¹⁹F Spin-lattice Relaxation of Perfluoropolyethers: Dependence on Temperature and Magnetic Field Strength (7.0-14.1T)

Abstract

Fluorine (¹⁹F) MRI of perfluorocarbon labeled cells has become a powerful technique to track the migration and accumulation of cells in living organisms. It is common to label cells for ¹⁹F MRI with nanoemulsions of perfluoropolyethers that contain a large number of chemically equivalent fluorine atoms. Understanding the mechanisms of ¹⁹F nuclear relaxation, and in particular the spin-lattice relaxation of these molecules, is critical to improving experimental sensitivity. To date, the temperature and magnetic field strength dependence of spin-lattice relaxation rate constant (R₁) for perfluoropolyethers has not been described in detail. In this study, we evaluated R₁ of linear perfluoropolyether (PFPE) and cyclic perfluoro-15-crown-5 ether (PCE) at three magnetic field strengths (7.0, 9.4, and 14.1 T) and at temperatures ranging from 256-323K. Our results show that R₁ of perfluoropolyethers is dominated by dipole-dipole interactions and chemical shift anisotropy. R₁ increased with magnetic field strength for both PCE and PFPE. In the temperature range studied, PCE was in the fast motion regime (ωτ_c < 1) at all field strengths, but for PFPE, R₁ passed through a maximum, from which the rotational correlation time was estimated. The importance of these measurements for the rational design of new ¹⁹F MRI agents and methods is discussed.

1. Introduction

Cyclic perfluoro-15-crown-5 ether (PCE) and linear perfluoropolyether (PFPE) molecules with repeating -CF₂CF₂O- units are increasingly being used for cellular and molecular MRI [1-4]. The use of ¹⁹F MRI has the advantage that there is no background signal in tissue, thus the imaging probe has high specificity. Moreover, quantification of the number of targeted probe molecules is feasible in vivo [5-6] leading to new cell tracking methods, such as in vivo cytometry [6]. For cell labeling, these molecules are formulated as an oil-in-water emulsion to enable use in biological applications [7]. PCE has desirable properties for imaging because each molecule has 20 chemically equivalent fluorine atoms giving rise to a single resonance peak. With these molecules, on the order of 10¹² – 10¹³ fluorine atoms can be loaded into a cell of interest, providing a detection limit of order 10⁴ – 10⁵ labeled cells per voxel [8]. One advantage of ¹⁹F MRI cell tracking is that, with a known labeling efficiency, the cell number can be estimated from ¹⁹F spin-density weighted images [5], for which the acquisition time is limited by R₁. Interestingly, unlike ¹H MRI of tissue water [9], spin-lattice relaxation rate constant (R₁) of PCE increases with increasing magnetic field strength [10], thereby allowing accelerated data acquisition at higher field strengths. PFPE is essentially a linear version of the cyclic PCE, which has a significantly long R₁ compared with PCE, making it an attractive label for in vivo cell tracking by MRI where enhanced imaging speed and sensitivity is desirable.

Understanding the molecular mechanisms of spin-lattice-relaxation in these two closely related molecules could aid the development of novel agents that are optimized for ¹⁹F cellular MRI [7]. In this study, we measured the temperature dependence of ¹⁹F R₁ for the linear PFPE and cyclic PCE between 256 K to 323 K at three different magnetic field strengths: 7.0 T (282 MHz), 9.4 T (376 MHz), and 14.1 T (564 MHz). These measurements were used to provide insight into the mechanisms ¹⁹F nuclear spin-lattice relaxation in these molecules and to estimate the apparent rotational correlation times.

2. Experimental

Sample preparation

PCE and PFPE with 98% purity were obtained from Exfluor LP (Round Rock, TX) and used without further modification. The molecular weights of PCE and PFPE were 580 and 1000 Da, respectively. The viscosity of PCE was 4.8 Pa s and PFPE was 14.74 Pa s. 200 μl of neat PCE and PFPE oil were transferred to a 2.5 mm NMR tube and purged with 100% nitrogen for 15 minutes to remove oxygen. Tubes were sealed gas-tight with epoxy resin. PCE and PFPE emulsions were obtained from Celsense (Pittsburgh, PA) at a concentration of 120 mg/ml. Emulsion samples for NMR measurements were prepared in the same way as described above.

NMR measurements

¹⁹F NMR measurements were made at 282, 376, and 564 MHz at temperatures between 256 to 323K using three different Bruker Avance III NMR spectrometers (Bruker Biospin, Billerica, MA). A 5mm Bruker QNP probe was used at 282 MHz and a BBFO-Plus probe was used at 376 and 564 MHz. On both these probes the inner radio frequency coil was used for ¹⁹F observation. The probe temperature was calibrated using ethylene glycol by measuring the chemical shift difference between the OH and CH₂ resonance [11] before every measurement. The longitudinal relaxation time constant, T₁ (1/R₁) measurements were made using an inversion recovery sequence with phase cycling for a total of 8 averages per sample. A non-selective 90° pulse length of 15.5 μs was used and the recycle delay was 20s. 14 recovery points were used for each relaxation measurement. T₁ was determined with a two-parameter monoexponential fit using Topspin software (Bruker). The ¹⁹F COSY spectrum was measured using 2048 and 128 TD points in the direct and indirect dimensions respectively with a recycle delay of 4 s and 8 scans were average per TD point in the F1 dimension. The data were processed with SI of 2048 × 1024. Spectral width of 100 ppm was used for both inversion recovery and COSY experiments. Data analysis was performed using Origin software (Originlab, Northampton, MA). The R₁ versus temperature data for PFPE was fit to a third degree polynomial. To calculate the maximum point, the first derivative of the fit was solved for f′(T)=0.

3. Results

The structures of PCE and PFPE are shown in Figures 1A and 1C, respectively. PCE has 20 fluorine atoms with equivalent chemical shifts at −92.8 ppm (Figure 1B) (relative to CFCl₃ (trichloro-fluoro-methane) at 0.00 ppm). PFPE is provided as a mixture of polymers with 28-36 fluorine atoms per molecule and major resonance peaks between −90.7 and −90.9 ppm that arise from the perfluoropolyether chain and minor peaks at −58 and −93 ppm that arises from the terminal perfluorocarbon moieties (Figure 1D). Theoretically, the fluorine atoms of perfluoropolyether backbone should only exhibit a single resonance peak; however, the large size and conformation of the molecule within the local environment can give rise to different chemical shifts. The range of chemical shifts could also result from a difference in the polymer chain lengths present in PFPE. The separation between two major resonance peaks (90.7 and 90.9 ppm) increases linearly with magnetic field ranging from 14 Hz (0.49 ppm) at 282 MHz, 19 Hz (0.50 ppm) at 376 MHz and 29 Hz (0.51 ppm) at 564 MHz, consistent with chemical shift separation and not spin-spin coupling, as this would display field independence. ¹⁹F-COSY experiments further confirmed that there is no spin-spin coupling between these two major resonance peaks (Figure 1E). A broad-band COSY experiment showed that there is a weak correlation between the major peaks and minor peak supporting the assignment of the minor peak to the end groups (Figure 1F). T₁ was measured at three different magnetic field strengths (7.0, 9.4, and 14.1T) and at temperatures ranging from 256 K to 323 K. T₁ was estimated using a two-parameter monoexponential recovery curve (Figure 2A and C). For PCE, R₁ decreased with increasing temperature for this range for all magnetic field strengths (Figure 2B). For PFPE, R₁ was calculated using the area integrated over the two major resonance peaks. For all magnetic field strengths, R₁ increased with temperature from 256 K to reach a maximum before decreasing (Figure 2D). To estimate the maximum point, the data was fit to a third order polynomial, followed by solving f′(T) = 0. The maximum R1 was observed at 281.6 K for 14.1T, 270.6 K for 9.4T and 264 K at 7T. No maximum was observed for PCE at these temperatures and magnetic field strengths. The T₁ of PCE and PFPE was then measured at 14.1 T in aqueous nanoemulsions for the same temperature range. The temperature dependence of R₁ was similar to that found for the neat preparations. For PCE, the R₁ decreased with increasing temperatures (Figure 3A), and R1 values of the nanoemulsions and neat preparations were similar. For PFPE, R₁ increased from 256 K to reach a maximum at 279.4 K and then decreased (Figure 3B). This temperature at which f′(T) = 0 is in good agreement with the neat measurement; however, for PFPE, the R₁ values were reduced by about 20% in the nanoemulsion.

Figure 1.

Structure and ¹⁹F NMR spectra of PCE and PFPE. (A) Structure of PCE and (C) PFPE (R=CF₂CF₃ or CF₃). (B) PCE has 20 equivalent ¹⁹F atoms showing a single peak at −92.8 ppm. (D) PFPE has about 28-36 ¹⁹F atoms with two major chemical shifts at −90.7 and −90.9 ppm. The inset shows the magnified view of the major peaks. (E) ¹⁹F COSY shows that there is no spin-spin coupling between the peaks. (F) ¹⁹F COSY spectrum of PFPE at broad bandwidth shows a weak correlation between major and minor resonances supporting the assignment of minor peak to the endgroup of the molecule

Figure 2.

R₁ versus temperature at 7.0, 9.4, and 14.1T. (A) A representative mono-exponential R₁ inversion recovery curve of PCE and (C) PFPE. (B) R₁ decreased with temperature and increased with magnetic field strength for PCE. (D) For PFPE, R₁ increased from 256 K until a maximum and then decreased. The data were fit to a third degree polynomial, and the maximum point was determined by solving f′(T)=0. The R₁ maximum was observed at 281.63 K (14.1T), 270.61 K (9.4T), and 264 K (7.0T). The rotational correlation time for PFPE was estimated to be 1.77×10⁻⁹ s at 281.63 K, 2.66×10⁻⁹ s at 270.61 K, and 3.55×10⁻⁹ s at 264 K. At all temperatures and magnetic field strengths, PCE has a slower R₁ compared to PFPE. (▲) = 14.1 T, (●) = 9.4 T, and (■) = 7.0 T.

Figure 3.

R₁ versus temperature of PCE and PFPE emulsions at 14.1T. (A) R₁ decreased with temperature for PCE emulsions. B) For PFPE, R₁ increased from 268 K until a maximum and then reduced. The data were fit to a third degree polynomial, and the maximum point was determined by solving f′(T)=0. The R1 maximum was observed at 279. 4 K.

We calculated the rotational correlation time (τ_c) for PFPE directly from the apparent maximum of R₁ versus temperature (Figure 2D). Assuming ω² τ_c² =1 at the R₁ maximum, the calculated rotational correlation times for the neat PFPE were 1.77×10⁻⁹ s at 281.6 K, 2.66×10⁻⁹ s at 270.6 K, and 3.55×10⁻⁹ s at 264 K. For the PFPE emulsion, a rotational correlation time of 1.77×10⁻⁹ s was calculated at 279.4 K. As expected, an inverse linear relationship between rotational correlation time and temperature was observed. The rotational correlation time for PCE could not be calculated from the range of temperatures and magnetic field studied. Measurements at higher magnetic fields and/or lower temperatures would be needed to find the maximum for R₁.

4. Discussion and Conclusions

The temperature and field strength dependence of R₁ for perfluoropolyethers is consistent with contributions from dipole-dipole and CSA interactions [12-13].

$$R_1={R_1}^{dipole}+{R_1}^{CSA}$$

$${R_1}^{dipole}={R_1}^{rot}+{R_1}^{trans}$$

$${R_1}^{rot}=\frac{1}{5}I(I+1){\gamma }^4{\hslash }^2{r}^{-6}\left[J\right(\omega )+4J(2\omega \left)\right]$$ Eq: 105, pg. 300, ref. 13

$${R_1}^{trans}=\frac{6{\pi }^2}{5}{\gamma }^4{\hslash }^2\frac{N\eta }{kT}$$ Eq: 115, pg. 302, ref. 13

$${R_1}^{CSA}=\frac{6}{40}{\gamma }^2{B_0}^2{\delta }^2\left(1+\frac{{\eta }^2}{3}\right)\left[J\right(\omega \left)\right]$$ Eq: 141, pg. 316, ref.13

where J(ω) is the spectral density function given by

$$J\left(\omega \right)=\frac{2{\tau }_c}{1+\frac{{\omega }^2}{{{\tau }_c}^2}}$$ Eq: 91, pg.297, ref.13

τ_c is the rotational correlation time and R₁ is a maximum at τ_c=1/ω

Our measurements show that R₁ increases with increasing magnetic field strengths due to CSA. The contribution of CSA increases with increasing magnetic field with a dependence of B₀². For tissue water in the fast motion regime (ωτ_c < 1), dipole-dipole interactions dominate nuclear relaxation and R₁ decreases with increasing magnetic field strength. The observed trend of R₁ versus temperature for the perfluorocarbon molecules supports contributions from both dipole-dipole and CSA interactions. However, we did not attempt to quantify the relative contributions of these two relaxation mechanisms. We calculated the τ_c for PFPE using the assumption that ω² τ_c² =1 at R1 maximum. From the equation for R1^rot, it follows that at R1 maximum, 4 ω² τ_c²=1 can also be assumed. The range of temperatures did not allow us to separate the contributions ofJ(ω) or J(2ω), but exploring a larger temperature range may allow separation of the rotation (J(ω) + 4J(2ω)) from CSA contributions (J(ω)). The decrease in R₁ from 293 K to 323 K for PFPE and 256 K to 323 K for PCE suggest that, at these temperatures, the molecules experience fast to intermediate tumbling motion within the NMR time scale (ωτ_c < 1). R₁ versus temperature trends observed in neat liquids at 14.1T were similar to that of the respective emulsions. For PFPE, the temperature at which the R₁ maximum was observed in emulsion was in good agreement with the R₁ maximum observed in neat liquid. However, unlike PCE, the PFPE R₁ was found to be about 20% lower in the emulsion compared to the neat liquid. The presence of residual O₂ in the neat liquid could contribute to relaxation, although all the samples were prepared by bubbling N₂ thought the samples. One could speculate that translational diffusion could be limited in the emulsion and translational intermolecular dipolar relaxation could make a significant contribution in the neat liquid.

In addition to temperature and magnetic field strengths, the spin-lattice relaxation of perfluorocarbons including perfluoropolyethers are influenced by the oxygen content. The paramagnetic properties of molecular oxygen increase the R₁ which has been used to measure tissue oxygenation in vivo [14, 15]. In vitro calibration studies at different magnetic field strengths have shown that R₁ exhibits a linear increase with pO₂ [10, 14, 15].

CSA is a predominant mechanism for NMR relaxation in many solids, however, in liquids, CSA components average out due to rapid tumbling motion. The motions that produce this average value can cause fluctuations in the local magnetic field, and these time-varying fields lead to relaxation [16]. Although PCE and PFPE are liquids in the temperature range studied, our data show that CSA makes a significant contribution to R₁. Perfluorocarbons are particularly interesting because of their low intermolecular dipole-dipole interactions and high vapor pressures compared to corresponding hydrocarbons of equal chain length. Low inter-molecular interactions are due to the large electronegativity of the F in C-F bonds, which effectively repel any other similar molecules in their vicinity [17].

Understanding the molecular dynamics underlying NMR relaxation, such as rotational correlation times can aid in the development of optimized perfluoropolyethers for ¹⁹F MRI. The rotational correlation time for PFPE was calculated from the maximum R₁ versus temperature, but the rotational correlation time of PCE could not be determined since the molecule remained in the fast motion regime over the temperature and field strength used in our study. However, our relaxation data support a shorter effective rotational correlation time for PCE than PFPE at a given temperature, likely a result of the lower molecular weight and viscosity [18]. In addition, the shape of the molecules may also influence the rotational tumbling motion [19]. PFPE has a long chain, and the strong electronegativity of C-F bonds tends to align the chains in a rigid linear structure compared to PCE, where the crown-ether structure gives rise to a compact alignment.

The increase in R₁ with increasing magnetic field strength observed in perfluoropolyethers is desirable for imaging at high magnetic field strengths because signal-to-noise ratio per unit time can be increased with an optimized T1-weighted sequence. However, at high field strengths, increased CSA and magnetic field inhomogenieties can lead to undesirable line-broadening. For cell tracking, however, ¹⁹F MRI is typically acquired at 2-4 times lower resolution than ¹H MRI, therefore, the effect of line broadening on signal localization can be minimal. PFPE has a long spin-spin relaxation time constant (T₂), which is also attractive for imaging applications. There are other perfluorocarbon molecules used for cellular imaging such as perfluorooctyl bromide [1, 2]; however, these molecules have multiple major resonance peaks over a broad chemical shift range resulting in a reduction in the sensitivity and confounding MRI results. Therefore, these molecules were not included in the study.

An ideal ¹⁹F contrast agent for molecular MRI should have long R₁ and short R₂. Based on our measurements, for PFPE and PCE, R₁ can be increased by increasing magnetic field strengths. For PFPE, R₁ maximum was observed in the R1 versus temperature plots, from which we estimated the rotational correlation times. For in vivo imaging, it is desirable to have a R₁ maximum at about 310 K (37°C). From our data, a right shift in R₁ versus temperature plots could achieve it. A right shift in R₁ maximum towards 310 K was observed with increasing magnetic field strengths suggesting that PFPE is an optimized agent for high field MRI. For imaging at clinical field strengths of 3T and below, PFPE can be optimized by increasing the chain length. For PCE, enlarging the crown structure could result in more signals per molecule and more desirable R₁ characteristics. The emulsion formulation can be optimized by increasing the size of the emulsion droplets and viscosity of the emulsions into an acceptable range without affecting the stability of the emulsion. For ex vivo imaging of tissues, the sensitivity can be increased by reducing the temperature of the samples. Understanding the fundamental principles of ¹⁹F NMR relaxation of these molecules will aid in the rational design of ¹⁹F contrast agents.

Highlights.

1. T1 of perfluoropolyethers can be explained by dipole-dipole interactions and CSA

2. Molecular motion determines the differences in R₁ between PCE and PFPE

3. The rotational correlation time of PFPE was estimated from R₁ vs. temp plots