| Summary: | <p>Monitoring the build-up or decay of hyperpolarization in nuclear magnetic resonance requires radio-frequency (RF) pulses to generate observable nuclear magnetization.
However, the pulses also lead to a depletion of the polarization and, thus, alter the spin dynamics. To simulate the effects of RF pulses on the polarization build-up and decay, we propose a first-order rate-equation model describing the dynamics of the hyperpolarization process through a single source and a relaxation term.
The model offers a direct interpretation of the measured steady-state polarization and build-up time constant.
Furthermore, the rate-equation model is used to study three different methods to correct the errors introduced by RF pulses: (i) a <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">1</mn><mo>/</mo><msup><mi>cos</mi><mrow><mi>n</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mi mathvariant="italic">θ</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="53pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="c78669eae3f1e1adb4c0ec8f1fa9d79f"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mr-4-175-2023-ie00001.svg" width="53pt" height="15pt" src="mr-4-175-2023-ie00001.png"/></svg:svg></span></span> correction (<span class="inline-formula"><i>θ</i></span> denoting the RF pulse flip angle), which is only applicable to decays; (ii) an analytical model introduced previously in the literature; and (iii) an iterative correction approach proposed here.
The three correction methods are compared using simulated data for a range of RF flip angles and RF repetition times.
The correction methods are also tested on experimental data obtained with dynamic nuclear polarization (DNP) using 4-oxo-TEMPO in <span class="inline-formula"><sup>1</sup></span>H glassy matrices.
It is demonstrated that the analytical and iterative corrections allow us to obtain accurate build-up times and steady-state polarizations (enhancements) for RF flip angles of up to 25<span class="inline-formula"><sup>∘</sup></span> during the polarization build-up process within <span class="inline-formula">±10</span> % error when compared to data acquired with small RF flip angles (<span class="inline-formula"><3</span><span class="inline-formula"><sup>∘</sup></span>).
For polarization decay experiments, corrections are shown to be accurate for RF flip angles of up to 12<span class="inline-formula"><sup>∘</sup></span>.
In conclusion, the proposed iterative correction allows us to compensate for the impact of RF pulses offering an accurate estimation of polarization levels, build-up and decay time constants in hyperpolarization experiments.</p>
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