Radiation Oncology Residents MR Physics Overview

Transcription

1 Radiation Oncology Residents MR Physics Overview Edward F. Jackson, PhD Department of Imaging Physics Example MR Images Introduction Image contrast in MRI depends on an extensive list of intrinsic and extrinsic parameters. Intrinsic parameters include: proton density velocity spin-lattice relaxation time (T 1 ) spin-spin relaxation time (T 2 ) chemical environment Extrinsic parameters include: echo time (TE) repetition time (TR) flip angle (α) contrast agents diffusion perfusion temperature saturation pulses inversion pulses flow compensation pulses (GMN) diffusion sensitization pulses 1

2 Introduction Basic ingredients: Non-zero magnetic moment nuclei Nuclear Static magnetic field, B o Magnetic Radiofrequency field, B 1 Resonance Magnetic field gradients, G x,y,z Nuclear Magnetic Resonance Only nuclei with non-zero magnetic moments can be imaged. A non-zero magnetic moment occurs for odd numbers of protons and/or neutrons. Most commonly, the nuclei have spin quantum numbers of 1/2, e.g., 1 H, or 3/2, e.g., 23 Na. Nuclear Magnetic Resonance Properties of some common nuclei with potential use in MR studies Natural Isotopic Abundance (%) Sensitivity Relative to 1 H (%)* Nucleus Spin Gyromagnetic ratio (MHz/T) 1 H 1/ C 1/ F 1/ Na 3/ P 1/ *At constant field for equal number of nuclei. 2

3 Nuclear Magnetic Resonance B o M o Longitudinal Magnetization μ M 0 M XY = 0 Net Excess Spins Aligned with B 0 Net Longitudinal Magnetization Note that all transverse components cancel so there is no net transverse magnetization, i.e., M xy = 0. Nuclear Magnetic Resonance The equilibrium distribution of spin up and spin down protons is given by the Boltzmann distribution, γ hb0 0 0 kt N / N = e + At room temperature and with a 1.5 T field, ~10 per 1 million spins are preferentially aligned with the applied magnetic field. 3

4 Nuclear Magnetic Resonance To generate time-dependent transverse magnetization that can be detected, transitions between the two allowed energy states (for a spin 1/2 nucleus) must be induced. The transitions result from the application h of a time-varying magnetic field with an energy equal to the difference in the energy levels, i.e., E = hω = γ hb o where h is Planck s constant, γ is the gyromagnetic ratio, and B o is the static magnetic field strength. Nuclear Magnetic Resonance The Larmor frequency is given by: ω = γ B o For protons in a 1.5 T field, the Larmor frequency is ~64 MHz. The radiofrequency field is commonly known as the B 1 field and, in addition to being applied at the Larmor frequency, must be applied perpendicular to the static field in order to induce the desired transitions. Nuclear Magnetic Resonance The effect of the applied B 1 field is to tip the net magnetization away from the longitudinal direction toward the transverse plane. It also results in the development of phase coherence of the precessing magnetic moments. The nutation angle, or flip angle, is determined by the B 1 field amplitude and duration of the pulse, i.e., α = γ B 1 t p 4

5 Spin Coherence μ M 0 = 0 M XY 0 Before RF Pulse Immediately After RF Pulse Free Induction Decay 1 Relative Signal Intensity Time (ms) Introduction to Relaxation Effects Immediately following the 90 0 pulse, the magnetic moments precess in phase, and N + = N -. This gives rise to the detected transverse magnetization, M xy. Following the B 1 pulse, two effects are observed: The transverse magnetization (M xy ) returns to the equilibrium longitudinal direction (M o ), and The magnetic moments begin to dephase. 5

6 Spin-Lattice Relaxation The B 1 field induced transitions between the spin up and spin down states due to its oscillation at the appropriate frequency, the Larmor frequency. There are other sources of time-varying magnetic fields within the tissues that also can induce transitions from the higher energy antiparallel state to the lower energy parallel state. These physiological sources of B(t) are primarily based on the random motion of the water protons in different tissues. Spin-Lattice Relaxation ΔB T 1 ω L ω slow MOTION fast ω bound ENVIRONMENT free large SIZE small Spin Lattice Relaxation M z (t)/m 0 (%) Fat WM GM CSF Time (s) Calculated longitudinal magnetization following a 90 0 pulse for tissues with varying T 1 relaxation times. (Assumes equal proton densities for the tissues.) 6

7 Spin-Spin Relaxation In addition to the T 1 relaxation that occurs following the application of a 90 0 pulse, the transverse magnetization begins to dephase immediately following the B 1 pulse that originally induced phase coherence. The dephasing is known as spin-spin relaxation. The time constant for the rate of dephasing is the T 2, or spin-spin, relaxation time. M xy (t) = M O e - t / T2 Spin-Spin Relaxation Many of the tissue-induced time-varying B-field processes that contribute to spin-lattice relaxation also contribute to spin-spin relaxation, particularly at the higher frequencies. Therefore, the frequency-dependent T 1 and T 2 relaxation curves are quite similar at high tumbling frequencies (for pure liquids, for example). However, T 2 relaxation rates are also affected by the more slowly varying tissue-induced B-fields that do not cause efficient T 1 relaxation. (Hence, T 2 T 1.) Spin-Spin Relaxation T 1 or T 2 T 1 T 2 slow MOTION fast bound ENVIRONMENT free large SIZE small ω 7

8 Spin-Spin Relaxation M Signal xy / M 0 (A.U.) (%) Fat GM WM CSF TE (s) Calculated transverse magnetization following a 90 0 pulse for tissues with varying T 2 relaxation times. (Assumes equal proton densities for the tissues.) T 1 and T 2 Relaxation Times 1 - >3 sec Macromolecules rigid lattice, restricted motion μs ms CC Hydration H 2 O structured or bound anisotropic 5-10 ms 2-3 s RE Bulk (Free) H 2 O isotropic rotation, translational diffusion 1-2 s ~250 ms T 1 Values Elster, Q&A in MRI (See Refs) Mobile Fatty Acids dipole-dipole interactions, J-coupling ~100 ms T 2 Values CC: cross-coupling RE: rapid exchange Reference Relaxation Times Tissue T1 T TT T1 T TT T2 (ms) White Matter (WM) Gray Matter (GM) Cerebrospinal Fluid (CSF) >4000 >4000 >2000 Fat Skeletal Muscle Liver Kidney Spleen Note that the T 1 relaxation times depend on the applied field strength, while the T 2 relaxation times are essentially independent of applied field strength. The proton densities, unlike the relaxation times, do not vary greatly with tissue type with the exceptions that the proton density in gray matter exceeds that of white matter by ~20%, and the proton density in CSF exceeds that of gray matter by ~20 %. Reference: Wood et al. Physical MR Desktop Data, JMRI 3(S): 19-26,

9 Combined T 1 and T 2 Relaxation M 0 M z M xy M e 0 t * T2 0 TR T1 ( M 1 e ) time B TR time Spin-Echo Sequence The FID following a 90 0 pulse decays with a time constant of T 2 *, which is influenced by the local magnetic field inhomogeneities. Given a good quality magnet, the inhomogeneities are typically a result of interfaces between tissues with varying magnetic field susceptibilities. B eff = (1+χ) B 0, where χ is the magnetic susceptibility. Therefore, at interfaces of differing susceptibility, there is an apparent inhomogeneity of ΔB eff = Δχ B 0, resulting in a shortened T 2 * and enhanced dephasing (signal loss). Spin-Echo Formation B 1 TE Dephasing Rephasing Spin Echo F S F S F S 9

10 Signal Intensity in Spin-Echo Imaging The signal obtained using a SE sequence is given by S SE ρ ( TR TE / 2) / T1 TR T1 ( 1 e + e ) TE / T2 / 1 e 2 H or, if TR >> TE, S SE ρ H-1 e -TE/T2 (1 - e -TR/T1 ) Signal Intensity in Spin-Echo Imaging It s instructive to consider three limiting cases: Case 1: Let TE ==> 0 and TR ==>, then the signal intensity equation becomes S SE ρ H-1 In this case, the signal intensity (and hence contrast) will depend solely on the proton density. Signal Intensity in Spin-Echo Imaging Case 2: Let TE > 0 and TR ==>, then the signal intensity equation becomes S SE ρ H-1 e -TE/T2 In this case, the signal intensity (and hence contrast) will depend on the choice of the extrinsic parameter TE as well as the intrinsic T 2 relaxation times and proton densities. TR = 30 s, Equal Densities T 2 -weighted images 100 Typ: TE ~ 100 ms CSF Long T 2 substances, e.g., CSF, edema, etc., 50 GM will be hyperintense. Signal (A.U.) Fat WM TE (s) 10

11 Signal Intensity in Spin-Echo Imaging Case 3: Let TE ==> 0 and TR <<, then the signal intensity equation becomes S SE ρ H-1 (1 - e -TR/T1 ) In this case, the signal intensity (and hence contrast) will depend on the choice of the extrinsic parameter TR as well as the intrinsic T 1 relaxation times and proton densities. TE = 0 s, Equal Densities T 1 -weighted images Fat 100 Typ: TR ~ 500 ms WM GM CSF Short T 1 substances, e.g., lipids, will be 50 hyperintense. Long T1 substances, e.g., CSF, will be hypointense. Signal (A.U.) TR (s) Contrast in SE Imaging Recall the signal intensity equation for SE imaging (TR>>TE): S SE ρ H-1 e -TE/T2 (1 - e -TR/T1 ) From this we see that the choices of TE and TR dictate the image contrast: Short TE/Short TR (~15/500ms): T1-weighted Short TE/Long TR (~15/3500ms): PD-weighted Long TE/Long TR (~100/3500ms): T2-weighted Spin-Echo Image Contrast Increasing TE ==> Increasing TE ==> Increasing TR ==> 11

12 Spatial Orientation The MR signals must be encoded in 3 dimensions z - slice selection x - frequency-encoded y - phase-encoded Note: the slice, frequency and phase encoding may be on any axis z y x Image compliments of Carl Keener, PhD Slice Selection Gradient along z-axis modifies B 0 to produce a range of Larmor frequencies which vary with position. ω = γ B ω 0 0 z = γ ( B 0 + zg z ) G z ω -z ω 0 ω z Image compliments of Carl Keener, PhD Slice Thickness Slice thickness is determined by Gradient strength G z Δz Bandwidth of RF pulse (transmitter bandwidth) Δω Δz Δω = Δ( γ B + zg )) Δω Δz = γ G z ( 0 z 12

13 Slice Position Slice position is determined by the transmit center frequency. f Hz f 0 f Hz G z z ω Hz ω 0 ω Hz Image compliments of Carl Keener, PhD Frequency Encoding To encode the spatial information in the x-axis, another gradient (G x ) is used: ω -x ω 0 ω x ω x = γ (B o + x G x ) <== one-to-one correspondence between frequency and position Image compliments of Carl Keener, PhD Frequency Encoding When the gradient is on frequencies vary along x-axis The signal is sampled while x- gradient is on frequency of signal encodes position along x-axis ω -x ω 0 ω x Image compliments of Carl Keener, PhD 13

14 Phase Encoding To encode the spatial information in the y-axis, a 3rd gradient (G y ) is used ω - φ y ω 0 ω + φ y Image compliments of Carl Keener, PhD RF G slice G phase G freq Signal k-space Spin Echo Imaging Sequence TE TR st echo 2nd echo Reconstructing the Image image has been phase-encoded in the one direction gradient applied before frequency-encoding & sampling image has been frequencyencoded in other dimension gradient applied during sampling Image compliments of Carl Keener, PhD 14

15 Image Formation Re[s(t,n)] 2D FFT Im[s(t,n)] S(ω,φ) Gradient-Echo Imaging z z M o α o Pulse M z α x y x M xy y Contrast in Gradient-Echo Imaging Compared with SE imaging, how are T1W, T2*W, and PDW images obtained using GRE imaging? Consider the case of TR=100ms: Case 1: T1W Imaging α is large (typically ~ ) to emphasize T 1 effects TE is as short as possible (~4-8 ms) to minimize T 2 * effects Case 2: T2*W Imaging α is small (typically ~20 0 ) to minimize T 1 effects TE is long (typically ~15-20 ms) to emphasize T 2 * effects Case 3: PDW Imaging α is small (typically ~20 0 ) to minimize T 1 effects - TE is as short as possible (~4-8 ms) to minimize T 2 * effects Most common use, e.g., breath-hold abdominal, MRA, etc. Susceptibility-based contrast, e.g., disk & nerve root spine imaging, detection of blood, etc. 15

16 Gradient-Echo Imaging FMPSPGR sequence Top: TE / TR = 4.2 / 110 ms Bottom: TE / TR = 1.8 / 110 ms Both: BW = 32 khz 8-6 mm sections with 2 mm gaps 256 x 128 matrix 1 NEX St:SI Gradient-Echo Imaging Compared to SE imaging, GRE imaging has a significant speed advantage. However, the absence of the spin echo refocusing pulse makes the GRE sequence much more sensitive to magnetic susceptibility-induced inhomogeneity artifacts. (Recall that GRE sequences are T 2 *-weighted not T 2 -weighted.) The frequently gives rise to artifacts on T 2 *-weighted images. Gradient-Echo Imaging 3 mm 5 mm 10 mm Ref: Wehrli, Fast-Scan Magnetic Resonance. Principles and Applications 16

17 3D Image Acquisition Commonly used for image-guided therapy planning (RT as well as surgical). Advantages: Thinner slices are possible (down to ~0.5 mm vs ~1.5 mm for 2D acquisitions). The SNR per unit time is better. (Since each slice-encoding provides a signal average.) Disadvantages: Motion artifacts and any data acquisition hardware errors are propagated across all slices, i.e., they are not localized to the slice that was being acquired when the motion or spike noise occurred. 3D Display Fast Spin Echo (FSE) Imaging Recall that gradient-echo sequences are sensitive to susceptibility effects since the local field inhomogeneities are not corrected (no 180 o pulses). Furthermore, susceptibility artifacts become worse as the echo time increases, which makes obtaining T 2 *-weighted GRE images difficult. The FSE sequence uses multiple 180 o pulses following each 90 o pulse. Each 180 o pulse yields a refocused echo from the selected slice. The number of 180 o pulses is known as the echo train length, or ETL. Advantage: The acquisition time can be decreased by a factor of (up to) ETL in FSE imaging! 17

18 Fast Spin-Echo Imaging Fast Spin Echo - Advantages 1) Speed Can acquire images faster! (Can use faster imaging rate to improve temporal resolution, spatial resolution, or SNR as compared to spin-echo imaging.) 2) Decreased susceptibility artifacts Less artifacts at interfaces such as tissue/air or tissue/bone in T 2 -weighted images as compared to GRE. (Even less susceptibility artifacts than obtained with SE imaging.) Fast Spin Echo - Disadvantages 1) Increased specific absorption rate (SAR) The use of multiple 180 o pulses in rapid succession deposits significant RF energy into the patient and may actually limit the speed advantage of the FSE sequence. (A 180 o pulse contains 4x the energy of a 90 o pulse.) 2) T 2 -blurring Increased blurring occurs in the phase-encoding direction when using short TE eff values. The effect is more evident for tissues with short T 2 values and for longer ETL values. 18

19 Inversion Recovery Sequences The basic inversion recovery (IR) sequence is a pulse followed by a inversion time (TI) delay and then a conventional SE, GRE, or other type of imaging sequence. The choice of TI plays a strong role on the image contrast. Appropriate choices of TI allow for T 1 -dependent suppression of tissues or for enhancing T 1 -contrast. FLAIR Imaging - fluid attenuated inversion recovery Desire a T 2 -weighted image (to demonstrate pathology) with low viscosity fluids (CSF, cysts, vitreous humor, etc.) suppressed. To suppress fluids, which have long T 1 values, the inversion time, TI, is on the order of 2000 ms ( ms is common). For good suppression, TR must also be long (typically ms). Using conventional IR sequence, this requires 20 min or more!!! Fast-FLAIR uses an inversion pulse followed by a fast spin-echo (FSE) sequence. Acquisition times are 3-4 min for whole brain. FLAIR Imaging 180 o TI 90 o 180 o CSF Parenchyma 19

20 FLAIR Imaging T2W-FSE FLAIR TE/TR = 98/3500ms, 5/1.5mm, ET:8 (split) TI/TE/TR = 2200/147/10000ms, 5/1.5mm 256x224, 1 NEX, 20x20 cm FOV, 3:23 256x160, 1 NEX, 20x20cm FOV, 3:40 Brain MRI - Anaplastic Astrocytoma T 1 SE T 2 FSE FLAIR T 1 SE +Gd Spine MRI T 1 SE T 1 SE T 2 FSE 20

21 Body MRI - Pelvis L R Axial T 1 SE Axial T 1 SE + Gd Axial T 2 FSE Body MRI - Abdomen T 1 FMPSPGR T 1 SE w/gd & Fat Sat T 2 FSE + Fat Sat R L T 1 BH FMPSPGR Body MRI - Knee T 1 SE T 2 FSE 21

22 Clinical MRI Clinical MR Angiography Diffusion imaging The addition of two diffusion-sensitizing gradients to an EPI SE sequence provides a means of generating diffusion-weighted images. RF G diff The degree of diffusion-weighting depends on properties of the diffusion-sensitizing gradient pulses, which are taken into account in the b-value (s/mm 2 ). In the presence of these gradients, the signal is attenuated according to S/S 0 = e -bd, where D is the diffusion coefficient (mm 2 /s). 22

23 Diffusion imaging Intracellular space: D intra Extracellular space: D extra ~ 10 D intra D measured = D V + D V V + V intra intra extra extra intra extra Diffusion imaging Tissue Sample A Tissue Sample B Freely Diffusing Water = Dark Restricted Diffusion = Bright Diffusion imaging - Ischemic injury normal tissue cells swell membranes break D normal D < D normal D > D normal 23

24 Diffusion imaging in acute stroke PDW T2W FLAIR Diffusion GE Medical Systems Applications Guide Diffusion tensor imaging Dxx Dxy Dxz D = Dxy Dyy Dyz Dxz Dyz Dzz λ D = E 0 λ2 0 E 0 0 λ 3 Diffusion tensor imaging (DTI) Using multiple diffusion encoding directions to determine the diffusion tensor terms, the eigenvalues/eigenvectors can be used to characterize the anisotropy (λ1-λ) + (λ2-λ) + (λ3-λ) FA = λ + λ + λ T, b=1576 s/mm 2, 6 directions 3.0T, b=1000 s/mm 2, 15 directions 24

25 Diffusion tensor imaging (DTI) Furthermore, fractional (or relative) anisotropy indices can be computed to more fully characterize the white matter tract directions. Red: Right/left Green: Anterior/posterior Blue: Superior/inferior DTI Applications Image-Guided Therapy Neurosurgical Planning and Guidance Stereotactic biopsies (frame based) Frameless procedures Stereotactic Radiosurgery IMRT MR-Guided Therapies Thermal (Laser, RF, High intensity focused ultrasound) Biopsies Resection 25

26 In-Plane Spatial Encoding in MRI Recall that the linear magnetic field gradients relate frequency and phase to spatial position. Example: Assume the frequency-encoding direction is x, then ω x = γ (B o + G x x) Therefore, anything that results in a spatially varying magnetic field inhomogeneity, i.e., ΔB o (x,y,z), results in distortion of the image in this direction, i.e., ω x = γ {B o + [G x + ΔB o (x)] x} Sources of Geometric Distortion System Limitations Poor B o homogeneity Linear scale factor errors in the gradient fields Field distortion due to induced eddy currents Nonlinearities of the gradient fields Object-Induced Chemical shift effects Magnetic susceptibility variations (patient induced) Sources of Geometric Distortion Poor B o Homogeneity Modern magnet designs and field engineering tools have made the error due to inhomogeneous B o fields quite small. Linear Scale Factor Errors in the Gradient Fields Usually due to miscalibration of the gradients. Readily addressed by careful calibration using a phantom of known dimensions. Field Distortion Due to Induced Eddy Currents Usually negligible (for standard sequences) in systems with actively-shielded gradients and gradient pre-emphasis corrections. 26

27 Eddy Currents Gradient Current Eddy Current Actual Gradient Field Gradient Current with Pre-Emphasis Actual Gradient Field Sources of Geometric Distortion Most significant causes of geometric distortions in MRI: Gradient Field Nonlinearities Barrel Aberrations Slice Distortions Resonance Offsets Chemical Shift Induced Local Magnetic Field Inhomogeneity Induced (Susceptibility Effects) Gradient Field Nonlinearities G zz z 27

28 Gradient Field Nonlinearity Effects - In-Plane Distortion Barrel Aberration Due to nonlinearities in the gradient fields used for phase- and frequency-encoding. Results in a warping of the image space. Can result in errors of ~4-5 mm on a 20 x 20 cm FOV (without correction). Typically corrected during reconstruction (to within 1 mm near isocenter) using the known error fields of the gradient coils. Gradient Field Nonlinearity Effects - In-Plane Distortion Slice Plane at Isocenter 20 cm FOV White circles: with gradient nonlinearity correction Black circles: without gradient nonlinearity correction Maximum error without correction: ~ 4.5 mm at ±10 cm from isocenter Maximum error with correction: < 1 mm at ±10 cm from isocenter Gradient Field Nonlinearity Effects - In-Plane Distortion Slice Plane at 20 cm from Isocenter 20 cm FOV White circles: with gradient nonlinearity correction Black circles: without gradient nonlinearity correction Maximum error without correction: ~ 5.5 cm at ±10 cm from isocenter Maximum error with correction: < 2 mm at ±10 cm from isocenter 28

29 Gradient Field Nonlinearity Effects - Slice Distortion Reference: Sumanaweera TS et al., Neurosurgery 35(4): , Potato Chip Distortion Due to nonlinearities in the gradient field used for slice selection. Results in a warping of the slice. Can result in errors up to ~4 mm on slices ~10 cm from isocenter with a 20 x 20 cm FOV (without correction). More difficult to correct when using 2D imaging techniques. Not as significant when using 3D (volume) imaging techniques. RF G slice G phase G freq Signal 3D Gradient Echo Imaging Sequence TE TR α 0 α k-space 1st echo 2nd echo Gradient Field Nonlinearity Effects To minimize spatial inaccuracy due to nonlinearity of the gradient fields: When possible, use 3D imaging techniques (typically T 1 - weighted gradient recalled echo sequences) to minimize slice distortions. Make sure barrel aberration distortions are being corrected during image reconstruction. To the extent possible, place the region of interest at or near the isocenter of the magnet, where gradient field nonlinearities are minimum. 29

30 Resonance Offset Effects The effects of resonance offsets result in spatial inaccuracy in the frequency-encoded direction only. The phaseencoded information is not effected by these effects. Chemical shift effects Magnetic susceptibility effects Resonance Offset Effects - Chemical Shift The chemical shift between the water and methylene fat resonances is ~215 Hz at 1.5T, and scales linearly with B o. The difference in resonance frequency gives rise to an apparent difference in spatial location of the fat and water protons since spatial position and frequency are related in the presence of an applied gradient field. Two primary effects: Fat and water pixels are mis-registered in-plane. Fat and water excitation slices are slightly offset. Resonance Offset Effects - Chemical Shift Larmor equation: ω = γ (B o + G x x) Let δ = ω fat - ω water = chemical shift of fat relative to water. then δ = γ G x Δx, or Δx (mm) = δ / (γ G x ) = δ (FOV / BW) where BW is the total sampling bandwidth in Hz, δ is the chemical shift in Hz, and FOV is the field-of-view in mm. 30

31 Resonance Offset Effects - Chemical Shift The magnitude of the in-plane chemical shift-induced spatial errors are: Directly proportional to B o (δ scales linearly with B o ) Inversely proportional to the amplitude of the frequencyencoding gradient field (G ν ) Inversely proportional to the sampling bandwidth, since decreasing BW results in decreasing G ν (for the same FOV) Resonance Offset Effects - Chemical Shift Good news: Chemical shift induced artifacts can be eliminated by applying fat suppression techniques during image acquisition. Bad news: You may suppress some of the anatomy of interest. Fat Suppression T1W images without (left) and with (right) fat suppression. 31

32 Resonance Offset Effects - Chemical Shift In-between news: Effects can be reduced by anything that increases the amplitude of the frequency-encoding gradient, including (while keeping all other parameters fixed): decreasing the FOV increasing the sampling bandwidth increasing the frequency-encoding matrix size Each of these options, however, decreases SNR! Resonance Offset Effects - Susceptibility Magnetic susceptibility effects are patient-induced. Modified Larmor equation: B = (1 + χ) B o, where χ is the magnetic susceptibility. A concomitant χ- dependent spatial shift will occur in the image. Interfaces between two substances with differing magnetic susceptibilities result in an apparent B o inhomogeneity (ΔB = Δχ B o ). Such areas give rise to local spatial accuracy errors in the image. Resonance Offset Effects - Susceptibility Material Signal ρ (g/cm 3 ) χ (ppm/cm 3 ) Air No 0.0 H 2 O Yes Bone (Cortical) Cu(SO) 4 + H 2 O (0.12 g/ml) No Yes 3.52 Pyrex No

33 Resonance Offset Effects - Susceptibility The modified Larmor equation provides a means of calculating the theoretical error in the frequency-encoding direction, Δ ν, in terms of the frequency-encoding gradient amplitude, G ν, applied static field, B o, and Δχ: Δ ν Δχ Β ο / G ν or, if BW is the total acquisition bandwidth: Δ ν (γ Δχ Β ο FOV) / BW Resonance Offset Effects - Susceptibility The most significant errors due to susceptibility changes occur for Air/bone interface Δχ = 8.86 ppm/cm 3 Air/tissue interface Δχ = 9.05 ppm/cm 3 Only minor errors occur for Bone/tissue interface Δχ = 0.19 ppm/cm 3 For a 1.5 T scanner with G ν = 3.1 mt/m, FOV=24 cm, and 256 pixels, this gives rise to theoretical errors of Air/tissue interface Δ = 2.15 mm Bone/tissue interface Δ = 0.05 mm Resonance Offset Effects - Susceptibility Minimizing Susceptibility-Induced Effects: As in the case of chemical shift-induced spatial errors, susceptibility-induced errors can be reduced by anything that increases the amplitude of the frequency-encoding gradient, including (while keeping all other parameters fixed): decreasing the FOV increasing the sampling bandwidth increasing the frequency-encoding matrix size Again, each of these options decreases SNR! 33

34 Resonance Offset Effects - Susceptibility Various investigators have published correction algorithms to reduce the magnitude of the susceptibilityinduced errors. Field mapping-based techniques to generate error fields that are used to correct the distortions Double acquisition techniques with frequency-encoding gradient amplitudes reversed At this time, however, vendors have not incorporated such algorithms into commercial products. Image Fusion Images Courtesy of Almon Shiu, Ph.D. Practical Tradeoffs In general, the SNR equation in MRI is given by 1 SNR ρ0 δυδφδs Nυ Nφ Nave B0 f where BWsamp ρ 0 is the proton density δ υ δ φ δ s is the voxel volume (δ s is the slice thickness) N υ is the number of frequency-encoded points N φ is the number of phase-encoding steps N ave is the number of averages (NEX, NSA, etc.) BW samp is the sampling bandwidth f is a variable that depends on sequence, TE, TR, coil, etc. 34

35 Practical Tradeoffs Defining δ x as FOV x /N x, then the SNR equation can be rewritten as: FOVυ FOVφ SNR ρ0 δs Nave B0 f Nυ Nφ BWsamp In addition to this expression for SNR, we should consider the equations for resolution and scan time: T scan = TR N ave N φ δ υ = FOV υ / N υ δ φ = FOV φ / N φ Acquisition time (ideal multislice imaging) Resolution in the frequency-encoding direction Resolution in in the phase-encoding direction Example Protocols Scenario # Bo T delta_fat_water Hz FOV mm BW (total FOV) Hz Num Freq Enc Pts Num Phase Steps NEX chem shift mm susceptibility shift mm relative SNR relative tacq resolution (freq) mm resolution (phase) Note: NEX<1 implies partial Fourier reconstruction. Summary While CT typically yields images that are spatially accurate to within a pixel (~1 mm), MR images can have errors that are up to 5 times worse. MRI imaging can yield quite similar accuracy to CT if: B 0 homogeneity is optimized by shimming Gradient field calibrations and eddy current corrections are accurate 3D acquisition sequences are used, when possible, and the volume of interest is positioned as close to the isocenter of the magnet to minimize errors due to nonlinearities in the gradient fields Fat suppression is utilized, if possible, to minimize chemical shift effects The FOV is made as small as practical and the sampling bandwidth as large as possible to reduce both chemical shift- and susceptibilityinduced errors 35

36 Summary (continued) Although it is preferable to use 3D image acquisition techniques, in some cases 2D image acquisitions must be used to obtain the necessary image contrast. Examples: non-enhancing lesions may best be seen using FLAIR (fluid attenuated inversion recovery) images and 3D FLAIR imaging times can be excessive. Studies have shown that 1 mm spatial accuracy can still be obtained (over the dimensions of the human head) for 2D spin-echo, gradient recalled-echo, and FLAIR imaging sequences if the MR systems are properly calibrated and maintained and appropriate acquisition parameters are used. Even for FOVs on the order of 40 cm, ~ 2 mm spatial accuracy, or better, is achievable with appropriate choices of acquisition sequences and parameters (and a good MR QC program). QA Guidelines ACR MRI accreditation testing guidelines: Phantom Test Guidance for the ACR MRI Accreditation Program Site Scanning Instructions for Use of the MR Phantom for the ACR Accreditation Program ACR Standards ACR MRI Quality Control Manual Some general MRI references: References Questions and Answers in Magnetic Resonance Imaging, A.D. Elster, 2nd edition, Mosby, St. Louis, Magnetic Resonance Imaging, D.D. Stark and W.G. Bradley, 2nd Edition, Volume 1, Mosby Yearbook, St. Louis, Biomedical Magnetic Resonance Imaging. Principles, Methodology, and Applications. F.W. Wehrli, D. Shaw, J.B. Kneeland, eds. VCH Publishers, New York, Magnetic Resonance Imaging: Physical Principles and Sequence Design. E.M. Haacke, R.W. Brown, M.R. Thompson, R. Venkatesan. Wiley-Liss, New York,

37 Spatial Accuracy References TS Sumanaweera, JR Adler, S Napel, GH Glover, Characterization of Spatial Distortion in Magnetic Resonance Imaging and Its Implications for Stereotactic Surgery. Neurosurgery 35(4): , 1994 TS Sumanaweera, GH Glover, TO Binford, JR Adler. MR Susceptibility Misregistration Correction, IEEE Trans Med Imaging 12(2): , J Michiels, H Bosmans, P Pelgrims, et al., On the Problem of Geometric Distortion in Magnetic Resonance Images for Stereotactic Neurosurgery, Magn Reson Imaging, 12(5): , L Walton, A Hampshire, DMC Forster, AA Kemeny. Stereotactic localization with magnetic resonance imaging: A phantom study to compare the accuracy obtained using two-dimensional and three-dimensional data acquisitions. Neurosurgery 41(1): ,