Single‐Shot 2D Radial Echo Planar Imaging for Functional MRI

ABSTRACT

Purpose

To develop a novel single‐shot radial echo planar imaging (ss‐rEPI) technique for rapid, distortion‐free brain imaging in functional MRI experiments.

Methods

Radial multi‐gradient echo (radial mGRE) data were acquired on a 3T clinical scanner using a 2D ss‐rEPI readout with small golden‐angle rotations between echoes. Images were reconstructed using an iterative conjugate‐gradient method incorporating coil sensitivities, B ₀ field inhomogeneities, transverse relaxation, and field‐drift correction to account for signal inconsistencies in the extended mGRE readout. Additional k‐space‐weighted image contrast (KWIC) filtering prior to reconstruction helped reduce model mismatches at low spatial frequencies. Single‐shot rEPI image quality, contrast, and distortion were assessed against multi‐shot radial mGRE reference data. Retrospective adjustment of the KWIC filter and target TE in the reconstruction allowed the generation of multiple T ₂*weighted and phase contrast images from a single ss‐rEPI scan, enabling quantitative T ₂* mapping and QSM. Visual BOLD fMRI experiments were conducted and evaluated against Cartesian EPI measurements.

Results

Twenty‐four 3 mm thick slices of distortion‐free, multi‐contrast brain images were obtained at 2 × 2 and 1.5 mm² (ramp‐sampled) in‐plane resolution with an acquisition time of under 1.7 s. In multi‐session fMRI experiments on two subjects, ss‐rEPI demonstrated BOLD activation in the visual cortex comparable to standard EPI while also enabling functional T ₂* measurements.

Conclusion

Single‐shot rEPI enables rapid, distortion‐free 2D multi‐contrast brain imaging, offering a promising alternative to Cartesian EPI. Accurate ∆B ₀ modeling is critical for ss‐rEPI performance. Advanced reconstruction techniques and self‐calibration methods could further enhance its speed, performance, and applicability across diverse MRI techniques.

1. Introduction

Magnetic resonance imaging is a powerful but inherently slow imaging technique and the acceleration of data acquisition remains a major focus of interest despite significant advances in the past decades [1]. Techniques to increase acquisition speed include parallel imaging [2, 3, 4] and advanced reconstruction methods [5, 6] that reduce the amount of sampling needed for image formation, as well as fast pulse sequences that acquire data in minimal time. One of the earliest and most prominent fast acquisition methods is echo planar imaging (EPI) [7]. It is commonly used in functional MRI (fMRI) and diffusion tensor imaging [8, 9, 10, 11, 12, 13, 14]. EPI trajectories consist of gradient echo trains that sample multiple phase‐encoding lines during the readout to reduce the number of excitations or “shots” needed to fill k‐space. In single‐shot EPI, the entire k‐space used for image formation is collected within a single readout making it particularly interesting for imaging applications at maximal speed. Basic implementations of EPI commonly suffer from susceptibility artifacts and non‐linear distortion along the slowly sampled phase direction as a result of phase accumulation during the extended readout [15]. Over the past years, several approaches have been developed to mitigate distortion artifacts including techniques based on ΔB ₀ field mapping and registration [16, 17]. In particular, echo planar time‐resolved imaging (EPTI) has received considerable attention due to its ability to generate highly accelerated multiparameter maps with minimal distortion artifacts [18, 19, 20]. Several implementations to exploit redundancies in k‐TE space of EPTI have been developed, including a very recent single‐shot 2D EPTI version based on a subspace reconstruction [21].

Other rapid sampling approaches include non‐Cartesian trajectories such as spiral [22, 23, 24] and rosette [25, 26] readouts that also enable single‐shot imaging and have been successfully applied to various MRI applications, including spectrally selective imaging and fMRI. Spiral imaging is particularly attractive due to its efficiency in both k‐space coverage and gradient usage, resulting in high acquisition speeds. Radial sampling has also been successfully adopted in fast MRI sequences such as fast low angle shot (FLASH) [27], fast spin echo (FSE) [28] and gradient‐ and spin‐echo (GRASE) [29] acquisitions and plays an important role in cardiac MRI [30] and MR fingerprinting [31]. Potential advantages of radial sampling include its robustness to motion, the ability to generate distortion‐free images, and its incoherent undersampling characteristics [32, 33].

The development of a radial EPI (rEPI), a fast gradient‐echo sequence analogous to EPI but based on radial sampling, has been proposed but received little attention due to poor image quality [34, 35]. A major difficulty of rEPI is associated with the phase accumulation during the extended readout when combining data with varying echo time during image reconstruction. In contrast to EPI or spiral imaging where these phase effects lead to distortion or blurring, the signal evolution between different echo lines in rEPI results in signal dropout and poor results in the image formation when left unaccounted for. The signal dropout in rEPI is a consequence of phase inconsistencies accumulating at low spatial frequencies around the center of k‐space. This is particularly problematic for long echo trains and has been a major challenge for the development of single‐shot rEPI (ss‐rEPI).

Model‐based reconstruction approaches have been successfully used to account for the signal evolution in radial mGRE acquisitions in quantitative imaging [36, 37], and more recently, fast imaging of the brain [38, 39, 40, 41]. The signal evolution in these approaches is modeled using R ₂/R ₂* and ∆B ₀ terms in the iterative reconstruction [42, 43]. In the specific case of radial sampling, k‐space weighted image contrast (KWIC) filtering can be additionally utilized to mitigate phase inconsistencies at low spatial frequency. KWIC filtering was originally used for the generation of T ₂ maps from a single radial FSE dataset by exploiting the sampling redundancy at the center of k‐space [44, 45]. The KWIC filter functions as a high‐pass filter to control contrast contributions from the different echoes of the multi‐echo dataset by removing low frequency data from echo lines that are distant to the target echo time. Different segments with varying cutoffvalues can be defined to fine‐tune the filter design. When applied to an mGRE acquisition, the narrowing of the echo time range at low frequency not only determines the contrast of the reconstructed images but also reduces the phase inconsistencies at the low frequency region of k‐space.

In this work, we propose an ss‐rEPI approach based on a reconstruction that models B ₀ field inhomogeneities and transversal relaxation using a small golden angle (GA) trajectory design in combination with a KWIC filter. Our results demonstrate that artifacts from phase inconsistencies are largely mitigated with this ss‐rEPI approach so that highly accelerated, distortion‐free multi‐contrast images can be obtained in a single shot and applied in blood oxygen level dependent (BOLD) fMRI of the brain.

2. Theory

2.1. General Considerations

Radial EPI is a fast MRI acquisition technique analogous to Cartesian EPI that samples k‐space along multiple radial gradient‐echo lines rotated around the k‐space center (see Figure 1). A defining feature of rEPI is the repeated sampling of low‐frequency k‐space data for each echo during the rEPI echo train. This oversampling provides valuable k‐TE information for quantitative parameter mapping but also poses challenges for image formation in fast imaging, as data from multiple echo times must be combined into a single image. In single‐shot rEPI, the entire 2D k‐space is acquired after a single excitation, typically requiring long echo trains to achieve Nyquist or near‐Nyquist sampling coverage. Without proper correction, signal evolution during the prolonged readout causes phase and magnitude inconsistencies between adjacent k‐space points and must be accounted for during reconstruction.

FIGURE 1.

(A) Design of the radial EPI k‐space trajectory using a small GA of α = 27.198…°, and two 5‐segment KWIC filter patterns (K4) showing the k‐space distribution, (B) the temporal distribution in TE space of the 5 KWIC segments for varying target echoes, and (C) k‐space and sampling density plots for 5 KWIC filter variations (K1–K5). Trajectory segments traversed during gradient ramp‐sampling and rotational blipping are marked in red. The transition points for the KWIC filter segments [7 13 20 33 53] are based on the generalized Fibonacci sequence for N = 6. The central region of k‐space is shown in more detail for target echoes 4 and 24, which are highlighted in the temporal distribution plot (B). KWIC filtering removes low frequency echo data at varying cutoff values for segments 2–5. The integration of a golden angle scheme into the KWIC filter design allows for flexible incoherent k‐TE sampling with relative uniform coverage of the rotational plane in k‐space for each segment. KWIC filter variation K1–K4 progressively remove more of the central k‐space data, narrowing the k‐TE sampling/TE window of the central echo lines in the first segment (blue) that pass through k ₀. K5 is based on K2 but defines the filter cutoff thresholds based on the sampling ratio R = 2. Corresponding sampling ratio and segment distribution in TE space are also shown for the target TE of 20.

2.2. Model‐Based Reconstruction

A model to describe the signal evolution during ss‐rEPI acquisition s(t) can be derived from the general signal Equation (1).

$$s(t)=\int M(\rho (r),\vartheta ,t,r)·e^{-i2\pi ·k(t)·r}\mathit{dr}$$ (1)

Here, r represents spatial coordinates, ρ(r) is the spin‐density distribution, ϑ denotes parameters modeling physiological or systemic effects such as relaxation (e.g., T ₁ and T ₂/T ₂*), molecular motion (e.g., flow, diffusion, or perfusion), and acquisition parameters (e.g., echo time (TE) and flip angle), and k(t) is the k‐space location sampled at time t along the radial trajectory. The magnetization term M(ρ(r), ϑ, t, r) encompasses biophysical factors that influence signal dynamics. It was explicitly designed to include B ₀ field inhomogeneity (ΔB ₀) and R ₂* relaxation (R ₂*(r)) in our model:

$$M(\rho (r),t,r)=\rho (r)·e^{i2\pi ·\mathrm{\Delta }{B}_0(r)·t-R_2^{*}(r)·t}$$ (2)

Incorporating coil‐sensitivity profiles c _i (r) of the multi‐channel arrays with $N_{\mathit{\text{coil}}}$ elements, the signal equation becomes:

$$s_i(t)=\int c_i(r)\rho (r)e^{-i2\pi ·k(t)·r+i2\pi ·\mathrm{\Delta }{B}_0(r)·t-R_2^{*}(r)·t}\mathit{dr},i=1,\dots ,N_{\mathit{\text{coil}}}$$ (3)

To reduce computational complexity, this equation is discretized for each echo time TE _j under the assumption that echo spacing (˜1 ms) is sufficiently short to disregard ∆B ₀ phase accrual and R ₂* decay within each echo. By substituting the Fourier transformation with a Non‐Uniform Fast Fourier Transformation (NUFFT), the discretized signal model for all $N_{\mathit{\text{echo}}}$ echoes is given by:

$$\begin{array}{cc}{s}_{j,i}& =\text{NUFFT}·\left[c_i(r)\rho (r)e^{i2\pi ·\mathrm{\Delta }{B}_0(r)·{\mathit{TE}}_j-R_2^{*}(r)·{\mathit{TE}}_j}\right],\\ & i=1,\dots ,N_{\mathit{\text{coil}}},j=1,\dots ,N_{\mathit{\text{echo}}}\end{array}$$ (4)

Replacing the spin density distribution $\rho (r)$ in [4] with the expression for a modulated contrast image $I_t(r)$ at a desired target echo time $\mathit{tTE}$, given in [5], leads to the modified signal Equation (6) that can be used directly to solve for images with adjustable phase or T ₂* contrast.

$$I_{\mathit{tTE}}(r)=\rho (r)·e^{i2\pi ·\mathrm{\Delta }{B}_0(r)·\mathit{tTE}-R_2^{*}(r)·\mathit{tTE}},\mathit{tTE}=\mathit{\text{target}}\mathit{TE}$$ (5)

$$s_{j,i,\mathit{tTE}}=\text{NUFFT}·\left[c_i(r)I_{\mathit{tTE}}(r)e^{i2\pi ·\mathrm{\Delta }{B}_0·(r)·\left({\mathit{TE}}_j-\mathit{tTE}\right)-R_2^{*}(r)·\left({\mathit{TE}}_j-\mathit{tTE}\right)}\right]$$ (6)

$$i=1,\dots ,N_{\mathit{\text{coil}}},j=1,\dots ,N_{\mathit{\text{echo}}.}$$

Multi‐contrast images $I_{\mathit{tTE}}(r)$ are generated from ss‐rEPI k‐space data ${\mathrm{Y}}_{j,i}$ using the linear inverse iterative reconstruction described in [7], where a total variation sparsifying transformation $\mathit{TV}$ is used to incorporate compressed sensing via the L1 regularization term, with $\mathrm{\lambda }$ being the regularization weight. The ${\mathrm{\Delta }B}_0(r)$ and $R_2^{*}(r)$ maps are derived from preparation scans and are held constant during the ss‐rEPI optimization to reduce the computational complexity.

$${\widehat{I}}_{\mathit{tTE}}={\mathit{\text{argmin}}}_{I_{\mathit{tTE}}}\sum _{j,i}{‖s_{j,i,\mathit{tTE}}-{\mathrm{Y}}_{j,i,\mathit{tTE}}‖}_2^2+\mathrm{\lambda }{\left|\left|\mathrm{TV}\left(I_{\mathit{tTE}}\right)\right|\right|}_1$$ (7)

2.3. Field Drift Compensation

In prolonged fMRI experiments, slow field drifts due to external effects such as gradient heating are induced during the acquisition of the image time series, causing model‐data mismatches [46]. The repeated sampling of the k‐space center in ss‐rEPI allows continuous monitoring and correction of field changes. The field drift over the time series $t_a$ including $N_{\mathit{rep}}$ repetitions is hereby approximated as spatially uniform within the 2D image plane [47], so that the resulting corrected $\mathrm{\Delta }{B}_o^{\mathit{\text{corr}}}\left(r,t_a\right)$ is described as the sum of a time invariant spatial map ${\mathrm{\Delta }B}_0(r)$ and a time‐dependent uniform drift $\mathrm{\Delta }f\left(t_a\right)$:

$$\mathrm{\Delta }{B}_o^{\mathit{\text{corr}}}\left(r,t_a\right)\approx \left({\mathrm{\Delta }B}_0(r)+\mathrm{\Delta f}\left(t_a\right)\right)$$ (8)

This is incorporated into the signal model as follows:

$$s_{j,i,\mathit{tTE},t_a}=\text{NUFFT}·\left[c_i(r)I_{\mathit{tTE}}(r)e^{i2\pi \mathbf{·}\left({\mathrm{\Delta }B}_0(r)+\mathrm{\Delta f}\left(t_a\right)\right)·\left({\mathit{TE}}_j-{\mathit{TE}}_t\right)-R_2^{*}(r)·\left({\mathit{TE}}_j-{\mathit{TE}}_t\right)}\right],$$ (9)

$$i=1,\dots ,N_{\mathit{\text{coil}}},j=1,\dots ,N_{\mathit{\text{echo}}},t_a=1,\dots ,N_{\mathit{rep}},\mathit{tTE}=\mathit{\text{target}}\mathit{TE}$$

The drift $\mathrm{\Delta }f\left(t_a\right)$ is estimated from the phase accrual at the k‐space center across all echoes ($1,\dots ,N_{\mathit{\text{echo}}}$) in the time series ($1,\dots ,N_{\mathit{rep}}$). The k ₀ frequency is filtered (Savitzky–Golay) and referenced to the midpoint k ₀ frequency value of the radial mGRE pre‐scan.

2.4. Trajectory and KWIC Filter Design

Radial sampling naturally oversamples the k‐space center, where low‐frequency data critically influences image contrast and is most vulnerable to errors and severe artifacts. To help stabilize ss‐rEPI against TE‐dependent inconsistencies, KWIC filtering can be applied as a stepwise high‐pass filter that selectively removes central k‐space data points. This restricts the low‐frequency contributions primarily to echo lines close to the target TE, while allowing more distant echo lines to contribute only higher spatial frequencies. Consequently, the effective echo footprint (and thus TE range) for the contrast‐determining low‐frequency data is reduced, thereby decreasing the TE‐dependent discrepancies and associated challenges for the model‐based reconstruction.

To implement an effective KWIC filtering scheme in ss‐rEPI, uniform echo weighting across k‐space is desirable when using all consecutive echo lines or subsets thereof (see Figure S1). Golden‐angle (GA) radial sampling introduces pseudo‐randomness with near‐uniform angular coverage and is, therefore, well suited to these purposes. Small GA rotations defined in Equation ((8), (9), (10)) [48], in particular, strike a balance between distributing consecutive echo lines across a wide angular span to maximize incoherence between k‐space position and TE (k‐TE incoherence), while minimizing gradient‐blipping downtime to preserve high sampling efficiency. These properties make small‐GA rotations particularly appropriate for ss‐rEPI. The small GA radial sampling scheme is most effective for generating uniform 2D k‐space coverage when echo lines are grouped according to elements of the generalized Fibonacci sequence $G_n$ see Equation (11) [49].

Small golden angle for N = 6:

$$\alpha =\pi (\tau +6-1)=27.198\dots {\hspace{0.17em}j}^{°},\mathrm{\tau }=\frac{1+\sqrt{5}}{2}$$ (10)

Generalized Fibonacci sequence (N = 6):

$$G_1^6={1;G}_2^6=6;G_n^6=G_{n-1}^6+G_{n-2}^6$$ (11)

In our ss‐rEPI approach, a stepwise KWIC filtering scheme with varying cutoff thresholds is applied retrospectively, using Fibonacci numbers as transition points between filter segments [44]. Echo lines are assigned to filter segments based on their proximity in echo space to the target TE (see Figure 1). For different target TEs, the segmentation scheme is shifted accordingly in echo space [50]. Each KWIC filter segment is characterized by a different high‐pass windowing threshold $k_{\mathit{\text{thresh}}}$, which controls the low‐frequency contribution of the corresponding echo data see Equation (12). The cutoff values for spatial frequencies in each KWIC segment are chosen to maintain sampling density above the Nyquist criterion (R = 1) up to the last segment (see Figure 1). The Nyquist threshold is hereby calculated assuming uniform radial sampling.

$$\text{KWIC threshold}:k_{\mathit{\text{thresh}}}=\raisebox{1ex}{$N_{\mathit{\text{filt}}}$}\!\left/ \!\raisebox{-1ex}{$N_{\mathit{xy}}*\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.$}\right.*k_{\mathit{max}},N_{\mathit{\text{filt}}}=G_n^6,n=3\dots 6$$ (12)

$$N_{\mathit{\text{filt}}}=[7,13,20,33]$$

2.5. K‐Space Simulations

K‐space simulations based on forward modeling can be used to mimic the effects of signal evolution in ss‐rEPI to provide a quantitative description of the issue.

Simulations of the signal model described above demonstrated the effect of phase and R ₂* inconsistencies in the case of ss‐rEPI trajectories. K‐space data were synthesized from input images using the forward operation ($A_{\mathit{\text{encode}}}$), filtered, and reconstructed with a basic CG‐SENSE reconstruction without including ΔB ₀ and R ₂* terms ($A_{\mathit{\text{recon}}}$). The application of different KWIC filter designs ($F_{\mathit{\text{KWIC}}}$) controlled the number of echo lines passing through the k‐space center (see Figure 1) thereby modulating the amount of signal inconsistencies at the low special frequency.

$${\rho }_{\mathit{sim}}(r)=A_{\mathit{\text{recon}}}{F}_{\mathit{\text{KWIC}}}{A}_{\mathit{\text{encode}}}{\rho }_{\mathit{\text{input}}}(r)$$ (13)

K‐space simulations were used to quantitatively describe the effect of B ₀ inhomogeneity and R ₂* relaxation on image quality in ss‐rEPI and to demonstrate the effect of KWIC filtering.

3. Methods

3.1. Trajectory and KWIC Filter Design

The ss‐rEPI trajectory used in this work was generated from a sequence of 53 radial readout gradients (see Figure 1) using a small GA rotation of α = 27.198…°. Retrospective KWIC filtering during reconstruction was based on the Fibonacci numbers 7, 13, 20, and 33, defining transitions between five distinct filter segments. In addition to the five‐segment KWIC scheme K4 with transitions at echoes [7 13 20 33], we tested simplified variants in which innermost segments were combined, yielding schemes K3 [13 20 33], K2 [20 33], and K1 [33] (see Figure 1C). The k‐space trajectory was designed with a maximum gradient strength of 30 mT/m and maximum slew rate of 150 T/m/s for 2 × 2 mm² in‐plane resolution imaging, resulting in an undersampling factor of approximately 3 at the outermost k‐space points (53 out of 165 echo lines required for fully sampled radial imaging). The duration of the 53‐echo readout was 48.8 ms, with an echo spacing of 0.9 ms. In addition to the standard ss‐rEPI trajectory, we tested a ramp‐sampled version (rs ss‐rEPI) that incorporated previously excluded gradient ramp and blip samples (highlighted in red in Figure 1A). These samples accounted for ∼40% of the total readout duration and extended coverage to k _max = 3.2 cm⁻¹. The continuous readout enabled imaging at 1.5 × 1.5 mm² resolution using the identical trajectory and KWIC filter designs.

3.2. Data Acquisition

All measurements were performed on a Siemens MAGNETON Prisma 3T (Erlangen, Germany) MRI scanner equipped with a 52‐channel head coil. Phantom and in vivo brain images were obtained from two healthy adult volunteers. Participants were recruited and scanned under informed consent using a protocol approved by the joint Institutional Review Board (IRB) of the Queens Medical Center and the University of Hawaii.

The brain and spherical phantom MRI data were acquired using a multi‐slice ss‐rEPI sequence with gradient spoiling (N _slice = 24, w _slice = 3 mm, TR/TA = 1.69 s, and nTE = 53, TE(1) = 5.0 ms, ΔTE = 0.9 ms). Slices were acquired in an interleaved manner, covering a combined 72 mm thick slab with a FOV_xy of 210 mm and an in‐plane resolution of 2 × 2 mm² (1.5 × 1.5 mm² when ramp sampling was included). Flip angles of 40° and 70° were used for the T ₂*‐weighted brain images and fMRI time series, respectively. Multi‐shot GA radial multi‐gradient‐echo (mGRE) reference data were acquired (N _shots = 100) with otherwise matching imaging parameters.

Reference fMRI experiments were performed using two Cartesian EPI protocols with matching imaging parameters (N _slice = 24 (interleaved), w _slice = 3 mm, FOV_xy  = 210 mm, and 2 × 2 mm² in‐plane resolution), TE = 29 ms, FA = 70°, with TR/TA = 1.60 s, GRAPPA = 3 (35 k‐space lines) and BW = 890 Hz/Px for EPI 1 and TR/TA = 1.69 s, GRAPPA = 2 (51 k‐space lines) and BW = 1202 Hz/Px for EPI 2 in “fast” gradient mode.

3.3. Image Reconstruction

Image reconstruction and fMRI processing were performed offline using Matlab (The Mathworks, Nattick, MA). The ss‐rEPI data were filtered using the KWIC filter described above. Prior to reconstruction, the multi‐coil k‐space data were compressed to 16 virtual coils via principal component analysis [51] (see Figure 2). A linear iterative conjugate‐gradient reconstruction was used modeling coil sensitivities (SENSE) [2], B ₀ field inhomogeneities, and transversal relaxation in the signal equation to generate final images. The reconstruction included a total‐variation constraint and was based on previously described implementations [33, 52]. Non‐uniform fast Fourier transformation (NUFFT) of k‐space data was performed using the NUFFT‐toolbox [53] and combined with a limited‐memory BFGS algorithm for minimization (Poblano toolbox). ΔB ₀ field maps (Projection onto Dipole Fields) [54], R ₂* maps (monoexponential fitting based on Auto‐Regression on Linear Operations) [55], and coil‐sensitivity maps (ESPIRiT) [56] for the reconstruction of the ss‐rEPI images were generated from a separate radial mGRE acquisition with matching imaging parameters. Radial multi‐gradient‐echo reference images were reconstructed using a conjugate gradient SENSE reconstruction (MIRT toolbox) [57]. A field‐drift adjustment for extended fMRI scans was carried out using the phase information at the k‐space center from all 53 echoes within the ss‐rEPI data as described above. The frequency drift (Δf) was then used to update the initial ΔB ₀ field map for each shot during the model‐based reconstruction of the fMRI time series (see Figure 2). The field‐drift correction was performed on a slice‐by‐slice basis. Single‐shot rEPI T ₂* maps were generated via monoexponential fitting (Levenberg–Marquardt), and quantitative susceptibility maps using the MEDI toolbox [58]. Reference and ss‐rEPI maps were derived from echoes 1–53 (TE = 5.0–22.4 ms) and echoes 4, 10, 16, 22, 28 (TE = 7.8–29.6 ms), respectively (QSM: λ _ref = 10 000, λ _ss‐rEPI = 1000). EPI images were used as reconstructed by the scanner, including the vendor's built‐in motion correction, and were processed using the TOPUP method [59] in FSL [60, 61] to mitigate distortion effects.

FIGURE 2.

Schematic overview of the image reconstruction process to obtain brain images with varying T ₂*‐ and phase contrast. The single‐shot rEPI data were retrospectively filtered by applying a dynamic sliding‐window segmentation scheme of the KWIC filter for a specific target TE. The filtered data were then fed into the informed model‐based reconstruction to generate the T ₂*‐weighted brain images at the desired echo time (target TE). ∆B ₀, R ₂*, and coil maps were obtained from a separate radial mGRE scan. In addition, a field‐drift adjustment (Δf), updating the initial ΔB ₀ field map during the model‐based reconstruction, was applied for each shot, which was determined form the k ₀‐phase evolution across the 53 echoes within the ss‐rEPI train. Brain images at different echo times were generated from a single ss‐rEPI acquisition and used to generate R ₂* and quantitative susceptibility maps (QSM).

3.4. fMRI Analysis

The fMRI tasks consisted of six blocks of 20 s flickering checkerboard for visual stimulation separated by 20 s resting periods, leading to a total duration of the paradigm of 4:20 min. BOLD analyses were carried out using a general linear model with a canonical hemodynamic response function after removal of first and second order temporal trends in the data. No spatial smoothing, masking, or corrections for multiple comparisons were applied. Functional MRI analyses were carried out on the T ₂‐weighted (T ₂ w) image series as well as the series of quantitative T ₂* maps. The fMRI task was designed to produce visual activation using the Cogent 2000 toolbox [62]. Mean BOLD t‐values were calculated within a data‐derived mask obtained by averaging t‐maps across all compared conditions (ss‐rEPI and EPI) and thresholding at t‐map > 5.

4. Results

4.1. Mitigation of Phase Inconsistency in ss‐REPI Using KWIC Filtering and Model‐Based Reconstruction

K‐space simulations using the unfiltered ss‐rEPI trajectory (no KWIC) revealed high susceptibility to B ₀ inhomogeneity, resulting in severe signal dropout (see Figure 3). In contrast, R ₂* relaxation primarily modulated image contrast (see Figure S2). Applying KWIC filters substantially reduced these artifacts, with narrower filters (e.g., K4) producing fewer ∆B ₀‐related errors than broader filters (e.g., K1). A KWIC filter with a higher spatial‐frequency cutoff (R = 2; filter K5) showed slightly larger sensitivity to off‐resonance effects than its lower‐cutoff counterpart (K2). The removal of central k‐space data was associated with reduced signal strength, indicating a potential trade‐off between artifact suppression and signal‐to‐noise ratio (SNR) loss.

FIGURE 3.

Impact of KWIC filter designs on ss‐rEPI for k‐space simulations (green frame) and experimental data (blue frame), with and without ΔB ₀ and R ₂* terms in model‐based reconstruction. Reference images (TE‐matched) and ΔB ₀ and R ₂* maps (mGRE) used for simulations are shown in (orange frame). Simulated images include resampled data with KWIC filters K1–K5, without (no ΔB ₀, R ₂*), and with ΔB ₀ and R ₂* effects (with ΔB ₀, R ₂*). Experimental data are reconstructed without KWIC filtering (no KWIC), with KWIC filters alone (KWIC only), and with ΔB ₀ and R ₂* terms included in the full model‐based reconstruction (ΔB ₀, R ₂* model). Simulations incorporating ΔB ₀ and R ₂* effects resemble experimental KWIC‐only reconstructions across filter designs. Including ΔB ₀ and R ₂* terms in the full model‐based reconstruction recovers most signal, yielding nearly artifact‐free images across KWIC filter designs and without KWIC filter for brain and phantom images at TE = 22.3 ms. For later TE values (shown for TE = 40.5), images reconstructed without KWIC filtering and to a lesser extend with K1 showed loss of contrast and increased blurring. SNR values are given for experimental brain and phantom images reconstructed with the full model. A reduced drop in SNR is observed going from no KWIC to K4 in brain scans with higher B ₀ inhomogeneity than phantom experiments at TE of 22.3 ms.

These simulation findings were confirmed experimentally and used to guide the optimization of our ss‐rEPI protocol. We evaluated the impact of the KWIC filter design (K1–K5) and model‐based reconstruction with in vivo ss‐rEPI brain data. KWIC filters K1–K5 were tested with and without ΔB ₀ and R ₂* terms in the model‐based reconstruction. Consistent with the simulations, the basic reconstruction (excluding ΔB ₀ and R ₂* terms) produced severe signal dropout in unfiltered images (see Figure 3) and the use of KWIC filters (K1–K5) markedly reduced dropout and off‐resonance artifacts, with progressively lower observed dropout for narrower filters (i.e., lower central k‐space sampling density, see Figure 1). Nevertheless, residual artifacts persisted with filtering alone. Full model‐based reconstruction incorporating ΔB ₀ and R ₂* terms dramatically improved image quality, reducing visible artifacts considerably across all KWIC designs—and even without KWIC filtering (bottom three rows, Figure 3C). However, reconstructions using the full model without KWIC filtering, and to a lesser extent with the broadest filter (K1), exhibited loss of contrast and increased blurring at later echo times (red arrows). The SNR followed the trend observed in simulations, decreasing with narrower filter designs. Filter K5 (the higher‐cutoff analogue of K2) had lower SNR than K2. Overall, filters K2–K4 provided the best compromise between artifact reduction and SNR preservation in our experimental data. Additional experimental results are shown in Figure S3–S5.

4.2. Multi‐Contrast Single‐Shot rEPI Images and Quantitative T ₂ * and Susceptibility Maps

Single‐shot rEPI brain images (24 slices) were acquired at 2 × 2 × 3 mm³ spatial resolution in less than 1.7 s and compared to radial mGRE reference images. Figure 4 shows five selected slices from a healthy brain scan at echo times (TEs) of 13.2, 22.3, 31.4, and 40.5 ms using the K4 KWIC filter design. Single‐shot rEPI images are displayed side‐by‐side with mGRE references at matched TEs, along with the corresponding difference maps. Close‐up views at the level of the basal ganglia are shown in Figure S6 for TEs of 13.2, 21.2, 34.2, and 40.5 ms, accompanied by profile plots. Key anatomical features were preserved in ss‐rEPI images across TEs, as evidenced by Figure 4 and profile plots in Figure S6 with no apparent distortion as confirmed by overlaying the mGRE reference outline onto ss‐rEPI images in Figure S6. The most prominent differences were observed in high‐intensity regions at later echo times and close to regions with high B ₀ inhomogeneity, which is reflected in the difference maps and slice average RMSE values. Furthermore, an increase in graininess was observed in earlier‐TE images, while later‐TE images exhibited greater blurring. These observations held across K2, K3, and K4 filters with no discernible trends in filter performance (see Figure S7).

FIGURE 4.

Comparison of single‐shot rEPI images with TE‐matched radial mGRE reference images, including the corresponding difference maps. Selected slices of a healthy brain are shown for echo times of 13.2, 22.3, 31.4, and 40.5 ms. Images were obtained using the 5 segment KWIC filter design K4. RMSE values based on mean‐normalized intensities are given for each slice.

Multi‐contrast ss‐rEPI images were used to derive quantitative T ₂* and susceptibility maps. The comparison of maps obtained with filter designs (K4 and K2) and the radial mGRE reference is shown in Figure 5. Both, T ₂* and QSM maps were generated from echo images 4, 10, 16, 22, and 28. The inclusion of later echoes [34, 40, 45] to cover the entire echo space introduced blurring in the corresponding maps. Compared to the mGRE reference, single‐shot rEPI T ₂* mapping overestimated T ₂* values in the brain (RMSE = 8.9 ms), with greater discrepancies in high T ₂* areas and those affected by off‐resonance effects. Similarly, QSM maps obtained with ss‐rEPI showed elevated noise but generally matched the mGRE reference closely (RMSE = 0.0173 ppm).

FIGURE 5.

Comparison of quantitative T ₂* and susceptibility maps from single‐shot rEPI and TE‐matched radial mGRE reference images including the difference maps between mGRE reference and ss‐rEPI K4 (a). Quantitative maps were generated from echoes 4, 10, 16, 22, and 28 (TE = 7.8–29.6 ms) for K2 and K4 (a) and with the inclusion of later echoes 34, 40, 46 (TE = 7.8–46.0 ms) for K4 (b). RMSE values for each slice are given for difference maps shown on the bottom.

4.3. Field‐Drift Correction

Single‐shot rEPI relies heavily on accurate B ₀ inhomogeneity estimation for model‐based reconstruction. In our implementation, ΔB ₀ maps are obtained from a radial mGRE prescan. To mitigate field drift during extended fMRI acquisitions, we implemented a retrospective correction scheme using multi‐echo k ₀‐phase information from the rEPI scan itself. Repetitive k‐space center sampling enabled shot‐by‐shot monitoring of echo‐to‐echo phase evolution throughout the acquisition. The resulting k ₀‐frequencies are plotted in Figure 6 (top left) across the full experiment, including a radial mGRE prescan, ss‐rEPI fMRI scan, and post‐fMRI mGRE scan. The frequency shift (Δf) derived from the multi‐echo k ₀‐phase differences closely matched the inter‐field‐map difference (averages: 17.5 vs. 17.6 Hz; Figure 6, top right). Consequently, corrected images (10th and 150th frames, bottom left) showed minimal degradation over prolonged ss‐rEPI acquisitions compared to uncorrected ones (bottom right), demonstrating the effectiveness of the approach.

FIGURE 6.

Frequency‐drift correction during MRI data acquisition. The multi‐echo, k ₀‐phase‐derived frequency drift (Δf) is plotted over the course of the acquisition, including multi‐gradient‐echo (mGRE) scans before and after the functional MRI (fMRI) acquisition, separated by dotted vertical lines. Δf is shown pre‐ (light blue) and post‐Savitzky–Golay filtering (dark blue) for each slice and averaged across slices in red. The light‐red background highlights the typical fMRI experiment, including a single mGRE pre‐scan. The estimated frequency drift is compared to the difference between pre‐ and post‐fMRI field maps (ΔB ₀ map). Two representative fMRI time‐series images (10th and 150th frames; bottom) are shown with and without Δf adjustment, along with the resulting difference map (bottom left and right, respectively).

4.4. Functional MRI Experiments

BOLD fMRI experiments using the ss‐rEPI method were conducted on two healthy volunteers with a flickering checkerboard paradigm. Results were compared to those from standard Cartesian EPI with matched acquisition parameters (EPI 1 AND EPI 2). In the case of ss‐rEPI, the time course of the T ₂* maps was analyzed in addition to those of conventional T ₂ w images at TE = 29.6 ms. Activation patterns in the visual cortex were observed for all methods (see Figure 7). Spatial details in the activation maps were well‐resolved in T ₂ w BOLD analyses and closely aligned between ss‐rEPI and EPI. Potential smoothing effects from ss‐rEPI image blurring were minor, allowing visualization of fine activation features. In the case of T ₂* mapping derived activation maps, spatial details were not resolved to the same degree, but the activation remained strong. The analysis of T ₂ w timeseries from six MRI sessions (3 sessions for each subject, 2 of which had EPI reference scans) demonstrated comparable performance between ss‐rEPI and EPI with slightly stronger activation for Cartesian EPI which was also reflected in the pixel‐time‐course comparisons (see Figure 8). In contrast, the temporal SNR (tSNR) was significantly higher in ss‐rEPI than in EPI time series (see Figure 9). Comparisons across KWIC filter designs revealed similar BOLD activation for K2–K4, which were significantly higher than without the use of a KWIC filter. Temporal SNR values were comparable across all KWIC filters and without filtering. Image distortion was compared between ss‐rEPI and TOPUP‐corrected EPI using mGRE as reference, revealing only small differences (see Figure S8). In both cases, deviations from the reference appear to be primarily driven by signal dropout.

FIGURE 7.

BOLD activation maps from ss‐rEPI (K4 filter, TR/TA = 1.69 s, FA = 70°) and EPI (TR/TA = 1.62 s, TE = 29 ms, FA = 70°, GRAPPA = 3, TE = 29 ms) fMRI experiments using a 4:20 min‐long block paradigm for visual stimulus (6 × 20 s). Activation maps derived from functional T ₂* mapping (T ₂* ss‐rEPI, top row) and conventional T ₂‐weighted imaging at TE = 29.6 ms (ss‐rEPI, center row) are shown together with those from T ₂‐weighted Cartesian EPI (EPI 1) reference scans (EPI, bottom row). Activation maps are overlaid on the corresponding T ₂‐weighted ss‐rEPI and EPI images (left). Close‐ups of selected regions of the visual cortex with adjusted windowing are shown on the right. No explicit spatial smoothing was applied in any of the analyses.

FIGURE 8.

Comparison of fMRI results from ss‐rEPI and Cartesian EPI experiments. (A) Selected slices of tSNR maps (top) and BOLD activation maps (bottom) from ss‐rEPI with no KWIC filter and with filter designs K2–K4, as well as from an EPI reference experiment (EPI 1). (B) Time course of pixel intensities of the T ₂ w image series of ss‐rEPI (K4) and EPI (EPI 1) plotted as a single pixel intensity time plot and a stack plot of signal intensity time courses (100 highest t‐values, rows representing voxel time courses). (C) Overview of average tSNR and t‐values obtained in three separate fMRI sessions for two subjects each using conventional T ₂ w fMRI.

FIGURE 9.

Ramp‐sampled structural ss‐rEPI images (A) and QSM (B) and quantitative T ₂* (C) maps derived from multi‐contrast ss‐rEPI data, compared across three datasets: MGRE reference (ref), ramp‐sampled ss‐rEPI (rs ss‐rEPI), and standard ss‐rEPI (ss‐rEPI). Multi‐echo GRE and rs ss‐rEPI were reconstructed at 1.5 × 1.5 mm² in‐plane resolution. Single‐shot rEPI was reconstructed at 2 × 2 mm² resolution and up‐sampled.

4.5. Extension to Ramp‐Sampled ss‐rEPI

The extension of the ss‐rEPI method to include ramp‐sampling enabled imaging at higher resolution compared to the basic implementation. Multi‐contrast images were reconstructed at 1.5 × 1.5 mm² resolution. An overview of the results is provided in Figures 9 and 10, including rs ss‐rEPI brain images, corresponding T ₂* and QSM maps, as well as results from fMRI experiments and the comparison to standard ss‐rEPI and mGRE. The inclusion of ramp‐sampled data improved the resolution by 22% compared to the standard radial‐only case (ss‐rEPI), which was apparent across the different contrasts, revealing details that were previously not resolved at 2 × 2 mm² resolution. The increase in resolution was accompanied by a reduction of tSNR in the fMRI time series. Despite the lower signal strength, rs ss‐rEPI images showed strong activation in task‐based fMRI experiments with only slightly lower levels of activation than the 2 × 2 mm² resolution standard ss‐rEPI. Additional figures are shown in Figures S9 and S10.

FIGURE 10.

Ramp‐sampled BOLD activation maps from visual fMRI experiment (A) with close‐ups of the activation pattern in selected slices through the visual cortex (B), along with tSNR maps (C). Multi‐echo GRE and rs ss‐rEPI were reconstructed at 1.5 × 1.5 mm² in‐plane resolution. Single‐shot rEPI was reconstructed at 2 × 2 mm² resolution and up‐sampled.

5. Discussion

Radial EPI (rEPI) combines the advantages of radial sampling with rapid gradient‐echo imaging, offering a compelling alternative to Cartesian EPI. This study focused on single‐shot rEPI, which generates images from a single RF excitation to minimize acquisition time. Previous work has described the principles of ss‐rEPI sampling [34, 35] but highlighted challenges due to the repetitive sampling of the k‐space center. Our approach mitigates these challenges and leverages the inherent k‐TE information, extending ss‐rEPI from a fast‐imaging technique to a versatile method for rapid multi‐contrast imaging. The ss‐rEPI technique described here is built on a model‐based reconstruction framework previously developed for radial quantitative imaging using a signal model accounting for B ₀ inhomogeneity and R ₂* relaxation effects [52]. This model addresses most signal inconsistencies in well‐controlled imaging experiments (e.g., spherical phantom), however, additional strategies, such as KWIC filtering and GA ordering, were found to consistently enhance the method's performance in structural brain images and fMRI experiments.

5.1. Trajectory and KWIC Filter Design

A key innovation of the sampling approach used in our method is the integration of GA rotations with KWIC filtering. This approach facilitates retrospective targeting of different echo times, enabling single‐shot multi‐contrast imaging. The KWIC filter controls the span of echo lines contributing to the central k‐space, reducing inconsistencies that need to be addressed by the reconstruction model. In simulation and imaging experiments, KWIC filtering increased the tolerance towards data inconsistencies and was found to have a crucial impact on the robustness of the method. The small GA rotation scheme ensures a uniform sampling distribution across KWIC filter segments for varying target echo times (see Figure S1). The temporal distribution of the filter segments (see Figure 1B) increasingly deviates from the ideal centric arrangement around the target TE at the extreme ends of TE‐space, possibly affecting results slightly. Due to the incoherent characteristic of the small GA sampling, residual inconsistencies between model and data are relatively well‐tolerated in the final images (see Figure S1). Notably, significant artifacts were observed when using a sequential inter‐echo rotation scheme with α = 3.40° (see Figure S3) in combination with the model‐based reconstruction.

In the case at hand, the rotation by the small GA was associated with about 40% downtime due to gradient ramping. Further reducing the rotation angle did not shorten the readout, as gradient ramping times of the radial lines slightly exceeded times required for the rotational blips. In our implementation, 53 echo lines were acquired over a 49 ms readout, resulting in an undersampling rate of approximately R = 3 at the k‐space edges (ss‐rEPI). Increasing the number of echo lines to enhance sampling density was deemed impractical due to prolonged readout times, while reducing echo lines increased blurring in reconstructed images (see Figure S3). The trajectories were designed using moderate‐to‐high slew rates and amplitude limits to avoid peripheral nerve stimulation during extended fMRI experiments. A systematic exploration of stronger gradients was not conducted, but faster gradients could exacerbate gradient imperfections, potentially degrading image quality. Adjusting trajectory parameters, such as the rotation angle or number of echo lines, may be necessary to mitigate these effects and optimize acquisition times. However, for the readout parameters used here, gradient imperfections seemed to be a minor factor as no significant improvements were observed when an actually measured gradient trajectory using the thin‐slice method (vs. the ideal ss‐rEPI trajectory) was used in the image reconstruction (results not shown) [63, 64].

Furthermore, the adherence to a generalized Fibonacci series to determine the number of echo lines and KWIC filter design can limit optional sequence parameter combinations including in‐plane resolution, undersampling factor, and TR.

The extension of ss‐rEPI to include data sampled during gradient ramping and blipping essentially resulted in a continuous readout similar to a rosette trajectory design with additional k‐space crossings at the edges of k‐space due to the alternating left‐ and right‐handed “turns”. Although the resulting acquisition deviated from strictly radial sampling, key radial characteristics, such as repeated k ₀ crossings, were preserved and imaging at higher resolution was enabled using the same acquisition and reconstruction approach.

In this work, we focused on single‐shot rEPI; however, the extension to multi‐shot/segmented rEPI is relatively straightforward and would include adjustments of the inter‐echo rotation scheme of the trajectory to consider the additional excitations of the segmented rEPI and number of gradient‐echoes [38]. Another potential extension of the 2D rEPI method would be to include simultaneous multi‐slice imaging to further accelerate data acquisition. Both multi‐shot versions have been presented previously by our group [38].

5.2. Model‐Based Reconstruction

The presented ss‐rEPI method relies on an iterative model‐based reconstruction that directly incorporates off‐resonance and R ₂* decay into the forward signal model during the optimization. This approach successfully captured the major sources of signal evolution throughout the prolonged single‐shot readout. Resulting multiple T ₂*w magnitude and phase images enabled rapid and accurate T ₂* and quantitative susceptibility mapping with no apparent distortion. Furthermore, robust T ₂ w time‐series were obtained in BOLD fMRI experiments producing comparable activation (magnitude and fine structure) to conventional Cartesian EPI. Across multi‐session experiments, the method proved remarkably stable, confirming the effectiveness of combining KWIC‐filtered GA sampling with the model‐based reconstruction.

Aside from conventional T ₂ w BOLD fMRI, the ability to generate multi‐contrast ss‐rEPI images was used to probe functional BOLD T ₂* mapping which could have potential implications for quantitative BOLD measurements. While comparable levels of activation were observed, spatial details in the activation maps were blurred compared to T ₂ w BOLD maps. These observations were made across different filter designs. Minor residual artifacts were also visible in structural images, most prominently grainy noise at very early TE and blurring at late echo times, coinciding with the strongest R ₂* and B ₀ modulation. These artifacts potentially arise from possible noise amplification and small mismatches between the assumed physics model (monoexponential fitting, dynamic effects, etc.) and the actual data or even residual sampling errors due to gradient imperfections. Although these effects were tolerable for the current applications, further refinement of the reconstruction strategy may be beneficial.

In the current implementation predetermined ∆B ₀, R ₂*, and coil‐sensitivity maps from a separate scan were used in a linear conjugate gradient SENSE reconstruction to generate the final images. Fixed maps significantly simplify the optimization problem. However, they also lead to potential sources of instability when inconsistencies between pre‐scan and ss‐rEPI acquisition arise. This is particularly problematic in the case of extended fMRI scans for which the potential for inconsistencies from motion, field drift, or other sources is elevated. The implementation of a field‐drift correction based on the repetitive sampling of k ₀ successfully mitigated the instability towards field drift; however, motion‐related inconsistencies were not addressed in the current implementation. Furthermore, subtle bias towards the reference image in the fMRI time series could also attenuate the BOLD signal. This might be an explanation for the improved tSNR but slightly weaker BOLD activation for ss‐rEPI compared to Cartesian EPI. The need for additional scans also limits the significance of the ss‐rEPI method for MRI applications other than fMRI, and methods to derive maps from the actual rEPI data itself would be highly desirable.

To further advance the ss‐rEPI method, a major focus will therefore be placed on the implementation of more sophisticated reconstruction techniques that adjust ∆B ₀ and R ₂ maps during the optimization [37, 41, 65] to potentially avoid the need for pre‐scans altogether. The inclusion of subspace reconstruction approaches could help to further accelerate the technique, as successfully shown for the Cartesian single‐shot EPTI case [20, 21].

6. Conclusion

In this work, the concept of single‐shot rEPI was revisited and extended by implementing a multilayered approach that enabled high‐quality single‐shot imaging. Sampling considerations such as a uniform echo‐time weighting of k‐space and the KWIC filter were adopted and combined with a model‐based reconstruction to account for phase evolution and T ₂* relaxation during the multi‐echo readout. Each contributed to the stability and integrity of the image formation and was critical for the successful application of the method in fMRI applications. This new single‐shot rEPI approach enabled rapid distortion‐free 2D imaging and the flexibility to modify R ₂* contrast from within a single dataset, demonstrating the potential of ss‐rEPI as a fast, multi‐contrast imaging alternative. However, further development of this technique, particularly towards self‐calibration, is desired to improve the significance of ss‐rEPI for other imaging applications.

Funding

This work was supported by National Institutes of Health, P20GM139753 and R01 EB028627.

Supporting information

Figure S1: Root‐mean‐square error (RMSE) plots for the KWIC filter K4 and plot showing the temporal distribution of the filter segments. The integration of a golden angle scheme into the KWIC filter design allows for flexible incoherent k‐TE sampling with relative uniform coverage of the rotational plane in k‐space for each segment as demonstrated by the RMSE plots shown. The RMSE between the ss‐rEPI and the ideal sequential angular echo line distribution (with $\alpha =\pi /N_{\mathit{seg}}$) is used as a sampling uniformity metric. For all segments RSME values are at or below the reference of the sequential small golden angle.

Figure S2: Simulated phantom and brain images modeling either ΔB ₀ or R ₂* effects at a target TE = 22.3 ms. Signal‐to‐noise ratio (SNR) values for the phantom images with no B ₀ inhomogeneity (ΔB ₀ = 0) are displayed above the images to illustrate the effect of removing central k‐space data during KWIC filtering on noise. As is evident from the brain images, tissue contrast is primarily regulated by the R ₂* term, whereas ΔB ₀ inhomogeneity can cause severe signal loss due to intravoxel dephasing.

Figure S3: (A) Single‐shot rEPI brain images obtained with R ₂* decay, ΔB ₀ off‐resonance, or both effects are excluded from the signal model during model‐based reconstruction. (B) Comparison of ss‐rEPI brain images acquired with golden‐angle (GA) rotation versus sequential small‐angle rotation (Δα = 3.40°) between successive echo lines. (C) Single‐shot rEPI brain images at increasing effective acceleration factors (R≈3 to R = 24) obtained by retrospective undersampling of the single‐shot trajectory. (D) Normalized difference images between mGRE reference and undersampled ss‐rEPI images shown in (C).

Figure S4: Impact of ΔB ₀ deviations on single‐shot images obtained with small GA KWIC filtered (K4) ss‐rEPI, small GA ss‐rEPI without KWIC filtering, and sequential echo ordering. Experimental data was reconstructed using differently scaled field maps (0.75–1.5×) ΔB ₀ to simulate potential deviations from the reconstruction model.

Figure S5: Impact of pre‐scan undersampling on ss‐rEPI image quality. Brain images obtained with coil, ΔB ₀, and R ₂* maps generated from the pre‐scan data with varying degree of retrospective undersampling (N _blades = 100, 50 25, and 12) and theoretical acquisition length for 24 slices (t _acq = 169, 85, 42, and 20 s, respectively) are shown alongside corresponding mGRE images and ΔB ₀ and R ₂* maps.

Figure S6: Close‐up views of a selected slice of brain ss‐rEPI images at the basal ganglia level for TE = 13.2, 22.3, 31.4, and 40.5 ms (top), alongside two intensity profile plots per echo time (bottom). The outline of the mGRE reference image is overlaid in red on the ss‐rEPI images to demonstrate geometric fidelity.

Figure S7: RMSE between ss‐rEPI brain images and mGRE references across selected slices for KWIC filters K1–K4 and without KWIC filtering. No significant differences in RMSE were observed with the only exception being the unfiltered case at the latest echo time (TE = 40.5 ms), which shows markedly higher RMSE due to severe contrast loss relative to the mGRE reference.

Figure S8: Left: Geometric fidelity assessment. Selected slices from the mGRE reference, ss‐rEPI at early (TE = 7.8 ms) and late (TE = 40.5 ms) echo times, and standard single‐echo EPI reference. The mGRE brain outline (red contour) is overlaid on all images to highlight distortion and signal drop‐out. Right: Multi‐echo ss‐rEPI analysis (KWIC filter K4). Mean tSNR and mean t‐values as a function of echo time are plotted on the top for TEs = 7.8, 13.2, 18.7, 24.2, 29.6, 35.1, and 40.5 ms. Temporal SNR maps and BOLD activation maps (5 < t‐values < 14) are shown below.

Figure S9: Close‐up views of a selected slice from ramp‐sampled ss‐rEPI brain images (1.5 × 1.5 mm² resolution) alongside TE‐matched radial multi‐echo gradient‐echo (mGRE) reference images at echo times of 13.2, 22.3, 31.4, and 40.5 ms. All ss‐rEPI images were reconstructed using the 5‐segment KWIC filter design (K4). Corresponding difference maps and RMSE values calculated from mean‐normalized intensities are provided for each echo time.

Figure S10: BOLD activation maps from ramp‐sampled ss‐rEPI (K4 filter, TE = 29.6 ms, TR/TA = 1.69 s, FA = 70°) fMRI experiment using a 4:20 min‐long block paradigm for visual stimulus (6 × 20 s). No explicit spatial smoothing was applied in the analysis. Activation maps are overlaid on ss‐rEPI images.

Data Availability Statement

The reconstruction code, raw k‐space data, and main scripts are available at https://github.com/crettenm/ss‐rEPI, and Zenodo.org (https://doi.org/10.5281/zenodo.19520791).