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In Vivo Bone 31P Relaxation Measurement and Its Implications on Mineral Quantification

Xia Zhao¹, Hee Kwon Song¹, and Felix W. Wehrli¹

¹University of Pennsylvania, Philadelphia, PA, United States

Synopsis

In MRI-based bone mineral assessment, pixel intensity of the bone is compared against that of the sample to estimate the 31P density after correcting for their relaxation properties. Knowledge of bone 31P relaxation times is therefore crucial. Using saturation-recovery spectroscopy and ZTE-PETRA, T1, T2* and density of bone 31P in healthy subjects (26 to 76 y/o) were measured yielding 36.8±1.4s, 196.9±10.1μs and 6.10±0.62 mol/L. Measured T1 and T2* errors are expected to be within 6% and 15%, resulting in an error of quantified [31P] of ≤ 6.3%. The small inter-subject variations may therefore obviate the need for individual T1 measurements.

Introduction

Bone mineral phosphorus has been shown to be quantifiable by solid-state ³¹P MRI [1]. While proper quantification requires accurate knowledge of the relaxation times, the T₁ of bone ³¹P is particularly difficult to measure since T₂*/T₁<<1 [1-4]. Therefore, assumed T₁ values have previously been used [5]. Here we measured T₁ of bone ³¹P in a cohort of healthy subjects with wide age range at 3 T, and the possible implications of errors in T₁ on ³¹P quantification. The accuracy of the technique was analyzed by simulation and the measured T₁ and T₂* were subsequently used to estimate bone mineral density from ³¹P zero echo time (ZTE) images. Repeatability was also evaluated in three subjects.

Methods

The tibial mid-shafts of ten healthy subjects (26 to 76 y/o) were scanned on a Siemens 3 T Trio system with a ¹H/³¹P dual frequency birdcage calf coil. T₁ of bone ³¹P was measured with the saturation recovery (SR) sequence in Figure 1. Since both the phosphate metabolites in muscle and bone mineral phosphate contribute to the spectroscopic signal, bone signal was isolated by creating two spectra: one directly from the acquired FID (Total_Spec) and a second one from the same FID after deleting the first 150 points (dominated by the fast-decaying bone signal; Metabolite_Spec). After phase correction, subtraction of the two spectra yielded the bone ³¹P spectrum (Figure 2), which was fitted to a Lorentzian. The integral of this resonance line was fit to a mono-exponential model to extract T₁. Errors in T₁ estimation due to interference from metabolite signals was evaluated via simulation using literature value of relaxation times [6], taking into account B₁ inhomogeneity of the coil measured with the Bloch-Siegert method [7]. ³¹P images were acquired with a custom-made ZTE-PETRA sequence [8, 9] and [³¹P] was quantified relative to a calibration sample [5]. Three subjects underwent three scans each for test-retest repeatability evaluation.

Results

Figure 3a plots percent error in quantified [³¹P] as a function of the error in relaxation times. Effects of relative contributions from metabolites to total signal on the relaxation times measured are shown in Figure 3b. Spectra generated from an in vivo dataset are shown in Figures 4a-b. Figure 4c displays bone ³¹P SR spectra after removal of the metabolite signals. The result of mono-exponential fitting is given in Figure 4d. Table 1 summarizes the relaxation times measured for all ten subjects as well as bone [³¹P] quantified from ZTE images using the measured relaxation values. Repeatability experiments yielded average coefficients of variation of 1.53% for T₁, 2.64% for T₂* and 4.77% for [³¹P]. Neither the relaxation times nor [³¹P] was found to be significantly correlated with age.

Discussion and Conclusions

According to Figure 3b, T₁ is progressively underestimated with increasing fraction of metabolite ³¹P in the total signal (since metabolite T₁s are shorter by about one order of magnitude). T₁ is underestimated by ~10% while T₂* is overestimated by ~24% when 15% of the total signal arises from the metabolites, which would result in [³¹P] being underestimated by 9.7% according to Figure 3a. However, using typical muscle metabolite concentrations [10], bone [³¹P] measured ex vivo [1] and muscle volume measured from gradient echo images, a rough estimate done on a few subjects indicated that over 90% of in vivo ³¹P total signal actually originates from bone, limiting the measurement error for T₁ and T₂* to within -6% and 15%, respectively. According to the simulation in Figure 3a, this magnitude of relaxation time error translates into an error in estimated [³¹P] of less than 6.3% if relaxation is the only error source, suggesting the reliability of the proposed method for measuring bone ³¹P relaxation. However, the variation in T₁ across subjects observed in this study is very small (36.8±1.4 s), which parallels the relatively small variation in T₁ (96.7±10.8 s measured at 7 T) for a group of 16 tibia specimens from donors aged 27 to 97 years at death [1], and no correlation with age was observed in that study as well. In addition, mean [³¹P] quantified using measured relaxation times in the present study (6.10±0.62 mol/L) is close to measurements ex vivo (6.74±1.22 mol/L) [1], where the experiment was free from interference of metabolites signal. In conclusion, the finding of the current study might obviate the need to measure individual bone ³¹P T₁ altogether, using instead estimated values, thereby shortening the scan protocol.

Acknowledgements

NIH R01-AR50068

References

1. Seifert, A.C., et al., Bone mineral 31P and matrix-bound water densities measured by solid-state 31P and 1H MRI. NMR in Biomedicine, 2014. 27(7): p. 739-748.

2. Seifert, A.C., et al., 31P NMR Relaxation of Cortical Bone Mineral at Multiple Magnetic Field Strengths and Levels of Demineralization. NMR in Biomedicine, 2013. 26(9): p. 1158-66.

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6. Meyerspeer, M., M. Krssak, and E. Moser, Relaxation times of 31P-metabolites in human calf muscle at 3 T. Magn Reson Med, 2003. 49(4): p. 620-5.

7. Sacolick, L.I., et al., B1 mapping by Bloch-Siegert shift. Magn Reson Med, 2010. 63(5): p. 1315-22.

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Figures

Figure 1. Saturation-recovery sequence used for T₁ measurement. The saturation (SAT) module consists of twelve hard pulses, each followed by a spoiler, used to saturate ³¹P spins of all phosphorus components within the coil volume. After a saturation recovery delay TSR, an FID is acquired at a bandwidth of 250 kHz. Due to B₁ amplitude limitation of the coil, both SAT and excitation pulses were set to 120 μs to achieve a 60° flip angle. Simulations show that twelve 60° pulses achieve 99.5% saturation. TSRs of 2, 4, 8, 16, 32, 64, 128 and 256s were chosen to sample the T₁ recovery (8.5 min).

Figure 2. Workflow for isolating the bone ³¹P spectrum from the composite signal containing both bone phosphorus and ³¹P metabolites.

Figure 3. (a) Error in quantified [³¹P] as a function of error in T₁ and T₂*. (b) Error in relaxation times measured with the method shown in Figure 2, versus metabolite signal fraction.

Figure 4. (a) Series of composite spectra (Total_Spec) as a function of saturation-recovery time; (b) Same after subtraction of short-T₂ components (Metabolite_Spec); (c) Bone ³¹P spectra along with their Lorentzian fits after subtraction of the metabolite signals; (d) T₁ fit from the data in panel (c).

Table 1. Measured relaxation times and quantified bone ³¹P concentrations.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)

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