Chapter 14:Physics of Magnetic Resonance

Transcription

1 Chapter 14:Physics of Magnetic Resonance Slide set of 141 slides based on the chapter authored by Hee Kwon Song of the publication (ISBN ): Diagnostic Radiology Physics: A Handbook for Teachers and Students Objective: To familiarize the student with the fundamental concepts of MRI. Slide set prepared by E. Berry (Leeds, UK and The Open University in London) International Atomic Energy Agency

2 CHAPTER 14 TABLE OF CONTENTS Introduction Nuclear magnetic resonance Relaxation and tissue contrast MR spectroscopy Spatial encoding and basic pulse sequences Diagnostic Radiology Physics: A Handbook for Teachers and Students - 14 (02/141)

3 14.1 INTRODUCTION 14.1 Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (03/141)

4 14.1 INTRODUCTION 14.1 Nuclear magnetic resonance (NMR) Nuclei in a magnetic field absorb applied radiofrequency (RF) energy and later release it with a specific frequency 1920s Stern and Gerlach particles have intrinsic quantum properties 1938 Rabi discovered phenomenon of NMR (Nobel prize 1944) 1946 Bloch and Purcell measured NMR signal from liquids and solids (Nobel prize 1952) But no imaging yet 9 Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (04/141)

5 14.1 INTRODUCTION 14.1 Magnetic resonance imaging (MRI) 1973 Lauterbur method to spatially encode the NMR signal using linear magnetic field gradients 1973 Mansfield method to determine spatial structure of solids by introducing linear gradient across the object i.e apply magnetic field gradients to induce spatially varying resonance frequencies to resolve spatial distribution of magnetization Milestone the beginning of MR Imaging Nobel prize in medicine in 2003 Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (05/141)

6 14.1 INTRODUCTION 14.1 Characteristics of MRI No ionizing radiation unlike x-rays and CT Superior soft tissue contrast compared with other modalities Can control image contrast among different tissues by adjusting acquisition timing parameters Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (06/141)

7 14.2 NUCLEAR MAGNETIC RESONANCE 14.2 Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (07/141)

8 14.2 NUCLEAR MAGNETIC RESONANCE 14.2 Nuclear magnetic resonance The nucleus: spin, angular and magnetic momentum External magnetic field and magnetization Excitation and detection Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (08/141)

9 14.2 NUCLEAR MAGNETIC RESONANCE THE NUCLEUS: SPIN, ANGULAR AND MAGNETIC MOMENTUM Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (09/141)

10 14.2 NUCLEAR MAGNETIC RESONANCE The nucleus: spin, angular and magnetic momentum Nuclei used for MRI MRI involves imaging the nucleus of hydrogen atom = proton Hydrogen abundant in human body in water and fat Water is 50-70% of total body weight Fat is 10-20% of total body weight Other nuclei are used in research carbon ( 13 C), phosphorus ( 31 P), fluorine ( 19 F), sodium ( 23 Na) relatively low abundance in vivo limited signal available Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (010/141)

11 14.2 NUCLEAR MAGNETIC RESONANCE The nucleus: spin, angular and magnetic momentum Properties of the nucleus Angular momentum p=ih where h is Planck s constant and I is the nuclear spin (or quantum number) for the hydrogen nucleus, I= ½ Because the proton is positively charged, the angular momentum also produces a nuclear magnetic moment p µ =γ where γ is the gyromagnetic ratio Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (011/141)

12 14.2 NUCLEAR MAGNETIC RESONANCE The nucleus: spin, angular and magnetic momentum Gyromagnetic ratio Specific to each type of nucleus For proton, roughly MHz T -1 Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (12/141)

13 14.2 NUCLEAR MAGNETIC RESONANCE The nucleus: spin, angular and magnetic momentum Common nuclei for MR Nucleus Relative Abundance (%) Spin (I) Gyromagnetic ratio (Hz/G) Relative sensitivity* Abundance in human body (% of atoms) 1 H / C / F 100 1/ Na 100 3/ P 100 1/ K / x * PER EQUAL NUMBER OF NUCLEI Adapted from Stark & Bradley, Magnetic Resonance Imaging, 2 nd edition Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (13/141)

14 14.2 NUCLEAR MAGNETIC RESONANCE EXTERNAL MAGNETIC FIELD AND MAGNETIZATION Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (14/141)

15 14.2 NUCLEAR MAGNETIC RESONANCE External magnetic field and magnetization Boltzmann distribution Consider a collection of these magnetic moments or spins No external magnetic field random alignment: zero net magnetization In external magnetic field B 0 each spin aligns parallel or anti-parallel to direction of applied field i.e. polarized parallel orientation has lower energy state slightly greater number of spins align along that direction Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (15/141)

16 14.2 NUCLEAR MAGNETIC RESONANCE External magnetic field and magnetization No external magnetic field Random alignment of spins Zero net magnetization In external magnetic field B 0 Each spin aligns parallel or anti-parallel to direction of applied field i.e. polarized Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (16/141)

17 14.2 NUCLEAR MAGNETIC RESONANCE External magnetic field and magnetization Boltzmann distribution Parallel orientation has lower energy state Slightly greater number of spins align along that direction N + E/ kt hωo kt = e = e / N Where N + is number of spins aligned parallel to direction of applied field N - is number of spins aligned anti-parallel to direction of applied field E is energy difference between the two states k is Boltzmann constant T is absolute temperature ω 0 is Larmor, or resonance, frequency Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (17/141)

18 14.2 NUCLEAR MAGNETIC RESONANCE External magnetic field and magnetization Precession and Bloch Equation Torque on magnetization causes it to precess about the direction of the magnetic field = µ dµ γ dt B ω =γ Will precess at the Larmor frequency, o B o Analogous to precession of spinning top about the direction of gravitational field top has angular momentum due to its spin precession arises from a torque acting on the top Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 5 (18/141)

19 14.2 NUCLEAR MAGNETIC RESONANCE External magnetic field and magnetization Larmor frequency ω o =γb o Under the influence of an external magnetic field B o, the spins precess about the direction of the field at the Larmor frequency which is proportional to B o e.g. at 1.5 T, ω 0 = 64 MHz Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 6 (19/141)

20 14.2 NUCLEAR MAGNETIC RESONANCE External magnetic field and magnetization Rotating frame of reference In stationary (or laboratory) frame of reference, precession: at Larmor frequency ω 0 about the direction of B 0 (z-axis) In rotating frame of reference, which rotates at Larmor frequency, precession: at Larmor frequency appears to be stationary at a different frequency ωin stationary frame, appears to precess at ω r, where ω = ω r ω o Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 7 (20/141)

21 14.2 NUCLEAR MAGNETIC RESONANCE External magnetic field and magnetization Net magnetization Total magnetization within a voxel net magnetization vector sum of all spins within the voxel aligned along +zdirection, the direction of B 0 **add diagram** Henceforth Magnetization = net magnetization of a collection of spins i.e. not magnetization of a single spin Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 8 (21/141)

22 14.2 NUCLEAR MAGNETIC RESONANCE External magnetic field and magnetization Bloch equation for net magnetization M dm dt =γm B In the presence of a constant external magnetic field B 0 net magnetization is aligned along the z-axis, remains stationary and does not precess about any axis magnetization is at its equilibrium magnetizationm 0. When additional fields applied, including time varying fields magnetization may deviate from equilibrium position magnetization may precess about an effective magnetic field Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 9 (22/141)

23 14.2 NUCLEAR MAGNETIC RESONANCE External magnetic field and magnetization Perturbation from equilibrium Arises from applied additional magnetic fields Such a perturbation is needed for signal detection Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 10 (23/141)

24 14.2 NUCLEAR MAGNETIC RESONANCE EXCITATION AND DETECTION Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (24/141)

25 14.2 NUCLEAR MAGNETIC RESONANCE Excitation and detection Effect of external radiofrequency (RF) field B 1 (t) Spins are in a magnetic field B 0 B 1 (t) is resonating at the Larmor frequency From Bloch equation magnetization will precess about effective magnetic field given by vector sum of static B 0 field and time varying B 1 field In the rotating frame B 1 field appears stationary magnetization is initially aligned along z-axis magnetization precesses about the direction of the B 1 field will continue to do so as long as B 1 is applied Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (25/141)

26 14.2 NUCLEAR MAGNETIC RESONANCE Excitation and detection Effect of external radiofrequency (RF) field B 1 (t) If RF field B 1 lies along the x-axis magnetization precesses, or nutates, about the x-axis Typically, apply B 1 field just long enough to cause a 90 rotation At end of the RF pulse, (2-3 ms), magnetization is aligned with y- axis note that diagram shows rotating frame with axes (x r, y r, z r ) Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (26/141)

27 14.2 NUCLEAR MAGNETIC RESONANCE Excitation and detection Effect of external radiofrequency (RF) field B 1 (t) Once magnetization is rotated into the transverse (x, y) plane RF is removed Precession is again about B 0 at the Larmor frequency (in stationary frame of reference) according to Bloch equation Can detect the rotating magnetization Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (27/141)

28 14.2 NUCLEAR MAGNETIC RESONANCE Excitation and detection Detection of a signal from rotating magnetization Use an RF coil By Faraday s law, changing magnetic flux through coil induces voltage changes Changes are detected by receiver Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 5 (28/141)

29 14.2 NUCLEAR MAGNETIC RESONANCE Excitation and detection Detection of a signal from rotating magnetization Overall strength of received signal depends on type and size of RF coil used for signal reception proximity of coil to the imaged object voxel size More in Chapter 15 Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 6 (29/141)

30 14.3 RELAXATION AND TISSUE CONTRAST 14.3 Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (30/141)

31 14.3 RELAXATION AND TISSUE CONTRAST 14.3 Relaxation and tissue contrast T 1 and T 2 relaxation Bloch equations with relaxation terms T 2 * relaxation Contrast agents Free-induction decay (FID) Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (31/141)

32 14.3 RELAXATION AND TISSUE CONTRAST T 1 AND T 2 RELAXATION Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (32/141)

33 14.3 RELAXATION AND TISSUE CONTRAST T 1 and T 2 relaxation Spin-lattice, or T 1, relaxation One of two mechanisms that drive magnetization back to its equilibrium state Some of energy absorbed by spins from RF pulse is lost to their surroundings - the lattice Time constantfor this phenomenon is T 1 depends on the mobility of the lattice efficiency of energy transfer from excited spins to the lattice Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (33/141)

34 14.3 RELAXATION AND TISSUE CONTRAST T 1 and T 2 relaxation Spin-lattice, or T 1, relaxation The longitudinal component (z-component) of the magnetization returns to its equilibrium state M 0 in an exponential fashion M z ( ) ( ) t/ T ( ) 1 t/ T1 t = M 0e + M 1 e z where M z (0) is the longitudinal magnetization immediately following RF excitation For a 90 excitation, M z (0) is zero After a time period of several T 1 s, the magnetization has nearly fully returned to its equilibrium state o Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (34/141)

35 14.3 RELAXATION AND TISSUE CONTRAST T 1 and T 2 relaxation Spin-lattice, or T 1, relaxation Light gray component After a time period of several T 1 s, the magnetization has nearly fully returned to its equilibrium state: amplitude M 0 aligned with z-axis Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (35/141)

36 14.3 RELAXATION AND TISSUE CONTRAST T 1 and T 2 relaxation Spin-spin, or T 2, relaxation In addition to interactions with the lattice, spins interact with each other spin-spin Each spin is essentially a magnetic dipole creates a magnetic field of its own slightly alters the field of its surroundings Any spin close to another will experience the additional field which slightly alters its precessional frequency Spins are in constant motion, so precessional frequency of each spin changes continuously Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 5 (36/141)

37 14.3 RELAXATION AND TISSUE CONTRAST T 1 and T 2 relaxation Spin-spin, or T 2, relaxation Result is a loss of phase coherence Leading to an exponential decay of signal in the transverse plane With time constant T 2 M xy t = M 0 ( ) ( ) t/ T2 xy e where M xy (0) is the transverse magnetization immediately following RF excitation Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 6 (37/141)

38 14.3 RELAXATION AND TISSUE CONTRAST T 1 and T 2 relaxation Spin-spin, or T 2, relaxation Dark gray component T 2 relaxation reduces the transverse component towards zero Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 7 (38/141)

39 14.3 RELAXATION AND TISSUE CONTRAST T 1 and T 2 relaxation Typical T 1 and T 2 values in human tissues at 1.5 T Tissue T 1 (ms) T 2 (ms) Muscle Fat Liver Blood (oxygenated) Blood (deoxygenated) White matter Gray matter Cerebrospinal fluid (CSF) T 1 and T 2 differ between tissue types T 1 and T 2 are field-strength dependent Adapted from Bernstein, King and Zhou, Handbook of MRI pulse sequences, 2004 Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 8 (39/141)

40 14.3 RELAXATION AND TISSUE CONTRAST T 1 and T 2 relaxation TR and image creation Repeat process of excitation and signal detection many times until have sufficient data for image reconstruction Time between successive excitations is repetition time (TR) From M z ( ) ( ) t/ T ( ) 1 t/ T1 t = M 0e + M 1 e z value of TR determines the extent to which tissues with various T 1 s have returned to their equilibrium state o Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 9 (40/141)

41 14.3 RELAXATION AND TISSUE CONTRAST T 1 and T 2 relaxation TR and image creation M z ( ) ( ) t/ T ( ) 1 t/ T1 t = M 0e + M 1 e z If TR is short tissues with short T 1 s which relax more quickly will appear brighter than those with longer T 1 values differences in T 1 between tissues will be emphasized o Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 10 (41/141)

42 14.3 RELAXATION AND TISSUE CONTRAST T 1 and T 2 relaxation TE and image creation Time between excitation and data acquisition is echo time (TE) M xy t = M ( ) ( ) t/ T2 If TE is long tissues with short T 2 s which relax more quickly will appear darker than those with longer T 2 values differences in T 2 between tissues will be emphasized More in Section xy 0 e Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 11 (42/141)

43 14.3 RELAXATION AND TISSUE CONTRAST BLOCH EQUATIONS WITH RELAXATION TERMS Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (43/141)

44 14.3 RELAXATION AND TISSUE CONTRAST Bloch equations with relaxation terms Bloch equations If the T1 and T2 relaxation constants are incorporated into the Bloch equation (slide 17/141) dm = γm B dt + M M xˆ o M x + zzˆ T T 1 2 M y yˆ Now includes effects of both static (B 0 ) and dynamic (B 1 ) magnetic fields relaxation of spins due to T 1 and T 2 relaxation Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (44/141)

45 14.3 RELAXATION AND TISSUE CONTRAST T 2 * RELAXATION Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (45/141)

46 14.3 RELAXATION AND TISSUE CONTRAST T 2 * relaxation Effect of magnetic field inhomogeneities In a homogeneous field, the transverse signal decays exponentially with intrinsic T 2 time constant Magnetic field inhomogeneities may arise from imperfect magnet shimming induced field perturbations (e.g. due to susceptibility differences at tissue boundaries) These lead to additional loss of coherence among the spins In an inhomogeneous field, the transverse signal may decay more rapidly Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (46/141)

47 14.3 RELAXATION AND TISSUE CONTRAST T 2 * relaxation Effect of magnetic field inhomogeneities Approximation for signal loss within a voxel Exponential decay with time constant T 2 * pronounced T- two star T 2 *<T 2 represents total transverse relaxation time i.e. both intrinsic T 2 and the component due to inhomogeneous field, T 2 T-two prime Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (47/141)

48 14.3 RELAXATION AND TISSUE CONTRAST T 2 * relaxation T2* relaxation 1 T * 2 = 1 T 2 + γ B 1 + T where Bis the field inhomogeneity across a voxel γ is the gyromagnetic ratio T 2 *is the total transverse relaxation time constant T 2 is the intrinsic transverse relaxation time constant T 2 is the transverse relaxation time constant due to the inhomogeneous field = 1 T 2 2 Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (48/141)

49 14.3 RELAXATION AND TISSUE CONTRAST T 2 * relaxation Most common incidences of field perturbations in vivo Near regions of air-tissue boundaries Sinus cavity in the head In trabecular (spongy) bone susceptibility difference between bone and bone marrow induces local field inhomogeneities within the marrow Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 5 (49/141)

50 14.3 RELAXATION AND TISSUE CONTRAST T 2 * relaxation Reversal of signal loss Signal loss due to intrinsic T 2 relaxation cannot be avoided Signal loss due to field inhomogeneities can be reversed Apply a second RF pulse known as a refocusing pulse This is basis of spin echo imaging Section Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 6 (50/141)

51 14.3 RELAXATION AND TISSUE CONTRAST CONTRAST AGENTS Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (51/141)

52 14.3 RELAXATION AND TISSUE CONTRAST Contrast agents Contrast Agents Further enhance contrast among tissues Highly paramagnetic enhance the spin-lattice interaction shorten T 1 time constant longitudinal signal restored more rapidly following excitation Commonly based on gadolinium 3+ ion seven unpaired electrons strongly paramagnetic Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (52/141)

53 14.3 RELAXATION AND TISSUE CONTRAST Contrast agents Relaxation rate R 1 R 1 1 = = T T + 1 r[ C] where T 10 is the intrinsic tissue T 1 without contrast agent ris relaxivity of contrast agent [C] is concentration of contrast agent 1 10 Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (53/141)

54 14.3 RELAXATION AND TISSUE CONTRAST Contrast agents Relaxivity Specific property of each type of contrast agent Varies significantly from one agent to another Both T 1 and T 2 are affected by contrast agents relaxivities roughly the same for both But, T 10 >> T 20 i.e. R 1 << R 2 So, for a given concentration of contrast agent, relative effect is greater on longitudinal time constant(t 1 ) than on transverse (T 2 ) time constant. Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (54/141)

55 14.3 RELAXATION AND TISSUE CONTRAST Contrast agents Imaging sequences in contrast-enhanced MRI Highlight enhancing structures by using short TR Most tissues do not recover sufficiently after excitation Only those tissues affected by contrast agent will recover sufficiently to produce a high signal as they have drastically shortened T1 values Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 5 (55/141)

56 14.3 RELAXATION AND TISSUE CONTRAST Contrast agents Clinical applications of contrast-enhanced MRI Tumour detection inject contrast agent into blood stream through vein in arm most tumours have a rich blood supply contrast agent diffuses from vessels into extra vascular space local reduction in T 1 enhance lesion signal intensity compared with surrounding tissue degree of signal enhancement may be used to assess tumour perfusion MR angiography Imaging of myocardial infarction Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 6 (56/141)

57 14.3 RELAXATION AND TISSUE CONTRAST Contrast agents Example of tumour detection Pre-contrast, no lesion is visible Post-contrast (intra-vascular administration), the lesion is enhanced due to high vascularity within the lesion Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 7 (57/141)

58 14.3 RELAXATION AND TISSUE CONTRAST FREE-INDUCTION DECAY (FID) Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (58/141)

59 14.3 RELAXATION AND TISSUE CONTRAST Free-induction decay (FID) Free induction decay (FID) Occurs following excitation with an RF pulse Evolution of the signal in the transverse plane exponential decay with T 2 time constant (ignoring the T 2 *effect) spins precess at Larmor frequency in laboratory frame of reference In homogeneous field, detected signal is perfectly sinusoidal modulated by exponential decay with T 2 time constant Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (59/141)

60 14.3 RELAXATION AND TISSUE CONTRAST Free-induction decay (FID) Frequency spectrum of free induction decay Take Fourier transform of the FID Result is a function, whose real component is a Lorentzian peak of Lorentzian function centred at the Larmor frequency full-width-at-half-maximum = Rapidly decaying signal broader spectrum Longer T 2 sharper peak in spectrum 1πT 2 Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (60/141)

61 14.4 MR SPECTROSCOPY 14.4 MR SPECTROSCOPY Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (61/141)

62 14.4 MR SPECTROSCOPY 14.4 MR spectroscopy Proton spectroscopy All hydrogen nuclei (protons) have same properties spin number, angular moment In a homogeneous magnetic field expect to precess at same frequency But local magnetic field differs for hydrogen nuclei of different chemical species different magnetic shielding from electron clouds So even if a homogeneous external field slight difference in precessional frequency for hydrogen nuclei in different molecules Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (62/141)

63 14.4 MR SPECTROSCOPY 14.4 MR spectroscopy Proton spectroscopy water and fat e.g. water and fat, frequency difference of 3.35 ppm (parts-per-million) 215 Hz at 1.5 T FID for an object containing both water and fat sum of two decaying sinusoids slightly different resonant frequencies different T 2 time constants Fourier transform of FID frequency spectrum superposition of two Lorentzians separated by 3.35 ppm Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (63/141)

64 14.4 MR SPECTROSCOPY 14.4 MR spectroscopy MR spectroscopy Within single molecule such as fat hydrogen nuclei resonate at different frequencies protons bound to carbon atom with single bonds vs. carbon atom with double bonds T 2 values could also vary Complex frequency spectrum multiple peaks of different amplitudes and widths MR spectroscopy use the information in spectrum to determine the chemical and structural properties of molecules Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (64/141)

65 14.4 MR SPECTROSCOPY 14.4 MR spectroscopy Chemical shift Separations between resonant peaks of different protons proportional to external magnetic field strength high field systems advantageous for MR spectroscopy higher spectral resolution Frequency shift due to different electronic environments known as chemical shift Diagnostic Radiology Physics: A Handbook for Teachers and Students 14.4 Slide 5 (65/141)

66 14.4 MR SPECTROSCOPY 14.4 MR spectroscopy Clinical applications of MR spectroscopy Monitor biochemical changes in tumours, stroke, metabolic disorders Commonly used nuclei proton, phosphorous, carbon Higher peak in spectrum associated with higher concentration of a compound or molecule E.g. in proton spectroscopy increased ratio of choline:creatine may indicate malignant disease high lactate levels may indicate cell death and tissue necrosis More in Chapter 15 Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 6 (66/141)

67 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES 14.5 Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (67/141)

68 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES 14.5 Spatial encoding and basic pulse sequences Slice-selection Frequency and phase encoding Field-of-view and spatial resolution Gradient echo imaging Spin echo imaging Multi-slice imaging Three-dimensional imaging Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (68/141)

69 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES SLICE-SELECTION Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (69/141)

70 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Slice-selection Slice selection In previous discussion RF pulse caused entire imaging volume to be excited In most applications though, an image of a thin slice of object is desired Achieve thin slice by applying a linear magnetic field gradient across the object during the RF pulse shaping the RF pulse to give desired slice profile Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (70/141)

71 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Slice-selection Slice profile RF pulse applied simultaneously with linear magnetic field gradient Excited slice profile in direction of gradient resembles Fourier transform of the shape of the RF pulse most accurate for small flip angles (< 30 ) acceptable for 90 excitation deviates at larger flip angles, but often assumed to hold Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (71/141)

72 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Slice-selection Slice profile To get rectangular slice profile Use sinc-shaped RF pulse The dotted box (left) indicates how the sinc pulse is often truncated to limit its width, and the ends may be tapered to create a smooth transition region in the slice profile Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (72/141)

73 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Slice-selection Shaping the excitation pulse Sinc pulse is infinitely long, so is truncated in practice usually include only one or two lobes on either side of main lobe To taper to zero at the ends, apply low pass smoothing Hanning or Hamming filter Without a low pass filter get abrupt truncations can lead to Gibbs ringing and excitation outside the desired slice Gaussian RF pulse shape could be used too Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 5 (73/141)

74 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Slice-selection Slice thickness The thickness of the excited slice zis a function of bandwidth of the sinc pulse, BW amplitudeof slice selection gradient, G z z = BW γ G z Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 6 (74/141)

75 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Slice-selection Slice selection gradient In MRI have three sets of linear gradient coils used for spatial encoding G x, G y andg z provide linear gradients long the x, yand zaxes respectively Slice selection gradient may be any one of these Or can obtain a slice plane in any spatial orientation by using more than one of the gradients Excited plane is perpendicular to the direction of the net gradient Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 7 (75/141)

76 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES FREQUENCY AND PHASE ENCODING Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (76/141)

77 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Frequency and phase encoding Spatial encoding within the selected slice After exciting desired slice use linear gradients along the two perpendicular in-plane directions G x and G y for an axial slice plane from G z gradient Linear gradient field will cause spins at different positions along direction of gradient to precess at different frequencies Frequency of precession varies linearly with position where G x is the applied magnetic field gradient along x axis and ω x is the resonance frequency of the spins at position x ω x = γg x x Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (77/141)

78 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Frequency and phase encoding Rotating frame of reference The precession frequency in the equation is relative to the rotating frame the additive frequency term due to the static B 0 field is not included Note that this also applies to subsequent equations Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (78/141)

79 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Frequency and phase encoding Frequency-encoding During MRI data acquisition spatial gradient applied along x-axis by convention spins resonate at linearly varying frequencies This is frequency-encoding Applied gradient is called readout gradient since data points are acquired while gradient is applied Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (79/141)

80 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Frequency and phase encoding Phase-encoding Arises from spatial gradient applied along y-axis by convention Applied gradient is called phase-encoding gradient Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 5 (80/141)

81 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Frequency and phase encoding The detected signal, frequency encoding only The detected signal S(t) is the sum of all the excited spins in the imaging volume Each spin is resonating at a frequency corresponding with its position along gradient direction S = ρ = ( ) ( ) jω t xe dx ( x) xt jγgxxt e dx where ρ(x) is the spin density T 1 and T 2 dependence have been ignored for simplicity Term in the exponent is a phase term ρ Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 6 (81/141)

82 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Frequency and phase encoding The phase term in the detected signal The phase term represents the relative phase accumulated in the rotating frame due to the frequency encoding gradient Typically, readout gradient is constant More generally, readout gradient may be time varying so the accumulated phase term must be replaced by a time integral of the readout gradient Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 7 (82/141)

83 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Frequency and phase encoding The phase term in the detected signal for a time varying readout gradient Define Then S k x = γ ( ) ( ) ( ) jkxx t S k xe dx x G = = ρ ( t) dt i.e. position variable xand the variable k x are a Fourier pair k x represents spatial frequency, in k-space Thus image space and k-space are a Fourier pair x Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 8 (83/141)

84 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Frequency and phase encoding Extend to 2D, i.e. both frequency and phase encoding Define Then Image space and k-space are a Fourier pair Once a sufficient amount of data S ( k ) x, k y are acquired in k- space Can obtain imaging object ρ( x, y) by Fourier transformation k x = γ S G x ( t) dt k ( k k ) ( x y ) x, y = ρ, y = γ e j G y ( t) dt ( kxx+ kyy) dxdy Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 9 (84/141)

85 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Frequency and phase encoding Data acquisition in 2D k-space Desired k-space data, S ( k ) x, k y, acquired by navigating through k-space Use G x and G y gradients, where k x = γ G x ( t) dt k y = γ G y ( t) dt Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 10 (85/141)

86 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Frequency and phase encoding Data acquisition in 2D k-space Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 11 (86/141)

87 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Frequency and phase encoding Data acquisition strategies in 2D k-space Can acquire data to fill k-space after a single excitation but signal may be small during data acquisition due to T 2 or T 2 * decay leading to blurring or other image artefacts Instead use multiple TRs Acquire data for a single line of k-space following each excitation Details of typical data acquisition strategies in sections , , Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 12 (69/141)

88 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES FIELD-OF-VIEW AND SPATIAL RESOLUTION Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (88/141)

89 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Field-of-view and spatial resolution Field of view (FOV) Determined by manner in which k-space is sampled Image space and k-space are Fourier pair have an inverse relationship image space, units of distance spatial position k-space, units of 1/distance spatial frequency Larger FOV: finer sampling in k-space Smaller FOV: coarser sampling in k-space Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (89/141)

90 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Field-of-view and spatial resolution Field of view (FOV) FOV given by inverse of the distance between adjacent sampled k-space points Can be different for the two in-plane directions FOV x = 1 FOVy k = 1 k y x where k x and k y are the spacing between adjacent k- space points along k x and k y Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (90/141)

91 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Field-of-view and spatial resolution Spatial resolution / pixel width The range of the sampled k-space region is important High spatial resolution requires larger region of k-space to be sampled Expressed in terms of pixel widths xand y x= 2 1 k x,max y= k y,max where k x, max and k y, max are the maximum positions, along k x and k y respectively, that are sampled 2 1 Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (91/141)

92 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES GRADIENT ECHO IMAGING Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (92/141)

93 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging Pulse sequences Set of instructions that control how MRI data are acquired application of G x, G y and G z magnetic field gradients the RF pulse data acquisition Many available Some optimized e.g. for rapid imaging estimating diffusion or flow robustness against motion Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (93/141)

94 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging Gradient echo pulse sequence One of the simplest imaging pulse sequences Slice-selective RF pulse which rotates the magnetization into the transverse plane (conventionally along the z-axis) Frequency-encoding, or readout, gradient (x-axis) Phase-encoding gradient (y-axis) Plus Slice rewinder Readout pre-phase gradient Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (94/141)

95 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging Gradient echo pulse sequence Following slice excitation, phase-encoding and readout pre-phase gradients are applied. Data acquisition subsequently follows in which one line of k- space data is acquired. The phase encoding gradient amplitude is linearly increased from one TR to the next in order to fill different k y lines of k-space. Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (95/141)

96 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging Slice rewinder Opposite polarity to slice-selection gradient amplitude Needed to undo the phase accumulation that occurs during RF pulse when a slice-selection gradient present spins at different positions along the z-axis will accumulate different amounts of phase during the RF pulse Apply rewinder gradient with area approximately half that of slice selection gradient reverses undesired phase dispersion aligns spins along same direction in the transverse plane Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 5 (96/141)

97 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging Readout pre-phase gradient For reconstruction of an MR image, require k-space to be filled symmetrically about its centre i.e. about k x = k y = 0 Can be achieved efficiently by acquiring a full line of data in a single readout Pre-phase gradient moves the k-space location to k x, max prior to each data acquisition position in k-space is the integral of the spatial gradients a negative G x pre-phase gradient will move k-space position along negative k x direction Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 6 (97/141)

98 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging Readout pre-phase gradient a) b) c) a) The pre-phase gradient of the readout axis moves the current k-space position to k x, max b) Subsequently, one complete line of data is acquired during readout c) Also apply the various phase-encoding gradients prior to readout to move along the k y axis two different phase-encoded acquisitions are shown, one positive and one negative Continue until the desired k-space region is filled (gray box). Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 7 (98/141)

99 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging Readout pre-phase gradient Without a pre-phase gradient data readout would begin at k x = 0 to fill the other half of k-space would need second readout in opposite direction Pre-phase gradient causes de-phasing of spins that element of de-phasing is then reversed by the readout gradient spins come back into phase and result in the echo signal Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 8 (99/141)

100 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging When to apply gradients One line of data acquired during each TR During each TR apply different phase-encoding amplitudes to sample different lines along k y axis Phase-encoding, pre-phase and slice rewinders must be applied after the end of the excitation pulse prior to beginning of readout window Could be applied simultaneously Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 9 (100/141)

101 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging Gradient amplitude and duration Total area under pulses is important since kis time integral of the gradient Area under the readout pre-phase gradient should be onehalf of the area of the readout gradient echo will occur midway through the readout window Achieve using same amplitude, but opposite polarity and half pulse width or maximum possible amplitude and a shorter pulse width good if short TE is desired Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 10 (101/141)

102 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging Image reconstruction Acquire desired data e.g. 256 phase-encoding lines 256 readout points per line Apply 2D discrete fast Fourier transform to k-space data Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 11 (102/141)

103 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging TE, echo time Time between peak of excitation pulse and centre of readout window (k x =0) above a certain minimum, can select value of TE to achieve desired image contrast During TE transverse magnetization decays with instrinsic T 2 relaxation time constant also loss of phase coherence among the spins from field inhomogeneity result is T2* decay of signal the gradient echo image is weighted by the factor exp(-te/t 2 *) Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 12 (103/141)

104 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging T 1 -weighted imaging T 1 relaxation takes place following each excitation and longitudinal magnetization recovers If TR short longitudinal magnetization for tissue with relatively long T 1 s remains low (insufficient time for recovery) lower signal in tissues with long T 1 s longitudinal magnetization greater for tissue with shorter T 1 s higher signal in tissues with short T 1 s T 1 -weighted images Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 13 (104/141)

105 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging T 1 -weighted imaging Image contrast results from difference in T 1 among the tissues TE kept to a minimum in T 1 -weighted imaging to minimise contrast from T 2 or T 2 * Both TR and TE are short Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 14 (105/141)

106 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging Fast imaging Applications such as dynamic imaging Multiple images are acquired rapidly to detect changes in the images over time TR needs to be short but short TR reduces time available for magnetization to recover So, use small excitation angles (e.g., 5 o 30 o ) so that acquired signal is maximised Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 15 (106/141)

107 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging Ernst angle θ E Flip angle that yields highest signal intensity for given TR known or approximate tissue T 1 Obtained by solving Bloch equation θ = cos ( / T) 1 1 E e TR Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 16 (107/141)

108 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Gradient echo imaging Drawback of gradient echo imaging Sensitive to magnetic field inhomogeneities imperfect shimming of main B 0 field along air tissue boundaries where susceptibility difference between regions distorts the local magnetic field Leads to additional signal loss from dephasing of spins (T 2 *decay) within affected voxels Results in reduced signal Or even complete loss of signal at long TE Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 17 (108/141)

109 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES SPIN ECHO IMAGING Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (109/141)

110 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Spin echo imaging Spin echo imaging Avoids reduction of signal due to magnetic field inhomogeneities A second RF pulse is applied following the initial 90 excitation pulse at time TE/2 180 flip angle Called a refocusing pulse Effect is to reverse the phase that a spin may have accumulated due to the inhomogeneous field Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (110/141)

111 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Spin echo imaging After the refocusing pulse After 180 refocusing pulse, magnetization again accumulates phase But, because of the phase reversal from the refocusing pulse, the total phase is reduced At the echo time TE the phase accumulated after the refocusing pulse cancels the phase accumulated before Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (111/141)

112 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Spin echo imaging Spin echo pulse sequence The spin echo sequence is similar to the gradient echo sequence phase-encoding, rewinder and prephase gradients Plus a 180 refocusing pulse to refocus any spin that may have dephased due to magnetic field inhomogeneities The refocusing pulse reverses any accumulated phase so polarities of both the phase encoding gradient and the prephase gradient of the readout are reversed Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (112/141)

113 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Spin echo imaging Spin echo pulse sequence in k-space Effect of refocusing pulse is to move current k-space location to its conjugate position i.e. to reflect the point about the k-space origin Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 5 (113/141)

114 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Spin echo imaging Acquired signal at TE Spin echo imaging evolves with the intrinsic T 2 time constant not affected by inhomogeneous fields Gradient echo imaging evolves witht 2 * is affected by inhomogeneous fields Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 6 (114/141)

115 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Spin echo imaging Fast imaging In gradient echo, use short TR and small angle excitation In spin echo, short TR not recommended due to rapid reduction of available magnetization 180 refocusing pulse inverts any positive longitudinal magnetization to z direction a short TR does not allow sufficient time for recovery Instead, reduce scan time by acquiring multiple lines of data following a single excitation pulse Fast spin echo or turbo spin echo Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 7 (115/141)

116 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Spin echo imaging Fast spin echo or turbo spin echo For each excitation pulse apply multiple refocusing pulses acquire multiple lines of data Typically 16, 32 or more lines of data per TR Single shot acquisitions possible e.g. 128 refocusing pulses and 128 readout lines following a single excitation pulse Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 8 (116/141)

117 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES MULTI-SLICE IMAGING Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (117/141)

118 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Multi-slice imaging Two approaches to get more than one slice Acquire multiple 2D slices by repeating the single slice strategy at shifted slice positions Use 3D imaging Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (118/141)

119 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Multi-slice imaging Multiple slice technique All gradient waveforms, including slice selection gradients, remain unchanged Vary location of each slice by modulating frequency of the excitation RF pulse modify the carrier frequency of the RF pulse Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (119/141)

120 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Multi-slice imaging Multiple slice technique Centre location of excited slice with respect to scanner isocentre, z slice, given by z slice f = γg where fis the offset frequency of the RF pulse relative to resonance frequency at isocentre and G sl is the slice selection gradient amplitude sl Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (120/141)

121 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Multi-slice imaging Multiple slice technique Typically acquire multiple 2D slices in an interleaved fashion Do not need to wait until the end of a TR following data acquisition from one slice before acquiring data from other slices there is dead time between end of data acquisition and next excitation pulse for a given slice excite a different slice, and acquire data, during dead time of the previous slice Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 5 (121/141)

122 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Multi-slice imaging Interleaved slice acquisition Three slices S1, S2 and S3 are acquired Each box can represent any imaging sequence Effective TR for each slice is period between acquisitions of the same slice corresponds to the time between excitations for any given spin Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 6 (122/141)

123 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Multi-slice imaging Interleaved slice acquisition Total scan time can be equal to scan time for a single slice if the dead time is sufficiently long Otherwise, repeat scan until all remaining slices are acquired Following data acquisition, images are reconstructed by applying separate 2D Fourier transforms for each slice Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 7 (123/141)

124 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES THREE-DIMENSIONAL IMAGING Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (124/141)

125 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Three-dimensional imaging 3D imaging Alternative approach to acquisition of multiple slices Excite a single large volume (instead of a single slice) Add phase encoding along slice direction Now have phase encoding in in-plane, and through-plane (slice) directions Just as in-slice spatial information is encoded using phase-encoding along y-axis Slice information is encoded using phase-encoding along z-direction Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (125/141)

126 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Three-dimensional imaging 3D gradient echo sequence Similar to 2D sequence But has additional phase encoding along the sliceencoding direction, G z Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (126/141)

127 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Three-dimensional imaging 3D imaging After data acquisition, images are obtained by 3D Fourier transform of the acquired k-space data Data for all slices acquired simultaneously in 2D scheme each data acquisition window receives data from only one slice Scan time in 3D is greater than that for 2D (for a single slice with the same TR) by a factor equal to the number of slices Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (127/141)

128 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Three-dimensional imaging Advantages/Disadvantages of 3D imaging 3D imaging preferred when multiple contiguous slices needed because slices are contiguous 3D imaging preferred if thin slices required because excitation of a large 3D volume requires much lower gradient amplitude than needed to excite individual thin slices 2D imaging preferred if arbitrary slice positions desired Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 5 (128/141)

129 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES MEASUREMENT OF RELAXATION TIME CONSTANTS Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 1 (129/141)

130 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Measurement of relaxation time constants Why measure T 1 and T 2? Determine disease status Track disease progress following treatment Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 2 (130/141)

131 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Measurement of relaxation time constants Measurement of T 1 Several approaches One example is the inversion recovery (IR) technique accurate and widely used Apply 180 pulse inverts spins from equilibrium position into the z axis Magnetization recovers from its inverted state towards equilibrium magnetization in exponential fashion, with longitudinal time constant T 1 t/ T according to ( ) ( ) ( ) 1 t/ T1 Mz t = Mz 0e + Mo1 e where M z ( 0) = M0 Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 3 (131/141)

132 14.5 SPATIAL ENCODING AND BASIC PULSE SEQUENCES Measurement of relaxation time constants Inversion recovery (IR) sequence Invert magnetization to the z axis by a 180 pulse Acquire data following an inversion time (TI) Repeat for different TI values (open circles) Fit data to equation to find T 1 Typically a fast imaging technique used such as turbo spin echo Diagnostic Radiology Physics: A Handbook for Teachers and Students Slide 4 (132/141)