_{1}

^{*}

Purpose: Recently it was demonstrated that spin-locking (SL) effects can manifest as pseudo magnetization transfer (MT). To our best knowledge the MT models proposed so far cannot distinguish between saturation effects caused by the MT preparation pulses and SL phenomena. Therefore a new MT model is proposed. Materials and Methods: A binary spin-bath model for magnetization transfer was extended in that sense that SL effects are considered. The new modified spin bath model was tested for a phantom with different agar concentrates (2%, 4%, 8%) and a MnCl
_{2} (0.3 mM) solution. Results: The mean fitting error is 3.2 times lower for the modified model compared to the original model. Especially the parameter F for the fractional part of the bounded proton pool describes the situation for the MnCl
_{2} (F = 0) better than the original model (F = 0.004). Conclusion: The proposed mathematical modifications of the binary spin-bath model considering SL seem to be a step in the right direction in that sense that the effects associated with SL are not interpreted as magnetization transfer.

The magnetization transfer (MT) contrast [

In this technical note the original spin-bath model proposed by Sled was extended in that sense that SL effects are considered. The new modified spin bath model was tested for a phantom with different agar concentrates (2%, 4%, 8%) and a MnCl_{2} (0.3 mM) solution.

The magnetization transfer is described by a system of modified Bloch Equations (1)-(3). As this system is not analytically solvable, Sled proposed a 3-step-strategy divided in a phase of instantaneous saturation of the free pool, the free precession of the free pool and the continuous saturation of the bounded pool. This procedure enables to decouple the transversal magnetization of the free pool from the other components. We follow this approach and start with the description of the longitudinal magnetization assuming that the transversal components are zero at the end of a pulse period

where

Equation (6) has the solution

In the context of the original model (1 - 5) a significant reduction of the signal intensities for off-resonance frequencies greater than 500 Hz (no direct saturation) would be interpreted as magnetization transfer effects. To avoid this, the new model must consider the spin-locking (SL) related changes of the z-component in equation (2):

The coupling parameter

In matrix form the differential equation system (1, 11) can be written as:

(bold type expresses matrices and vectors) where

The effect of both the MT pulse and the excitation pulse on the free pool is modelled as an instantaneous fractional saturation

in which

The general solution of (12) is

From the periodicity property of the sequence

The steady state magnetization

With

Nonlinear fitting was performed with a Levenberg-Marquardt algorithm within a Matlab (R2014a) framework.

The free fitting parameters are

setting 60uT.

The sequence is a 2D-FLASH sequence. The sequence parameters are as follows: flip angle 540 degree (MT preparation pulse), 15 degree (excitation pulse), 30 slices, gap 0, voxel size = 2 mm isotropic, 10 frequency samples, matrix size = 128, TR/TE = 30/4.8 ms, BW = 390 Hz/Px.

Imaging was performed on a 3.0Tesla whole body scanner. The phantom (

The mean MT-effects for Agar 8%, 4%, 2%, MnCl_{2} according to the intensity values listed in

In _{SL} is not considered as a free adjustable degree of freedom but if it is set to a constant (e.g. 1, assuming the spin locking is generally present).

Numerical post processing according to the original model provides F values 200 ± 2.3, 100 ± 3.3, 45 ± 5.9,

MT meas MT fit | meas-fit |

41 ± 3.5 for Agar 8%, 4%, 2%, MnCl_{2} (

The non-vanishing F values and the significant fitting error within the MnCl_{2} region in the case of the original spin-bath model are present regardless of the T1 or T2 values (which were set to arbitrary values for test purposes, e.g. 1000 or 10,000 ms) which means that indeed SL effects have to be considered in general (the measured T1/T2 values of MnCl_{2} are 140/12 ms (literature 144/14 ms)).

The values of the T_{2,b} parameter for the original and modified model are very similar: T_{2,b} (Agar 8%) = 12.95

Intensities | F = 16 [kHz] | 12 | 10 | 8 | 4 | 2 | 1 |
---|---|---|---|---|---|---|---|

Agar 8% | 184.15 | 181.14 | 180.14 | 179.14 | 174.14 | 162.13 | 135.11 |

Agar 4% | 201.12 | 200.12 | 199.11 | 198.12 | 196.12 | 188.11 | 170.11 |

Agar 2% | 182.12 | 181.13 | 181.12 | 181.12 | 180.13 | 177.13 | 166.12 |

MnCl_{2} | 507.25 | 507.26 | 506.25 | 506.26 | 504.26 | 498.26 | 479.25 |

± 2.4 μs, T_{2,b} (Agar 4%) = 12.98 ± 0.2 μs, T_{2,b} (Agar 2%) = 12.98 ± 0.5 μs, T_{2,b} (MnCl_{2}) = 1 μs. The T_{2,b} values for distilled water and MnCl_{2} are arbitrarily set to one because the z-spectrum in the context of the new model is just a constant, except at the resonance (zero).

The k_{f} values using the original model are k_{f} (Agar 8%) = 4.25 ± 0.6, k_{f} (Agar 4%) = 1.66 ± 0.6, k_{f} (Agar 2%) = 0.56 ± 0.1, k_{f} (MnCl_{2}) = 0.42 ± 0.1. The k_{f} values using the modified model are k_{f} (Agar 8%) = 1.98 ± 0.2, k_{f} (Agar 4%) = 1.02 ± 0.1, k_{f} (Agar 2%) = 0.37 ± 0.1, k_{f} (MnCl_{2}) = 0.

The proposed mathematical modifications of the binary spin-bath model considering spin-locking seem to be a step in the right direction in that sense that the effects associated with spin-locking are not interpreted as magnetization transfer furthermore. This could be verified by the F parameter which is really zero within the region of MnCl_{2} using the modified model. The T_{2,b} values of 13 μs for the agar solutions correspond very well with the literature [

This work was supported by the Ruth & Arthur Scherbarth foundation, grant 2249.