Fluorinated Paramagnetic Complexes: Sensitive and Responsive Probes for Magnetic Resonance Spectroscopy and Imaging

Fluorine magnetic resonance spectroscopy (MRS) and magnetic resonance imaging (MRI) of chemical and physiological processes is becoming more widespread. The strength of this technique comes from the negligible background signal in in vivo 19F MRI and the large chemical shift window of 19F that enables it to image concomitantly more than one marker. These same advantages have also been successfully exploited in the design of responsive 19F probes. Part of the recent growth of this technique can be attributed to novel designs of 19F probes with improved imaging parameters due to the incorporation of paramagnetic metal ions. In this review, we provide a description of the theories and strategies that have been employed successfully to improve the sensitivity of 19F probes with paramagnetic metal ions. The Bloch-Wangsness-Redfield theory accurately predicts how molecular parameters such as internuclear distance, geometry, rotational correlation times, as well as the nature, oxidation state, and spin state of the metal ion affect the sensitivity of the fluorine-based probes. The principles governing the design of responsive 19F probes are subsequently described in a “how to” guide format. Examples of such probes and their advantages and disadvantages are highlighted through a synopsis of the literature.


FLUORINE MRS AND MRI
Fluorine magnetic resonance imaging (MRI) was first reported in 1977, just four years after the development of 1 H MRI, by Holland who acquired phantom images of NaF and perfluorotributylamine (Holland et al., 1977). In 1985, McFarland obtained the first 19 F in vivo MR images of a rat using a fluorinated probe which accumulates in the liver, Fluosol-DA (McFarland et al., 1985). These pioneering studies demonstrated the key advantages of fluorine nuclei for magnetic resonance spectroscopy (MRS) and imaging (MRI). Today, these advantages are still exploited for monitoring a variety of biological analytes and processes.
The fluorine nuclei ( 19 F, I = ½) is attractive due to its 100% abundance and high receptivity (83% that of 1 H). These attributes make it comparable to the 1 H nuclei (Knight et al., 2011;Ruiz-Cabello et al., 2011). Further, the similar gyromagnetic ratios (γ) of 19 F and 1 H allow images to be collected on broadband 1 H MRI scanners provided broadband amplifiers and dedicated radiofrequency coils are employed to accommodate the slower Larmor frequency of 19 F (Stares et al., 2018). The primary advantage of 19 F probes over 1 H MRI contrast agents is that the background signal in 19 F MRI is negligible. The body contains low amounts of fluorine that are primarily embedded in the solid matrices of bones and teeth. As a result, those fluorines have very short transverse relaxation times (T 2 ) and very broad signals that are easily removed with appropriate pulse sequences (Yu et al., 2013a). On the other hand, T 1 (longitudinal relaxation times) and T 2 -based 1 H MRI contrast agents, which are primarily gadolinium-and iron oxide nanoparticle-based, generate contrast by modulating the relaxation rates of the naturally-occurring water molecules. The significant background from the endogenous water can render certain imaging more difficult. In addition, 19 F nuclei have a large chemical shift range, >300 ppm, that readily allows for the design of fluorine probes featuring two distinct resonances that can be independently imaged if they are sufficiently separated. As will be discussed later, this property is advantageous in the design of ratiometric responsive 19 F MRI probes. Ratiometric probes can independently map the distribution of the probe and target analyte in vivo and enable tracking of different cell types or monitoring of multiple markers simultaneously.

IMPROVING THE SENSITIVITY OF 19 F PROBES
Despite the advantages of 19 F MRS and MRI, this field is limited by its low sensitivity that requires the use of high concentrations of probe, typically between 10 and 50 mM. In comparison, Gdbased T 1 contrast agents can be readily detected in vivo at substantially lower concentrations (0.1 µM) (Helm et al., 2018). This low sensitivity is due in part to the fact that only the 19 F nuclei of the probe are detected. Those nuclei are inherently less concentrated than the 1 H of H 2 O used in 1 H MRI, hence the lower sensitivity. This issue is usually addressed by increasing the local concentration of 19 F nuclei. A second underlying problem of 19 F probes, and particularly diamagnetic ones, is the long T 1 relaxation times of 19 F, typically 0.5-3 s for small diamagnetic compounds, which necessitate long image acquisition times in order to obtain sufficient signal-to-noise ratio (SNR). This issue is best addressed via the incorporation of appropriate paramagnetic metal ions that shorten the relaxation rates of the 19 F nuclei.

Increasing Sensitivity by Increasing the Density of 19 F Nuclei
The most straightforward approach to increasing 19 F MRS/MRI signal intensity is simply to increase the local concentration of 19 F nuclei. This is most often accomplished by increasing the number of 19 F nuclei on the probe. Complications of this approach are attributed to the hydrophobicity of fluorine which decreases the solubility of a probe in water and affects biodistribution and clearance. Nonetheless, many perfluorocarbons have successfully been used as 19 F MRS/MRI oximetry sensors and 19 F cell tracking agents provided they are injected as stable emulsions formulated to optimize clearance (Janjic and Ahrens, 2009;Ruiz-Cabello et al., 2011). Highly fluorinated molecules are mostly inert and considered non-toxic, which has facilitated their use in vivo and translation to humans. For instance, fluorinated nano-emulsions are undergoing a phase I clinical trial for 19 F MRI cell tracking applications (Ahrens and Zhong, 2013;Ahrens et al., 2014). However, not all fluorinated compounds can be assumed to be entirely non-toxic, especially at the high concentrations required for 19 F MRS/MRI. For instance, perfluorooctane sulfonate (PFOS) and perfluorooctanoic acid (PFOA) are both known to affect the function of the pancreas, thyroid, and liver (Chang et al., 2014;Kamendulis et al., 2014).
An often overlooked complication of perfluorinated probes arise when their 19 F nuclei are not chemically equivalent. Nonequivalent 19 F nuclei of a probe that have small frequency differences between the 19 F resonances result in blurry MR images that are the result of incomplete overlap of the images resulting from each 19 F resonance (Janjic et al., 2008). This substantially complicates image acquisition, can lead to artifacts, and decreases SNR. It is thus best to increase the number of fluorines in such a way that they remain chemically equivalent.
One of the most efficient ways to ensure that each 19 F nuclei is chemically equivalent is to incorporate high molecular symmetry in the design. Transition metal and lanthanide complexes with C 3 or C 4 symmetry are ideally suited for this application if the ligands are fluorinated appropriately. The macrocyclic DOTA (1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid) ligand, for instance, adopts a pseudo C 4 symmetry in which the acetate arms are arranged in a propeller-like fashion above the plane of the coordinating nitrogen atoms. Four possible isomers exist for this system based on the combination of two macrocyclic ring configurations (square prismatic or square antiprismatic) and the two possible arrangements of the acetate arms (Caravan et al., 1999;Benetollo et al., 2003). The substituents on the acetate arms and the Ln III ion both influence the ratio of isomers observed by NMR such that one isomer can be favored over the others (Parker et al., 2002). The judicial choice of the macrocycle's arms has a notable impact on the 19 F NMR spectra of this class of macrocycles and on their effectiveness to function as 19 F MRS/MRI probes. Ln(F-DOTPME) − (1,4,7,10,-tetraazacyclododecane-1,4,7,10tetrakis(methanephosphonic acid mono(2 ′ ,2 ′ ,2 ′ -trifluoroethyl) ester)), the lanthanide complex of the tetra trifluoroethylsubstituted DOTMP (1,4,7,10-tetraazacyclododecane-1,4,7,10tetrayl-tetrakis(methylphosphonic acid)) analog (1, Figure 1; Kim et al., 1997), for instance, exists in solution at room temperature as a mixture of all eight isomers, which results in the presence of eight distinct 19 F peaks within a 12 (Yb III ) to 70 ppm (Tm III ) range. As discussed above, the presence of these different isomers limits the efficacy of these complexes to function as 19 F MR probes. The metal complexes of the tetra substituted DOTA with aryl-CF 3 groups (11, Figure 1; Chalmers et al., 2010) exist primarily as one isomer, whose proportion depends on the nature of the lanthanide ion. This ligand is therefore better suited for 19 F MRI applications. The problem of multiple isomers is not limited to tetra-substituted macrocyclic derivatives. In fact, many DOTA analogs with only one or two fluorinated arms are present in solution as more than one isomer (2-4), the percentage of which varies according to the lanthanide (Kenwright et al., 2008;Chalmers et al., 2010;Placidi et al., 2013;Cakic et al., 2016).
Substitution of one or more carboxylate arms with bulky phosphinate groups or the introduction of substituent at the α-position to the ring nitrogen affects this dynamic process. For instance, Chalmers et al. reported two DOTA derivatives incorporating two trifluoroaryl groups and either two carboxylic acid or two glutaric acid substituents at the α-position to the ring nitrogen (5 and 6, Figure 1) (Chalmers et al., 2011a,b). In solution the carboxylic acid derivative, unlike the glutamic acid one, favors one major isomer which accounts for 80% of the 19 F NMR spectrum. The selectivity for one isomer can also be improved via the use of a phosphinate arm. For instance, all lanthanide complexes of 7 exist primarily (>87%) as one isomer. In extreme cases, a single isomer of a DOTA analog fluorinated on a single arm can be obtained, as for compounds 8-10 (Figure 1) (Jiang et al., 2011;Davies et al., 2015).
A single isomer for a tetra-substituted DOTA complex which exploits the symmetry of the ligand in order to maximize the number of equivalent fluorines can nonetheless be obtained. Examples include M-DOTAm-F12 (2,2 ′ ,2 ′′ ,2 ′′′ -(1, 4,7,10-tetraazacyclododecane-1,4,7,10-tetrayl)tetrakis(N-(2,2, 2-trifluoroethyl)acetamide)) (12, Figure 1; Srivastava et al., 2017a,b) and more recently the redox-responsive Eu-complex 39 (Figure 9) (Basal et al., 2017). Both of these complexes contain 12 19 F nuclei linked to the macrocycle via four amide arms. Importantly, they both exist as a single isomer for which all 12 19 F nuclei remain chemically equivalent. This increases the sensitivity of the 19 F MR probe and the resolution of the images that can be obtained with it. The high symmetry of the DOTA scaffold can also be exploited with certain transition metals. The unusual but stable 8-coordinate structure of the Fe II -DOTAm-F12 maintains a high symmetry and chemical equivalency for its 12 fluorine nuclei (Srivastava et al., 2017a). The higher solubility in water of the M-DOTAm-F12, >100 mM, renders it particularly promising for further development and imaging applications. In summary, the C 3 or C 4 symmetry of metal complexes can be exploited to increase the number of chemically equivalent 19 F nuclei on a probe, but the drawback of multiple stable isomers in solution remains a challenge.

Increasing Sensitivity With Paramagnetic Metal Ions
Increasing the number of 19 F nuclei per agent can only go so far in terms of increasing the sensitivity of 19 F probes. Ultimately, there is a limit to the number of 19 F nuclei that can be added to a molecule in such a way that they are chemically equivalent all the while maintaining sufficient water solubility for in vivo applications. A complementary approach to increasing the number of 19 F nuclei that is often used simultaneously is to decrease the T 1 of the 19 F nuclei. Diamagnetic molecules typically have T 1 of 19 F nuclei in the range of 0.5-3 s. For in vivo imaging applications, that are limited by time, the long T 1 of diamagnetic fluorine probes hinders their sensitivity (Harvey et al., 2012b). It is thus preferential to decrease the T 1 of the 19 F nuclei of fluorine probes. This is best achieved by incorporating paramagnetic metal ions such as lanthanides(III) or iron(II). The metal should be selected with care as different paramagnetic metal ions have different effects on the relaxation of nearby nuclei.
The effect of a paramagnetic metal ion on the T 1 and T 2 of a 19 F nuclei is described by the Bloch-Wangsness-Redfield theory. A 19 F nuclei adjacent to a paramagnetic center in a magnetic field can relax via five different mechanisms: (1) chemical shift anisotropy, (2) inter-nuclear dipole-dipole interaction, (3) electron-nucleus contact interaction, (4) electron-nucleus dipoledipole interaction, and (5) Curie relaxation (Chalmers et al., 2010). Of these, chemical shift anisotropy is negligible for a single 19 F nuclei or CF 3 group, and inter-nuclear dipoledipole mechanisms are minimal, accounting for <1% of the total relaxation. The electron-nucleus contact interaction is also negligible since ligand geometries generally locate the 19 F nuclei further than 4.5-7.5 Å away from the metal ion, resulting in coupling values of zero. Thus, only the electron-nucleus dipoledipole and Curie relaxation processes contribute significantly to the relaxation of the 19 F nuclei. Given this, the longitudinal (R 1 = 1/T 1 ) and transverse (R 2 = 1/T 2 ) relaxation rates of 19 F nuclei in paramagnetic metal complexes are described by Equations (1) and (2), respectively (Chalmers et al., 2010).
In these equations, d is the distance separating the 19 F nuclei from the paramagnetic metal ion, µ 0 is the permeability of vacuum, γ F is the gyromagnetic ratio of the 19 F nuclei, T is the temperature in K, k is Boltzmann's constant, and ω F is the Larmor angular frequency of 19 F. The effective magnetic moment, µ eff , is proportional to the effective electron g-factor (g J ), the Bohr magneton (µ B ), and the electron angular momentum, J(J+1) according to Equation (3). The electron angular frequency (ω e ) is a function of the magnetic field strength (B 0 ) according to Equation (4) in whichh is the reduced Planck's constant. The τ R+e term is dependent on the rotational correlation time FIGURE 1 | Chemical structures of non-responsive paramagnetic 19 F probes (1, Kim et al., 1997;2, Cakic et al., 2016;3, Placidi et al., 2013;4, Chalmers et al., 2010;5-6, Chalmers et al., 2011a;7, Chalmers et al., 2011a,b;8-9, Davies et al., 2015;10, Jiang et al., 2011;11, Chalmers et al., 2010;12, Srivastava et al., 2017a,b;13, Blahut et al., 201613, Blahut et al., , 2017. (τ R ) and the electron spin longitudinal relaxation time (T 1e ) according to Equation (5). In Equations (1) and (2), the first term represents the dipolar relaxation characterized by the stochastic electron magnetization of the electron-nucleus dipole-dipole interaction. The second term is the Curie relaxation arising from the interaction between the fluorine nuclear spin and the magnetic dipole induced by the applied magnetic field. Together, they relate R 1 and R 2 to the effective magnetic moment (µ eff ) of the paramagnetic metal, the 19 F-metal distance (d), the rotational correlation time (τ R ), the applied magnetic field strength (B 0 ), and the temperature (T). Optimizing the sensitivity of 19 F MRS/MRI probes requires understanding each of these relationships.

Dependence on the Nature of the Metal Ion
The effective magnetic moment (µ eff ) of the paramagnetic metal affects both the electron-nucleus dipole-dipole interaction and, to a greater extent, the Curie relaxation mechanism. The effective magnetic moment of transition metal complexes is a function of both their oxidation state and their ligand fields. Each lanthanide ion has a characteristic µ eff value ( Table 1).
The effect of the nature of the transition or lanthanide ion on the relaxation rates of the 19 F nuclei of fluorinated complexes and the sensitivity of the resulting fluorine probe has been explored via a series of non-responsive probes. Several fluorinated ligands have been investigated, which enables a more in-depth evaluation of the influence of the structure of the ligand on the 19 F relaxation rates of the probe (Figure 1, Table 2). Studies by Parker and coworkers focused on a DOPA ([(4,7,-di{[hydroxyl(methyl)phosphoryl]methyl}-10-({[2-(trifluoromethyl)phenyl]carbamoyl}methyl)-1,4,7,10tetraazacyclododecan-1-yl)methyl](methyl)phosphinic acid) ligand monosubstituted with ortho aryl-CF 3 (7) and DOTA ligand scaffold tetra substituted with aryl-CF 3 groups (11) (Chalmers et al., 2010(Chalmers et al., , 2011a. In this scaffold, ortho substitution of the CF 3 group lead to a greater decrease in relaxation times due to the shorter distance separating the 19 F nuclei from the lanthanide ion (Senanayake et al., 2007;Chalmers et al., 2010). In agreement with the Bloch-Wangsness-Redfield theory, this first study demonstrated that paramagnetic lanthanide ions  (Gysling and Tsutsui, 1971;Tilley et al., 1980;Garcia and Allen, 2012). b (Gysling and Tsutsui, 1971;Bertini et al., 1993a;Chalmers et al., 2010). c (Bleaney, 1972). d aqua ion, 2.1 T (Alsaadi et al., 1980). e value for Eu II was calculated using formula in Burai et al. (2003). f Bertini et al. (1993b).
can increase the R 1 by up to two orders of magnitude, with the greatest change observed with those metal ions with the highest µ eff , notably, Tb III , Dy III , Ho III , and Er III ( Table 2). Unfortunately, the poor solubility of the tetra substituted complexes in water limited further in vivo studies. Recently, our lab reported the relaxation properties of the Fe II and Ln III complexes of another macrocyclic ligand, DOTAm-F12 (12) (Srivastava et al., 2017a,b). Complexes of this series, including the Fe II complex, have a number of advantageous properties for 19 F imaging. The complexes each contain 12 fluorine nuclei that are chemically equivalent, resulting in a single 19 F resonance. As discussed above, a high number of fluorine nuclei and their equivalency are two necessary components in the design of sensitive 19 F probes for MR imaging. The complexes are also highly soluble in water; they can be dissolved in concentrations of up to 100 mM, a necessity for any biological applications. The Fe II complex is notable as it is stable both in air and water and is a rare example of an eight coordinate iron complex (Srivastava et al., 2017a). Importantly, for both the Fe II and the Ln III complexes, the structure of the macrocycle places the fluorine nuclei from 5.22 to 6.84 Å from the metal ion. As will be discussed later, this is an optimum distance since it minimizes the effect of the shortened T 2 of the 19 F nuclei. As in Parker's study, the paramagnetic metal ions decrease the T 1 of the 19 F nuclei by up to two orders of magnitude with the greatest decrease observed with those metal ions having the highest µ eff , namely Tb III , Dy III , Ho III , and Fe II . Paramagnetic Ni II cyclam complexes featuring trans-trifluoroethyl groups were also recently reported by Blahut et al. (2016Blahut et al. ( , 2017. The trans-[Ni(te2f2p)] 2− (13, Figure 1) with phosphate ligands has a 19 F-Ni distance of ∼ 5 Å which facilitates a nearly 180-fold reduction in T 1 vs. the free ligand ( Table 2). This Ni II complex and Fe II -DOTAm-F12 (12) exemplify that the diverse electronic and structural parameters of transition metal complexes can also be exploited to optimize 19 F paramagnetic relaxation enhancement (PRE).
The sensitivity of an agent, estimated by comparing SNR of solutions of complexes at the same concentration, is dependent not only on T 1 but also on T 2 . The line-broadening characteristic of the shorter T 2 of the fluorines of certain paramagnetic complexes significantly affect the sensitivity of the probe. An extreme example being the Gd III complex of DOTAm-F12 that has such a short T 2 that the complex could not be observed by MRI. Note that for such complexes with rapid transverse relaxation, the use ultrashort TE (UTE) and zero TE (ZTE) acquisition pulse sequences can sometimes increase the SNR in 19 F-MRI (Kislukhin et al., 2016).
Not all paramagnetic metals affect T 2 to the same degree as T 1 . Therefore, the most sensitive metal-based probes are not those whose metal ions have the highest µ eff , but those whose 19 F have the highest T 2 /T 1 ratio. For M-DOTAm-F12 in water, these are Fe II , Ho III , Tm III , and Yb III . Importantly, the media also has a substantial effect on the relaxation times, and particularly on the transverse one. The T 2 of all M-DOTAm-F12 complexes decrease substantially in blood. This affects the sensitivity of all metal complexes. Ho III -DOTAm-F12, for instance, is the most sensitive probe in water, yet it could not be detected in blood. The lower T 2 value of M-DOTAm-F12 complexes in blood in comparison to water could be due to different parameters. Coordination to albumin or other serum proteins and the resulting increase in rotational correlation time can affect both T 1 and T 2 . Blood is also more viscous than water, and this increase in viscosity also affects τ R , T 1 , and T 2 . One should therefore not assume that a probe that is sensitive in water is necessarily appropriate for in TABLE 2 | 19 F chemical shift and relaxation properties for non-responsive paramagnetic fluorine probes.    (Cakic et al., 2016). b (Placidi et al., 2013). c (Chalmers et al., 2011a). d (Jiang et al., 2011). e (Chalmers et al., 2010). f (Srivastava et al., 2017b). g (Blahut et al., 2016). h Major isomer. i Minor isomer.
vivo applications where it will accumulate in blood or tissues. It is therefore recommended that the sensitivity of probes be evaluated not only in water but also in the media in which they are intended to be used. Also note that the greatest effect is not necessarily obtained with lanthanide ions. In blood, the most sensitive probe is Fe II -DOTAm-F12 whose limit of detection (300 µM) is more than an order of magnitude lower than that of small diamagnetic probes. Similar trends have been observed with other lanthanide complexes, such as 2-5, 7, and 10-12 (Figure 1, Table 2). In general, the stronger relaxing metals with the higher µ eff near 10, Tb III , Dy III , and Ho III decrease both T 1 and T 2 the most. Lanthanides such as Er III , Tm III , and in the extreme case Gd III , have lower T 2 /T 1 ratio and hence lower sensitivity ( Table 2) (Chalmers et al., 2010(Chalmers et al., , 2011aJiang et al., 2011;Harvey et al., 2012b;Placidi et al., 2013;Blahut et al., 2016;Cakic et al., 2016;Srivastava et al., 2017b). Do note that the PRE effect is determined by other parameters beyond the µ eff of the metal ion; it is also dependent on the magnetic field strength and on the distance separating the 19 F nuclei and the paramagnetic metal ion (Equation 1-5). As mentioned above, transition metals such as Fe II (µ eff ∼ 5) and Ni II (µ eff ∼ 3) (complexes 12 and 13, respectively) can also generate high 19 F MRI SNR ratios of 20-30 despite their lower magnetic moments.
Even at greater 19 F-M distances, the effect of the paramagnetic metal ion on the relaxation rates of the fluorine nuclei can be notable. The fluorinated complex of Jiang (10, Figure 1) is a DOTA-based complex containing three equivalent trifluoromethyl groups separated by a polyethylene glycol linker that positions the 19 F nuclei more than 10 Å away from the paramagnetic metal ion. Despite this great distance, paramagnetic metals such as Tb III , Dy III , Ho III , Er III , Gd III , Fe III , Ni II , and Cu II reduce T 1 and T 2 by >95% (Jiang et al., 2011). A noteworthy conclusion of this study is that the 19 F relaxation times of these paramagnetic metal complexes are relatively constant (<5% change) with respect to environmental fluctuations in pH, temperature, and the concentration of either O 2 or bovine serum albumin (BSA) (Jiang et al., 2011). It is thus the identity of the paramagnetic metal ion that is the primary contributor to both the chemical shift and the relaxation rates of the fluorines. This observation is important for the development of responsive probes (vide infra).

Dependence on the 19 F-Metal Distance
From the Bloch-Wangsness-Redfield Equations (1-5) given above, both the R 1 and the R 2 of the fluorine nuclei have a steep dependence on the distance d separating the 19 F nuclei from the metal ion. The 19 F-M distance is a key parameter in determining the sensitivity of metal-based fluorine probes. The effect of the paramagnetic metal ion on R 2 extends to longer distances than that of R 1 . Both too long and too short a distance can be detrimental. Too long a 19 F-M distance and the effect of the paramagnetic metal ion on the relaxation times of the fluorine nuclei is severely diminished. Too short a distance, and the substantial shortening of T 2 decreases the sensitivity of the fluorine probe. A higher T 2 /T 1 ratio and thus a more sensitive fluorine probe is obtained if the 19 F nuclei are positioned between 4.5 and 7.5 Å from the metal ion (Harvey et al., 2012b).
Within this range, even minor changes in 19 F-M ion distance can have an impact on the relaxation rates of fluorine nuclei and the sensitivity of the agent. One such example are the lanthanide complexes containing a single aryl-CF 3 moiety positioned either on an acetate-based DOTA (4, Figure 1) or a phosphinate-based DOPA (7, Figure 1) scaffold. The DOTA complexes (4) exists in solution as a mixture of multiple isomers with the primary species representing only 50% of the fluorine signal intensity by NMR. On the other hand, the principal isomer of the phosphinate analog (7) accounts for 87% of the total 19 F signal intensity (Chalmers et al., 2011a). The R 1 and R 2 of lanthanide complexes of these two ligands are different. The R 1 of complexes of DOPA scaffold are 10-67% greater than those of the DOTA scaffold ( Table 2). However, the R 2 of complexes (Ho III , Er III , and Tm III ) of DOPA scaffold are 5-12% smaller than those of DOTA scaffold with an exception of Tb III and Dy III being 14-124% greater than those of DOTA complexes. Global fitting of the relaxation rates collected at multiple field strengths to the Bloch-Wangsness-Redfield theory determined that the differences in R 1 and R 2 are due to a 0.3 Å shorter 19 F-Ln distance in the DOPA complex than in the DOTA one (Chalmers et al., 2010(Chalmers et al., , 2011a. Interestingly, the highest T 2 /T 1 ratio with the DOTA-based scaffold was obtained with Tb III . For the DOPA-based scaffold, it was instead Ho III (0.84), Er III (0.79), Tm (0.75), and Dy (0.74) that yielded the highest T 2 /T 1 ratio. As is apparent from this example, the best metal ion for one fluorinated ligand is not necessarily the same for another one.
The effect that such minor modifications of the ligand and the structure of the complex have on the T 2 /T 1 ratio and the sensitivity of the probe has been observed with other complexes. The Yb III -DO3A (1,4,7,10-tetraazacyclododecane-1,4,7-tris(acetic acid))-based complex with a fluorinated aryl phosphonate of Angelovski, (3, Figure 1) positions the 19 F nuclei 7 Å from the metal, a 19 F-Yb distance 0.7 Å greater than in Yb-DOTAm-F12 (Placidi et al., 2013). At 7 T, the T 1 of 273 ms is nearly twice that in Yb III -DOTAm-F12. More noticeably, the very short T 2 of the fluorines of this complex, 4.2 ms, results in a much smaller T 2 /T 1 ratio and hence a much less sensitive probe than Yb III -DOTAm-F12. Supramolecular self-assembly enables more facile synthesis of paramagnetic fluorine probes via the formation of ternary complexes. Given the hardness of lanthanide ions, fluorinated carboxylate ligands are particularly well-suited for this approach (8 and 9, Figure 1) (Davies et al., 2015). These assemblies also decrease the relaxation times of the fluorine to a similar degree as observed in the complexes discussed above, although the relatively weak affinity of the carboxylate ligand for the lanthanide (log K a ∼ 4.9) may result in decomplexation of the fluorinated moiety under biological conditions.
These previous examples positioned the paramagnetic metal ions on the surface of the nanoparticles and, thus, a significant distance away from the 19 F nuclei. To resolve this issue Kislukhin et al. designed nanoparticles that incorporated the paramagnetic metal ions directly into the fluorous core, thereby decreasing the 19 F-M distance (Kislukhin et al., 2016). Despite the electronegativity of the fluorine atoms that reduce the basicity FIGURE 2 | Schematic representations of paramagnetic perfluorocarbon nanoparticles. Gd-complexes are embedded into lipid monolayers that encapsulate perfluorocarbon cores (14, Neubauer et al., 2008;15-16, Hu et al., 2011;17-19, de Vries et al., 2014) or perfluorocarbon substituted parmagnetic metal complexes form nano-emulsions (20, Kislukhin et al., 2016).
of the ligand, fluorinated β-diketone ligands form neutral, hydrophobic complexes that are sufficiently stable and dispersible in the perfluorocarbon core (20, Figure 2). Three different paramagnetic metal ions were evaluated: Fe III , Mn II , and Gd III . Of these, Fe III had the greater impact on the R 1 of the 19 F nuclei, increasing it 13-fold, and the sensitivity of the nanoparticles, increasing it 5-fold. In comparison, Mn II and Gd III increased R 1 7-and 5-fold, respectively. Both Mn II and Gd III induced severe line broadening which decreased the sensitivity of the assembly. Advantageously, these nanoparticles are readily taken up by glioma cells. Since the nanoparticles also have low cytotoxicity (they reduce the viability of glioma cells by only 20%), they can be used to track cells in vivo 24 h post injection in mice. Do note, though, that it is not possible to distinguish between live and dead cells labeled with fluorine probes 24 h post injection, especially if the cells are engrafted subcutaneously.

Dependence on the Magnetic Field Strength
As the Bloch-Wangsness-Redfield theory indicates, both the R 1 and R 2 of fluorine nuclei depend on the strength of the magnetic field (Figures 3A,B, respectively). The magnetic field dependencies of R 1 and R 2 are also a function of the µ eff of the metal ion and as such, different metal ions are better suited for either low field or high field experiments. A steeper increase in R 1 with respect to magnetic field strength is observed for Dy III and Ho III complexes of para-hydroxyl derivative of 4 than for its Tm III and Tb III , and Er III complexes (Chalmers et al., 2010;Harvey et al., 2012b). For this ligand scaffold, the stronger relaxing ions such as Ho III are thus more appropriate for experiments performed at lower magnetic field strengths, whereas the weaker Tm III and Er III provide adequate relaxation enhancement above 7 T (Chalmers et al., 2010;Harvey et al., 2012b).
The higher relaxation rates of fluorine nuclei of paramagnetic complexes allow for the collection of more data per unit time. Consequently, PRE increases both the spectral sensitivity and the SNR of paramagnetic fluorine agents compared to their diamagnetic analogs. Chalmers et al. demonstrated that the Dy III of fluorinated DOPA complex (7) increased the image SNR ∼ 13-fold compared to the diamagnetic Y III analog (Chalmers et al., 2011a,b). The improved SNR correlates with a T 2 /T 1 ratio closer to l. With such a ratio, the benefit of increased R 1 is not diminished by the increased signal broadening due to rapid transverse relaxation. Similar conclusions were drawn with complexes of DOTAm-F12 (Srivastava et al., 2017b). In theory, sensitivity gains of 15-20 times that of diamagnetic analogs can be achieved with fluorinated lanthanide complexes between 1.5 and 9.4 T, the magnetic fields of clinical relevance (Harvey et al., 2012b). The use of paramagnetic metal ions is thus the most effective strategy to increase the sensitivity of probes for 19 F MRS/MRI, enabling imaging of sub-millimolar concentrations of probe in <15 min with adequate SNR (>4) (Chalmers et al., 2011a,b).

The Effect of the Rotational Correlation Time, τ R
Both the R 1 and R 2 of fluorine nuclei are affected by their rotational correlation time (τ R ) as well as by the field strength of the instrument (B 0 ) and the temperature of the sample. Both R 1 and R 2 increase as the magnetic field strength (B 0 ) increases. This increase is far more significant if the rotational correlation time, τ R , is also optimized. Macromolecules, which tumble more slowly (longer τ R ), have higher R 2 . As can be seen in Figure 3B, R 2 increases drastically for 19 F nuclei with τ R > 1,000 ps, especially at high magnetic field (>7 T). The resulting extreme line broadening explains why fluorines embedded in bones and teeth in the body are not visible by MRI. The effect  (1) for R 1 or (2) for R 2 and is done at 37 • C using the mean 19 F-Tm III distance determined from X-ray crystallography (6.26 Å), assuming a magnetic moment, µ eff , of 7.6 BM and an electronic relaxation time, τ e , of 0.20 ps, values typical of Tm III complexes.
of τ R on R 1 is more complicated (Figure 3A). R 1 increases to a maximum when the tumbling rate of the M-19 F vector (τ −1 R ) equals the Larmor frequency of the 19 F nuclei; i.e., when ω 2 F τ 2 R = 1 ( Modo and Bulte, 2007). Monomolecular lanthanide complexes, such as those discussed in this review, have rotational correlation times on the order of 200-350 ps (Chalmers et al., 2010;Harvey et al., 2012b). Unlike for R 2 , there is an optimal τ R beyond which R 1 decreases sharply especially at high magnetic field. The optimal τ R is a function of the µ eff of the paramagnetic metal ion. For Tm, an optimal τ R of 200 ps increases R 1 substantially, particularly at high magnetic field. Unlike for Gd IIIbased T 1 contrast agents (Caravan et al., 1999), there is not much advantage to macromolecular paramagnetic fluorine probes with longer τ R .
There are limited examples in the literature of macromolecular fluorinated probes that feature a paramagnetic center. They are mostly used to increase the number of 19 F nuclei per unit. For example, the polymeric Dy III -chitosan conjugate, 21 (Figure 4), increases the relaxation rates of the fluorines via the PRE effect (De Luca et al., 2014). As for the small molecules described earlier in this section, the aryl trifluoro groups are advantageously positioned close, but not too close (6.5 Å) from the lanthanide ion. This macromolecular complex features 10 trifluoro groups of equivalent 19 F nuclei appended to glycol chitosan, a linear polysaccharide selected for its biocompatibility. The increase in τ R from 83 ps to 8 ns due to polymerization of the chitosan was evaluated with Gd III -complexes similarly conjugated to the chitosan monomer (22) and polymer (23) (De Luca et al., 2014). In this case, the R 1 of the fluorine nuclei of the Dy chitosan conjugate 21 remained constant before and after polymerization (186 s −1 at 9.4 T), whereas the R 2 decreased from 440 to 367 s −1 , which is unusual for a polymer (De Luca et al., 2014). Of note, this polymer is a rare example of a metallic fluorine probe that was successfully used in vivo to image tumors in mice. Although a dose of 0.54 g/kg was used in this study-a dose higher than typically used with Gd-based contrast agents-the sensitivity of the probe remained poor and a very long imaging time of 7 h was required to have sufficient SNR (De Luca et al., 2014). Although this probe was more sensitive than small molecule fluorine probes, the very long imaging time remains a significant hurdle to the application of 19 F probes.
One should note that although macromolecular paramagnetic fluorine probes are rare, their diamagnetic analogs are more common. Several macromolecular structures based on hyperbranched polymers, dendrimers, or nanoparticles that incorporate a high number of 19 F nuclei have been described (Du et al., 2008;Criscione et al., 2009;Jiang et al., 2009;Peng et al., 2009;Ogawa et al., 2010a,b;Thurecht et al., 2010), and recently reviewed (Yu, 2013;Zhu et al., 2013). A macromolecular architecture is more advantageous for diamagnetic fluorine probes than for paramagnetic ones: the increase in τ R decreases T 1 , and, if designed correctly, can increase the solubility of the probe in water as well as its in vivo retention time.

Applications of the Bloch-Wangsness-Redfield Theory to the Design of Responsive Fluorine Probes
Advantageously, a paramagnetic metal ion that alters T 1 and T 2 of the fluorine nuclei can also modulate their chemical shift ( 19 F δ). Since variations in each of these three variables can readily be observed both by MRS and by MRI, paramagnetic fluorine complexes offer unique mechanisms for the development of responsive MR probes that often yield much greater response than their purely organic analogs (Yu et al., 2013a). Two different effects of paramagnetic metals can be exploited to design responsive molecular probes. The first is the PRE effect. It is governed by the Bloch-Wangsness-Redfield theory, affects both relaxation times (T 1 and T 2 ) and is a function primarily of the nature of the paramagnetic metal ion and the distance d separating it from the fluorine nuclei. The second is the lanthanide induced shift (LIS) effect. It is just as readily be observed with 19 F than with 1 H nuclei and  is governed by the McConnell-Robertson theory. Unlike PRE, LIS is affected not only by the nature of the paramagnetic lanthanide ion and the distance d separating it from the fluorine nuclei, but also by the second order crystal field coefficient of the complex, B 0 2 , and the angle θ between the metal-fluorine vector and the principle magnetic dipolar axis of the lanthanide. Coupling either of these effects with the extensive range of chemical shifts available to 19 F offers valuable opportunity to design ratiometric responsive MR probes that can distinguish between changes in signal intensity due to the presence of an analyte vs. that due to a change in the concentration of the probe.
The PRE effect described in the previous section of this review is the basis for the improved sensitivity on a per 19 F basis of paramagnetic probes as compared to their organic counterparts. It is the substantial shorter T 1 and higher T 2 /T 1 ratio of paramagnetic fluorinated complexes that enables more scans to be acquired in the same amount of time thereby yielding higher SNR both by 19 F MRS and MRI. Analysis of the Bloch-Wangsness-Redfield Equations (1-5) indicate that at constant applied magnetic field (the same scanner) and for the same metal ion, T 1 and T 2 are a function of primarily one parameter: the distance d separating the 19 F nuclei from the metal ion. This parameter can be altered significantly by binding to or reacting with a substrate. Herein lies a substantial advantage of paramagnetic metal ions in fluorine probes: they readily enable the design of responsive and ratiometric molecular probes.
The dependence of T 1 and T 2 on the distance separating the fluorine nuclei from the lanthanide ion has already been applied to the design of responsive paramagnetic fluorine probes. As depicted in Figure 5, this distance can be altered either by reacting with a target or by induced conformational change upon binding to the desired analyte. The former approach yields an irreversible response, although one that can enable the detection of targets such as enzymes that are present at lower concentrations. The latter approach can lead to a reversible response but given the enduring limits in the sensitivity of fluorine probes, it is more appropriate for biological analytes present at substantially higher concentrations such as pH or certain small molecules or metal ions.
Current examples of this class of responsive probes use for the most part Gd III . As described in the previous section, Gd III has a notable effect on the T 1 of nearby nuclei, and, importantly, a substantially more pronounced one on T 2 . Indeed, among the lanthanides, Gd III typically offers the lowest T 2 /T 1 ratio ( Table 2). As a result of this very low ratio, the peaks of 19 F nuclei near Gd III ions broaden to the point of no longer being observable neither by MRS nor by MRI. Increasing the distance between the 19 F nuclei and the Gd III increases T 2 ; this enables the 19 F signal to reappear.
A greater effect will be observed if the linker separating the 19 F nuclei from the Gd III ion is completely cleaved by the target (Figure 5A). As the fluorinated moiety diffuses away from the Gd III complex, its relaxation times increase by orders of magnitude and, consequently, so does the 19 F signal intensity. This approach is particularly well-suited for the detection of enzymes that cleave peptides or sugars. Indeed, the first example reported by Kikuchi and coworkers targeted caspase 3 (24, Figure 6). Adroit positioning of the 19 F nuclei on the amino acid substrate of the enzyme that was directly tethered to the Gd III complex resulted in a complete off/on response (Mizukami et al., 2008). This first probe, and its dual 19 F MRI/fluorescence analog (25, Figure 6) (Mizukami et al., 2009), exemplified a distinct advantage of 19 F molecular probes over both Gd IIIand nanoparticle-based responsive contrast agents: a substantial response with zero background such that presence of a signal can only result from co-localization of both the MR probe and the enzyme target. In comparison, 1 H MRI contrast agents have to contend with the intrinsic high 1 H background signal due to the high concentration of water of the biological milieu. With these agents, an increase in signal intensity does not necessarily correlate with the presence of the target; an identical response can simply result from higher local concentration of the contrast agent. Do note, however, that since such agents are not ratiometric they do not eliminate the possibility of false negative. That is, they cannot distinguish between a lack of signal due to a lack of enzyme as opposed to a lack of 19 F probe.
This approach was recently extended by both the Kikuchi and the Engelmann groups to other enzymes, β-galactosidase (26 and 27) (Keliris et al., 2011(Keliris et al., , 2012Mizukami et al., 2011), β-lactamase (28) (Matsushita et al., 2012), and matrix metalloprotease-2 (29, Figure 6; Yue et al., 2014Yue et al., , 2017 thereby opening the possibility of directly imaging gene expression by MRI. In each case, hydrolysis of the enzyme's substrate generates a self-immolative linker that releases the fluorinated moiety from the Gd III probe thereby turning on the 19 F MR signal. This approach is not limited to enzymes and cleavable linkers. Similar responses can be obtained with an analyte-induced conformational changes that either increase (turn on) or decrease (turn off) the 19 F-Gd distance (Figure 5B,C, respectively). Fujimoto and coworkers used this approach to the PRE effect to extend the traditional molecular beacon motif commonly used to detect DNA (or RNA) by luminescence to that by 19 F NMR (30, Figure 6) (Sakamoto et al., 2011). Hybridization with the target nucleotide sequence causes the stem loop of the probe to unfold, thereby increasing d and thus also the T 2 and signal intensity of the 19 F nuclei.
Similar responses can be obtained with paramagnetic transition metals. Yu and Mason reported three fluorinated probes for β-galactosidase that use the same principle but in the opposite direction (31-33, Figure 7) (Yu et al., 2012(Yu et al., , 2013b. Hydrolysis of the sugar moiety by β-galactosidase releases a fluorinated Fe III chelator. The T 2 of this ligand decreases substantially upon subsequent coordination to the transition metal. As opposed to Kikuchi's and Engelman's examples, in this case the 19 F signal of the probe is turned off by the enzyme. The practicality of such probes for in vivo imaging, however, is likely limited given that iron is tightly regulated in the body and is essentially unavailable (Raymond et al., 2003).
The same approach readily leads to the development of fluorine probes for paramagnetic metal ions. An example for Mn II is 34 developed by Datta and coworkers ( Figure 7B) (Sarkar et al., 2017). Coordination of Mn II results in a 101-fold decrease of T 2 and, therefore, significant line broadening which decreases the signal intensity of the 19 F nuclei.
By extension, this strategy can readily be adjusted to design probes that signal the redox potential of their surroundings. If the metal is chosen correctly, a change in its oxidation state enables it to switch between a diamagnetic and a paramagnetic state (Figure 8). In the paramagnetic state, the metal attenuates the 19 F signal by substantially decreasing their T 2 . Conversion to the diamagnetic state lengthens T 2 resulting in a "turn on" response. Early examples that utilize metal redox state to modulate the relaxation of 19 F nuclei, and in turn signal intensity, were reported by Chujo's lab (Tanaka et al., 2009;Kitamura et al., 2012). Their probes, Fc-POSS (35) and Cu-POSS (36) contain either a redox sensitive ferrocene or a Cu complex with a bis(2pyridylmethyl)amino ligand (PMEA) along with trifluoromethyl groups appended to a cubic polyhedral oligomeric silsesquioxane (POSS) for water solubility (Figure 9A). The oxidation of Fe II in 35 reduces the 19 F signal intensity 3-fold due to the shortened relaxation time. The nitroxyl (HNO) mediated reduction of paramagnetic Cu II in 36 to diamagnetic Cu I modestly increased T 1 (from 1180 ms to 1460 ms) and T 2 (from 420 to 540 ms) causing a 3-fold increase in signal intensity. Thus, their work demonstrates the ability to apply PRE to the design of 19 F redox sensitive responsive probes. Que's laboratory utilized this strategy and the PRE of Cu II to detect cellular hypoxia by 19 F MR . Reduction of CuATSM-F 3 (37, Figure 9A) from Cu II (d 9 , paramagnetic) to Cu I (d 10 , diamagnetic) and subsequent ligand dissociation increases T 2 of the 19 F and restores their signal intensity. A second generation version of this probe (38) was designed to be more sensitive (Xie et al., 2017). It includes a higher density of 19 F nuclei, a polyethylene glycol linker that increases the hydrophilicity of the probe and positions the 19 F nuclei at an optimal distance from the copper ion. With a 19 F-Cu distance of ∼ 18 Å, the 19 F signal is attenuated but remains visible by NMR when the probe is in the Cu II state. Reduction to Cu I generates a sharp signal which is 6-fold more intense, leading to a 4.5-fold increase in SNR in the 19 F MRI images obtained at 7 T. FIGURE 6 | Responsive fluorinated probes whose signals are modulated by the paramagnetic relaxation enhancement effect of Gd III (24, Mizukami et al., 2008;25, Mizukami et al., 2009;26, Mizukami et al., 2011;27, Keliris et al., 2012;28, Matsushita et al., 2012;29, Yue et al., 201429, Yue et al., , 201730, Sakamoto et al., 2011).
Frontiers in Chemistry | www.frontiersin.org 13 May 2018 | Volume 6 | Article 160 The large differences in relaxation times between the two species allow them to be independently imaged using short (TE = 10 ms for Cu II ) or long (TE = 100 ms for Cu I ) echo pulse sequences (Xie et al., 2017). Allen's laboratory used an analogous approach with Eu in the design of their temperature and redox responsive 19 F probe (39, Figure 9A). This Eu-DOTAm (1,4,7,10tetrakis(carbamoylmethyl)-1,4,7,10-tetraazacyclododecane) complex with a p-trifluoromethylphenyl arm, has 12 equivalent fluorine nuclei (Basal et al., 2017). In its +2 oxidation state, Eu significantly shortens the T 2 of the 19 F and hence quenches their signal. In its +3 oxidation state, Eu III has a much lower µ eff (3.40-3.51 B.M.) than Eu II (7.6-8.0 B.M.; Tilley et al., 1980;Garcia and Allen, 2012) (Table 1) and thus a limited effect on the relaxation times of the fluorine which consequently reappear. In 19 F MRI images, oxidation of Eu II to Eu III results in a 6-fold increase in SNR. This responsive probe was successfully used to image non-hypoxic regions in vivo by 19 F MRI.
This approach also enables direct detection of reactive oxygen species. Oxidation of Co-NODA-CF 3 (2,2 ′ -(7-(2-oxo-2-((2,2,2trifluoroethyl)amino)ethyl)-1,4,7-triazonane-1,4-diyl)diacetic acid) (40, Figure 9A) with H 2 O 2 from paramagnetic Co II (d 7 ) to diamagnetic Co III (d 6 ) shifts the 19 F signal by 3.6 ppm and increases the T 1 and T 2 of the 19 F nuclei 60-and 121-fold, respectively (Yu et al., 2016). This, in turn, results in a 23-fold increase in signal intensity in spin-density weighted 19 F MR images. Although the oxidation of the probe is reversible, the long (2 h) reaction time and the low sensitivity of the probe compared to in vivo levels of H 2 O 2 still limit the application of this probe to in vivo imaging.
There are two main disadvantages to using paramagnetic metals that primarily affect T 2 in the design of responsive fluorine probes. The first, as mentioned above, is that such probes are not ratiometric. A lack of signal can be attributed both to a lack of target and to a lack of probe. Similarly, signal intensity is not a direct measure of the concentration of the target as it is equally affected by the concentration of the probe. The second disadvantage is that upon release, the organic fluorine moiety regains its very long T 1 . Such probes are thus plagued by the same sensitivity issue as the purely organic fluorinated probes (Yu et al., 2005(Yu et al., , 2013a. Their T 1 of 0.4-5 s are10-to 500-fold longer than their paramagnetic counterparts, which greatly limits the number of scans that can be acquired per amount of time. The low sensitivity of such probes practically restricts the markers that they could measure in vivo. In theory, both of these problems can be resolved with the use of a paramagnetic ion that has a more limited effect on T 2 and maintain as high a T 2 /T 1 ratio as possible. Fe II , Tm III , and Ho III are particularly well-suited for this approach (Srivastava et al., 2017b), but examples are not represented in the literature.

Applications of the McConnell-Robertson Theory to the Design of Responsive Fluorine Probes
One of the first applications of lanthanides in NMR spectroscopy was as induced shift reagents (Sanders et al., 1972). This application has surprisingly rarely been applied to 19 F NMR spectroscopy. Yet the same theory and equations developed for 1 H apply to 19 F and as such they can readily be exploited for the rational design of paramagnetic 19 F shift reagents. Lanthanide induced shift (LIS) is traditionally defined as the difference in chemical shift, δ, between a paramagnetic complex and its diamagnetic analog ( δ = δ paraδ dia ). In terms of responsive paramagnetic fluorine probes, the induced shift, 19 FLIS, is defined as the difference between the chemical shift of a 19 F nuclei in the presence and absence of the probe's analyte FIGURE 9 | Responsive fluorine probes which function by altering either (A) the oxidation state of a redox active metal (35, Tanaka et al., 2009;36, Kitamura et al., 2012;37, Xie et al., 2016;38, Xie et al., 2017;39, Basal et al., 2017;40, Yu et al., 2016) or (B) the spin state of Fe II (41-42, Thorarinsdottir et al., 2017).
This shift is the sum of the contributions from the contact shift, δ c , and the pseudocontact shift, δ pc (Peters et al., 1996;Allegrozzi et al., 2000;Harvey et al., 2012b). If the fluorine nuclei is kept 5 Å or more from the paramagnetic metal center, the contribution from the contact shift is negligible, and the observed 19 FLIS is primarily due to the pseudocontact shift. This pseudocontact shift, δ pc , is the result of the dipolar interaction between the 19 F nuclei and the unpaired electrons on the metal ion that experiences a Curie magnetization in the applied magnetic field. Thus, an anisotropic metal ion can amplify the chemical shift inequivalence between a fluorine nucleus in the presence and absence of the probe's analyte, resulting in greater resonance shift that are ultimately necessary for each nuclei to be imaged independently by MRI. Under the condition that the 19 F nuclei is at least 5 Å away from the metal ion, the pseudocontact shift is a function of the nature of the metal, its coordination environment, and the metal ion (Figure 10). This relationship is defined by the McConnell-Robertson equation (Equation 7) (Harvey et al., 2012b) 19 FLIS = δ pc = C j β 2 60(kT) 2 3 cos 2 θ − 1 Where d is the 19 F-metal distance, θ is the angle between the principal magnetic dipolar axis of the metal ion and 19 F nuclei, B 0 2 is the second order crystal field coefficient that is dependent on the coordination environment of the metal ion, and C j is the Bleaney coefficient for the specific metal. Both the direction and magnitude of the shift are dependent on the identity of the metal ion as denoted by its Bleaney coefficient (Table 1). One can thus rank metals by relative pseudocontact shift (PCS) strength, which in turn indicates their efficacy as 19 FLIS agents. Dy III and Tb III are undeniably excellent shift agents. However, given the necessity to maintain as high a T 2 /T 1 ratio as possible to maximize 19 F sensitivity (see above), Tm III and Ho III are the best choices in the design of 19 FLIS probes for MRI.
According to the McConnell-Robertson equation, the design of responsive fluorinated lanthanide MR probes can be based on three parameters: the distance separating the 19 F nuclei from the metal ion, d (Figure 5), the angle θ between the main dipolar magnetic axis of the metal and the metal-19 F vector (Figure 11A), and the second order crystal field coefficient, B 0 2 , which is a function of the direct coordination environment of the metal (Figures 11B,C).
The second order crystal field coefficient, B 0 2 , which is a function of the direct coordination environment of the lanthanide or transition metal, has been used in the design of responsive fluorine probes. Advantageously, this approach enables the use of ligands of similar chemical structure as those used with gadolinium-based responsive contrast agents. Swapping Gd III for Tm III , Ho III , or Dy III and adding a fluorinated moiety within 4-7 Å of the metal is often all that is necessary. For example, the Parker group developed citrate-responsive 19 F probes, which are essentially fluorinated versions of Ln-DO3A (43 and 44, Figure 12A) (Harvey et al., 2012a). Coordination of citrate to a Tm III complex results in the displacement of the two inner-sphere water molecules; the resulting change in B 0 2 causes a 19 FLIS of 4.7 ppm. Such 19 F probes are unfortunately marked with the same selectivity problem as the gadolinium responsive contrast agents that function by varying the number of inner-sphere water molecules (q-based responsive contrast agents) (Pierre et al., 2018). The selectivity of 43 and 44 for citrate over other hard anions that also have good affinity for the oxophilic lanthanides, such as bicarbonate, phosphate and lactate, is rather poor. The efficacy of the probe in blood and in cells is thus likely limited.
The same approach was used to design the Ca II responsive fluorine probes 45 and 46 ( Figure 12A). These probes are derivatives of a Gd III -based responsive contrast agent which displays a change in longitudinal proton relaxivity, r 1 , in the presence of calcium (Harvey et al., 2012a). For 45 and 46 to bind Ca II , one of the amide arms of the macrocycle must release the lanthanide. In doing so, it is replaced by a water molecule. The resulting change in B 0 2 causes a 19 FLIS of 3.0 or 3.9 ppm depending on the lanthanide ion (Dy III or Tm III , respectively) (Harvey et al., 2012a). Seemingly minor modifications on the structure of the probe can thus result in a substantial difference in its response.
The Parker group used a similar approach to develop four pH responsive probes. In 47 and 48 ( Figure 12B) (Senanayake et al., 2007;Kenwright et al., 2008), protonation of a sulfonamide group coordinating the lanthanide at pH <5 breaks the N-Ln bond, which opens up a coordination site for a water molecule. The resulting change in B 0 2 due to the differing coordination FIGURE 11 | Modulating the response of fluorinated paramagnetic probes by altering (A) the angle θ between the 19 F-M vector and the principle magnetic dipolar axis of the metal ion, (B) the lanthanide coordinating environment and thus the second order crystal field coefficient, B 0 2 through chelation of the analyte that partially decomplexes the metal or direct coordination of the analyte onto the lanthanide that displaces one or more water molecules, (C) the angle θ, B 0 2 , and the 19 F-M distance, d, through analyte induced changes in the coordination environment. environment of the lanthanide ion, and in the angle θ due to conformational change through rotation of the arm, cause a 19 FLIS of −6 and +2 ppm between pH 8.5 and 4.2 for the two inequivalent 19 F in the Eu III complex 47. The 19 F resonance of the related Ho probe, 48, shifts upfield by 40 ppm upon deprotonation (Chalmers et al., 2010). Note the greater 19 FLIS for Ho III , which has a Bleany's coefficient of greater magnitude, than for Eu III .
The other two pH probes, 49 and 50, also rely on protonation of a coordinating arm, but in these cases the aryl amide does not release the lanthanide at acidic pH ( Figure 12B) (Kenwright et al., 2008;Chalmers et al., 2010). Instead, deprotonation of the amide changes both B 0 2 and θ between the Ln-19 F vector and the principal magnetic dipolar axis of the Ln III ion. The latter is due to the differing conformation of the arm. The combination of these two effects result in a substantial 19 FLIS of 18 and 23 ppm for 49 and 50, respectively.
The chemical shift of fluorine nuclei can also be modulated by altering the spin state of the metal ion. A recent example exploits the temperature induced transition of Fe II from low spin (S = 0) to high spin (S = 2) in hexadentate triazacyclonone ligands with fluorinated 2-picolyl substituents (41 and 42, Figure 9B) to image temperature by 19 F MRI (Thorarinsdottir et al., 2017). In these probes, the 19 F are positioned at an optimal distance away from the Fe II center so as to maximize 19 F δ. Increasing the temperature from 4 to 60 • C, causes the 19 F resonances of 41 to shift downfield 28.3-24.6 ppm. The single resonance of 42 instead shifts 12 ppm upfield. On a per • C basis, 41 is therefore a more sensitive probe than 42. Importantly, the response of these two probes to temperature is nearly identical in water and fetal bovine serum (FBS), which bodes well for future in vivo applications.
The standard approaches that are used in the design of diamagnetic fluorine probes can also be applied to their paramagnetic analogs. An example is the α-chymotrypsin esterase probe 51 ( Figure 12C). Hydrolysis of the ester, followed by self-immolation of the linker, yields a carboxylated fluorine moiety whose 19 F nuclei signal is positioned 6.2 ppm away from the starting material (Harvey et al., 2012a). These probes function essentially like their purely organic analogs recently FIGURE 12 | Responsive 19 F-Ln probes that induce a chemical shift ( 19 F δ) by (A) modulating the coordination environment of the Ln III and hence its second order crystal field coefficient, B 0 2 , (43-44, Harvey et al., 2012a;45-46, Harvey et al., 2012a), (B) altering B 0 2 and the angle θ between the Ln III -19 F vector and the principle magnetic dipolar axis of the lanthanide upon changes in protonation (47, Senanayake et al., 2007;48-49, Kenwright et al., 2008;50, Chalmers et al., 2010), or (C) following a chemical reaction (51, Harvey et al., 2012a). reviewed by Mason (Yu et al., 2005). The advantage of the paramagnetic version resides in the sensitivity of the probe (see section Improving the Sensitivity of 19 F Probes). In this case, the lanthanide ion functions only to increase the sensitivity of the probe. Ho III shortens the T 1 and T 2 of the fluorine, thereby significantly increasing the number of scans that can be recorded in a given amount of time, and thus improving the SNR of the probe.
Although this review has focused on 19 F MR imaging, a significant advantage of 19 F probes is their ability to also function in other modalities. Fluorinated polyaminocarboxylatebased complexes, for instance, can also be effective chemical exchange saturation transfer (CEST) MR contrast agents. Such dual-modalities are particularly well-suited for the design of ratiometric agents. False negatives are more readily avoided if one of the two modalities is responsive to the targeted marker while the other one is not. This enables the distribution of the contrast agent to be mapped independently of that of the marker. Two examples of dual 19 F-CEST agents have been reported. A fluorinated Eu-DOTAm-Gly complex with two trans trifluoromethyl groups (2, Figure 1) generated sufficient 19 F and CEST contrast in vitro despite multiple isomers in solution (Cakic et al., 2016). Unfortunately, the contrast agent was not detected in ex vivo by 19 F MRI, possibly due to interactions with tissues that substantially reduced T 2. This first dual-modality 19 F contrast agent is not responsive.
Fe-DOTAm-F12 which was developed in our lab, has 12 equivalent fluorine nuclei and one isomer in solution (12, Figure 1). It functions both as a 19 F MR probe and a paraCEST contrast agent. Importantly, whereas the 19 F signal intensity is independent of pH, the CEST signal is modulated by pH. The % saturation transfer of the complexes increases 5-fold between pH 4 and 6.2. The complex accurately determines the pH independently of the concentration of the contrast agent between pH 6.9 and 7.4, a range that is relevant to cancer diagnosis. Advantageously, the similar sensitivity of the agent in both modalities facilitates ratiometric determination of pH.

OUTLOOK
The development of paramagnetic fluorine probes over the last decade mirrors, in many ways, that of paraCEST agents, the paramagnetic derivatives of CEST contrast agents. The introduction of paramagnetic metal ions in the design of fluorine probes, most notably lanthanides, iron, and cobalt, offer several advantages. Those include increased sensitivity of the fluorine probes due to decreased R 1 of the fluorine nuclei and increased chemical shift spectral window due to the paramagnetic induced shift.
Advantageously, both the effects on relaxation rates and chemical shift offer new approaches to the development of responsive fluorine probes that are not available with their diamagnetic counterparts, and these strategies lead to a significantly greater response. Indeed, paramagnetic fluorinated complexes can be readily designed such that the chemical shifts and/or the relaxation times T 1 and T 2 of the fluorine nuclei change substantially upon binding to or reacting with a desired analyte. This causes either the appearance, disappearance or notable chemical shift of the 19 F peaks. Moreover, the absence of background signal in 19 F MRI is an added advantage of this class of probes over the more common Gd-based and iron oxide nanoparticle-based contrast agents which have to contend with the signal of endogenous water. The recent work published on paramagnetic fluorine probes, backed by accurate theoretical models, enable scientists to design molecules with maximum sensitivity by optimizing the nature, specially the oxidation and spin state, of the paramagnetic ion and its distance from the fluorine nuclei all while maximizing the number of chemically equivalent 19 F nuclei. Those same parameters are used in the design and optimization of responsive probes. Notably, the large spectral windows of paramagnetic fluorine probes enable the design of ratiometric responsive probes which can independently report on both the distribution of a probe and that of its targeted analyte. Paramagnetic fluorine probes are also uniquely suited to multicolor, or multifrequency, imaging, which enables the tracking of different types of cells.
Paramagnetic fluorine probes have drawbacks too that should be kept in mind. The increase in sensitivity due to lower R 1 induced by the paramagnetic ion is minimal at high magnetic fields. These probes are better suited for use with scanners of low and medium magnetic field strengths, below 6 T. The structure and conformation of the probe in solution, parameters that can be more difficult to predict, have a significant impact on the properties of the probe. Complexes existing as a single isomer in solution with all fluorine nuclei chemically equivalent are more sensitive and easier to image, but many lanthanide complexes exist in solution as interconverting isomers. The potential toxicity of the complex should also be kept in mind, especially given the high concentrations of probes required for in vivo imaging. Although the toxicity and pharmacological properties of this new class of probes has not yet been evaluated, conclusions drawn from Gd-based contrast agents are likely to extend to paramagnetic fluorine probes. Kinetically labile lanthanide complexes, for instance, are expected to present higher toxicity. Nonetheless, we foresee that these first generation of paramagnetic fluorine probes will open avenues for many more applications for in vivo imaging. In particular, the ability of these probes to track different cells and biomarkers, and their response to different stimuli, render them particularly promising for molecular imaging.

AUTHOR CONTRIBUTIONS
VP, KP, and KS: searched and analyzed the literature; VP, KP, and KS: co-wrote the manuscript.