Fast 3D Magnetic Resonance Fingerprinting (MRF) For a Whole Brain Coverage

Abstract

Purpose

The purpose of this study was to accelerate the acquisition and reconstruction time of 3D Magnetic Resonance Fingerprinting (MRF) scans.

Methods

A 3D MRF scan was accelerated by using a single shot spiral trajectory with an undersampling factor of 48 in the x-y plane, and an interleaved sampling pattern with an undersampling factor of 3 through plane. Further acceleration came from reducing the waiting time between neighboring partitions. The reconstruction time was accelerated by applying SVD compression in k-space. Finally, a 3D pre-measured B₁ map was used to correct for the B₁ inhomogeneity.

Results

The T₁ and T₂ values of the ISMRM/NIST MRI phantom showed a good agreement with the standard values, with an average concordance correlation coefficient of 0.99 and coefficient of variation of 7% in the repeatability scans. The results from in vivo scans also showed high image quality in both transverse and coronal views.

Conclusion

This study applied a fast acquisition scheme for a fully quantitative 3D MRF scan with a total acceleration factor of 144 as compared to the Nyquist rate, such that 3D T₁, T₂ and M₀ maps can be acquired with whole brain coverage at clinical resolution in less than 5 minutes.

Introduction

Magnetic Resonance Fingerprinting (MRF)(1) is an acquisition and processing framework that utilizes a variable acquisition scheme to enable simultaneous quantification of multiple tissue properties, such as T₁ and T₂. Currently, most MRF implementations and in vivo applications utilize two dimensional (2D) (2–10) and multi-slice acquisitions(11–13). However, in order to achieve higher through plane resolution, and better tissue characterization, extension to a 3D acquisition is desirable.

In general, the two main concerns of a 3D MRF scan are 1) long acquisition time due to the increased number of excitations necessary to acquire the data and 2) signal intensity inhomogeneity across the 3D volume due to excitation profile imperfections and local changes in the B₁ field. Since 3D acquisitions potentially allow a higher acceleration factor and more flexible undersampling schemes as compared to 2D acquisitions, several fast 3D methods have been proposed previously by using non-Cartesian trajectories(14–19), fast sampling schemes(20–22), and incorporating parallel imaging and compressed sensing methods(23–25). Any inhomogeneity in the flip angle can cause errors, which lead to inaccurate T₁ and T₂ results for many quantitative measurements including MRF scans(26–28). The two common ways to correct for the flip angle error are to premeasure the B₁ or flip angle map(3,29,30), or to quantify B₁ at the same time as tissue parameters(28,31,32).

The purpose of this study was to accelerate the 3D MRF scan and to correct for the flip angle error, in order to provide accurate T₁ and T₂ maps of a whole brain scan in a clinically acceptable time. Specifically, this study applied a simple accelerated acquisition scheme similar to k-t BLAST(21) for the 3D MRF scan to allow a total factor of 144 acceleration as compared to the Nyquist rate, so that 3D T₁, T₂ and proton density (M₀) maps can be acquired from a whole brain with a resolution of 1.2×1.2×3 mm³ in less than 5 minutes. In addition, since the 3D MRF scan acquired over 1000 undersampled volumes, a singular value decomposition (SVD) compression(7) was applied in k-space prior to reconstruction to substantially reduce the computing memory and accelerate the post-processing time. To correct for the flip angle error, a 3D slab-selective RF pulse with an optimized excitation profile was used to minimize the excitation profile variation across partitions (or slices in a 3D volume) and a 3D B₁ map that was premeasured using the Bloch-Siegert method(3,29) was used to measure the B₁ inhomogeneity. The B₁ values were then simulated into the dictionary to correct for inaccurate flip angles and improve the accuracy of the resulting T₁ and T₂ values.

Method

3D Acceleration Scheme

The 3D slab-selective MRF with the FISP-based readout(2) was implemented by adding phase encoding lines along k_z direction from the 2D MRF. As a quick summary of the 2D MRF sequence(1,2), the MRF sequence was designed based on a TrueFISP or FISP sequence, but with randomized flip angles (FA) and repetition times (TR). To capture sufficient temporal information for multi-parametric quantification, 1000 to 3000 time points (or TRs) were acquired and one image was reconstructed at each time point. The resulting signal evolution in each pixel as a function of time was matched to a pre-defined dictionary to obtain multiple tissue properties (such as T₁, T₂ and proton density) simultaneously. In this study, the 3D acquisition acquired data along time points in the x-y plane first. After acquired all the time points at a certain phase encoding line in k_z, the k_z increased and the same acquisition pattern (FA, TR and spiral trajectories) was repeated. For each time point at each k_z, a variable density spiral trajectory was used to sample the kx-ky data (note that spiral trajectory was designed to require 48 arms to fully sample the k-space) (2,33). After all sampling was complete, the spiral trajectory in kx-ky (in-plane) and Cartesian phase encoding in kz (through-plane) constitute a stack-of-spiral sampling pattern at each time point. However, in order to preserve the temporal fidelity of the rapidly changing MRF signals, the sampling order of this stack-of-spiral MRF acquisition is different from other time-resolved three-dimensional acquisitions that acquire all kz lines for a time point before proceeding to the next time point.

If this data were acquired at the Nyquist rate, the scan duration would be prohibitively long. As shown in previous MRF studies, individual time point can be greatly undersampled to reduce imaging times. Here, the acceleration scheme including both in-plane and through-plane acceleration is proposed. In-plane acceleration was achieved by using a single spiral arm in each time point (or TR) and for each kz. To improve spatial-temporal incoherence, a 7.5° (360/48) rotation of the trajectory was applied from one time point to the next, such that aliasing artifacts from neighboring time points are different. This yielded an in-plane acceleration factor of 48. Through-plane acceleration was achieved by uniformly undersamping the kz lines in an interleaved fashion by a factor of three.

An example of this undersampled 3D MRF acquisition is shown in Figure 1 for a scan using nine kz lines. These nine kz lines were divided into groups based on the through-plane acceleration factor (in this case there are three groups for the undersampling factor of three). Specifically, in the first repetition, the first kz line was acquired at the first time point, then the second kz line was acquired at the second time point, then the third kz line at third time point, followed by the first kz line at the fourth time point, and so on. Additionally, because the rotational angle of the spiral trajectory was repeated in every 48th time point, at the 49^th time point, instead of acquiring the first kz line, the second kz line was acquired in group 1. Thus, in addition to shifting the kz line by one for each time point, the index of the kz line was shifted by one at each multiple of 48 time points. After the kz lines at all time points were acquired in the first group, a waiting time with no excitation was applied to allow for the signal recovery, followed by the acquisition of the second group of kz lines, starting with the first kz line at the first time point again. After all undersampled 3D MRF data were acquired, this resulted in an undersampled, interleaved, stack-of-spirals sampling. This sampling pattern is similar to k-t BLAST and k-t SENSE(21), which was used to shift the aliasing artifacts. The additional benefit of this sampling scheme was that the sampling density of each kz line as well as the sampling times of each rotational angle of the spiral trajectory were the same after the entire acquisition.

Figure 1.

Undersampling scheme (a), flip angle pattern and TR pattern (b) of the 3D MRF scan. In (a), the sampling scheme of a 3D MRF scan with nine partitions is illustrated. The acquisition starts with the time domain first. Along the time points, the rotational angles of the spiral trajectories are changed with a step of 7.5 degrees. With an acceleration factor of three, nine partitions are divided into three groups or repetitions. The colored kz lines are the ones that are acquired in the accelerated scan while the gray kz lines are the ones that are skipped.

The scan time is further reduced by shortening the waiting time between neighboring groups. Although traditional relaxometry methods require spins to be fully relaxed before sampling each kz, MRF can account for partial relaxation of the spins by simulating the known waiting time between neighboring kz lines in the dictionary. This property of MRF provides some inherent acceleration as it allows the minimization of the waiting time between neighboring groups.

Data Acquisition

All scans were performed in a 3T scanner system (Skyra, Siemens). For both phantom and in vivo studies, a field of view (FOV) of 300×300×144 mm³ with a matrix of 256×256×48 and an image resolution of 1.2×1.2×3 mm³ was acquired. Under an acceleration factor of three, 16 acquisition groups (or repetitions) were acquired. For each group, 1440 time points (30 repetitions of 48 rotation angles) were acquired with an acquisition time of 14 seconds, followed by a 3 second waiting time before the next group, in order to allow for relaxation and to improve signal to noise ratio (SNR). The flip angle and TR patterns are shown in Figure 1(b). An asymmetric 3D slab selective RF pulse with a duration of 2048 us was used for excitation. Adiabatic inversion pulses were added at the first and the 1201^th time points at each repetition in order to improve sensitivity to T₁. The total acquisition time was 4.6 minutes.

A 3D B₁ map was acquired separately using the Bloch-Siegert method before each MRF scan(3,29). To accelerate the scan, a B₁ map with a spatial resolution of 2.3×2.3×3 mm³ was first acquired. The B₁ map in each partition was then interpolated to a spatial resolution of 1.2×1.2 mm² to match the spatial resolution of the tissue maps. The total acquisition time was 1.6 minutes.

The accuracy and repeatability of the 3D MRF scan were first validated using the ISMRM/NIST MRI phantom which has T₁ and T₂ layers, each containing 14 spheres, with T₁ values ranging from 20 ms to 2 seconds and T₂ values ranging from 8 ms to 600 ms(34,35). The phantom was scanned in five consecutive days by both B₁ and 3D MRF scans. The mean and standard deviations of the T₁ values in the T₁ layer as well as T₂ values from the T₂ layer were compared to those values measured by NMR experiment from the physical measurement laboratory at the National Institute of Standards and Technology(34).

The in vivo experiments were performed in five asymptomatic volunteers in an IRB-approved study, including written informed consent before each scan. B₁ measurement and MRF scans were performed at the same 3D location. In the T₁ and T₂ maps from each volunteer, six regions including caudate nucleus, centrum semiovale, middle cerebellar pedencle, putamen, frontal white matter and parietal white matter were selected. The T₁ and T₂ values in each tissue type were first averaged for each volunteer, and then the mean and standard deviation of T₁ and T₂ values among five volunteers were calculated.

Dictionary Simulation

The dictionary used in the matching algorithm was simulated using the Bloch equations in MATLAB (MathWorks, Natick, MA) and was introduced previously(1). In each TR, signal evolutions due to RF excitation with nominal flip angles, relaxation during TE and TR times, and a 2π dephasing at the end of the TR from 200 isochromats was simulated. Since a 3D slab-selective RF pulse with an optimized excitation profile was applied, the RF profile was not simulated in the dictionary. In order to simulate the waiting time, the entire acquisition was simulated twice. At the end of first repetition, relaxation during the waiting time was simulated. The resulting magnetization became the starting magnetization of the second repetition, where the whole acquisition was simulated again. Based on the simulation from a wide range of T₁ and T₂ combinations, the starting magnetization was stable after the second repetition. Each isochromat was simulated independently for the whole sequence before summing over the voxel.

The B₁ values were simulated as an additional dimension of the dictionary, with a range between 0.7 to 1.5 in steps of 0.02. The actual flip angles were calculated as nominal flip angles multiplied by B₁. For each B₁ value, a total of 12001 signal evolutions, each with 1440 time points, were simulated for a range of possible T₁ values (2 to 100 ms in steps of 2, 120 to 2000 ms in steps of 20, and 2000 to 3000 ms in steps of 40ms) and T₂ values (2 to 130 ms in steps of 2 ms, 140 to 200 ms in steps of 10 ms, 200 to 1000 ms in steps of 20 ms, and 1040 to 2000 in steps of 40 ms). The simulation time was 5.7 minutes for each B₁ value and 3.4 hours for the whole dictionary on a standalone PC.

Accelerated Post-Processing

Since 1440 undersampled 3D volumes were acquired, which could lead to a large memory requirement and long computing time for both reconstruction and template matching, a singular value decomposition (SVD) compression method(7) was applied to the k-space data prior to the reconstruction. Specifically, the SVD of the full dictionary was first computed, which takes four minutes.

$$D=U\mathrm{\sum }{V}^{\ast }$$ [1]

The first k=25 of the singular vectors were used to project the raw data and the full dictionary to the SVD space.

$$D\approx U_k{\mathrm{\sum }}_k{V}_k^{\ast }$$ [2]

$$Y_k=U_k^{\ast }Y$$ [3]

$$X_k=G^{\ast }{Y}_k$$ [4]

$$D_k=U_k^{\ast }D$$ [5]

where in equation [2], U_k ∈ ℂ^t×N_k is the first N_k of the left singular vector of the dictionary, t is the number of TRs. In equation [3], Y ∈ ℂ^t×M is the sampled k-space data, where M = N_coils × N_{samples_per_spiral} × N_spirals × N_kz, and Y_k ∈ ℂ ^N_k×M is the compressed k-space data in the SVD space. After projecting the raw data to the SVD space, instead of reconstructing 1440 undersampled 3D volumes, only 25 3D volumes with the compressed k-space data were reconstructed, which substantially reduced the computational effort. Each 3D volume was reconstructed using the GPU-NUFFT toolbox(36) with separately measured spiral trajectories(37). In equation [4], X_k is the reconstructed images, with the size of 25×256×256×48, and G is the NUFFT operator. To correct for B₁ inhomogeneity, the same U_k as to compress the raw data was also used to project the full dictionary with different B₁ values to the SVD space. In equation [5], D ∈ ℂ^{t×N_t1t2×N_B1} is the full dictionary and D_k ∈ ℂ^{N_k×N_t1t2×N_B1} is the compressed dictionary. In this way, pattern recognition could be performed between X_k and D_k, which are much smaller than the original full matrix X and D. Based on the measured B₁ map, the compressed signal evolution in each pixel was matched to those entries in the compressed dictionary that have the closest B₁ values as measured. The maximum inner-product value from the match gave rise to T₁, T₂ and M₀ values. The post-processing time of generating B₁ corrected T₁, T₂ and M₀ maps for a matrix size of 256×256×48 was 48 minutes in MATLAB (The MathWorks,Inc. Natick, MA).

Results

Figure 2 shows the accuracy and repeatability results of the 3D MRF scan before and after the B₁ correction, with bi-directional error bars representing the standard deviation of five measurements. Figure 2(a, b) shows the results from all 14 spheres of each layer and Figure 2(c, d) shows the same results but with a reduced T₁ range between 181 to 2038 ms and a reduced T₂ range between 26 to 143 ms, which correspond to the main physiological range of the brain tissues. The linear regression and R² of the results before and after the B₁ correction are also listed in each plot. As shown in the figure, although the B₁ correction has little impact on the T₁ results, it greatly improves the accuracy of the T₂ results. After the B₁ correction, MRF results in general are in good agreement with the results from the reference values, with a concordance correlation coefficient (CCC)(38) of 0.99 for both T₁ and T₂. The MRF scans also demonstrate high repeatability, with an average coefficient of variation (CV) of 6.9% for T₁ and 6.6% for T₂.

Figure 2.

The accuracy and repeatability of the qMRI phantom scan. (a, b) T1 values and T2 values from 14 spheres from the ISMRM/NIST phantom are compared to the values from the spin echo (SE) measurement. (c, d) The same results but with a reduced T1 range between 181 to 2038 ms and a reduced T2 range between 26 to 143 ms. The blue line and red line in each plot are the linear regression results before and after B1 correction, respectively.

Figure 3 and 4 illustrate the T₁ and T₂ maps in the axial view and coronal view, respectively, from one of the volunteer scans. To illustrate the B1 effects, Figure 3 shows the B1 maps, as well as T1 and T2 maps before and after B1 correction. Similar to the phantom results, the B1 effects are more visible from T2 maps. Table 1 summarizes the T₁ and T₂ values from six regions of the brain maps. The T₁ and T₂ values along with the size of the regions of interest, as well as the mean±std of the T₁ and T₂ values among the five volunteers are listed. Based on Table 1, the T1 and T2 values from each region are relatively consistent among these five healthy volunteers.

Figure 3.

B1, T1 and T2 maps from a 3D in vivo scan in axial view.

Figure 4.

3D T1 (ms) and T2 (ms) maps from an in vivo scan in Coronal view.

Table 1.

In vivo T1 and T2 values along with the size of the regions of interest from five volunteers scanned from a 3T scanner. (units: ms)

		v1	v2	v3	v4	v5	mean±std
Caudate Nucleus	T1	1397.2	1493.5	1293.5	1397.9	1368.9	1390.2±71.7
	T2	42.1	38.9	53.4	40.9	44.7	44.0±5.6
	ROI	38	27	17	23	24
Centrum semiovale	T1	875.9	866.6	823.1	863.1	866.4	859.0±20.6
	T2	39.7	33.6	40.3	34.4	41.2	37.8±3.5
	ROI	108	102	145	149	207
Middle Cerebellar Pedencle	T1	874.7	942.5	906.1	918.9	881.5	904.7±27.7
	T2	52.7	38.7	25.7	37.8	49.0	40.8
	ROI	72	54	47	75	87
Putamen	T1	1285.9	1314.0	1169.5	1238.4	1234.3	1248.5±55.3
	T2	40.7	36.9	43.0	38.6	39.1	39.7±2.3
	ROI	37	52	24	32	55
Frontal_wm	T1	843.1	854.3	794.8	809.1	818.1	823.9±24.5
	T2	30.8	29.1	42.6	35.1	35.6	34.6±5.3
	ROI	51	68	61	78	85
Parietal_wm	T1	783.3	817.9	904.5	793.7	781.2	816.1±51.5
	T2	46.8	37.7	36,8	36.1	43,1	40.1±4.6
	ROI	79	85	45	31	100

Discussion

In this study, a fast acquisition scheme was applied for a fully quantitative 3D MRF scan in less than 5 minutes of acquisition time, demonstrating T₁, T₂ and M₀ maps with 1.2×1.2×3 mm³ resolution and a whole brain coverage. A separate 1.6 minute B₁ measurement scan was performed before the 3D scan. The resulting B₁ map was used to correct for B₁ inhomogeneity effects and improve the accuracy of T₁ and T₂ estimates. In fact, both B₁ and 3D MRF scans can be further accelerated. A fast Bloch-Siegert scan has been proposed to measure the 3D B₁ maps in only 32 seconds(39,40). By incorporating advanced reconstruction methods, substantial reduction of the scan time or/and further improvement of the spatial resolution can be achieved for 3D MRF scans. For example, by using low rank reconstruction methods(41,42), the scan time of the 3D MRF scan with the same spatial resolution and tissue coverage can be reduced to only 2.7 minutes(43). Optimization of the MRF scan could also lead to a reduction of the scan time(44,45). In addition, method has been proposed to simultaneously quantifying B₁ as well as tissue properties without compromising the scan time(46).

The acceleration of the acquisition was achieved in 3 steps: intrinsic acceleration using short waiting times between neighboring phase encoding lines, in-plane acceleration factor of 48 and through-plane acceleration factor of 3. The in-plane acceleration has been demonstrated previously in 2D MRF scans, which took the advantage of the variable density spiral sampling pattern in order to generate incoherent aliasing artifacts both in each image and through time. The through-plane acceleration was achieved using a uniform undersampling pattern similar to the k-t sampling pattern. This pattern shifted the aliasing artifacts from one time point to the next, in order to create incoherent artifacts through time. This pattern also guaranteed that all 48 rotational angles of the spiral trajectory were used at the same rate (30 times for each spiral angle) and all kz lines were sampled at the same density. For this reason, no density compensation was needed along kz, although density compensation was still needed in the kx-ky plane for the image reconstruction.. In this study, all maps were generated by direct reconstruction and template matching. Advanced reconstruction methods that have been recently proposed for the 2D MRF could be applied in 3D MRF in order to further reduce the acquisition time or improve the image quality(47,48). Other sampling schemes such as variable density sampling can also be applied to the partition direction to potentially improve the sampling efficiency and increase the undersampling factor(49,50).

For a 3D scan with large volume coverage, B₁ variation and its effect on the resulting T₁ and T₂ estimation are not negligible. In this study, the Bloch-Siegert B₁ mapping method was performed separately before each MRF scan, and the resulting B₁ map was used to correct for the B₁ effect. Other approaches to correct for the B₁ effect, such as quantifying B₁ at the same time as T₁ and T₂, can also be applied(28,31). However, none of these methods has been effectively applied to 3D scans with such a high undersampling ratio. Although a separate scan to measure B₁ takes an additional time, it reduces the sensitivity to potential tissue or system parameters, and thus reduces the amount of information and acquisition time required for the MRF scan. In addition, a prior knowledge of the B₁ map reduces the dimensionality of the dictionary in pattern matching to estimate the tissue properties, which can lower the risk of mismatch and error propagation, especially in the present of strong aliasing artifacts and with low SNR from accelerated scans.

Based on the results obtained from the ISMRM/NIST MRI phantom, the 3D MRF scan shows high accuracy and repeatability as compared to the reference measurement. As described in our previous 2D study(51), we’ve consistently seen T₂ difference between our results after B₁ correction and literature reported values acquired using fast spin echo methods(2,52,53). Many groups have shown similar T₂ reduction by correcting for stimulated echoes(54), slice profile(27,51), magnetization transfer(55) and finite RF pulse effects(56). The lower T₂ values may also be related to tissue microstructure, intra voxel dephasing(57), and diffusion effect from the spoiling gradients used in the FISP sequence(58). These effects may also cause the T₂ variation between frontal and parietal white matter regions as shown in Table 1. An exact analysis of this phenomenon is the subject of a future investigation.

In this study, a 3D MRF scheme with the FISP readout was used, which is less sensitive to the B₀ inhomogeneity for large volume coverage. Therefore, this 3D MRF scheme has the potential to be used in other parts of the body. In addition, with a large flexibility on the MRF sequence design, navigation and magnetization preparation can be added to the sequence to make the 3D MRF scan robust to different applications.

Conclusions

A fast acquisition scheme for a 3D MRF scan with a whole brain coverage was presented. 3D T₁, T₂ and M₀ maps with a spatial resolution of 1.2×1.2×3 mm³ can be generated in 4.6 minutes. An additional 1.6 minute B₁ scan was used to reduce the system and subject related variations, and thus improve the accuracy of quantitative estimates. Given that this FISP-based sequence is also insensitive to the B₀ inhomogeneity, the proposed MRF scan could have wide and robust clinical applications.