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Quantitative Magnetization Transfer: A Comparison of State-of-the-Art Acquisitions
Fritz M. Bayer1, Peter Jezzard1, and Alex K. Smith1

1Wellcome Centre for Integrative Neuroimaging, FMRIB, University of Oxford, Oxford, United Kingdom

Synopsis

As development of quantitative magnetization transfer (qMT) has progressed, different sequences have been developed and independently optimised. Here, we present a comparison of the three main qMT acquisition sequences: spoiled gradient echo (SPGR), selective inversion recovery with fast spin echo (SIR-FSE) and balanced steady-state free precession (bSSFP). A novel comparison is accomplished by optimising each protocol using Cramér-Rao lower bounds (CRLB) theory. Our results indicate that SPGR qMT may introduce additional uncertainty due to the low sensitivity surrounding T2f, while bSSFP may provide a robust alternative for efficient 3D acquisitions.

Introduction

Quantitative magnetisation transfer (qMT) is a technique that can be used to detect the signal of protons attached to relatively immobile macromolecules, such as myelin1-5. As development of this technique has progressed, three main qMT sequences have been proposed and independently optimised: spoiled gradient echo (SPGR), selective inversion recovery with fast spin echo (SIR-FSE) and balanced steady-state free precession (bSSFP)6-8. However, due to their independent evolution, no comparison of each optimised sequence has been performed. Recently, the SIR-FSE and SPGR sequences have been optimised with great success using Cramér-Rao lower bounds (CRLB) theory, reducing their scan times while increasing precision9,10. In this work, we use CRLB theory to optimise the bSSFP sequence for the first time, which allows for an equitable comparison of all three acquisitions. By applying the optimisation to all three acquisition types, we derive sequence parameters which maximise parameter map accuracy while minimising acquisition time. Alongside, we present the results of a sensitivity analysis for all three sequences, revealing deeper insights into effective sequence design.

Methods

Numerical data simulations were performed by solving the Bloch-McConnell equations for each sequence using typical brain tissue parameters (Table 1, Assumed Values).

Each qMT acquisition follows a similar approach: By varying acquisition variables, an analytical model can be fitted to the signal data to find the parameter estimates. By means of a simple least-squares fit, the qMT specific parameters have been determined: macromolecular-to-free pool size ratio F, macromolecular-to-free pool exchange rate kmf, longitudinal relaxation rate R1f and transverse relaxation time T2f of the free pool. Acquisition details are described in Figure 1. By means of CRLB theory, optimal acquisition schemes for Q unknown parameters $$$\boldsymbol{\theta}$$$ can been determined, minimizing the following CRLB objective function11:

$$V=\sum_{i=1}^{Q}[J^{-1}]_{ii}\theta_i^{2}T_{cost}$$

As precise acquisition schemes can come at the cost of longer scan times, an additional cost function $$$T_{cost}=\sqrt{TR}$$$ has been included into the optimisation7,9. Varied acquisition parameters and further details on the optimisation are described in Figure 1. The objective function is largely defined by the Fischer matrix J, which calculates the sensitivity of the signal S as follows:

$$J_{jk}=\frac{1}{\sigma^2}\sum_{n=1}^{N}\frac{\partial S}{\partial\theta_j}\frac{\partial S}{\partial\theta_k}$$

where $$$\sigma$$$ is the SD of the noise and $$$\theta_j$$$ is the jth qMT parameter. To further optimise each sampling scheme, a sensitivity analysis has been performed for each sequence9:

$$S_{eff}=\frac{\partial S}{\partial\theta_l}\frac{1}{\sqrt{\text{TR}}}$$

This expresses the sensitivity of each qMT parameter on the measured signal S as a function of the acquisition parameters. All computations were performed in MATLAB (MathWorks, Natick, MA), with partial solutions taken from qMRlab toolbox12. Statistical analyses were performed using the Brown-Forsythe test and one-sample t-test using a significance of p<0.05.

Results

A comparison of all three sequences in typical brain tissue is shown in Table 1. Looking at the clinically most relevant parameter F: in white matter SIR-FSE showed a significant bias (p<0.001) compared to SPGR and bSSFP. Comparing kmf, all three sequences appear to be interchangeable, although SPGR shows significantly higher SD (p<0.001) in some cases. T2f is poorly described by SPGR (p<0.001 in WM and MS lesion), which agrees with our expectations, as the sequence operates at high offsets that do not affect the free water pool. In contrast, bSSFP measures T2f with high precision in all tissues.

In Figures 2 and 3, contoured areas mark high sensitivity Seff for each qMT parameter, illustrating the impact of CRLB theory, and demonstrating that the sensitivity of the respective model strongly depends on the choice of acquisition parameters. For instance, the grey area in Figure 2 (b) at low frequencies illustrates the poor T2f description in SPGR when operating at large offsets (i.e. offsets > 2.5 kHz).

By applying CRLB optimisations to the bSSFP acquisition scheme, we were able to reduce the number of sampling points from 16 to 8. This halves the original acquisition time, while maintaining precision of the parameter estimates. For instance, in simulations of white matter we see only minimal changes: F$$$\thinspace$$$=$$$\thinspace$$$14.0$$$\thinspace$$$±$$$\thinspace$$$0.9$$$\thinspace$$$%, kmf$$$\thinspace$$$=$$$\thinspace$$$10.1$$$\thinspace$$$±$$$\thinspace$$$0.9 s-1 (original acquisition); F$$$\thinspace$$$=$$$\thinspace$$$14.0$$$\thinspace$$$±$$$\thinspace$$$0.6$$$\thinspace$$$%, kmf$$$\thinspace$$$=$$$\thinspace$$$10.0$$$\thinspace$$$±$$$\thinspace$$$0.6 s-1 (CRLB acquisition).

Conclusion

We have demonstrated that CRLB optimisations can increase qMT acquisition efficiency without sacrificing parameter accuracy. By using these optimisations, scan time can potentially be halved, which provides time to acquire higher resolution data or increase the spatial coverage. Additionally, our results indicate that SPGR qMT may introduce additional parameter uncertainty compared to SIR-FSE and bSSFP due to its low sensitivity surrounding T2f. In particular, bSSFP has been shown to be a robust alternative to SPGR, indicating this method may be ideal for rapid quantification of the pool size ratio F. Future work involves applying these optimisations in healthy controls to confirm our hypotheses.

Acknowledgements

This work is supported by the German scholarship Cusanuswerk.

References

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  2. Ou X, Sun SW, Liang HF, Song SK, Gochberg DF. The MT pool size ratio and the DTI radial diffusivity may reflect the myelination in shiverer and control mice. NMR in Biomedicine: An International Journal Devoted to the Development and Application of Magnetic Resonance In vivo. 2009 Jun;22(5):480-7.
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  4. Underhill HR, Rostomily RC, Mikheev AM, Yuan C, Yarnykh VL. Fast bound pool fraction imaging of the in vivo rat brain: association with myelin content and validation in the C6 glioma model. Neuroimage. 2011 Feb 1;54(3):2052-65.
  5. Garcia M, Gloor M, Radue EW, Stippich C, Wetzel SG, Scheffler K, Bieri O. Fast high-resolution brain imaging with balanced SSFP: Interpretation of quantitative magnetization transfer towards simple MTR. Neuroimage. 2012 Jan 2;59(1):202-11.
  6. Yarnykh VL, Yuan C. Cross-relaxation imaging reveals detailed anatomy of white matter fiber tracts in the human brain. Neuroimage. 2004 Sep 30;23(1):409-24.
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  8. Gloor M, Scheffler K, Bieri O. Quantitative magnetization transfer imaging using balanced SSFP. Magnetic resonance in medicine. 2008 Sep;60(3):691-700.
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Figures

Figure 1: Schematic illustration of the acquisition sequences SPGR, SIR-FSE and bSSFP6,7,8,12. The acquisition parameters optimised over were as follows: offset frequency $$$\Delta$$$ and amplitude $$$\alpha_{mt}$$$ for SPGR, predelay time td and inversion recovery time ti for SIR-FSE as well as flip angle $$$\alpha$$$ and RF pulse duration tRF for bSSFP. The optimisation has been performed over a span of typical brain parameters (Table 1, assumed values) and a genetic algorithm has been used for minimizing V to ensure a global minimum is found.

Table 1: Comparison of all three sequences for typical qMT tissue parameters: pool size ratio F, exchange rate kmf and relaxation rate of the free pool R1f, relaxation time of the free pool T2f. Results represent mean values over 100 simulations and errors show the SD. The SPGR and bSSFP models can not determine R1f and T2f simultaneously. The SIR-FSE model is independent of T2f, but fits a further parameter Sf9. Remaining parameters have been kept fixed, similar to previous studies5-9. WM I=frontal white matter, WM II=internal capsule white matter, GM=grey matter and MS lesion=multiple sclerosis lesion. Assumed tissue values are taken from5,8,9.


Figure 2: Sensitivity analysis of bSSFP (a) and SPGR (b) in frontal white matter (Table 1). Contoured areas mask the 85th percentile of Seff for each qMT parameter, revealing areas that are suitable for precise and efficient acquisitions. It can be taken as a guidance when acquisition parameters are chosen or changed due to experimental constraints (e.g. acquisition parameters can be varied within sensitive areas with minimal loss of precision). The SPGR model is shown to be sensitive for T2f at low offsets only, which is in agreement with our expectations, as there is no direct saturation of the free pool at higher offsets.

Figure 3: Sensitivity analysis of SIR-FSE in frontal white matter (Table 1), reproducing the findings by Dortch9. Contoured areas mask the 85th percentile of Seff for each qMT parameter, revealing areas that are suitable for precise and efficient acquisitions. It can be taken as a guidance when acquisition parameters are chosen or changed due to experimental constraints (i.e. acquisition parameters can be varied within sensitive areas with minimal loss of precision).

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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