Pulse sequences

The package mainly revolves around two pulse sequences for diffusion encoding with either

1. monopolar, or

2. bipolar diffusion encoding gradients.

For these pulse sequences one can calculate the b-value (API)

\[b = p \gamma^2G^2\delta^2(\Delta-\frac{\delta}{3})\]

where p takes values 1 for a monopolar pulse sequence and 2 for a bipolar pulse sequence, \(\gamma\) is the gyromagnetic ratio, G is the gradient strength, and \(\delta\) and \(\Delta\) are the duration and separation of the gradient pulses.[1]

In a similar way, the c-value (flow sensitivity) can be calculated (API)

\[c = p \gamma G\delta\Delta\]

Note that the equation above applies for non-flow-compensated diffusion encoding.[2]^,[3] For a flow-compensated diffusion encoding, c = 0 by design.[4]

The module also provides functions for calculating the gradient strength given a b-value (API) and generation of cval files similar to the commonly used bval files (API).

References:

[1]

Le Bihan D, Breton E, Lallemand D, Grenier P, Cabanis E, Laval-Jeantet M. MR imaging of intravoxel incoherent motions: application to diffusion and perfusion in neurologic disorders. Radiology. 1986;161(2):401-407. doi: https://doi.org/10.1148/radiology.161.2.3763909

[2]

Le Bihan D, Breton E, Lallemand D, Aubin ML, Vignaud J, Laval-Jeantet M. Separation of diffusion and perfusion in intravoxel incoherent motion MR imaging. Radiology. 1988;168(2):497-505. doi: https://doi.org/10.1148/radiology.168.2.3393671

[3]

Kennan RP, Gao JH, Zhong J, Gore JC. A general model of microcirculatory blood flow effects in gradient sensitized MRI. Medical Physics. 1994;21(4):539-45. doi: https://doi.org/10.1118/1.597170

[4]

Ahlgren A, Knutsson L, Wirestam R, Nilsson M, Ståhlberg F, Topgaard D, Lasic S. Quantification of microcirculatory parameters by joint analysis of flow-compensated and non-flow-compensated intravoxel incoherent motion (IVIM) data. NMR in Biomedicine. 2016;29(5):640-649. doi: https://doi.org/10.1002/nbm.3505

API

ivim.seqs.lte

ivim.seq.lte.calc_b(G: ndarray[Any, dtype[float64]], Delta: float, delta: float, seq: str = 'monopolar') → ndarray[Any, dtype[float64]]

Calculate b-value given other relevant pulse sequence parameters.

Parameters:

• G – gradient strength [T/mm] (Note the units preferred to get b-values in commonly used unit)

• Delta – gradient separation [s]

• delta – gradient duration [s]

• seq – (optional) pulse sequence (monopolar or bipolar)

Output:

b: b-value [s/mm²]

ivim.seq.lte.calc_c(G: ndarray[Any, dtype[float64]], Delta: float, delta: float, seq: str = 'monopolar', fc: bool = False) → ndarray[Any, dtype[float64]]

Calculate c-value (flow encoding) given other relevant pulse sequence parameters.

Parameters:

• G – gradient strength [T/mm] (Note the units preferred to get b-values in commonly used units)

• Delta – gradient separation [s]

• delta – gradient duration [s]

• seq – (optional) pulse sequence (monopolar or bipolar)

• fc – (optional) specify is the pulse sequence is flow compensated (only possible for bipolar)

Output:

c: c-value [s/mm]

ivim.seq.lte.G_from_b(b: ndarray[Any, dtype[float64]], Delta: float, delta: float, seq: str = 'monopolar') → ndarray[Any, dtype[float64]]

Calculate gradient strength given other relevant pulse sequence parameters.

Parameters:

• b – b-value [s/mm²]

• Delta – gradient separation [s]

• delta – gradient duration [s]

• seq – (optional) pulse sequence (monopolar or bipolar)

Output:

G: gradient strength [T/mm]

ivim.seq.lte.cval_from_bval(bval_file: str, Delta: float, delta: float, seq: str = 'monopolar', cval_file: str = '', fc: bool = False) → ndarray[Any, dtype[float64]]

Write .cval based on .bval file and other relevant pulse sequence parameters.

Parameters:

• bval_file – path to .bval file

• Delta – gradient separation

• delta – gradient duration

• seq – (optional) pulse sequence (monopolar or bipolar)

• cval_file – (optional) path to .cval file. Will use the .bval path if not set