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.
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.
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.
Discussion and Conclusion