MRI with Sub-Millisecond Temporal Resolution

Abstract

Purpose:

To demonstrate an MRI technique – Sub-millisecond Periodic Event Encoded Dynamic Imaging or SPEEDI – for capturing cyclic dynamic events with sub-millisecond temporal resolution.

Methods:

SPEEDI is based on an FID or an echo signal in which each time point in the signal is used to sample a distinct k-space raster, followed by repeated FIDs or echoes to produce the remaining k-space data in each k-space raster. All acquisitions are synchronized with a cyclic event, resulting in a set of time-resolved images of the cyclic event with a temporal resolution determined by the dwell time. In SPEEDI, spatial encoding is accomplished by phase-encoding. SPEEDI was demonstrated in two experiments at 3 Tesla to (a) visualize fast-changing electric currents that mimicked the waveform of an action potential, and (b) characterize rapidly-decaying eddy currents in an MRI system, with a temporal resolution of 0.2 ms and 0.4 ms, respectively. In both experiments, compressed sensing (CS) was incorporated to reduce the scan times. Phase difference maps related to the dynamics of electric currents or eddy currents were then obtained.

Results:

In the first experiment, time-resolved phase maps resulting from the action-potential-mimicking current waveform were successfully obtained and agreed well with theoretical calculations (normalized root-mean-square error = 0.07). In the second experiment, spatially resolved eddy current phase maps revealed time constants (27.1±0.2 ms, 41.1±3.5 ms, and 34.8±0.7 ms) that matched well with those obtained from an established method using point sources (26.4 ms, 41.2 ms and 34.8 ms). For both experiments, phase maps from fully-sampled and CS-accelerated k-space data exhibited a high structural similarity (>0.8) despite a two- to three-fold acceleration.

Conclusions:

We have illustrated that SPEEDI can provide sub-millisecond temporal resolution. This capability will likely lead to future exploration of ultra-fast, cyclic biomedical processes using MRI.

Introduction

Increasing temporal resolution has been a major impetus for MRI technical development for several decades. Time-efficient strategies of k-space sampling, coupled with advanced image reconstruction (1–5) and radiofrequency (RF) coil technologies (6), have advanced temporal resolution of MRI to the order of ~ 10 – 100 milliseconds, making it possible to study many rapid dynamic processes such as cardiac motion (7) and kinetic movements (8). Despite these exciting developments, a number of important biological and physical processes on a temporal scale of milliseconds or sub-milliseconds remain invisible by MRI.

Many ultra-fast physiological, biophysical, or physical processes are periodic, offering an opportunity to capture these processes in multiple cycles. The use of periodicity to visualize a dynamic process is demonstrated in many electrocardiogram-gated cardiac MRI studies, where the time scale is approximately one second for human subjects (7). To extend this strategy to the millisecond or sub-millisecond time scales, however, traditional MRI pulse sequences fall short because the temporal resolution in these sequences is limited by the sequence length, readout duration, or the time required to sample at least one k-space line. In solid-state imaging where excessive line broadening arising from anisotropic dipolar interactions considerably accelerates the decay of an NMR signal, k-space can be sampled point-by-point, instead of line-by-line (9). This approach, known as single-point imaging, was extended to acquiring multiple time points along an FID or a spin echo for measuring the spatial distribution of dynamic eddy current changes (10). In a method known as SPREEDY (SPatially-REsolved EDdY current measurement), successive time points during the course of an NMR signal are used to capture the time evolution of spatially varying eddy currents with a temporal resolution of the order of 10 μs to 0.1 ms (10). Although this method is fully capable of producing a time-resolved 2D or 3D image, its implementation was in 1D on a set of point sources in order to reduce the total imaging times. Extension of this approach to 2D imaging was recently demonstrated on water phantoms, primarily for visualizing the dynamic evolution of magnetization dephasing under the influence of a gradient (11).

Built upon prior work (9–11), we herein describe an MRI technique, which we call Sub-millisecond Periodic Event Encoded Dynamic Imaging or SPEEDI. This technique is capable of capturing a periodic event with a sub-millisecond temporal resolution in 2D or 3D imaging where the scan times can be reduced by using compressed sensing (CS) (4). We demonstrate SPEEDI by employing two examples: (a) visualization of fast-changing electric currents that mimic an action potential in a phantom, and (b) characterization of rapidly decaying eddy currents in an MRI system. Through these specific examples, we show the technical feasibility of using SPEEDI to capture ultra-fast, cyclic processes that have not been previously visible by MRI.

Methods

SPEEDI Sequence

A conceptual 2D SPEEDI pulse sequence is shown in Fig. 1 which uses an FID signal as an example. Unlike conventional MRI in which an FID or an echo signal is used to encode spatial or chemical shift information, SPEEDI uses the signal to resolve a dynamic event with a temporal resolution determined by the dwell time Δt. Following slice selection with an excitation RF pulse, 2D in-plane spatial encoding is accomplished by two orthogonal phase-encoding gradients, with each phase-encoding step synchronized with a periodic event under study (the vertical red arrows in Fig. 1 indicate synchronization). In doing so, the same time-point t_j in the FID (i.e., any point in the set {t₁, t₂, …, t_j, …, t_N}) from M acquisitions, each synchronized with the periodic event, can be grouped together into a single k-space matrix consisting of M data points. Each k-space matrix is reconstructed individually to produce an image that corresponds to a specific time point t_j in the FID. A collection of all N time points over the course of the FID provides a time-resolved description of the periodic event. With SPEEDI, the temporal resolution of MRI is no longer determined by how fast k-space is traversed or how long the readout window is, but instead by the dwell time Δt (e.g., 50 μs with a receiver bandwidth rBW of ±10 kHz; Δt = 1/(2 · rBW)). The 2D sequence in Fig. 1 can be extended to 3D by applying a third phase-encoding gradient along the “slice-selection” direction. In addition, the FID signal can be substituted with a spin-echo signal, a stimulated echo signal, or other NMR signals.

Figure 1:

A 2D SPEEDI pulse sequence diagram using an FID. Each TR is synchronized with a periodic event. Each time point t_j from the set {t₁, t₂, …, t_j, …, t_N} in the FID corresponds to an individual k-space matrix. After repeating the sequence M times, N k-space matrices, each containing M points, can be obtained and reconstructed into N time-resolved images. The temporal resolution is determined by the acquisition bandwidth or the dwell time.

Due to the reliance on phase-encoding for spatial encoding, the scan time in SPEEDI can be long. However, this problem can be mitigated by using lower spatial resolution or sparse k-space sampling and the associated reconstruction techniques such as parallel imaging (1–3), CS (4), and others (12). The exclusive use of phase-encoding for spatial encoding in SPEEDI provides the flexibility to obtain an arbitrary k-space sampling pattern by manipulating the phase-encoding gradient areas. Thus, SPEEDI meshes nicely with a number of advanced reconstruction techniques (such as CS) by offering a sparse, random, and uncorrelated k-space sampling pattern.

Experimental

The SPEEDI sequence in Fig. 1 was implemented on a 3T GE MR750 scanner (General Electric Healthcare, Waukesha, Wisconsin). To demonstrate the feasibility of SPEEDI for capturing ultra-fast periodic events, two experimental studies were conducted using an 8-channel head coil. In the first experiment, a phantom was constructed with a 5.0 cm × 2.5 cm rectangular copper wire loop submerged in distilled water inside a plastic bottle with a square cross-section of 5.5 cm × 5.5 cm (Figs. 2A and 2B). The magnetic field produced by the wire loop with dynamic current I(t) is given by the Biot-Savart law:

$$B\left(t\right)={\int }_0^{l}dB=\frac{{\mu }_{0}I\left(t\right)}{4\pi d}\left(sin{\beta }_2-sin{\beta }_1\right),$$ [1]

where l is the length of the wire, μ₀ is the magnetic permeability, t is time, and the other geometric parameters are defined in Fig. 2C. The corresponding time-dependent phase change φ(t) in the image can be calculated from:

$$\phi \left(t\right)=\gamma {\int }_0^{t}B\left(t^{\prime }\right) d{t}^{\prime }.$$ [2]

Figure 2:

A custom-made water phantom (A) for electric current measurement, a wire loop in the phantom (B), and the magnetic field $\overrightarrow{B}$ (C) generated in a segment of the wire with a length of l and a current of I. The geometric parameters in the figure are used in Eq. [1]. In the experiment, the imaging plane was perpendicular to the wire loop and intersected in the middle of the wire as shown by the dash line in (B).

To deliver a time-varying current I(t) to the wire loop, a programmable pulse generator, PulsePal (Sanworks, Stony Brook, NY; Fig. 3A) (13), was used in synchrony with the SPEEDI pulse sequence shown in Fig. 1 by employing the RF unblanking signal from the scanner as a trigger. Two current waveforms were used in the study: (a) a rectangular waveform with a duration of 50 ms and an amplitude of 3 mA (Fig. 3B), and (b) a waveform imitating the shape of an action potential across a neuron membrane using a Hodgkin–Huxley model (14) with the parameters shown in Fig. 3C. With each current waveform, the following parameters were used in the SPEEDI sequence: flip angle = 90°, TR = 122 ms (to reduce signal saturation), TE = 2.0 ms, slice thickness = 3 mm, FOV = 8 cm × 8 cm, matrix = 64 × 64, rBW = ±2.5 kHz (temporal resolution Δt = 0.2 ms), number of sampling points = 256, and scan time = 8 min 20 sec for full k-space acquisition. To decrease the scan time to 4 min 10 sec, CS acquisition with an acceleration factor of two was performed (see Supporting Information Figure S1A). The acquisition was performed twice, with and without the current in the wire loop, to enable a phase difference calculation so that the phase errors caused by the unwanted temporal B0-field instability (such as B0 drift) and/or spatial B0-field inhomogeneities were removed.

Figure 3:

Two current waveforms used in the first experiment: a rectangular current waveform (B) and an action-potential-mimicking waveform (C). Both waveforms, which were generated using the pulse generator PulsePal in (A), were recorded using an oscilloscope while scanning. The RF unblanking signal from the scanner was used to trigger the PulsaPal without a delay in (B) and with a 5 ms delay in (C). The duration of the rectangular waveform was 50 ms with a current amplitude of 3 mA. The waveform in (C) was 5 ms with an interval of 15 ms and a peak current amplitude of 3 mA.

In the second experiment, dynamic evolutions of spatially resolved eddy currents were investigated. Time constants τ and amplitudes α of eddy currents on a commercial 3T MRI scanner were measured with two point sources using an established method (15). The eddy current measurements included B0, on-axis linear, and cross-term linear terms (16). All the measured eddy current terms were compensated except for one of the following three terms: (a) B0 term (τ = 26.4 ms); (b) linear cross-term from y to x (y→x; τ = 41.2 ms); and (c) linear cross-term from y to z (y→z; τ = 34.8 ms), where x, y, and z denote the three physical gradient axes. In each of the three cases, a spherical silicone phantom was scanned in the coronal plane using a modified SPEEDI sequence by placing a trapezoidal eddy-current testing gradient (G_test; amplitude = 45 mT/m, ramp times = 0.25 ms, and duration = 3 ms) along the physical y-axis 10 ms prior to the excitation RF pulse in the SPEEDI sequence. The acquisition parameters were similar to those used in the first experiment except for TR = 200 ms, FOV = 16 cm × 16 cm, bandwidth = ±1.25 kHz (temporal resolution = 0.4 ms), scan time = 13 min 40 sec for full k-space acquisition, and 4 min 33 sec for CS acquisition with a 3-fold acceleration (see Supporting Information Figure S1B). Similar to the first experiment, the acquisition was performed twice, with and without the eddy-current testing gradient G_test, to enable a phase difference calculation so that the phase changes irrelevant to eddy currents (such as slow B0 drift) could be eliminated.

In both experiments, phase difference image reconstruction was performed at each time point along the FID on the fully-sampled and CS-accelerated k-space data using a standard algorithm (16) and a CS-based reconstruction method (4), respectively. All image reconstructions were accomplished with customized Matlab programs (MathWorks, Inc., Natick, MA).

Image Analyses and Computer Simulations for Comparison

To compare the phase maps obtained from fully-sampled and CS-accelerated acquisitions, three quantitative image analyses were performed. First, relative errors between the phase maps from the fully-sampled and CS-accelerated aquisitions (denoted by IMG_full and IMG_cs, respectively) were calculated with the following equation:

$$err=\frac{IM{G}_{\mathit{\text{full}}}-IM{G}_{cs}}{IM{G}_{\mathit{\text{full}}}} \times 100\%.$$ [3]

The full width at half maximum (FWHM) of the phase error histogram was used to qunatify the errors. Second, the structural similarity (SSIM) of the phase maps from the two acquisitions was evaluated (17):

$$\mathit{\text{SSIM}}=\frac{\left(2M_{\mathit{\text{full}}}{M}_{cs}+c_1\right)\left(2{\sigma }_{\mathit{\text{full}},cs}+c_2\right)}{\left(M_{\mathit{\text{full}}}^2+M_{cs}^2+c_1\right)\left({\sigma }_{\mathit{\text{full}}}^2+{\sigma }_{cs}^2+c_2\right)} \times 100\%,$$ [4]

where M_full and σ_full are the average and standard deviation for IMG_full, respectively. The corresponding parameters for IMG_cs are defined similarly. σ_full,cs is the cross-covariance for IMG_full and IMG_cs; c₁ = (0.01L)² and c₂ = (0.03L)² are two stabilization parameters where L is the dynamic range of the pixel intensities; and the peak SNR (PSNR) of IMG_cs to IMG_full was determined by using:

$$\mathit{\text{PSNR}}=10lo{g}_{10}\left(\frac{{\rho }^2}{MSE}\right),$$ [5]

where ρ is the peak value of the phase map, and MSE is the mean-squared error between IMG_full and IMG_cs.

To establish a gold standard for validating the results from the first experiment, a computer simulation was performed with a set of parameters identical to those used experimentally. Using Eqs. [1] and [2], a series of time-resolved phase maps were first generated in a plane corresponding to the imaging plane. A comparison was then performed between the phase evolution obtained experimentally using SPEEDI and the theoretical phase evolution obtained from the simulation. Quantitatively, a normalized root-mean-square error (NRMSE) was evaluated between the experimental and theoretical phase evolutions by using:

$$\mathit{\text{NRMSE}}=\frac{\sqrt{\frac{1}{n}{\sum }_j{\left(x{\left(j\right)}_{acq}-x{\left(j\right)}_{sim}\right)}^2}}{\text{max}\left({\mathit{x}}_{\mathit{s}\mathit{i}\mathit{m}}\right)-\text{min}\left({\mathit{x}}_{\mathit{s}\mathit{i}\mathit{m}}\right)},$$ [6]

where n is the number of samples in the phase map, j indicates the jth point, and x_acq and x_sim are the experimentally obtained and the simulated phases, respectively.

For the second experiment, the time evolution of eddy-currents-induced phases was plotted pixel by pixel. For each plot, a time constant was estimated by fitting an exponential model to the phase evolution curve (18,19). The mean and standard deviation of the time constants were obtained from a circular region of interest (ROI) placed at the center of the phantom (~10 pixels in radius). These mean time constants were compared with the corresponding time constants obtained using a conventional eddy current measurement method (15).

Results

First Experiment: Visualization of Fast-changing Currents

The time evolution of the phase difference maps, resulting from the rectangular current pulse, was captured with a temporal resolution of 0.2 ms (Fig. 4A). Each phase map corresponds to a specific time point in the FID (numbered by 1, 2, …, 100), and the collection of the images spans a duration of 20 ms. Figures 4B and 4C display a pair of representative phase maps obtained from the fully-sampled and CS-accelerated SPEEDI acquisitions, respectively. Both phase maps were consistent with the simulation results (Fig. 4D), as evidenced by the matching dipole pattern. In addition, the phase map from the CS-accelerated k-space acquisition exhibited almost identical features to those from the fully-sampled acquisition, despite a two-fold scan time reduction. The SSIM and PSNR were 0.856 and 33.99 dB, respectively, indicating a high degree of similarity. The histogram (Fig. 4F) of the relative error map (Fig. 4E) between the two acquisitions showed that the FWHM of the error distribution was within −11.1% and 15.1%, further supporting a good agreement between the two acquisitions.

Figure 4:

A set of 100 phase difference maps (A), acquired with full k-space sampling, covering a total time span of 20 ms with a temporal resolution of 0.2 ms. The phase evolution as a result of the rectangular current waveform can be visualized in the time series. The first row on the right panel of the figure shows a zoomed phase difference map with full k-space acquisition (B), a corresponding phase difference map with CS-accelerated acquisition (C), and a phase different map from the simulation (D) which was intentionally off-centered to match the experimental results. All these phase maps corresponded to a TE of 20 ms. The CS-accelerated acquisition halved the scan times without noticeably degrading the image quality. The CS-accelerated and fully-sampled phase maps exhibited a high degree of similarity with an SSIM of 0.856 and a PSNR of 33.99 dB. The relative error map between (C) and (B) is displayed in (E), together with the histogram of the relative errors in (F), with an FWHM between −11.1% and 15.1%.

Figure 5A shows time evolution of the phase difference maps associated with the action-potential-current waveform with a temporal resolution of 0.2 ms. Figure 5B displays the applied current waveform (blue line), together with the dynamic phase change (black line) at a randomly selected point in the image (indicated by the arrow in Fig. 5A) and the simulated phase evolution (red line) using Eq. [2]. The experimentally measured and theoretically simulated phase evolution curves agreed well with each other with an NRMSE of 0.07.

Figure 5:

In (A), representative dataset from a stack of time-resolved phase maps with a temporal resolution of 0.2 ms is displayed. The action-potential-mimicking current waveform (blue line) leading to the phase evolution in (A) is shown in (B), together with the dynamic phase change (black line) at a randomly selected point in the image (indicated by the black arrow in (A)) and the simulated phase evolution (red line) using Eq. [2]. The total duration of the input current was 35 ms, including a 5 ms delay at the beginning.

Second Experiment: Characterization of Eddy Currents

Figure 6 shows the first 10 phase difference maps with a temporal resolution of 0.4 ms from fully-sampled (Fig. 6A) and CS-accelerated acquisitions (Fig. 6B) in the eddy current characterization experiment. Each sub-figure contains three rows of images, corresponding to B0 eddy currents (τ = 26.4 ms), y→x cross-term linear eddy currents (τ = 41.2 ms), and y→z cross-term linear eddy currents (τ = 34.8 ms), respectively. The phase maps associated with the B0 eddy currents were spatially uniform, as expected, but temporally varying as a result of the dynamic nature of eddy currents. In contrast, the phase maps of cross-term linear eddy currents varied both spatially and temporally, with a linear phase change along the direction of the eddy-current recipient axis (x- or z-axis). Even with an acceleration factor of three, the phase difference maps from the CS-accelerated acquisition were virtually identical to those from the fully-sampled acquisition. The SSIMs for the three rows of phase maps between Figs. 6A and 6B were 0.988±0.003, 0.977±0.012, and 0.933±0.021, respectively, and the corresponding PSNRs were 44.79±1.68 dB, 33.26±2.51 dB, and 29.00±1.62 dB, respectively.

Figure 6:

The first 10 out of a total of 256 time-resolved phase difference maps arising from eddy current perturbations obtained from fully-sampled (A) and CS-accelerated (B) k-space data. In each sub-figure which has a temporal resolution of 0.4 ms, the time constants of uncompensated B0, y→x, and y→z linear eddy current terms were 26.4 ms, 41.2 ms, and 34.8 ms, respectively. The CS-accelerated acquisition with a three-fold reduction in scan times produced comparable phase difference maps as the fully-sampled acquisition. The SSIMs for the three rows of phase maps between (A) and (B) were 0.988±0.003, 0.977±0.012, and 0.933±0.021, respectively, and the corresponding PSNRs were 44.79±1.68 dB, 33.26±2.51 dB, and 29.00±1.62 dB. The CS acquisition resulted in smoother edges (indicated by the arrows) than the fully-sampled acquisition likely due to the denoising feature of CS reconstruction.

Figure 7 displays a set of phase evolution curves for different types of eddy currents with a temporal resolution of 0.4 ms from two randomly selected points in the image. All the phase evolution curves were in agreement with the eddy current model described by Jehenson et al. (19). Using the phase maps from the fully-sampled acquisition, the time constants calculated within the circular ROI for the three different types of eddy currents were 27.1±0.2 ms, 41.1±3.5 ms, and 34.8±0.7 ms, respectively, which matched well with those measured using an established method (15) as a gold standard (26.4 ms, 41.2 ms and 34.8 ms, respectively; Table 1). The time constants obtained from the phase maps of the CS-accelerated acquisition were also consistent with the reference standard, as shown in Table 1. It is worth noting that the two exponential curves from B0 eddy current were similar due to their spatially independent nature. In contrast, the exponential curves from linear cross-term eddy currents showed opposite trends, reflecting their spatial dependency.

Figure 7:

Phase evolutions (normalized to their maximum phase value) from two randomly selected points in the image under various eddy current perturbations (blue, green and red colors are for B0, y→x, and y→z linear eddy currents, respectively). The temporal resolution for all curves was 0.4 ms. The time constants in the figure were estimated by curve fitting using the eddy current model in reference (19). The mean value of the time constants within the white circle for each of the three types of eddy currents is given in Table 1.

Table 1:

Comparison of the time constants calculated from the fully-sampled and CS-accelerated acquisitions for measuring the three different types of eddy currents.

	B0	y→x	y→z
Gold standard	26.4 (ms)	41.2 (ms)	34.8 (ms)
Full acquisition	27.1±0.2	41.1±3.5	34.8±0.7
CS acquisition	27.0±0.4	39.7±2.9	32.8±3.7

Discussion

We have described an ultra-fast MRI technique – SPEEDI – that offers sub-millisecond temporal resolution. With this capability, we have experimentally observed fast-changing electric currents in a phantom and the dynamics of spatially varying eddy currents in an MRI system. These examples provide a proof-of-concept demonstration of SPEEDI and illustrate that the temporal resolution of MRI can be improved by 2–4 orders of magnitude compared with the temporal resolutions currently in use.

Unlike the vast majority of fast MRI techniques, SPEEDI is based on the idea that a non-frequency-encoded MRI signal can be utilized to provide an ultra-high temporal resolution that is determined by the dwell time. By using phase-encoding exclusively for spatial localization, the conventional frequency-encoding domain is freed up to resolve rapid dynamic changes with sub-millisecond temporal resolution. Due to the reliance on phase encoding to perform spatial localization in multiple dimensions, an obvious issue is the lengthened acquisition times. The use of CS can mitigate this problem, as demonstrated in this study which showed consistent results between the fully-sampled and CS-accelerated acquisitions, despite a 2- to 3-fold scan time reduction. In addition to CS, SPEEDI can also benefit from many recently developed techniques on sparse sampling and the associated image reconstruction techniques (20). For example, SPEEDI can be combined with SENSE (2), GRAPPA (3), SMS (21), low-rank (22) and sparse matrix decomposition (12), etc. Alternately, the acquisition times can be reduced by reducing the spatial resolution.

Although our experimental demonstrations were performed on physical systems, the potential of extending SPEEDI to investigating ultra-fast, cyclic biological processes is clear. The ability to achieve sub-millisecond temporal resolution can open a range of possibilities to investigate cyclic biological processes and phenomena that have not been previously accessible by MRI, including tracking the dynamic evolution of neuronal currents (23), visualizing aortic valve opening/closing (24), monitoring transcranial alternating current stimulation (tACS) (25), and assessing vocal fold oscillations (26). In particular, neuronal currents elicited by a stimulus can provide a more direct measure of neural activities than the widely used blood-oxygen-level-dependent (BOLD) contrast for studying brain functions (27–29). The inadequate temporal resolution, however, has been one of the factors that prevent MRI from capturing the dynamic evolution of neuronal currents (23). Although other challenges (such as a minute neuronal current amplitude) are also present, the sub-millisecond temporal resolution afforded by SPEEDI can at least help address a technical barrier towards MRI-based visualization of neuronal currents. The potential applications of SPEEDI can expand beyond phase images. Magnitude SPEEDI images may be able to visualize the dynamics of rapid opening and closing of aortic valve, which occurs on the order of several tens of milliseconds (24). Abnormalities of aortic valve opening and closing are common and lead to stenosis and regurgitation which are important causes of morbidity and mortality. However, due to the limited temporal resolution of current MRI, valvular abnormalities are examined using 2D or 3D echocardiography in clinical practice. With the sub-millisecond temporal resolution, SPEEDI may help expand cardiac MRI into this important area.

The SPEEDI sequence can also be expanded from a technical perspective. First, the concept of SPEEDI can be extended to a number of NMR signals beyond FID, including spin echo, stimulated echo, and multiple spin echoes. Another variation of SPEEDI is to use gradient echo train or spin echo train to provide sub-millisecond temporal resolution with each echo-readout corresponding to an image (30). By employing both phase and frequency encodings, this variation can considerably reduce the scan times. Second, SPEEDI can also be extended to 3D imaging, especially when combined with advanced sparse sampling techniques to reduce the scan times. Lastly, each SPEEDI image corresponds to a different TE. As a result, a T2* map can be readily produced from the SPEEDI magnitude images by employing an exponential fitting. This can be particularly useful to measure ultra-short T2* values (e.g., ≤ 1 ms).

In this study, we have directed our effort to achieving the highest possible temporal resolution that is determined by the receiver bandwidth. Some physical or biological events, however, do not require an exceedingly high temporal resolution. A number of strategies can be used to make SPEEDI adaptive to a range of temporal resolutions needed for specific applications. First, a narrow receiver bandwidth can be selected to intentionally reduce the temporal resolution. Second, a broad receiver bandwidth can be kept, followed by averaging the neighboring time points in the signal to degrade the temporal resolution while achieving a higher SNR. Third, the piece-wise temporal segments (e.g., every 16 points) can be used to incorporate spatial encoding, thereby reducing the required phase-encoding steps and consequently the overall scan times. This approach essentially trades the temporal resolution for spatial resolution. The above three strategies are illustrating examples; and other strategies may also exist.

One obvious limitation of SPEEDI is the varying T2*-weighting in the magnitude images at different time points. The use of phase images as shown in this study can reduce the impact of T2* decay, although T2* affects the SNR. For SPEEDI applications requiring magnitude images, T2* mapping can be performed with a low spatial resolution, followed by a T2* correction to remove the T2*-induced modulations in SPEEDI (31). In situations where T2* is sufficiently longer than the time-scale of the dynamic process under investigation, the effect of T2* on SPEEDI images may be neglected. Another limitation arises from SPEEDI’s reliance on periodicity. To understand such reliance, we performed additional electric current experiments in which random trigger delays within a specific range of variations were introduced. Even with 50% random variations in trigger delay from a perfect trigger delay time of 5 ms, SPEEDI continued performing well (see Supporting Information Figure S2 and Table S1), boding well for future biological applications in which imperfect periodicity exists. For more excessive temporal variations, a strategy of discarding some affected data is likely needed, in a similar fashion to those employed in cardiac triggered or respiratory triggered acquisitions. In addition, like many other ultra-fast imaging methods, the achievable SNR must be carefully considered. Besides the T2* effect on SNR, spatial resolution must be properly selected to ensure an adequate SNR within a specific scan time. Given SPEEDI’s reliance on phase-encoding and synchronization, signal averaging may not be a preferred means to increase the SNR due to scan time considerations. Finally, to ensure data consistency across different TRs, a steady state must be maintained especially when a short TR is employed. This can be accomplished with a number of discarded data points at the beginning of an acquisition, similar to what is typically employed in gradient-echo pulse sequences.

In conclusion, through two examples of capturing rapidly changing electric currents and eddy currents, we have illustrated that MRI is capable of providing sub-millisecond temporal resolution using SPEEDI. Although our demonstrations were limited to phantom experiments on physical systems, the technical feasibility illustrated in this study will likely lead to future investigations of using SPEEDI to explore ultra-fast biomedical processes that are cyclic or pseudo cyclic.

Supplementary Material

Supplementary materials

Supporting Information Figure S1: CS acquisition pattern used in the electric current experiment with a two-fold acceleration (A) and the eddy current experiment with a three-fold acceleration (B). In (A), the CS acquisition pattern was designed based on a PDF using the magnitude of k-space acquired from a conventional gradient echo sequence, whereas in (B), a polynomial function was used as the PDF.

Supporting Information Figure S2: The phase evolution curves from a randomly selected point in the electric current experiment with randomly varying trigger delays of 0%, 20%, 50%, and 70% of the intended trigger delay of 5 ms. Compared with the perfect periodicity without any variation (0%; black curve), variable trigger delays produced noisier phase evolution curves whose deviation was quantitatively assessed with NRMSE by using the theoretically simulated phase evolution as a reference. Selected points with prominent deviations are indicated by the black arrows. However, even with a 50% variation in trigger delays, the phase evolution curve (blue curve) continued to match well with the simulation result (purple curve).

Supporting Information Table S1: The normalized RMS errors corresponding to different trigger delay variations in the electric current experiment.