Spatial Encoding in MRI PDF

Spatial encoding in MRI Nov.,26, 2024 (4th year /Medical Physics) By Dr. Manal Jabbar khalifa 1  Spatial encoding Spatial localization is based on magnetic field gradients, applied successively along different a...

Spatial encoding in MRI Nov.,26, 2024 (4th year /Medical Physics) By Dr. Manal Jabbar khalifa 1  Spatial encoding Spatial localization is based on magnetic field gradients, applied successively along different axes. Magnetic gradient causes the field strength to vary linearly with the distance from the center of the magnet. These gradients(z, y, and x) are employed for slice selection, phase encoding and frequency encoding. 2 3 4 Magnetic field gradients Spatial encoding relies on successively applying magnetic field gradients. First of all, a slice selection gradient (GSS) is used to select the anatomical volume of interest. Within this volume, the position of each point will be encoded vertically and horizontally by applying a phase encoding gradient (GPE), and a frequency-encoding gradient (GFE). Gradient equivalence in the three directions of space means that slices can be selected on any spatial plane. Representation of a slice plane and the phase encoding directions of the gradients in our example : frequency encoding slice selection 5 6 1.Slice selection gradient (GSS) Spatial encoding relies on successively applying magnetic field gradients. First of all, a slice selection gradient (SSG) is used to select the anatomical volume of interest. Z-axis 7 Factors affecting slice properties 1. RF pulse bandwidth The RF pulse bandwidth is the range of frequencies within the pulse. Large bandwidth = large range of frequencies = larger slice 2. RF pulse frequency Changing the RF pulse frequency moves the slice selected up Slice selection - Changing RF bandwidth and down the z-axis. 8  3. Gradient strength Altering the gradient strength alters the steepness of the gradient. The same RF pulse will then activate (select) a different size of slice Larger gradient = smaller image slice Smaller gradient = larger image slice Slice selection - gradient strength Summary 1.A magnetic field gradient is applied in the z-axis 2.The Larmor frequencies of the nuclei vary along the z-axis 3.An RF pulse with a frequency matching the Larmor frequency of the nuclei we want to select is applied 4.In this way, a slice along the z-axis is selected (correlates with an axial slice of the patient) 5.The phases of the nuclei are reset by reversing the gradients 9  2. Phase encoding The second step in spatial encoding consists in applying a phase encoding gradient, which we will choose to apply in the vertical direction. The phase encoding gradient (PEG) intervenes for a limited time period. While it is applied, it modifies the spin resonance frequencies, inducing Y-axis dephasing, which persists after the gradient is interrupted. This results in all the protons precessing in the same frequency but in different phases. The protons in the same row, perpendicular to the gradient direction, will all have the same phase. This phase difference lasts until the signal is recorded. 10 on receiving the signal, each row of protons will be slightly out of phase. This translates as their signals being more or less out of phase. To obtain an image, it is necessary to multiply the different dephased acquisitions, which are regularly incremented. 11  3.Frequency encoding Read-out gradient We have now selected a slice by applying a gradient in the z-axis. Should we want to select a section of the slice in the x-axis (i.e a column), all nuclei along the x-axis of the slice will have different amplitudes X-axis (indicating different brightness values) but they will have the same frequency and phase. Adding all the signals together results in one large wave of the same frequency. This is of no use if we want to localise the signal in the x- axis as all locations will have the same frequency. 12  As this gradient is applied simultaneously on receiving the signal, the frequency data is included. Summary 1.Gradient applied in z-axis to select axial slice 2.Dephase gradient applied along x-axis 3.Rephase read-out gradient applied along x-axis 4.Gradient echo signal received (combination of all signals along the x-axis) 5.Fourier transfer applied to combined signals 6.Signals separated out by frequency: 1. Each frequency relates to location along x- axis 2. Each frequency’s amplitude gives the signal brightness 13  3D spatial encoding The excitation of a complete volume at each repetition (volume = « thick slice »), rather than one thin slice spatial encoding in 3D by adding phase encoding in the 3rd dimension in relation to the phase and frequency encodings used in 2D imaging multiplication of the number of repetitions of a factor equal to the number of « slices» (partitions) in the third particularities of 3D acquisitions are: dimension to fill all the 3D k-space reconstruction by 3D Fourier transform. Duration of a 3D imaging sequence 14 15  Question 2. What is the role of the magnetic field gradients in MRI? The primary function of gradients is to allow spatial encoding of the MR signal. 16  Resolving the Third Dimension Frequency Encoding B H H Review of Spatial Resolution: H H 1. Apply slice selection gradient and choose a slice based H on precession frequency. H H H 2. Apply and turn off phase encoding gradient. This H H gets hydrogen in the x-axis out of sync. H H 3. Apply a third gradient, now we can distinguish hydrogen in the y-axis based on the precessional H H H H speeds. Slice plane y z x 17 -We have now resolved all three dimensions! But now , what do we do with all this info….? 18  Fourier’s Transform Fourier transform The pick up coil (RF coil) receives many different The 1D Fourier transform is a frequency oscillations. mathematical procedure that Use Fourier’s Transform to process the data. allows a signal to be decomposed into its frequency components. 1.5 1.5 Signal Strength Signal Strength 1 Transform 1 Time [s] 4 0.25 0.5 1.0 Frequency [Hz] -1 f = 1/T = ¼ =.25 -1.5 f = 1/T = ½ =.5 19 f = 1/T = 1/1 = 1 Fourier Transform The pickup coil does not distinguish between the input of each hydrogen. They are all read together, and constructively and destructively interfere. Fourier’s allows us to determine which frequencies are along the axis. For instance, if there are two hydrogen at different frequencies along an axis: 1 1 1 Signal Strength 4 Current Time [s] + Time [s] = Time [s] 4 4 -1 -1 -1 Signal Strength 1 1 1 Fourier 0.25 0.25 0.25 0.25 1 0.25 1 20 Frequency [Hz] Frequency [Hz] Frequency [Hz] 2D Fourier Transform Recall that the second axis is resolved with a phase encoding gradient. These hydrogen have the same frequency, but interfere with each other due to phase shift. Signal Strength 1 1 1 4 + 4 = 4 Time [s] - - - 1 1 1 ◼ A 1D Fourier Transform cannot distinguish between shifted phases. ◼ But if we take the Fourier Transform again, orthogonal to the first access the phase encoding gradient can be distinguished! ◼ The resulting data is known as a K-Space. 21 2D Imaging via 2D Fourier Transform 1DFT 1D Signal 1D “Image” 2DFT ky y kx x 2D Signal 2D Image  K-Space A 2D Fourier transform is conducted by performing two Fourier transforms orthogonal to each other. This yields a “K-Space” An example is seen on the right. The “K-Space” undergoes an Inverse Fourier Transform. Following this mathematical step, we finally have an image. 23 http://www.revisemri.com/tutorials/what_is_k_space/what_is_k_space_files/fullscreen.htm Sampling k-space x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x FT x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Perfect reconstruction of an object would require measurement of all locations in k-space (infinite!) Data is acquired point-by-point in k-space (sampling) Sampling k-space kx ky kx 2 kxmax 1. What is the highest frequency we need to sample in k-space (kmax)? 2. How close should the samples be in k-space (k)?