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Optimal control RF pulses for dual-angle T₁ measurements in ³¹P magnetization transfer spectroscopy

Clemens Diwoky¹, Christina Graf², Armin Rund³, and Rudolf Stollberger²
¹Institute of Molecular Biosciences, University of Graz, Graz, Austria, ²Institute of Biomedical Imaging, Graz University of Technology, Graz, Austria, ³Institute for Mathematics and Scientific Computing, University of Graz, Graz, Austria

Synopsis

Keywords: Pulse Sequence Design, CEST & MT

Herein, we show for the first time the application of optimal control (OC) to the design of RF pulses for dual-angle T₁ measurements as needed for ³¹P magnetization transfer spectroscopy. Phantom measurements highlight that OC RF pulses are able to produce precise T₁ maps within the relevant coil's sensitivity range. The resulting enlarged spin ensemble leads to high SNR and excellent T₁ prediction if used in non-selective spectroscopic application. In addition, OC pulses were optimized for operation at a large bandwidth suitable for ³¹P spectroscopy (± 15 ppm), which is often a problem when adiabatic BIR-4 pulses are used.

Introduction

The measurement of enzymatic exchange rates in vivo by magnetization transfer (MT) is a unique feature of magnetic resonance spectroscopy (MRS) [1,2]. ³¹P-MT spectroscopy relies on the accurate measurement of the apparent T₁ of a phosphate group (e.g. inorganic phosphate (Pi)) which is under enzymatic exchange with a second phosphate group (e.g. γ - ATP through ATP synthase) upon saturation of the latter [3]. In a typical MT-MRS experiment, T₁ needs to be validated at different binding-sites with distinct chemical shift offsets [4]. The low signal and therefore time consuming acquisition of phosphor MRS imposes two additional constraints: first, high SNR surface transmit/receive coils are used, and second, a fast two-angle T₁ measurement is employed [5]. When using the two-angle method, the inhomogeneous transmitting field brings adiabatic excitation pulses into play [6,7]. However, robustness to frequency offsets and B⁺₁ insensitivity of adiabatic excitation is limited [8]. Therefore, we propose the use of optimal control pulses [9,10] that provide high flip angle precision, strong B⁺₁ insensitivity, and a bandwidth optimized for phosphor excitation at 7 Tesla.

Methods

Measurements were carried out on a 7 Tesla platform (Bruker Biospec 70/20, Ettlingen, Germany) with a custom built ³¹P T/R surface coil of 11 mm inner diameter. In order to visualize coil (B⁺₁) dependent errors in the T₁ measurement, a 2D-slice phantom was built filling a 5 ml syringe with 475 μl of 98% ortho-phosphoric acid (4 mm slice). Dual-angle (α = 15° / β = 60°) T₁ measurements were performed according to the work of Bottomley and Ouwerkerk [5]. The phosphoric acid singlet was fixed to -5.8 ppm (center of ³¹P spectrum with PCr assigned to 0 ppm). Stability to frequency offsets was tested by changing the center frequency of the excitation pulses from f = 6.2 ppm (Δf = 12 ppm) to f = -17.8 ppm (Δf = -12 ppm) in steps of -1.5 ppm. For excitation of the dual-angle T₁ acquisitions, the following frequently used pulses were compared: hardpulse (BP, T_p = 0.05 ms, B⁺₁ = 48.4/193.5 μT, 15°/60° resp.), adiabatic B1-independent rotation pulse based on a sech-tanh modulation function as designed in [8] including phase cycling [11] (BIR-4, ζ = 10, κ = atan(20), Δω_max = 3.5 kHz, T_p = 4 ms, peak B₁⁺ = 500 μT), and a newly developed optimal control design pulse [10] optimized for T₁ mapping in ³¹P-MT spectroscopy (OC, bw = ± 15 ppm, ΔB⁺₁ = 0.4-1.2 x B⁺_1nom, T_p = 1.64/2.47 ms, 15°/60° resp., peak B₁ = 500 μT). The other imaging parameters were: TR = 800 ms, TE = 2 ms, FOV = 20 mm x 20 mm, matrix = 64 x 64, NEX = 12. A B⁺₁ map was acquired with the same parameters as above, but with TR = 10 s, BP excitation and two flip angles α = 60° / β = 120° [12]. Images were masked corresponding to SNR > 0.1 · SNR_max of the OC(60°) scan. Ground truth T₁ was determined as the mean of the voxels within ± 2.5 % B⁺_1nom and the dual-angle measurement of the BP excitation.

Results

Figure 1 demonstrates the superior accuracy of OC excitation pulses optimized and applied to dual-angle T₁ measurements in ³¹P-MT spectroscopy. Comparing OC with BIR-4 excitation, ΔB⁺₁ and/or frequency offsets cause strong (yellow and dark blue coded) deviations of the BIR-4 measurement from the true T₁ value (T₁ = 1.71 ± 0.17 s). The signal distribution of the surface coil in Figure 2 (b,c) shows that those erroneous areas within the BIR-4 measurement account for approx. 20 % of the overall signal and thus significantly modulate the sum signal and hence the measured T₁ (Fig. 1, b). T₁ measurement based on BIR-4 excitation overestimates T₁ throughout the whole bandwidth. This appears to be the result of incomplete phase compensation during the (phase cycled) composite parts of the pulse [11]. BP excitation underestimates T₁ because lots of measured signal originate from spins that are under-excited, which directly leads to an underestimation of T₁[5]. OC design pulses performed best in measuring T₁ till the outermost end of the coil detectable rim with the smallest mean error of -1.6 ± 25.2 % (mean ± standard deviation of the mean) compared to all RF pulses investigated (Figure 3).

Discussion and Outlook

Based on phantom measurements we showed that OC outperform non-adiabatic (hardpulse) and adiabatic (BIR-4) excitation by accurate measuring T₁over the relevant coil's sensitivity range. Its successful application in MT spectroscopy depends on the consistent performance of the excitation over the observed chemical shift offsets. If T₁ values depend (incorrectly) on the frequency offset of spins, as shown here for a phase corrected BIR-4 excitation, the recorded enzymatic exchange rates also exhibit - possibly critical - deviations depending on the binding site investigated. Therefore, for any quantitative analysis using MT spectroscopy, it is absolutely critical to choose the excitation that is most stable to variations in the desired Δ B⁺₁and chemical shift range, such as the OC excitation presented here. In this regard, the use of optimal control pulses is not limited to ³¹P and should be considered in any other application of X-nuclei spectroscopy.

Acknowledgements

No acknowledgement found.

References

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[5] Bottomley P.A., Ouwerkerk R.: The Dual-Angle Method for Fast, Sensitive T1 Measurement in Vivo with Low-Angle Adiabatic Pulses. JMR, B, Volume 104, Issue 2, June 1994, Pages 159-167 https://doi.org/10.1006/jmrb.1994.1070

[6] De Graaf R.A., Nicolay K.: Adiabatic rf pulses. Applications to in vivo NMR. Concepts Magn Reson 9: 247–268, 1997 https://doi.org/10.1002/(SICI)1099-0534(1997)9:4<247::AID-CMR4>3.0.CO;2-Z

[7] Garwood M., Ke Y.: Symmetric pulses to induce arbitrary flip angles with compensation for rf inhomogeneity and resonance offsets. Journal of Magnetic Resonance (1969), Volume 94, Issue 3, p. 511-525. https://doi.org/10.1016/0022-2364(91)90137-I

[8] De Graaf R.A., Nicolay K.: Adiabatic rf pulses: Applications to in vivo NMR. Concepts in Magnetic Resonance (1997), Volume 9, Issue 4, p. 247-268. https://doi.org/10.1002/(SICI)1099-0534(1997)9:4<247::AID-CMR4>3.0.CO;2-Z

[9] Graf C. et al.: Advanced design of MRI inversion pulses for inhomogeneous field conditions by optimal control. NMR Biomed. 2022, https://doi.org/10.1002/nbm.4790

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Figures

Figure 1: T₁ mapping error using the dual-angle approach and a surface coil for different excitation pulses (hardpulse BP, adiabatic BIR-4, optimal control OC) and frequency offsets (a). Measured total T₁ (b). Optimal control pulses match closely the ground truth of T₁ = 1.71 $$$\pm$$$ 0.17 s (dashed gray line). Representative ³¹P spectrum with major phosphate signals (inorganic phosphate Pi, phosphocreatine PCr, γ, β, α phosphate of adenosine triphosphate ATP) demonstrates the need to cover a wide frequency span (c).

Figure 2: B⁺₁map (a) and visualization of the spatial distribution of the total coil signal (b). BIR-4 and OC at -3 ppm off-resonance (f = -8.8 ppm) (c,d). The ROI marked in red shows the area furthest from the coil, which is still responsible for 20 % of the received signal.

Figure 3: Descriptive statistics of the on-resonant (f = -5.8 ppm) T₁ maps within a mask corresponding to 90 % of the total coil signal (Figure 2 b red to yellow areas). T₁ mean and standard deviation was weighted corresponding to the measured B⁺₁ field to account for coil sensitivity during reception. Measured gound truth T₁ = 1.71 ± 0.17 s.

Proc. Intl. Soc. Mag. Reson. Med. 31 (2023)

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DOI: https://doi.org/10.58530/2023/3429