' (o,p)(1!ab/v Z)!/V W If e is applied, P rotates with a temporal freq. &(o) = e o For TE(i.e., moment of the measurement): P o,p, = P ' (o,p)(1!ab/v Z)!/V W!"j s(!at) 17 Receiver measures a signal from the excited spins in the whole opplane: w ] = v o,p (1!ab/V Z)!/V W!"js(!at) dodp!w v o,p = net magnetization density in (o,p)at time = 0 the spin or proton density ]()describes a trajectory in the Fourier domain of the image y(o,p)to be reconstructed: ] = F y(o,p) = {(,0) = e ( TE) y o,p = v o,p (1!ab/V Z)!at/V W, the weighted spin density Similarly, nonzero p(thus, ) component signal can be reconstructed by applying a gradient in the p-direction 18

10 -theorem For 3D functions Angular frequency: &(},) = d }() w!w Measured signal: ] = v o,p,c (1!ab/V Z)!/V W!" R d }() $ dodpdc The -theorem states that the time signal ]()is equivalent to the Fourier transform of the image y(o, p, c) to be reconstructed: ] = F y(o,p,c) = {(,, % ) () = R ' d S ƒs y o,p,c = v o,p,c (1!ab/V Z)!at/V W, weightedspin or proton density distribution Weights» (1!ab/V Z)= the growth of longitudinal component»!at/v W = the decay of transverse component» Short TR X -weighted images» Long TE X -weighted images» Long TR & short TE v-weighted or proton density weighted images 19 20

11 Dephasing Breakdown of phase coherence due to different spin vectors of individual magnetic moments with different Larmorfrequencies, hence resulting in a small and noisy signal in the receiver Dephasing by spin-spin interactions (irreversible) Dephasing by magnetic field inhomogenieties(reversible) Dephasing by magnetic field gradients (reversible) 21 Undo dephsing of inhomogenieties Applying a 180 pulse at = TE/2, thereby creating the spin-echo(se) signal at = TE 22

12 Undo dephsing of gradients Applying another gradient with the same duration but with opposite polarity to make the at phase shift [Φ TE = R d }()d] be zero, thereby creating the gradient-echo(ge) ' signal at = TE 23 Spin-echo pulse sequence 2D Fourier transform SE imaging is the mainstay of clinical MRI SE pulse sequence (to sample the -space) Apply a slice selection gradiente % with a 90 & a 180 RF pulse To avoid dephasingof the first e %, use the longer second e % (the same effect of using the negative first e % ) Apply a phase-encoding gradiente (= : ) with a temporal phase shift p = e px ˆ, and which results in = : X ˆ Dephasingof e implies position encoding Apply a frequency-encoding gradiente to measure the signal ]() To avoid dephasingof the e, apply a compensating gradient before the 180 pulse Perform the inverse FT Note that the gradients encode by means of the angular frequency and initial phase of the magnetization vector during measurements e causes an initial phase shift dependent on p, p e yields an angular frequency &that depends on o 24

13 k y 25 Gradient-echo pulse sequence SE imaging requires long imaging times Primarily used for fast 2D & 3D acquisition of X -weighted images Difference of the GE pulse sequence compared with the SE sequence Use a flip angleq 90 No spin-echo because there is no 180 pulse Rephasing is done by means of gradient reversal only Signal characteristics are influence by X 26

14 3D imaging Further encode the z-position by a second phase-encoding gradient ladder I %, hence p,c = (: px ˆ +I % cx JJ ) 27 Chemical shift imaging The Larmor frequency slightly depends on the molecular structure the proton belong to This frequency differenceis called the chemical shift: & J 2By J Perform multiple imaging for different frequencies y J chemical shift imaging (CSI) Require two phase-encoding gradient ladders for e & e in 2D and three ladders for e, e, & e % in 3D imaging Acquisition time for CSI is an order of magnitude larger than for regular imaging 28

15 Acquisition time Acquisition time TA = # excitations interval between two successive excitations TA = Ž ˆTR Ž ˆ = # in-plane phase-encoding steps TA = Ž ˆŽ JJ TR Ž JJ = # phase-encoding steps in the slab-selection direction e.g., X -weighted 3D SE imaging with TR = 2000 ms TA = hours!!! e.g., X -weighted 3D GE imaging with TR = 40 ms TA = minutes (acceptable) 29 Very fast imaging sequences Multiple echoes per excitation& sampling within the same excitation TA = ab ta ETL= the echo train length(i.e., # echoes per excitation) To reduce TA : 1 Decreasing TR(e.g., GE pulse sequences) 2 Decreasing Ž ˆ (e.g., truncated& half-fourierimaging) 3 Increasing ETL(> 1) Filtered version of signal š, = œ, š(, )due to the dephasingeffect» š(, )= the signal with ETL = 1(without dephasing) Degrading the spatial resolution 30

16 Examples TurboSE& TurboGE e.g., TurboSEsequences for X -weighted brain imaging with 4 echos/expiation TA = ab ta Echo planar imaging(epi) = '' žÿ = 160 seconds The fastest 2D imaging sequence without 180 pulses Typ image size & TAwith 100 msor lower FunctionalMRI Diffusion and perfusion imaging 31 Imaging of spin motions In practice, the spins move due to various human body motion Motions in the human body (see the Table) can be visualized by imaging spin motions Since moving spinsexperience a change in (, the total phase shift and signal respectively given by &(},) = R d }()ds ' Motion type ] = R v (})!" } Z } W!"} $ ƒ} } v (}) = v } (1!ab/V Z)!at/V W ' R d Motion-induced dephasing! ds Diffusion Perfusion CSF flow Venous flow Arterial flow Stenotic flow Velocity range 10 µm/s 0.1 mm/s 0.1 mm/s 1 mm/s 1 mm/s 1 cm/s 1 cm/s 10 cm/s 10 cm/s 1 m/s 1 m/s 10 m/s spin position depends on time due to spin motion, = 0,1,2, the thorder gradient moment Smaller and noisier signal Position artifact (e.g., ghosting) if phase shift is small and coherent within a single voxel 32

17 Magnetic resonance angiography Obtain hyperintensevessel signals for blood flowing at a constantvelocity by rephasingthe motion-induced dephasing: ] = R v (})!" } Z } W!"} $ ƒ} } Time-of-flight(TOF) MRA GE-based sequences Enhance vascular contrast using the signal difference between the inflowing spins of the blood and the stationary spins of the tissues 33 Phase-contrast MRA Additional bipolar pulse and reversed bipolar pulse sequences Derive the blood velocity from a phase differenceimage of moving spins by subtracting the phase images of the twosubsequent acquisitions 34

18 Contrast-enhanced MRA 3D GE sequence with short TE& TR Use a contrast agentin the blood Paramagnetic, superparamagnetic, & ferromagnetic substances e.g., chelates of the rare earth metal gadolinium (superparamagnetic) Disturb the local magnetic field Decrease X Hypointensefor a X -weighted sequence Hyperintensefor a X -weighted sequence 35 Diffusion Spin-echo EPI sequences (or pulsed gradient spin-echo, PGSE) Visualize molecular Brownian motion by emphasizing the dephasingcaused by random thermal motion of spins in a gradient field š = š '!ª š ' = signal when no diffusion = «e e = the gradient amplitude «= the on-time of each of the gradients = the time between the application of the two gradients = the diffusion coefficient(mathematically, a tensor) Covariance matrix describing the displacement of the Brownian random motion in each direction Diffusion tensor imaging(dti) Visualize both the principal (diffusion) direction and its anisotropy by color coding the hue and brightness respectively 36

19 Perfusion Blood perfusion of tissues refers to the activity of the capillary network, where exchanges between blood and tissues are optimized Investigate perfusion by visualizing blood flow using a contrast agent such as gadolinium chelate X or X sensitive EPI sequences 37 Functional imaging Visualize the brain function using the dependence of brain tissue relaxation on the oxygenation level in the blood BOLD (blood oxygenation-level dependent) effect Influences the MR signal Oxyhemoglobin Oxygen-rich hemoglobin in the arteries Diamagnetic Deoxyhemoglobin Oxygen-poor hemoglobin in the capillaries Paramagnetic (causing magnetic field inhomogenieties) 38

20 Contrast Signal for a SE sequence (with Q = 90 ) is proportional to v (1!ab/V Z)!at/V W Parameters affecting the image contrast: Tissue-dependent parameters Relaxation times X & X Spin or proton density v(actually net magnetization density) Technical parameters Repetition time TR Echo time TE Type TR TE v-weighted X -weighted X -weighted long short long short short long Signal for a GE sequence (with Q < 90, e.g., FLASH sequence) is proportional to v!at/v W (! ±/² Z)Ÿ³ µ! ±/² Z Ÿµ 39 Resolution In the Fourierspace o Nyquisttheorem 1 2o ¹ = 1 FOV 1 2p ¹ = 1 FOV -theorem Resultantrestriction = 2B e e 2B FOV p = 2B X ˆ X ˆ 2B FOV In the imagespace Note that "the PSF defines the highest frequency ¹ available in the signal", ¹ e s, ¹ Ž V ˆ 40

21 Noise I I I J ħg $ ¼ ½ V = ! I J I J = I +I I & I = the number of spins with energy. &., respectively g = Boltzmann's constant X= the absolute temp. of an object P (ħ)w M N g $ ¼ ½ V Typically quite small (vulnerable to noise!) e.g., 1-L water at X= 310 K & ( ' = 1 T I J & P 3 10! J/T (very small value) Thermal noisein the patient and in the receiver part of the MR imaging system 41 Artifacts Due to 1) technical imperfections, 2) inaccurate assumptions about the data, & 3) numerical approximations System failure, inappropriate shielding of the magnet room or interaction with unshielded monitoring equipment Assumption that is homogeneous(to avoid unnecessary dephasing, which causes signal loss and geometric deformations) In real, inhomogeneous inhomogeneous RF field spatially varying Q lowfrequency signal intensity modulation(called the bias field) 42

22 43 Assumption that the data are independent of X If this fails (e.g., multiple echoes per excitation), the spatial resolution decreases Assumption that tissues are stationary Motion yields dephasing artifact The magnetic susceptibilityof tissues or foreign particles & implants yields dephasing Truncationerrors during digital image reconstruction may produce visual artifacts Truncated FT yields ripples at high-contrast boundaries (known as the Gibbs artifact or ringing artifact) Inadequate sampling yields aliasing, known as the wrap-around artifact 44

23 Phase cancellation artifact Dephasingin voxels that contain both water and fat elements (due to the chemical shift between water and fat) 45 Chemical shift artifact Mutual spatial misregistration due to a phase difference between water and fat 46

24 MRI systems 47 Magnets Desirable with compact designs with higher field homogeneities Superconducting magnets Higher field strengths, higher SNR Permanent & resistive magnets Lower field strength (poor homogeneity), lower SNR Interventional MRI Open MR systems for MR-guided procedures (e.g., surgery or therapy) All surgical instruments must use MR-compatible materials RF radiation from electronic equipment must be shielded from the RF of the MR system and vice versa Electrical leads with the RF field can produce hot spot; hence causing skin burns (preferred to use fiberoptic technology) 48

25 Gradient system Linearity for correct phase-encoding Maximum amplitude& its rise timefor fast imaging RF system For sensitivity & in-plane homogeneity of signal detection 49 Clinical use Anatomical imaging All parts of the human body that contain hydrogen (e.g., soft tissue, cerebrospinal fluid, edema, ) 50

26 Better contrast(using a various v-, X -, & X -weighted images) between different soft tissues than with CT 51 Tissue characterizationdue to the availability of v-, X -, & X -weighted images 52

27 Imaging with contrast agents Gadolinium compounds (not captured by cells) Iron oxide (taken up by specific cells) 53 Statistical image analysis 54

28 Perfusion imaging e.g., after brain tumor resection to exclude tumor residue or recurrence e.g., after myocardial infarction to assess tissue viability 55 Diffusion imaging To investigate microscopically small displacements of hydrogencontaining fluid 56

29 57