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Multinuclear Absolute MR Thermometry

Leeor Alon^1,2, Emilia Silletta³, Alexej Jerschow³, and Guillaume Madelin^1,2

¹Radiology, New York University School of Medicine, New York, NY, United States, ²Center for Advanced Imaging Innovation and Research (CAI2R), New York University School of Medicine, New York, NY, United States, ³Department of Chemistry, New York University, New York, NY, United States

Synopsis

Absolute MR thermometry has been unachievable clinically since the advent of MR and MR practitioners mostly rely on relative measurement of thermal changes using the proton resonance frequency shift method. Here, we introduce the JAMS method for reconstruction of absolute temperature using multinuclear frequency measurements. The method takes advantage of different frequency shifts with temperature of different nuclei (e.g. proton and sodium) for the reconstruction. Theory of the method is presented and proof-of-principle experiments validating the approach.

Introduction

While the body routinely regulates temperature throughout its tissues and organs, localized thermal changes can be associated with injury or disease¹²³. Absolute MR thermometry is currently unachievable clinically and MR practitioners mostly rely on relative measurement of thermal changes using the proton resonance frequency shift method (PRF)⁴. Non-thermal B0 changes, such as patient movement, magnetic field drift or flow, limit the applicability of the PRF method in vivo⁵. To measure absolute temperature, an internal frequency reference at each voxel is desired. Internally referenced chemical shift methods have been investigated in the brain using the amid proton in N-acetylaspartate (NAA) peak. However, due to the low concentrations of NAA⁶, challenges with water suppression and low signal-to-noise (SNR), in vivo absolute thermometry has not been translatable to clinical practice so far³. Here, we introduce a new method, referred to as “JAMS” (after the names of the researchers), which takes advantage of the resonant frequency shifts of sodium ions and protons with temperature to reconstruct absolute temperature. Theory is presented here and NMR experiments on a sample with a physiological concentration of sodium in water is used to demonstrate proof-of-principle of multinuclear absolute thermometry.

Theory

The Larmor frequency is defined by the magnetic field that the nucleus experiences, $B_{nuc}$ , and the gyromagnetic ratio, $\gamma$ of a nucleus of interest. $B_{nuc}$ is the result from a screening constant, $\sigma$ , altering the macroscopic magnetic field, $B_{0}$ , according to:

$f=\frac{\gamma}{2\pi}B_{nuc}=\frac{\gamma}{2\pi}(1-\sigma)B_{0} [1]$

The screening constant is expressed as:

$\sigma=\sigma_{0}+\sigma_{\chi}+\sigma_{\epsilon} [2]$

where $\sigma_{0}$ is the intramolecular screening constant, $\sigma_{\epsilon}$ is the intermolecular electric screening effect, and $\sigma_{\chi}$ is the volume magnetic susceptibility screening effect. Both $\sigma_{\chi}$ and $\sigma_{\epsilon}$ change with temperature; however, the macroscopic susceptibility experienced by the two nuclei within the same medium is identical. The precession frequency of nuclei A and B is expressed as:

$f_A(T)=\frac{\gamma_{A}}{2\pi}[1-\sigma_{0_A}-\sigma_{\chi_A}-\sigma_{\epsilon}(T)_A]B_{0} [3a]$

$f_B(T)=\frac{\gamma_{B}}{2\pi}[1-\sigma_{0_B}-\sigma_{\chi_B}-\sigma_{\epsilon}(T)_B]B_{0} [3b]$

Equations. [3a] and [3b] can be independently scaled with the a-priori known quantities $\frac{\gamma_{A}B_{0}}{2\pi}$ and $\frac{\gamma_{B}B_{0}}{2\pi}$ , respectively. Subtracting eq. [3b] from eq. [3a] (assuming $\sigma_{\chi_A}=\sigma_{\chi_B}$ ) yields:

$\frac{f_{A}}{\frac{\gamma_AB_0}{2\pi}}-\frac{f_{B}}{\frac{\gamma_BB_0}{2\pi}}=[\sigma_{0_B}-\sigma_{0_A}]+[\sigma_{\epsilon}(T)_B-\sigma_{\epsilon}(T)_A] [4]$

The result can be modeled using a constant term- $[\sigma_{0_B}-\sigma_{0_A}]$ , defined by the intramolecular screening constants and a linear term with temperature, $[\sigma_{\epsilon}(T)_B-\sigma_{\epsilon}(T)_A]$ , defined by the electric screening constants of the two nuclei, that can be calibrated in samples at known temperatures.

Methods

Experiments were carried out on an 11.7 T NMR Bruker Avance I spectrometer (Bruker BioSpin) operating at 500.19 MHz for ¹H, and 132.3 MHz for ²³Na, using a 5 mm double resonance broadband probe. A test tube with 1% NaCl w/v was placed inside the spectrometer where the sample temperature can be controlled using gas flow and a temperature sensor providing a precise, stable and reliable temperature regulation. After each desired temperature was reached, a standard FID pulse sequence was used with a 90° pulse. The duration of the pulse is 11 μs and 9 μs for ¹H and ²³Na, respectively, 8 averages were used with TR = 15 s for ¹H, and 0.5 s for ²³Na, dwell time = 100 μs, spectral width = 5 kHz. The center of the peak at each temperature was then determined by tracking its central moment. We conducted a set of 11 experiments: first, 3 spectrum measurements at 25, 30 and 40^oC were used to calibrate the JAMS model (eq. 5). The sample was then brought to 3 random temperatures where the person conducting the absolute temperature reconstruction was blinded to the actual physical temperature of the sample. Lastly, the sample was brought to 5 more random temperatures (blinded) where the shim was randomly changed. The data was processed in Matlab and absolute temperatures were reconstructed and plotted against the real sample temperatures.

Results

The frequency shifts of sodium and water at 25, 30 and 40^oC are shown in Fig. 1. Fig. 2 illustrates the linear fit used to calibrate the JAMS model (eq. 5). Once the model is calibrated, temperature and shims where randomly changed and absolute temperature was reconstructed (blindly) with mean squared error (MSE) of 0.18^oC (Fig. 3).

Discussion and Conclusion

In this work, we present the JAMS method for multinuclear absolute thermometry which takes advantage of the different frequency shift coefficients of sodium and protons with temperature. The method is validated on a fluid sample with physiological concentration of NaCl with precise temperature control, which make this method highly likely to be usable in vivo for both spectroscopy and phase imaging acquisitions. The JAMS method was shown to be immune to

$B_{0}$ changes which is imperative for thermometry studies in the clinical setting and was validated in blinded tests. The method is now being implemented on clinical scanners.

Acknowledgements

Funding from NIH through P41EB017183, R01NS097494, R01EB026456, R21CA213169.

References

1. E. Y. K. Ng, et al. J. Med. Eng. Technol. 25, 253–263 (2001). 2. Segàle, M. J. Exp. Med. 29, 235–49 (1919). 3. Wang, H. et al. Front. Neurosci. 8, 307 (2014). 4. De Poorter, J. Magn. Reson. Med. 34, 359–367 (1995). 5. Peters, R. D. Thesis (2000). 6. Rigotti, D. J. et al. Am. J. Neuroradiol. (2011).

Figures

Figure 1. A. Proton and sodium NMR Frequency shifts with temperature. Central moment was used to track center frequencies (purple). Sensitivity of sodium NMR and proton NMR to temperature was -0.0207 ppm/^oC and -0.0097 ppm/^oC, respectively. The frequency difference between the slopes 0.011 ppm/^oC indicates the normalizes sensitivity of the JAMS method to absolute thermometry.

Figure 2. JAMS method (eq. 5) fit (linear) conducted to calibrate absolute thermometry at three temperatures: 25, 30 and 40 ^oC.

Figure 3. Absolute temperature reconstruction from blinded experiments. First 3 experiments were at random temperatures with no shim changes. Last 5 experiments included both random temperatures and shim changes.

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

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