Concurrent Excitation and Acquisition (CEA) was shown to be feasible in MRI at a preclinical field strength [1] as well as a 3T clinical MR system with transmit array [2], but the signal acquisition features and contrast mechanisms have not been addressed comprehensively. In MRI with CEA, frequency modulated radiofrequency (RF) excitation pulses are applied. Thus, magnetization across the sample is excited sequentially by the combined action of the magnetic field gradients and the RF pulse. Gradient directions change during data acquisition which results in TR variation across the sample (Fig. 1), leading to changes in transverse magnetization. This signal modulation causes a non-ideal point spread function (PSF), and is a potential source of artifacts.

In this work, the T₁-modulation effects were investigated for frequency-swept excitation schemes in CEA, and changes in PSFs of 2D and 3D virtual point sources were analyzed for various acquisition schemes. Our findings lead to an optimal approach in designing pulse sequences for CEA, and can be generalized to other pulse sequences such as SWIFT [3].

CEA sequences with a radial inside-out acquisition scheme was simulated for 3 different k-space ordering methods: (1) Equidistant spokes based on the algorithm developed in [4], (2) segmented equidistant trajectory with 16 segments, and (3) the golden angle trajectory. A point source was defined on a 2D grid, and for each radial acquisition, the effective TR, TR_eff, was calculated as a function of distance from isocenter, d_n and the default TR (here: 4.2 ms), assuming a chirp excitation with a sweep range of f_o - Δf to f_o + Δf over 2 ms along with a constant gradient. Note that TR_eff changes from one radial spoke to the next for all off-isocenter positions. Transverse magnetization (M_xy) was prepared to reach steady state after 200 dummy scans, then, modulations in M_xy were calculated iteratively as a function of TR_eff, T₁ and the flip angle, α:

$$ M_{n}=M_{n-1} cos(\alpha) e^{-TR_{eff}(n-1)/T_{1}}+(1-e^{-TR_{eff}(n-1)/T_{1}}) $$

$$ M_{xy}=M sin(\alpha) $$

Using the central slice theorem [5], 2D k-space is formed by weighting each radial spoke signal by the modulation in the magnitude of the M_xy as a result of the variation in TR. Image reconstruction with zero-order gridding was used to obtain PSF of the point source located at the edge of FOV on a 512x512 grid. In extension to 3D calculations, similar steps were followed and PSFs were calculated. Segmentation and golden angle ordering was applied only along the azimuthal angle. Resulting k-space data was reconstructed using gridding with Kaiser-Bessel interpolation. PSF comparison was based on scaling and subtracting the reconstructed data obtained with T₁-modulated magnetization values and the data which was reconstructed under constant TR assumption.

In Fig. 2, TR_eff for the three different trajectories and the resulting modulations in M_xy are shown using a 2D sequence with α=10° for a point source with T₁ = 100 ms placed at (x,y)=(150,150) on a 512x512 grid. The oscillations in M_xy is more evident for golden angle trajectory. In Table 1, resulting amount of change in TR_eff, M_xy, and the PSF for appoint source at the edge of the field of view (FOV) are summarized for all 2D and 3D trajectories for T₁ values of 10 and 100 ms and α values of 10° and 30°.

T₁-modulation effects for sequential ordering of equidistant points were below 0.2% for all conditions. However, with segmented ordering, changes up to 1.8% are calculated in PSF. Golden angle trajectory resulted in the most extreme modulations in TR_eff, M_xy and PSF for majority of the simulated conditions. The maximum change in PSF of 5.2% was observed for 2D golden angle trajectory (cf. Fig.3).

As a result of sequentially satisfying the resonance conditions in frequency-swept pulses, the k-space representation of the signal is also affected. Although in most of the cases the PSF-related signal change is less than 5%, modulations can cause blurring artifacts under extreme conditions (radial segmentation schemes with lines far apart, short T₁, and/or high α). To avoid PSF artifacts, readout gradients should preferably be adjusted to follow sequential ordering of equidistant points in k-space, and low flip angles are more preferable.