We present a novel approach to maximize the excitation accuracy while limiting the RF power in parallel transmission through integrating full 3rd order dynamic field monitoring in single-shot measurements with exquisite precision and high bandwidth and alternatively gradient impulse response estimations into the RF pulse design problem.

Theory: The iterative reVERSE method (2) is based on the assumption that the k-space trajectory associated with the RF pulse design problem is unchanged at each iteration. From the s-domain perspective, the equation defining the spin rotation under VERSE reshaping has to be modified by an additional gradient field deviation term to account for aforementioned time-varying local gradient field perturbations given that $$ \boldsymbol{\widetilde{\mathrm{G}}}(s)=\boldsymbol{\mathrm{G}_{nom}}(s)-\boldsymbol{\mathrm{G}_{act}}(s) $$ $$\phi^\prime(s,\boldsymbol{\mathrm{r}}) = - \sqrt{\vert{W(s)\vert^2 + (\boldsymbol{\mathrm{g}}(s).\boldsymbol{\mathrm{r}} + \frac{\boldsymbol{\widetilde{\mathrm{G}}}(s).\boldsymbol{\mathrm{r}} + \Delta\omega(\boldsymbol{\mathrm{r}})}{\gamma \vert{\boldsymbol{\mathrm{G}}(s)\vert} })}}$$ $$\boldsymbol{\mathrm{n}}(s,\boldsymbol{\mathrm{r}})\propto(\frac{B_{1,x}(s)}{\vert\boldsymbol{\mathrm{G}}(s)\vert},\frac{B_{1,y}(s)}{\vert\boldsymbol{\mathrm{G}}(s)\vert},\boldsymbol{\mathrm{g}}(s).\boldsymbol{\mathrm{r}}+\frac{ \boldsymbol{\widetilde{\mathrm{G}}}(s).\boldsymbol{\mathrm{r}} + \Delta\omega(\boldsymbol{\mathrm{r}})}{\gamma \vert{\boldsymbol{\mathrm{G}}(s)\vert}})$$ where $$$\phi^\prime(s,\boldsymbol{\mathrm{r}}) $$$ is the incremental rotation angle about the axis of rotation $$$\boldsymbol{\mathrm{n}}(s,\boldsymbol{\mathrm{r}})$$$. $$$\boldsymbol{\mathrm{k}_{act}}$$$ (actual) or $$$\boldsymbol{\mathrm{k}_{H}}$$$ (predicted) k-space trajectories were associated in pulse design problem and in case the resulting peak RF amplitude exceeds the given limits then the variably-stretched gradient waveforms are calculated by using the time-optimal VERSE method (Fig.1).

Dynamic Field Monitoring and GIRF estimation: Spatio-temporal field measurements were performed with a dynamic field camera comprising a 16-channel acquisition system and the Tx/Rx chains to operate a set of NMR field sensors (3). Determining the dynamic evolution of the field inside the sample is based on the assumption that the field can be expanded into a low number of spatially smooth basis functions which are selected as spherical harmonics here. The field inside the object was directly interpolated using the computed probe position and the obtained field measurement. Subsequent data processing includes routing the probe signal by means of transmit/receive switches to receive chains (preamplification, analog filtering, second amplifier stages) and sampling and digital conversion to 1 MHz output bandwidth by a custom-configured spectrometer based on high-speed ADC (14 bit, 250 MS/s) and field programmable gate arrays. GIRF approach (4) relies on the assumption that the system is largely LTI implying that most critical terms affecting the field are linear. We used frequency-swept pulses to successively excite the different frequencies in the bandwidth. Probe signal were acquired with a duration of 70 ms providing a frequency resolution of about 14.3 Hz and GIRFs were calculated for each gradient axis (Fig.2). 2D spatially-selective parallel RF pulses were designed for an excitation pattern of a 30 x 30 mm2 square based on a single-shot spiral-in excitation k-space trajectory which is radially undersampled to accelerate (2x) the excitation.

By applying the reVERSE method, peak RF magnitude was gradually reduced below the target magnitude (12 μT) in 5 iterations. Figure 3.a shows the individual RF waveforms and Figure 3.b shows the corresponding peak RF values. However both the magnitude and pattern of the actual gradient fields significantly deviates from their nominal counterparts which are shown here as the resulting reVERSE’d gradient waveforms at the final iteration (Figure 3.c). Figure 3.d illustrates the discrepancy of the associated k-space trajectories iteration to iteration which is assumed to be unchanged by reVERSE algorithm. Figure 4.a shows the excitation results at 7T for the cases of nominal, GIRF predicted and monitored k-space trajectories were used in the pulse design algorithm. The knowledge of either GIRF predicted or directly measured k-space trajectories highly improves the parallel RF excitations (i.e. NRMSE is reduced from 48% to 9% for the GIRF predicted and 8% for the directly measured gradient waveforms at 5th iteration) while the peak RF is limited to the given threshold of 11 μT. While the excitation accuracies are very close to each other for GIRF predicted and monitored gradients, there is a slight difference in NRMSE up to 2% which is most likely reflecting the individual fluctuations in multiple channel RF waveforms. Figure 4.b compares the initial and reVERESE’d RF pulses and Figure 4.c shows the iterative reduction of peak RF power for different cases.A method for parallel transmit VERSE pulse design is proposed based on dynamic field monitoring to maximize the excitation accuracy under strict RF power and SAR constraints. The performance of the VERSE’d pulses would even degraded more in case the roughness of the reshaped gradients increases as a result of high acceleration factors in parallel transmission, aggressive RF attenuation and large flip angles. Our approach highly improves the multidimensional parallel excitation while achieving time optimality as well (5). Any k-space trajectory can be associated and SAR can be controlled via setting the RF upper bound.