1. G Practical MRI 1
Gradients

2. The Gradients

3. The Gradients Role Important components and parameters Impact
Select excited volumes
Encode spatial information
Important components and parameters
Components: gradient coils, gradient amplifiers
Parameters: gradient strength, slew rate, homogeneity volume, length
Impact
Increased imaging speed/efficiency
Improved velocity and diffusion encoding
Short TE/TR

4. The Gradient Coils B0 ∆B “Fast” spins “Slow” spins
Lauterbur & Mansfield
Nobel Prize in Physiology or Medicine, 2003

5. X, Y and Z Gradient Coils

6. Modern Gradient Coils

7. Introduction
In MRI, magnetic field gradients refer to the spatial variation of the z component of the magnetic field:

8. Introduction
In MRI, magnetic field gradients refer to the spatial variation of the z component of the magnetic field:
Gradient amplitudes are typically measured in mT/m or G/cm (10 mT/m = 1 G/cm)
When a gradient driver produces its maximal current, its associated coil produces its maximal gradient strength (h)
When a gradient driver produces its maximal voltage, the amplitude of the associated gradient field undergoes its largest rate of change, called the maximum gradient slew rate (SR)
Typical values for whole-body gradient systems are h ~ mT/m and SR ~ T/m/s

9. Useful Definitions
The product hSR (∝ max power) is a measure of the gradient system’s performance
Limit on dB/dt to avoid peripheral nerve stimulation

10. Useful Definitions
The product hSR (∝ max power) is a measure of the gradient system’s performance
Limit on dB/dt to avoid peripheral nerve stimulation
Limit on duty cycle to avoid thermal heating
With linear ramps, the rise time is r = h/SR
Gradient lobe refer to a single gradient pulse shape that starts and ends with zero amplitude
Examples of lobes include triangles and trapezoids
Gradient waveform refers to all gradient lobes on a single axis within a pulse sequence

11. Simple Gradient Lobes
The area A of a gradient lobe when plotted versus time is typically determined by the prescribed imaging parameters (e.g. FOV, matrix size, BW)
Often also the shape is determined by imaging constraints
The shortest duration gradient lobe is normally used in order to minimize timing parameters such as TE and TR
For gradient systems that use linear ramps, the simple lobe shapes with the shortest duration will be triangular or trapezoidal

12. Trapezoidal and Triangular Lobes
The ramps have maximal slope in both cases:
Bernstein et al. (2004) Handbook of MRI Pulse Sequences
We select the most efficient shape based on the gradient area:
Triangle with
Trapezoid with

13. Sinusoidal Lobes A half-sine lobe that starts at t = t0 is given by:
Bernstein et al. (2004) Handbook of MRI Pulse Sequences
Maximal slew rate is at its beginning and end:
The lobe area is:

14. Problem: Calculate the gradient amplitude and duration for a sinusoidal lobe that satisfies both the gradient amplitude and slew-rate constraints

15. Sinusoidal Lobes A half-sine lobe that starts at t = t0 is given by:
Maximal slew rate is at its beginning and end:
The gradient amplitude that satisfies both the gradient amplitude and slew-rate constraints is:
Bernstein et al. (2004) Handbook of MRI Pulse Sequences
The lobe area is:

16. Bridged Gradient Lobes
Advantages:
more compact gradient waveform
rb is less than r1 + r2
less acoustic noise
less gradient heating
less eddy currents
The plateau of the second lobe must be increased to preserve
the gradient area
Bernstein et al. (2004) Handbook of MRI Pulse Sequences

17. Any questions?

18. Frequency Encoding Gradients
Frequency encoding is employed by many pulse sequences, including projection acquisition and Fourier imaging
A frequency-encoding gradient can be applied along any physical direction
The polarity of the frequency-encoding gradient can be either positive or negative
The waveform typically consists of two portions, a prephasing gradient lobe and a readout gradient lobe
The amplitude and duration of the readout gradient lobe are related to image resolution, receiver BW, FOV and γ
In multi-echo pulse sequences (e.g. EPI) the second half of the readout gradient can serve as prephasing gradient for the subsequent readout

19. Qualitative Description
Bernstein et al. (2004) Handbook of MRI Pulse Sequences

20. Spin Echo and Gradient Echo
When the prephasing gradient is applied the spins accumulate phase (differently with location). After the 180° pulse, they will continue to accumulate phase under the influence of the readout gradient and will refocus at the echo time.
The echo is maximum when the area of
the readout gradient is equal to the area
of the prephasing lobe
If the echo coincide with the RF echo,
then off-resonance effects are minimized
In the gradient echo sequence we don’t have the refocusing pulse, so the prephasing lobe has the opposite polarity. What does this tell you about an important difference with spin-echo?
Bernstein et al. (2004) Handbook of MRI Pulse Sequences

21. Readout Gradient Design
The duration of data acquisition Tacq is determined by the receiver bandwidth ±BW and the number of k-space data points along the readout direction nx ( ∆t = sampling time)
The amplitude of the readout gradient plateau can be derived from the FOV along the readout direction Lx
Which for a constant readout gradient has a simple k-space expression
The higher the readout gradient amplitude, the smaller the FOV that can be achieved. This can be done also by reducing the receiver bandwidth: why the former approach is preferable?

22. Prephasing Gradient Design
In a full-echo acquisition (techo = Tacq/2), at techo the readout gradient area equals the prephasing gradient area (techo defines the point when the center of k-space is sampled):
Spin-echo
Gradient-echo
In gradient echo with partial-echo (readout is not applied symmetrically with respect to techo) acquisition, if nx,f points are acquired prior to the center of the echo (nx,f ≤ nx/2), before using the above equation, techo must be calculated as:
There is no requirement on the amplitude of the prephasing gradient as long as the area satisfies the equations above.
max amplitude can be used to minimize echo time (e.g. in angiography)
longer duration and smaller amplitude reduce the effect of eddy currents

23. See you next week!