MRF & Synthetic MRI: How Does It Work?
Anagha Deshmane1
1Max Planck Institute for Biological Cybernetics, Tübingen, Germany

Synopsis

Synthetic MRI is gaining interest as a way to perform a rapid comprehensive MRI exam, and more vendors have added synthetic MRI capabilities to their product portfolios. This talk provides a brief overview of the methods behind synthetic MRI. We will learn about two main ingredients of synthetic MRI: the signal models of commonly acquired weighted image contrasts, and rapid multi-parametric quantitative mapping sequences, including MR fingerprinting. We will explore emerging synthetic MRI contrasts for neuroimaging applications. Finally, we will cover the challenges of robustness, accuracy, and reproducibility in multi-parametric quantitative MRI and synthetic MRI, and their potential solutions.

What is Synthetic MRI?

Synthetic MRI is a technique to use just a few measurements to produce the weighted contrast images which might normally be acquired in the course of a clinical MR exam, including T1-weighted, T2-weighted, proton-density-weighted, FLAIR, etc. This is possible with the knowledge of the underlying quantitative MRI tissue relaxation properties, namely T1, T2, and proton density. These quantitative relaxation values can themselves be mined for information using, for example, machine learning and radiomics. But the extremely attractive clinical utility of synthetic MRI is the ability to retrospectively adjust or even switch the weighted contrast of the image without having to acquire more measurements or repeat the exam (1).

Relaxation properties, Pulse sequence parameters, and Image contrast

MRI pulse sequences provide a mechanism to manipulate spins and observe their relaxation. Radiofrequency (RF) pulses tip the equilibrium magnetization away from the longitudinal axis and towards the transverse plane (where it can be measured). RF pulses used to prepare (ex, invert) magnetization or excite spins for imaging are characterized by the flip angle (θ). The repetition time (TR) of the sequence determines the amount of time that the magnetization has to recover to its equilibrium state according to T1 relaxation. The echo time (TE) is the time between excitation and the recorded echo, and determines how much transverse magnetization is measured after T2 relaxation. Together, the sequence parameters θ, TE, TR, and other timing parameters between RF pulses determine the amount of T1 and T2 weighting in the measured signal.

How are relaxation properties quantified?

Quantification is a two-step process that involves
  1. several measurements over which one or more sequence parameters (ex, θ, TE, TR) are varied, and
  2. fitting the measured signal to a corresponding model to estimate the desired relaxation parameter.
Gold-standard quantification methods aim to minimize the effects of other parameters and are typically quite long measurements and clinically impractical for in-vivo application. Much research has been devoted to faster T1 and T2 quantification, though often at the cost of some measurement bias or accuracy limitation.

Measurement of T1 can be achieved using a spin- or gradient echo by varying the time after a magnetization preparation (inversion or saturation) RF pulse, or varying the FA or TR. Suitable methods include the inversion recovery (gold-standard), Look-Locker, variable flip angle, and MP2RAGE techniques (2,3).

Measurement of T2 can be achieved using a spin-echo by varying the time between excitation and refocusing pulses, effectively the TE. Suitable methods include the single-echo spin echo (gold-standard), multiple-echo spin echo/CPMG, GRASE, or T2-prepared rapid imaging sequences (2,3).

Measurement of proton density requires a pulse sequence which ideally minimizes T1 and T2 weighting. This involves very long TR and very short TE, and is experimentally difficult to achieve. Two practical approaches to estimating PD are by fitting/extrapolation of quantitative T1 or quantitative T2 measurements, or exploiting the relationship between T1 and free water content (2).

Why is synthetic MRI now a trending technology?

In recent years, synthetic MRI has been touted as a way to perform a rapid comprehensive MRI exam, and more vendors have added synthetic MRI capabilities to their product portfolios. The enabling technology that makes synthetic MRI so fast is the multi-parametric quantitative relaxometry sequence. These techniques aim to rapidly and simultaneously measure T1, T2, and PD values by combining three key elements:

  1. specialized pulse sequences which efficiently sensitize the signal to both T1 and T2,
  2. fast acquisition so that multiple measurements can be made at different phases of the relaxation process within one exam, and
  3. corresponding signal models and algorithms to quantify the effects of different relaxation properties on the measured signal.
Multi-parametric quantitative relaxometry methods have the advantage that the resulting quantitative parameter maps are inherently co-registered. Most pulse sequences for multi-parametric quantitative MRI can roughly be divided into two types: interleaved and steady-state.
One group of multi-parametric quantitative relaxometry approaches involve interleaving pulse sequence blocks which provide T1 and T2 sensitivity (4,5). A widely deployed approach is to use an inversion or saturation pulse in a preparation module to provide T1 sensitivity followed by a multiple-echo spin echo/CPMG readout for T2 sensitivity (QRAPMASTER/MDME). A more recently developed approach (3D-QALAS) uses the magnetization preparation module to encode the T2 weighting, with a fast Look-Locker readout to provide T1 sensitivity. These sequences pair well with multi-slice acquisitions and established acceleration techniques such as parallel imaging, and readily provide multi-slice or 3D coverage for efficient acquisitions.
Another class of multi-parametric quantitative relaxometry approaches takes advantage of the mixed T1 and T2 sensitivity of steady-state free precession sequences (5). Inversion-recovery balanced steady-state free precession (IR-bSSFP) combines an inversion pulse for increased T1 sensitivity with a fast bSSFP echo train with T2 sensitivity (6). Sequences with RF phase cycling and balanced SSFP readouts (PLANET, MIRACLE) additionally take advantage of the frequency sensititivity of bSSFP signals to quickly sample tissue-specific profiles (7,8).
Steady-state and interleaved sequences for multi-parametric quantitative relaxometry have relatively complicated signal models and require sophisticated optimization algorithms for fitting of the T1, T2, and proton density parameters from a small series of images with different contrast weightings. Alternatively, signals for different combinations of T1 and T2 can be modeled in advance and stored in a dictionary or look-up table.

How does MR Fingerprinting work?

Like the techniques mentioned above, Magnetic resonance fingerprinting (MRF) uses the three multi-parametric quantitative MRI elements to simultaneously encode T1, T2, and PD (9,10). However the approach differs from those listed above in important ways, which enable more flexibility in the acquisition. The unique features of MRF are:
  1. the specialized pulse sequence which simultaneously sensitizes the signal to both T1 and T2 is implemented as a series of time-varying pseudo-random excitation parameters. Unlike the other approaches, this avoids that the signal recovery follows an exponential time course or is in a steady state, making tissue-specific relaxation time courses more unique from each other.
  2. the fast acquisition is achieved through variable, highly accelerated sampling. The high acceleration factor ensures that the images capture a time point in the relaxation time course without introducing blurring. The variable sampling pattern yields different aliasing artifacts at each time point, which effectively generates a noise-like pattern over the signal time course.
  3. the relaxation properties are identified not by fitting but by looking up the signal time course in a pre-calculated dictionary. Each dictionary entry is simulated for a single expected T1, T2 pair by using the Bloch equations to simulate each step of the pseudorandom sequence. This simulation avoids the challenge of modeling the complicated signal evolution of a non-exponential, non-steady state sequence. The pattern recognition approach used for the dictionary matching process is robust to the noise-like undersampling artifacts, and yields accurate T1 and T2 estimates. The relative scaling between the dictionary elements and measured signal provides an estimate of proton density.
The MRF approach forms a framework through which each of these three elements has several options for modification or customization (11). First, the MRF pulse sequence can be modified to encode properties other than T1 and T2. For example, the original MRF work used pulse sequence blocks similar to a bSSFP experiment, which are also sensitive to off-resonance effects and enable mapping of B0 inhomogeneity. Gradient echo sequence blocks or modifying phases of the RF pulses can be used to encode T2*. Several recent approaches also integrate B1+ mapping. Second, the fast image encoding can be achieved in a variety of ways. The original work called for a time-varying single-shot spiral. Other approaches have tried exotic music-based trajectories or simpler EPI readouts. The key requirement is that each image can be acquired fast enough that it represents a unique timepoint in the voxel signal evolution without blurring. The choice of readout will affect the range of achievable echo times and therefore T2 times which can be measured accurately. Finally, the dictionary simulation and matching approach offers some flexibility to model additional parameters. Accurate parameter quantification is a function of the range and ordering of the time-varying sequence parameters as well as the range and resolution of the dictionary. Interpolation methods and deep learning have recently been proposed to circumvent the large memory requirements for dictionary storage and look-up.

How do we make synthetic MR images?

MR images are typically collected from either spin-echo or gradient-echo pulse sequences with additional features such as inversion pulses or gradients to sensitize the echo signal to particular tissue properties. A contrast equation describes the relationship between the tissue relaxation properties and the voxel signal or image contrast based on the pulse sequence design and protocol parameters used to acquire that image (12,13).

T1, T2, and PD-weighted
The T1 or T2 weighted MR signal can be modeled using the spin-echo signal equation which takes into account the voxel relaxation properties and the sequence parameters, TR, and TE:
$$S \propto PD(1-e^{-TR/T_1})e^{-TE/T_2}$$
By adjusting TR and TE we can alter the contrast in the image. Long TRs reduce T1 weighting, while short TEs reduce T2 weighting.

Inversion Recovery
If an inversion pulse is used followed by a delay time TI, the following spin-echo signal equation applies, assuming a 180 degree inversion pulse and 90 degree excitation flip angle:
$$S \propto PD(1-2e^{-TI/T_1}+e^{-TR/T_1})e^{-TE/T_2}$$
As before, the choice of TR and TE determine the degree of T1 or T2 weighting. The choice of TI relative to the tissue T1 determines the degree to which that particular tissue signal is suppressed.

Technical challenges with multi-parametric qMRI, MRF, and synthetic MRI

The quality of synthetic MRI images depends on the quality of the underlying quantitative relaxometry parameter maps. Recent work on has investigated the number and type of parameters quantified, as well as improvements to the resolution and field of view, speed, and encoding efficiency of MRF. Careful attention has been paid to mitigate confounding factors, ensure accuracy & reproducibility of quantified values, and implement accurate signal models (1,2,17,18).

Confounding factors in quantitative relaxometry include B1+ inhomogeneity or transmit RF effects for T1 mapping, B0 inhomogeneity & stimulated echo effects for T2 mapping, and B1- (receiver profile) effects in proton density mapping, as well as k-space encoding artifacts, motion and flow artifacts. Some of these effects may be mitigated by careful choice of protocol parameters, good shimming or additional, independent measurements. Expanded signal models are often required to account for errors in the fitting or dictionary simulation processes.

Accuracy and precision are important characteristics for quantitative MRI measurements. Accuracy helps us understand to what degree reference values for disease characteristics can be established. Especially for neuroimaging, in which white matter, gray matter, cerebrospinal fluid (CSF), and lesions have widely different relaxation characteristics, it is important to choose a multi-parametric mapping sequence and protocol which is accurate over a sufficiently large range of relaxation times and is relatively insensitive to diffusion, flow, or pulsation. Standardized quantitative MRI phantoms can be used to perform quality assurance and aid in experimental calibration. Population studies are also conducted to investigate the repeatability & reproducibility of quantitative MRI methods. These metrics determine to what degree the quantified values can be compared across patient populations and for the same subject who may be scanned repeatedly over a long period of time or at multiple clinical sites.

Synthetic MRI weighted images are computed under certain assumptions, especially that every spin in the voxel exhibits the same relaxation characteristics which are estimated in the quantitative maps. The signals measured, however, are an aggregate of signals from all the spins in the voxel, which may span tissue boundaries or be better characterized by multiple tissue compartments. One place where these assumptions give rise to errors is in synthetic FLAIR images, which have characteristic hyperintensities at tissue/CSF boundaries (19). The pseudorandom signal behavior of MRF allows for CSF partial volume errors to be modeled and mitigated (20).

Finally, synthetic MRI cannot yet reproduce all weighted contrasts acquired in a clinical setting and is currently limited to contrasts that can be estimated from quantitative T1 and T2 mapping. For example, a comprehensive and quantitative neuroimaging exam may include diffusion-weighted imaging, T2* or susceptibility-weighted imaging, or arterial spin labeling. Each of these sequences contains specialized features (RF pulses, gradients, and timing elements) which specifically encode these parameters. While some effort has been made to incorporate these elements into MRF sequences, these are still in the experimental phase and not yet clinically available.

Acknowledgements

Support of the Max Planck Society is gratefully acknowledged.

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