Introduction to Biomedical Imaging
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1 Alejandro Frangi, PhD Computational Imaging Lab Department of Information & Communication Technology Pompeu Fabra University
2
3 MRI advantages Superior soft-tissue contrast Depends on among others proton density, relaxation times 3D acquisitions possible Free orientation of tomographic scan planes No ionizing radiation No iodinated contrast agent Non-invasive Imaging of anatomy/pathology and function
4 MRI Principle Based upon: nuclear magnetic resonance Resonance phenomenon of nuclear spins (magnetic moments of atomic nuclei) in a strong external magnetic field A rotating charge has an electromechanical momentum (μ) which has a direction coincident with the rotation axis and a magnitude proportional to the angular momentum of electrons and protons by the expression The electromechanical momentum is known as nuclear spin In the presence of an external magnetic field (B) all spins line up with it yielding a net macroscopic moment (M); otherwise they are randomly distributed with no net macroscopic momentum Not all atoms have a zero spin. The spin is non-zero when the atom has an odd number of protons or nucleons (p is odd or p+n is odd) Practically speaking a spin can be seen as a kind of elemental magnet Most important proton in the human body is Hydrogen
5 Precession Spins presses around the direction of the external field (Bo) at a frequency (Larmor frequency) proportional to Bo The proportionality constant is known as gyro magnetic constant For hydrogen, γ = MHz / T Magnetic Resonance Imaging ω =γb o From quantum mechanics it seems that only a limited number of spin states are possible (each with their own energy). E.g.: for H only ± 1/2
6 Net magnetization The spins altogether form a net magnetization vector M M depends on the external field and the temperature
7 Resonance phenomenon Magnetization can be flipped toward the xy-plane by adding energy to the system by applying an RF pulse at the Larmor frequency M-vector rotates toward the xyplane over an angle θ (flip angle) θ=γ Bdt 1
8 Situation before RF pulse Longitudinal vs. transverse magnetization After RF pulse only longitudinal magnetization (Mz) Mz is static and, hence, cannot produce induction signal
9 Situation after RF pulse RF perturbs the magnetization vector Both longitudinal (Mz) and transverse (Mxy) components exist Mxy component rotates at Larmor frequency M is now time-varying and an induction signal can be measured with a receive coil (Free Induction Decay FID)
10 Relaxation processes The perturbation of the magnetization has a limited life-time Relaxation returns M to its original (lower energy) state (exponentially) Longitudinal relaxation increases Mz to M T1 relaxation constant M t M e z t/ T1 () = (1 ) o Transverse relaxation reduces Mxy to zero T2 relaxation constant M () t = M e xy o t/ T 2 The increase of Mz can be slower than the decrease of Mxy The nature of T1 and T2 relaxations is different! T1 is related to spin-lattice interactions (between H protons and its surroundings) T2 is related to spin-spin interactions (between protons themselves) They depend on molecular structure, physical state (solid or liquid), temperature, external field strength, T1 [ms] T2 [ms] Fat WM GM
11 Why is MR becoming so important? Provides nice contrast between soft tissues (vs. hard/soft tissue contrast in CT) Each tissue has characteristic MR properties T1, relaxation time for Mz T2, relaxation time for Mxy Proton density This allows to obtain application-specific tissue-contrast by designing appropriate RF pulse sequences Provides additional possibilities through flow-dependent phenomena or using saturation pulses
12 Free Induction Decay (FID) RF pulse creates transverse magnetisation Mxy Precession of transverse magnetisation at Larmor frequency Amplitude of Mxy is initially dependent on proton density Signal decays exponentially with time constant T2* Signal can be measured using receive coil: Free Induction Decay (FID)
13 Measurement Strategy Free induction decay Hard to measure (directly after the RF pulse) Fast decay (T2*) For imaging: echo techniques Signal is recalled after some time (echo) Two methods: Spin echo techniques Gradient (recalled) echo techniques
14 Spin Echo Magnetization is flipped to transverse plane through a RF pulse Dephasing due to local field inhomogeneities Inversion pulse (180º) for spin refocusing at TE/2 TE = echo time Spin rephasing First echo is recalled thus reconstructing the FID TE
15 MR image formation Main scanner components Magnet: constant main magnetic field Bo Gradient coils: fields that vary in space RF coils: for transmitting and receiving RF signals
16 Image formation Static field gives a net magnetization RF pulse excites nuclei and creates transverse magnetization Spatial encoding of the signal using gradient fields Echo read-out (using receive coil) Magnetic Resonance Imaging Reconstruction of image from measured echoes (mostly Fourier reconstruction) Pulse sequence Series of events in time: sequence Pulse sequence contains components necessary to produce an MR image Components: RF pulses, gradients, echo sampling Nature and order of components determines kind of scan: sequence design Spatial encoding Slice selection Frequency encoding Phase encoding Localization if based upon the fact that spins presses at the Larmor frequency, which depends on the local value of the magnetic field B
17 Spatial encoding: slice selection The excitation pulse can be selective or non selective S: Only spins in a given slice are excited NS: All spins covered by the transmit coil are excited Thickness and location of slice are determined by the bandwidth of the RF pulse and gradient in direction of slice selection Slice selection Gradient field encodes space in frequency Larmor frequency depends on local strength of magnetic field B: f ~ B RF excitation pulse has finite bandwidth Spins within a limited range of frequencies are excited: selective excitation Slice thickness: determined by the shape of the pulse (bandwidth) and the gradient strength
18 Spatial encoding: slice selection Gradient field causes dephasing within the slice An inversion pulse is applied to achieve rephasing and thus yield maximal signal Selection and rephasing lobes
19 Spatial encoding: frequency encoding (also read-out gradient) Magnetic Resonance Imaging By applying a gradient Gx along the x-direction, every position along the x-axis is associated with its own unique Larmor frequency: frequency encoding The Fourier transform of the detected signal is a projection onto the x-axis The amplitude of each frequency component is proportional to the summed signal in the y-direction for that x position By repeated rotation and application of the readout gradient, spatial information in more than one direction can be obtained Lauterbur used this technique in combination with backprojection reconstruction to generate the first MR images
20 Spatial encoding: frequency encoding Magnetic Resonance Imaging Signal has now been encoded in slice (z) en frequency (x) directions A third gradient is needed for full localization Phase encoding gradient is kept on for a certain duration Precession at different frequencies during that period of time gives different phases along the gradient direction: phase encoding
21 Spatial encoding: phase encoding Combination of frequency and phase encoding gives spatial signal encoding in 2D plane First step: phase encoding (y gradient) Between excitation and echo read-out Second step: frequency encoding (x gradient) Gradient switched on during echo read out (a.k.a. read out gradient) Image formation using Fourier transform on all acquired echo data Data collection: sampling With the frequency encoding gradient switched on (here: x-direction) Nx data points are sampled (digitized echo read-out) Read out is performed for all Ny phase encoding steps: Ny phase encoding steps give Ny echos Result Nx Ny data points per slice: MATRIX This signal matrix exists in so-called k-space 2D Fourier transform used to reconstruct an image from k-space
22 Spatial encoding All spins have same precessional frequency
23 Spatial encoding Apply Phase Encoding Gradient Slower Unchanged Faster
24 Spatial encoding After Phase Encoding Gradient is turned off All spins have same frequency again, but different phase
25 Spatial encoding Apply Frequency Encoding Gradient Faster Unchanged Slower
26 K-space k-space contains raw scan data (sampled data points) In 2D x-direction in k-space is frequency encoding: measured echoes y-direction is phase encoding direction (gradient strength during phase encoding)
27 K-space: interpretation K-space is the Fourier domain of the target image Trivial reconstruction: Inverse Fourier Transform
28 K-space: interpretation Duality between image and k space Field of View (FOV)
29 K-space: interpretation K-space allows to think in terms of frequency content
30 K-space: interpretation Low frequencies = image contrast
31 K-space: interpretation High frequencies = image details and edges
32 K-space filling strategies By thinking in terms of frequency content one can devise non linear filling strategies which can have advantages in certain applications Warning! These strategies may impose hardware constrains as the field gradients may need to switch very fast (slew rate limitations) Standard Echo planar imaging (EPI) Interleaved EPI Spiral Scanning
33 3D Imaging Concept of spatial localization can be expanded to 3D by adding an extra phase encoding in the slice direction Thick slab volume excitation is used
34 Angiographgy
35 MR Scanners
36 MR Coils Brain coil General purpose flex coil Torso coil Split head coil Extremity coil
37 MR Scanner Console
38 MR Images
39 MR Images
40 References & Acknowledgements References Amersham Health Basics of MRI - Joseph P. Hornak Basic Principles of MR Imaging Philips Medical Systems Medical Imaging D. Liley Acknowledgements for some material used in these lectures ImPACT Magnetic Resonance Imaging W. Bartels
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