MRI image formation Indiana University School of Medicine and Indiana University Health Disclosure No conflict of interest for this presentation 2 Outlines Data acquisition Spatial (Slice/Slab) selection Spatial encoding (using frequency and phase) Image reconstruction K-space Fourier Transform Signal-to-noise ratio Signal intensity Source of noise 3 1
Free Precession f = γb 0 B 0 M 4 Excitation f RF = f M B 0 B 1 B 1 M 5 Signal f = γb 0 B 0 S(t) = Ae i[2πft+φ 0 ] T2* M t 6 2
Chemical Shift (CS) f = γb 0 + CS B 0 M t 7 SPATIAL SELECTION AND ENCODING 8 Slice/Slab Selection Gradient Tx Frequency Water 9 3
Slice/Slab Selection Gradient Tx Frequency Water 10 Slice/Slab Selection Gradient Tx Frequency RF TxBW Water Fat 11 TxBW (~ 2kHz) Slice/Slab Selective Excitation Tx Frequency Thin Slice Gz Tx Offset Thick Slice 12 4
Rx Band Width (RxBW) Rx Band Width (RxBW) 8/3/2016 Slice Selective Excitation and Refocusing https://www.imaios.com/en/e-courses/e-mri/magnetic-resonance-spectroscopy-mrs/single-voxel-spectroscopy 13 Frequency Encoding Gradient Rx Frequency S(t) = ΣA x e i(2πγxg xt) t Water 14 Frequency Encoding Gradient Rx Frequency Water Fat 15 5
Frequency Encoding Implementation Rx Frequency RxBW / FOV x -> G x RxBW (+/- 8 128 khz) FOV x (in Frequency Encoding direction) 16 Precession Frequency Phase Encoding Phase diff. φ = 0 t=0 17 Phase Encoding Gradient Precession Frequency Phase diff. φ = 0 t=0 18 6
Phase Range (0 2p) Phase Encoding Steps (N phase = 4) 8/3/2016 Phase diff φ t = τ Phase Encoding Gradient S(t ) = ΣA y e i(2πγyg yτ) φ(y) = g y G y t t G y Fat 19 Phase Encoding Implementation τgy 1 S = S k e iφ k (τgy 1 ) τgyn S = S k e iφ k (τgyn) 20 Spatial Selection and Encoding in 2D MRI G z G y G x k y k x Frequency Encoded Points (N Freq = 8) 21 7
Frequency Encoding Chemical Shift Artifact http://mri-q.com/chemical-shift-artifact.html 22 Chemical Shift Artifact in SS-EPI G x G y E1 E2 E3 E4 E5 E6 GRE Train (~64) Phase Encoding Blips Without FatSat With FatSat 23 Frequency and Phase Encoding Each encoded data point is a Fourier series. Frequency encoding More efficient, no aliasing (using a low pass filter) Frequency Encoding typically used in the direction of higher resolution or greater coverage Chemical shift artifact (can be minimized with high RxBW) Phase encoding More time consuming (N PE * TR), does improve SNR Can be used more than once 24 8
Spatial Selection & Encoding Heavily rely on the imaging gradients Gradient non-linearity -> Spatial distortion Gradient performance -> Acquisition time and min. FOV Gradient stability -> Artifacts Any combinations of the three orthogonal physical gradients can be used for spatial selection or encoding 25 K-SPACE AND FOURIER TRANSFORMATION 26 K: Wave Number or Wave Index I I I I I x x x x x K= 0 1 2 3 4 I Image Space I K Space x 0 1 1 K x 27 9
2D Image <-> 2D K-space K y K x 28 k-space <-> Image space Magnitude K-space FT Image space Phase 29 Information in K-space Inner k-space (Low spatial freq.) -> Intensity/Contrast. Outer k-space (High spatial freq.) -> Edges/Details. K-space resolution (DK) -> Image FOV. K-space range (K max ) -> Image resolution. Symmetry -> Allows partial k-space acquisition. 30 10
SIGNAL-TO-NOISE RATIO (SNR) 31 Signal and Noise Proton Density (PD) Voxel size (Dx Dy Dz) Field Strength (B 0 ) Receiver coil sensitivity Sequence type and parameters Relaxation Properties. Averages (NE) Patient / Object. Components (receiver coils & electronic components) in receiving chain. 32 Noise and K-space filter Noise in MRI Stochastic Process / thermal motion of electrons White noise High SNR Low SNR Intensity Signal (Limited BW) Noise (Wide BW) 0 K Low-pass filter 33 11
Signal to Noise Ratio (SNR) SNR: Signal / Noise Signal: Average of pixel intensity (in a signal region) Noise: Fluctuation (Stdev ) of pixel intensity (in a noise region) SNR ~ f(sequence Type, FA, TR, TE, TI ) * PD B 0 Dx Dy Dz ( N phase * NE / rbw ) 1/2 Scan time = N phase * NE * TR SNR Efficiency = SNR / Scan Time Contrast to Noise Ratio (CNR) = S Tissue1 S Tissue2 / Noise 34 Thank you! clin1@iupui.edu 12