Molecular Mechanism of Transverse Relaxation in Whole Blood with Plasma Contrast Reagent: Simulations of Bulk Magnetic Susceptibility and Water Exchange
Gregory J Wilson1, Charles S Springer2, Sarah Bastawrous1,3, and Jeffrey H Maki1

1University of Washington, Seattle, WA, United States, 2Oregon Health and Science University, Portland, OR, United States, 3Puget Sound VA HCS, Seattle, WA, United States

Synopsis

Previously reported T2* values in oxygenated whole blood with gadolinium based contrast reagents are very small. This has important implications for optimization of contrast-enhanced MR angiography and quantification of arterial input functions. To investigate the molecular mechanism of these short T2* values, we have performed Monte Carlo simulations of signal dephasing that predict the reported values remarkably well. Intracellular water signal experiences a frequency shift that is dependent on the orientation of the RBC in the magnetic field. The resulting frequency distribution in combination with trans-membrane water exchange results in rapid dephasing of water signal.

Introduction

Small 1H2O T2* (≡ 1/R2*) values in whole blood containing plasma gadolinium based contrast reagents (GBCRs) are widely reported. Gadoteridol (PH) relaxivities (r2* ≡ (R2* - R20*)/[CR]: [CR] is the whole blood GBCR concentration, and R20* is R2* in the absence of GBCR) are reported from 15.07 (± 1.93) to 23.6 (± 1.8) s-1/mM at 1.5T, and 38.64 (± 3.80) to 50.3 (± 5.4) s-1/mM at 3.0T.1,2 Whole blood r2*s are much larger than plasma relaxivities and exhibit almost no r2* variation between different GBCR chelates. In addition, the vast majority of signal dephasing is reversible by spin echo (SE; i.e., R2 << R2′ [≡ R2* - R2]). The large r2* is likely due to GBCR exclusion from the intracellular red blood cell (RBC) space, creating a bulk magnetic susceptibility (BMS) difference between the intra- and extracellular (plasma) spaces. This produces magnetic field gradients and intracellular frequency shifts that cause signal dephasing. To better understand the molecular mechanism, we performed Monte Carlo simulations of the signal dephasing and found remarkable agreement with experimental data with no adjustable parameters.

Theory

In SI units, the extracellular space magnetic susceptibility increases linearly with [CRe] according to: $$\chi_{e}=0.31\left[CR_{e}\right]-9.1$$ while the intracellular susceptibility is constant ($$$\chi_i = - 9.19$$$, for oxygenated RBCs). If the RBC’s are approximated as ellipsoids in a uniform external magnetic field B0, the extracellular field is inhomogeneous, but the intracellular magnetic field is uniform.3 In a general compartment c, Bc = {1 + Dc}B0 + Ic, where Dc is the homogeneous and Ic the inhomogeneous contribution. The extracellular inhomogeneous field (Ie) can be approximated as the field surrounding a sphere of radius R: $$I_{e}=\frac{\chi_{i}-\chi_{e}}{3}\left(3\cos^{2}\alpha-1\right)\frac{R^{3}}{r^{3}}$$ where r is the positional vector from the center of the sphere, and α is the angle r makes with B0. The extracellular homogeneous term (De) is equal to $$$\chi_e/3$$$. The Di value inside an ellipsoid varies with the latter’s orientation in B0, and is approximated as the case inside an infinite disk: $$D_{i}=\frac{\chi_e-\chi_i}{3}\left(3\cos^2\phi-1\right)+\frac{\chi_e}{3}$$ where $$$\phi$$$ is the angle the ellipsoid normal makes with B0.

Methods

Monte Carlo simulations of water molecule random walks were performed for 13,000 molecules through an ensemble of 2744 cells (spherical, R = 3.2 mm). The cell membrane water permeability coefficient (PW) was adjusted such that the mean intracellular residence time was 10 ms (a well established value for the RBC).4 The diffusion coefficient was set to 1.5 μm2/ms with step duration 1 μs, thus the rms step length was 0.09 μm (Figure 1). For each step, the local Larmor frequency was calculated using either Ie or Di, phase accumulated accordingly, and net signal calculated as the vector sum of all 13,000 spins. For spin echo simulation, the accumulated phase was reversed at intervals corresponding to the echo spacing (TE) in the previously reported in vitro experiments.2 Signal data was sampled at time points corresponding to the in vitro sampling, and fitted to mono-exponential decays using non-linear least squares, yielding relaxation time constants Sim R2* and Sim R2. Similarly, Sim R2e* and Sim R2e relaxation rate constants were predicted for the extracellular inhomogeneity contribution only (i.e., the intracellular dephasing was turned off for the entirety of the walk).

Results

Figures 2-4 show the results of the full simulations (filled circles) and the extracellular contribution only (filled diamonds). The full simulation R2ʹ agrees remarkably well with the in vitro experimental R2ʹ (Fig. 4, open circles) for gadoteridol (PH). The full simulation accurately predicts the large, reversible dephasing. The results obtained from the extracellular dephasing predict much smaller R2* that is mainly irreversible (i.e., the reversible component Sim R2eʹ is near zero). Hence, intracellular dephasing due to the RBC orientation-dependent frequency differences accounts for the majority of in vitro dephasing, and is mainly reversible.

Discussion

With Monte Carlo simulations of signal dephasing due to intracellular frequency differences Di and extracellular field inhomogeneities Ie, we accurately predicted transverse relaxation in oxygenated whole blood and the [CR]-dependence. Additional simulations (not shown) of the no-exchange-limit (setting PW = 0; i.e., no trans-membrane exchange) showed that water exchange is crucial to accurately predict SE behavior. Without exchange, intracellular spins dephase only via the relatively small R20 (R2 in the absence of GBCR) in SE experiments. Thus intracellular BMS frequency differences and water exchange are essential to the GBCR-induced rapid transverse relaxation in whole blood.

Acknowledgements

Research grant from Bracco Diagnostics, and NIH UO1 CA154602 and R44 CA180425.

References

1. Blockley NP, Jiang L, Gardener AG, Ludman CN, Francis ST, Gowland PA. Magn Reson Med 60:1313-1320 (2008).

2. Wilson GJ, Springer CS Jr., Woods M, Bastawrous S, Bhargava P, Maki JH. PISMRM 22:3862 (2014).

3. Springer CS. Physicochemical principles influencing magnetopharmaceuticals. Chapt. 5 in NMR in Physiology and Biomedicine, Ed. by Gilles RJ, Academic Press, San Diego, pp 75-99 (1994).

4. Wilson GJ, Woods M, Springer CS Jr., Bastawrous S, Bhargava P, Maki JH. Magn Reson Med 72:1746-54 (2014).

Figures

Figure 1. Example water molecule random walk through randomly oriented RBC ensemble. In this example, the RBCs are oblate ellipsoids. This is a 2D projection of semitransparent RBCs so the random path can be visualized. The cell membrane water permeability is prescribed in the simulation. Details in text.

Figure 2. Simulated [CR]-dependences of R2* from the full simulation (Sim R2*; filled circles) and the extracellular dephasing simulation (Sim R2e*; filled diamonds). The full simulation includes signal dephasing from intracellular frequency differences in addition to the extracellular dephasing, and shows the majority of signal dephasing results from intracellular frequency differences.

Figure 3. Simulated [CR]-dependences of R2 from the full simulation (Sim R2; filled circles) and the extracellular dephasing simulation (Sim R2e; filled diamonds). The majority of irreversible dephasing results from extracellular signal dephasing.

Figure 4. Simulated [CR]-dependences of R2′ from full (Sim R2′; filled circles) and extracellular dephasing simulations (Sim R2e′; filled diamonds). Sim R2′ matches the in vitro experimental data (open circles) remarkably well. Extracellular dephasing is not reversible (i.e., Sim R2e′ is near zero), so R2′ results mainly from the intracellular frequency differences.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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