New insights into rotating frame relaxation at high field

Abstract

Measurements of spin-lock relaxation rates in the rotating frame (R1ρ ) at high magnetic fields afford the ability to probe not only relatively slow molecular motions, but also other dynamic processes, such as chemical exchange and diffusion. In particular, measurements of the variation (or dispersion) of R1ρ with locking field allow the derivation of quantitative parameters that describe these processes. Measurements in deuterated solutions demonstrate the manner and degree to which exchange dominates relaxation at high fields (4.7 T, 7 T) in simple solutions, whereas temperature and pH are shown to be very influential factors affecting the rates of proton exchange. Simulations and experiments show that multiple exchanging pools of protons in realistic tissues can be assumed to behave independently of each other. R1ρ measurements can be combined to derive an exchange rate contrast (ERC) that produces images whose intensities emphasize protons with specific exchange rates rather than chemical shifts. In addition, water diffusion in the presence of intrinsic susceptibility gradients may produce significant effects on R1ρ dispersions at high fields. The exchange and diffusion effects act independently of each other, as confirmed by simulation and experimentally in studies of red blood cells at different levels of oxygenation. Collectively, R1ρ measurements provide an ability to quantify exchange processes, to provide images that depict protons with specific exchange rates and to describe the microstructure of tissues containing magnetic inhomogeneities. As such, they complement traditional T1 or T2 measurements and provide additional insights from measurements of R1ρ at a single locking field. Copyright © 2016 John Wiley & Sons, Ltd.

Keywords: T1ρ; T1ρ dispersion; chemical exchange; diffusion; spin-locking; susceptibility.

Figure 1.

Schematic diagram of the chemical exchange of labile hydrogen nuclei between water and hydroxyls on a single glucose molecule. Water is represented as pool a and glucose as pool b, and so the corresponding exchange rate from water to glucose is k_ab and from glucose to water is k_ba.

Figure 2.

An example of four nuclei exhibiting random Brownian motion through local magnetic field gradients manifested from the presence of spherical perturbers of susceptibility χ in an external magnetic field. This illustrates the local field shifts experienced by a diffusing nucleus through the superposition of dipole fields.

Figure 3.

(a) The application of an on-resonance B₁ pulse tips the magnetization into the transverse plane. (b) The B₁ spin-lock pulse, together with the field offset ΔΩ, comprises the effective field B_eff, about which the magnetization precesses for the duration of the locking time.

Figure 4.

R_1ρ dispersions of 200 mm glucose solutions (pH 7.4) in phosphate-buffered saline (PBS) with the specified concentration of D₂O are shown at 4.7 T in (a) and at 7 T in (b). The R₁ values of each concentration in (c) decrease at both 4.7 and 7 T.

Figure 5.

The low locking field limit of R_1ρ versus the percentage of protons is plotted and fitted to a linear model. The increased slope at 7 T indicates how the chemical exchange effect becomes more prominent, whereas the decreased y-intercept value at 7 T reveals the decreased dipolar contribution to relaxation.

Figure 6.

(a) R_1ρ dispersions of 200 mm glucose (pH 7) at 7 T for various temperatures. (b) The estimated exchange rate, calculated from the parameters used in the dispersion fits, plotted versus temperature. (c) R_1ρ dispersions of 200 mm glucose (T = 19 °C) at 7 T for various pH values. (d) The estimated exchange rates plotted versus pH.

Figure 7.

(a) R_1ρ dispersions of 200 mm glucose (T = 19 °C) at 7 T over a more relevant range of pH values shows a more exponential trend in the estimated exchange rates shown in (b).

Figure 8.

(a) R_1ρ dispersions simulated using three pools with 1% pool fractions of the exchanging pools, ΔΩ_b = 0.75 ppm, ΔΩ_c = 0.5 ppm, k_ba = 1 kHz and k_ca = 3 kHz. The red and blue curves are single dispersions (one exchange pool), the yellow curve is the addition of the two single dispersions and the black curve is the simulated double dispersion (two exchange pools). (b) The effect of exchange between minor pools on the double dispersion. (c) Similar simulations with pool c exchanging much faster at 30 kHz. (d) The corresponding simulations with the addition of minor exchange.

Figure 9.

(a) Experimentally measured R_1ρ dispersions at 7 T for creatine, glucose and a mixture. The single dispersions were fitted to the Chopra model in Equation ((3)), whereas the double dispersions were fitted to the double Chopra model in Equation ((4)). (b) The full blue lines indicate the individual dispersions estimated from the fitting of the black double dispersion curve, whereas the broken lines are the experimental single dispersions. The estimated curves cannot be accurately estimated when the exchange rates are too close. (c) R_1ρ dispersions at 7 T for creatine, uracil and a mixture. (d) The estimated single dispersions are much more accurate when the exchange rates are very different. PBS, phosphate-buffered saline.

Figure 10.

(a) Simulated R_1ρ dispersions with three pools using various volume fractions of the slowly exchanging pool. (b) Exchange rate contrast (ERC) analysis of the previous double dispersions for various pool fractions with the full black line indicating the location of the peak in the case of no fast exchanging pool, which is the upper limit of the ERC shift. (c) The ERC values of each curve that intersect with the full back line in (b).

Figure 11.

(a) R_1ρ map at 545 Hz for glucose and uracil samples of specified concentrations. (b) The entire R_1ρ dispersion of each sample shown on the R_1ρ map. (c) Exchange rate contrast (ERC) map at 545 Hz of the same samples; note the increased intensity of the 200 mm glucose sample as a result of the dependence on exchange rates, not relaxation rates. (d) Mean ERC values of each sample calculated by region of interest (ROI) analysis over each specific sample. PBS, phosphate-buffered saline.

Figure 12.

(a) Simulated R_1ρ dispersions for an array of packed spheres for various radii. (b) The correlation time, calculated from the parameters of the fitted dispersion curves, increases with radius as there is more space between spheres. (c) Simulated correlation times are plotted together with the experimental correlation times estimated from the dispersions of polystyrene microspheres in pure water. The curves overlap well for small radii.

Figure 13.

(a) R_1ρ double dispersions measured in whole bovine blood at 7 T for various oxygen saturation levels to vary the amount of deoxyhemoglobin present. (b) The individual dispersion components are plotted from the double dispersion fits in (a). Note how the exchange component stays relatively constant, whereas the low-frequency dispersion diminishes with higher oxygen saturation. (c) The gradient parameter, estimated from the dispersion fits, decreases with oxygen saturation.

Figure 14.

Inflection points of R_1ρ dispersions are plotted against the exchange rate for various B₀ field strengths with a chemical shift of ΔΩ_b = 1 ppm in (a) and ΔΩ_b = 3.5 ppm in (b).

Figure 15.

The ratio of [R_1ρ(0) – R_1ρ(∞)]/[R_1ρ(Ω₁) – R_1ρ(∞)] versus the exchange rate at three static field strengths. The maximum value of the ratio decreases at higher fields because of the dominance of the increase in chemical shift frequency offset.

Figure 16.

(a) R_1ρ dispersions of 200 mm glucose at 4.7 T over the pH range 6–7.4. Note that the magnitude of the pH 7.4 dispersion does not continue to increase relative to the pH 7.02 dispersion. (b) The dispersion magnitudes plotted against exchange rate at various B₀ fields; note that the peak shifts to higher frequencies at higher fields.