Magnetic Field Gradients Spatial information is obtained by the application of magnetic field gradients (i.e. a magnetic field that changes from point-to-point).
Gradients are denoted as Gx, Gy, Gz, corresponding to the x, y, or z directions. Any combination of Gx, Gy, Gz can be applied to get a gradient along an arbitrary direction (gradients are vector quantities).
Depending on the gradients function, these gradients arecalled Slice-select gradient The read or frequency-encoding gradient The phase-encoding gradient
Slice Selection GradientGradient coils provide a linear variation in Bz with position.Result is a resonant frequency variation with position.w = g (B0 + Bz)
Selective ExcitationFrequencyMagnitudeTimeRF AmplitudePositionSlope = 1g GFrequencyRF Pulse (Resonance Freq and Bandwidth)Slice
(position &thickness) Thickness = BW/Bz
RF Pulse for ExcitationThe bandwidth of an RF pulse depends on its length and shape. Fourier Transform of a RF pulse displays bandwidth.
A RF pulse with a sinc profile is commonly used in MRIfor slice selection.
After having defined a slice through the subject, we need to resolve features along the other two directions (x and y) using frequency-encoding (along x) and phase encoding (along y)A smallest volume element in this slice is called a voxel.
The frequency encoding gradient is applied when we read-out signals
Image Acquisition Gradient causes resonant frequency to vary with position.Receive sum of signals from each spin.
Image ReconstructionReceived signal is a sum of tones.The tones of the signal are intensities of objects.This also applies to 2D and 3D images.FourierTransformReceived SignalFrequency(position)
Phase EncodingPhase encoding resolves spatial features in the vertical direction (y) by using the phase information of precessing spins. To get enough data to make an image, we need to repeat the phase encoding process many times, each time with a different strength of phase encoding to impart a different phase angle to the voxel.
Number of Phase Encoding StepThe # of phase encoding steps = # of rows in image (i.e. the resolution in the y-direction).The phase shift between adjacent rows is Dq = 360 / # rows
Pulse SequencesExcitation and imaging are separate.Pulse sequence controls:RF excitationGradient waveformsAcquisitionReconstruction information as well.
1D-Pulse Sequence Detailed!RFGzGxAcq.Phase, Modulation FrequencyFinite amplitude, slew rate Demodulation frequency, phase Sampling rate and duration
2-D Image SequenceRFGzGxAcq.ExcitationReadoutGyPhase-encoding
2D Image ReconstructionFrequency-space(k-space)Image spaceFT(phase-encoding)readout
ResolutionImage resolution increases as higher spatial frequencies are acquired.
k-Space Trajectories2D FourierTransformEcho-PlanarSpiral
Get rid of the equation??Probably nix this slideDo we want to animate these??Perhaps omit this / Replace with K-space Image space slide.