Velocity Encoding#

This module contains functions defining compositions of building blocks commonly used in flow MRI

Functions:

bipolar(system_specs, venc, direction[, ...])

Simplified definition of a bipolar M0-compensated gradient waveform:

flow_comp(system_specs, venc_eff, direction)

Defines a sequence of concatenated trapezoidals with flow-compensation over the full duration.
bipolar(system_specs, venc, direction, duration=<Quantity(0.0, 'millisecond')>, repetitions=1, start_time=<Quantity(0.0, 'millisecond')>)#

Simplified definition of a bipolar M0-compensated gradient waveform:

.                      | Delta |                        .
.                      _____________   _______              .
.                     /             \         |             .
.                    / |             \        G             .
.                   /  |              \       |             .
.                  /   |               \ _____|             .
.                 |    |                                    .
.                  delta                                    .
\[\begin{split}M1 =& (3 \delta \Delta + \Delta^2 + 2 \delta^2) G \\ \delta =& G/s_{max} \ \ (use\ max\ slew) \\ 0 \stackrel{!}{=}& G\Delta^2 + \frac{3G^2}{s_{max}} \Delta + \frac{2G^3}{s_{max}^2} - M1\end{split}\]

Solve the quadratic equation to obtain the flat duration \(\Delta\)

Example Plots
../_images/bipolar_venc.svg
Parameters:

  • system_specs (SystemSpec) – SystemSpecifications

  • venc (Quantity) – Quantity[Length/Time] velocity that corresponds to a phase accrual of 2pi

  • direction (ndarray) – Vector (3, ) denoting the direction of velocity encoding

  • duration (Quantity) – Quantity[Time] denoting the duration of applied VENC-gradients. If 0. the resulting gradients will be the shortest for given system limits

  • repetitions (int) – number of repetitions

  • start_time (Quantity) – Quantity[Time]

Return type:

Sequence

Returns:

sequence object

flow_comp(system_specs, venc_eff, direction, period=<Quantity(0.0, 'millisecond')>, repetitions=1, start_time=<Quantity(0.0, 'millisecond')>)#

Defines a sequence of concatenated trapezoidals with flow-compensation over the full duration.

Example Plots
../_images/flow_compensated.svg
Parameters:

  • system_specs (SystemSpec) –

  • venc_eff (Quantity) –

  • direction (ndarray) –

  • period (Quantity) –

  • repetitions (int) –

  • start_time (Quantity) –

Return type:

Sequence

Returns: