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Magnetic resonance fingerprinting (MRF) is a quantitative magnetic resonance imaging (MRI) method whereby a set of MRI parameters (e.g., T1 or T2) are concurrently estimated with a single acquisition. MRF uses a pseudorandomized MRI sequence which results in unique signal evolutions, termed fingerprints, for each combination of relevant parameters. These underlying parameters are then estimated by matching the acquired fingerprint with an existing database of fingerprints whose corresponding parameters are known. MRF operates much like its eponym, fingerprint identification, in which an anonymous fingerprint is measured and compared against a database of known fingerprints in order to discover the identity of the person. In addition to producing multiple parameter maps from a single acquisition, MRF displays robustness to undersampling. This robustness allows for fast, clinically feasible scan times. MRF has been demonstrated for a number of clinical applications including from cranial, cardiac, and full abdominal scans.

Background
MRI is one of the most utilized imaging modalities in diagnostic medicine since its development in the 1970s and 1980s. However, most clinical MRI is qualitative. Any information in the produced image is contained in contrast between materials with different physical properties. Many of these properties are related to or are themselves magnetic resonance (MR) parameters since they directly affect the acquired signal from an MRI scan. Thus, it is possible to “weight” these images differently based on their parameters (e.g., T1 and T2 weighting). However, these weightings only provide relative information about the underlying parameters and are subject to external factors such as the scanner type and setup. As a result, diagnoses based on qualitative MRI are reliant on potentially inconsistent data which cannot capture global changes to a subject.

The goal of quantitative MRI is to directly estimate the values of the MR parameters in the materials of interest or of the system itself. These parameters primarily include longitudinal relaxation time (T1), the transverse decay time (T2), proton density, apparent diffusion coefficient, and static magnetic field (B0) and radiofrequency field (B1) inhomogeneities/off resonance frequencies. Typically, the desired output of a quantitative MRI task is a per-pixel map of a particular parameter. Traditional methods for quantitative MRI involve hand-designed sequences for isolating the parameter of interest and consequently require a separate process for each parameter of interest. For example, simple T1 mapping utilizes an inversion recovery sequence in which the magnetization is first inverted and then allowed to recovered with multiple acquisitions taken at different times along the recovery; the data is then fit to an exponential to obtain T1. Though theoretically simple, these sequences are often imperfect in isolating a single parameter and thus suffer from inconsistencies depending on the type of sequence used. MRF attempts to instead estimate all parameters of interest simultaneously in a single process, making the total time to estimate the set of desired parameter maps clinically feasible. MRF has been used to estimate a wide range of parameters including T1, T2, T2*, B0 and B1 inhomogeneities, the apparent diffusion coefficient, proton density, perfusion and microvascular properties.

Mechanism
Consider scanning a volume with an unknown distribution of MR parameters. Each point in the volume has some unknown T1, T2, proton density, etc. In MRF, a series of excitations and readouts of the entire volume are performed, each with different pulse sequence parameters. Thus, the acquired measurement is a series of images of the volume, one image for each readout or time point, each with different contrast for different MR parameters. The “fingerprint” of each voxel in the image is the signal intensity from that voxel over time (a 1D signal). Each voxel’s fingerprint is then matched to its MR parameter values with some pattern matching algorithm. In the original MRF paper, each fingerprint is matched with every entry in a simulated dictionary of parameter values and their corresponding fingerprints. The final result is a quantitative map for each parameter that shows the parameter value at each voxel. The primary design choices in MRF are the choice of pulse sequence for generating fingerprints and the pattern matching algorithm used to determine parameter values from an acquired fingerprint.

MRF sequence design
In order for the pattern matching algorithm to successfully and robustly match parameter values to fingerprints, the pulse sequence used must generate maximally uncorrelated and unique signal evolutions for each combination of desired parameters. In MRF, this is accomplished with a pseudorandomized pulse sequence, which will naturally minimize the correlations between signal evolutions from different parameter values. Typically a “base” sequence is chosen and then its parameters are randomized, such as randomly picking a sequence of flip angles (FA) and repetition time (TR). After the sequence of random parameters is chosen, it is fixed and used for both dictionary generation and data acquisition. During each TR, a fast k-space readout is performed.

In the seminal MRF experiment, an inversion-recovery balanced steady state free-precession (IR-bSSFP) sequence was used with randomized FA and TR. IR-bSSFP was chosen for its known sensitivity to T1, T2, and off-resonance. For each TR a variable density spiral readout was performed after the RF pulse, allowing for a quick readout. The spiral was rotated every readout as a way to minimize undersampling error correlation. In order to fix the banding issues inherent in IR-bSSFP, a fast imaging with steady-state precession (FISP) sequence was later used as the base MRF sequence. As with bSSFP, a sequence of FA and TR are randomized to create the final MRF sequence.

Dictionary generation
In the original MRF paper, the pattern matching procedure involves matching to a precomputed dictionary of fingerprints. This dictionary contained over 500,000 entries for different values of T1, T2, and off-resonance, focusing on values likely to occur in a scan of the brain. The fingerprints for each entry were simulated with a Bloch simulator after the random sequence parameters were chosen. They report that the dictionary generation took only a few minutes on a modern desktop computer.

Fingerprint matching
In the original MRF paper, the matching procedure is straightforward: the signal evolution from each voxel was compared with every fingerprint in the dictionary, and the inner product between the two was computed. The entry with the highest inner product was then chosen as the set of parameter values for that voxel. Since then, work has been done to accelerate and improve the pattern recognition algorithm. First, McGiveney, et al. compressed the dictionary by using singular value decomposition (SVD) to generate a low-rank approximation. Then, each acquired fingerprint is transformed into that lower dimensional space, and matching can be done faster. There has also been significant work on more sophisticated methods that move completely away from the idea of matching with a dictionary, and instead try to invert the Bloch equations that underlie the signal generation mechanics of MR. Unlike a discrete dictionary, this allows for recovery of the entire continuous space of parameter values. Davies et. al. use compressed sensing theory to formulate an iterative optimization approach that directly works with the linear algebraic Bloch equations. Alternatively, Hoppe et. al. train a deep neural network on simulated data, and it implicitly learned how to invert the Bloch equations.

Error tolerance
A major benefit of using pseudorandom pulse sequences is tolerance to all kinds of artifacts caused by non-idealities in the scanning system or process, such as undersampling and patient motion. Error tolerance means that artifacts do not interfere majorly with the fingerprint matching process, i.e. do not cause one fingerprint to be mistaken for another. Intuitively, because the different acquisitions over time are random relative to each other, their artifacts are uncorrelated too. Therefore, artifacts will look like noise in the acquired signal evolution, but the “shape” will still look like the underlying signal, so the fingerprint can still be identified correctly. The original MRF paper successfully demonstrates robustness to severe undersampling, acquiring only a single spiral for each readout, about 1/48th of the normally required data, and seeing minimal interference with fingerprint matching. They also test patient motion by instructing a subject to move randomly during a scan; this also barely interfered with the results. Error tolerance in the clinical setting can enable faster acquisitions, endure some movement artifacts, and allow the use of less expensive and precise MR machines while maintaining current performance.

Clinical use
As of early 2021, MRF remains in the research stage of development, and is not widely used in clinical practice. However, the quantitative and error tolerant nature of MRF offers several advantages to traditional MR scan techniques that would make it useful in clinical practice. Despite these advantages, MRF still has hurdles to overcome before it is ready for widespread clinical use.

Diagnostics
As bodily tissue changes due to disease, injury, age, or other factors, the corresponding MR parameters of that tissue also tend to change. For example, T1 times can significantly lengthen in certain tumor types. However, parameters do not always change measurably, so information about many parameters can help determine if something is medically relevant. MRF offers the ability to rapidly acquire these parameters, allowing for accurate assessment of functions and disease progression within the body. Access to these parameters also opens up possibilities for using MRF as a screening tool for a variety of conditions. If one can define a unique set of MR parameters for a condition, the presence of those parameters would alert doctors to the existence of a problem. Additionally, quantitative information could enable computer-assisted or completely automated tissue segmentation. For example, given the parameters that differentiate an epileptic nodule from healthy brain tissue, a computer could automatically separate the two. This automatic separation gives doctors a non-subjective way to image and diagnose patients.

Challenges
Since MRF acquires information by matching simulations to measurements, there is inherent uncertainty in the technique. Simulation or measurement errors could potentially cause a fingerprint mismatch, or several fingerprints could equally match one sequence. This becomes increasingly less likely as more samples are taken, but it remains a statistical measure. The error bars of MRF need to be well established and understood before it can be used in a clinical setting. Additionally, many use cases of MRF assume that the MR parameters of a wide variety of tissue types are known, which is not necessarily the case. The evolution of MR parameters due to different diseases also needs to be well quantified in a large and diverse population before it can be used for accurate diagnoses.

Relationship to compressed sensing
MRF is strongly related to the concept of compressed sensing (CS), which is a statistical theory that justifies how randomness can be utilized to recover information from undersampled but sparse signals. Because MRF uses pseudorandom pulse sequences, artifacts caused by undersampling k-space in each readout will be uncorrelated (“incoherent” in the terminology of CS) between different acquisitions. In other words, artifacts will look like noise in the signal, and will not coherently interfere with the fingerprint matching process. This robustness to undersampling greatly decreases MRF’s scan time and maximizes the amount of information that can be collected and recovered.