OSRT MRI Seminar February 2019 Barry Southers M

OSRT MRI Seminar February 2019 Barry Southers, M. Ed, RT(R)(MR)

Spatial Encoding and Data Collection

Spatial Encoding • • MRI Gradients Coils of wire Adjust for shim of magnet Alter and influence magnetic field so that each signal can be related to an exact location • X, Y, and Z directions

Spatial Encoding • All three gradients help create images in: • Axial • Coronal • Sagittal • Oblique

Spatial Encoding Axial Oblique Coronal Sagittal Images from http: //www. med. harvard. edu/AANLIB/cases/case. NA/pb 9. htm and http: //www. ajnr. org/cgi/reprint/22/6/1149

Spatial Encoding • Gradients responsible for spatial encoding – Determining where signal is coming from within patient

Spatial Encoding # of phase encoding steps is our PHASE MATRIX #of frequency data points per PE step is our FREQUENCY MATRIX This makes up our image resolution!

Spatial Encoding • MR system must be able to locate signal spatially in three dimensions • Necessary to position each signal at the correct point on the image • First, a slice is located • Next, the signal is located, or encoded, encoded along both axes of the image • These tasks are performed by gradients

Encoding and the gradients Plane Slice selection Frequency encoding Phase encoding Sagittal X Z Y Axial (body) Z X Y Axial (head) Z Y X Coronal Y Z X

Spatial Encoding Gradient adds to the magnetic field Gradient subtracts from the magnetic field Gradient field interacts with B 0 so that the magnetic field strength along axis of gradient coil is altered linearly

Spatial Encoding Precessional frequency of magnetic moments decrease according to Larmor equation 1. 2. 3. Precessional frequency of magnetic moments increase according to Larmor equation When a gradient is switched on, the magnetic field along its axis is sloped or graded Precessional frequency of magnetic moments increase/decrease according to Larmor equation This depends on the magnetic field strength they experience along different points of gradient axis

Spatial Encoding Precessional frequency of magnetic moments decrease according to Larmor equation Precessional frequency experienced by nuclei along axis of gradient can be predicted – this is spatial encoding Precessional frequency of magnetic moments increase according to Larmor equation

Spatial Encoding

Spatial Encoding • Slope of gradient is the amplitude of magnetic field gradient and determines rate of change of the magnetic field along that gradient’s axis • Steep gradient slopes alter magnetic field more than shallow gradient slopes • Steep gradient slopes alter precessional frequency of nuclei more than shallow gradient slopes

Slice selection • When a gradient is switched on, the magnetic field along its axis is sloped or graded • Precessional frequency of magnetic moments increase/decrease according to Larmor equation • This depends on the magnetic field strength they experience along different points of gradient axis

Slice selection • Therefore, a specific point along the axis of gradient has a specific precessional frequency • Therefore, nuclei within a designated slice have specific precessional frequencies • A slice can be selectively excited, by transmitting RF with a band of frequencies coinciding with the precessional frequencies of spins in a particular slice (this is defined by slice select gradient)

Slice selection • Resonance occurs within that particular slice because RF appropriate to that position is transmitted • Nuclei within other slices DO NOT RESONATE…. WHY? • Their precessional frequencies are different due to the presence of gradient (with gradient being sloped and altering magnetic field strength, precessional frequencies will be different depending on location)

Phase/frequency encoding • MR image consists of a matrix of pixels – # of lines filled in k-space (phase matrix) – # of data points within each line (frequency matrix)

Phase encoding • Signal must be located along short axis of anatomy – this is called phase encoding • When phase encoding gradient is switched on, magnetic field strength/precessional frequency of nuclei is altered along gradient axis – Nuclei that have sped up due to presence of gradient move further around their precessional path – Nuclei that have slowed down due to presence of gradient move further back around their precessional path

Phase encoding

Phase encoding • Watch analogy: • Imagine a watch telling time at 12 o’clock being equivalent to the phase of a magnetic moment of nucleus in B 0 • Phase encoding gradient is then switched on • Magnetic field strength, precessional frequency, and phase of magnetic moments of nuclei change according to position along gradient axis

Phase encoding • Magnetic moments experiencing lower field strength LOSE phase (move further back around the watch to say 8 o’clock) – They travel slower when phase encoding gradient is switched on

Phase encoding • Magnetic moments experiencing higher field strength GAIN phase (move further around the watch to say 4 o’clock) – They travel faster when phase encoding gradient is switched on

Phase encoding • There is now a phase difference or (phase shift) among magnetic moments of nuclei along gradient axis • When gradient is switched off, magnetic field returns to main magnetic field strength • When gradient is switched off, precessional frequencies return to Larmor Frequency

Phase encoding • Their phases (or positions) are now different because of gradient being previously on • These differences are used to determine their position along phase encoding gradient

Frequency encoding • Once slice has been selected, signal from slice must be located along both axes (long and short axes) of image • Signal from long axis of anatomy is located by frequency encoding • Done by frequency encoding gradient

Frequency encoding • When frequency encoding gradient is switched on, magnetic field strength along axis of gradient is altered linearly • Precessional frequency of signal is therefore altered • Gradient produces frequency difference along its axis • Signal can then be located along its axis according to its frequency in a particular slice

Frequency encoding

Receive Bandwidth and Sampling • Enough frequencies must occur during readout to achieve sufficient data points • This is determined by receive bandwidth (r. BW) – This is band of frequencies to be sampled or digitized during readout – Center frequency is selected, then defines the upper/lower limits of frequencies to be digitized on both sides of center frequency of echo – Receive bandwidth determines # of frequencies available to be digitized during readout

Receive Bandwidth and Sampling • The Nyquist theorem: – Tells us how fast to sample when several frequencies are to be digitized – Relevant in MRI because echo contains many different frequencies – The Nyquist theorem states that “in order to adequately sample a signal, it must be sampled twice at its highest frequency” (i. e. , sampling frequency must be at least twice the highest frequency in signal)

Receive Bandwidth and Sampling • Based on the Nyquist theorem, the sampling frequency must be twice as high as the r. BW

Sampling • Receive Bandwidth Example: • if 256 frequency samples are collected (i. e. 256 frequency matrix) and the readout or sampling time is 8 milliseconds, then frequencies in the signal are sampled once every 0. 00003125 s, or a sampling frequency of 32 KHz (32, 000 Hz) • 256/0. 008 s = 32, 000 Hz • According to Nyquist theorem, this is twice the highest frequency in the receive bandwidth, so r. BW is what? • 32 KHz, or 32, 000 Hz, or highest freq is 16, 000 Hz