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
1H
2O T
2* (≡ 1/R
2*)
values in whole blood containing plasma gadolinium based contrast reagents
(GBCRs) are widely reported. Gadoteridol (PH) relaxivities (r
2* ≡ (R
2*
- R
20*)/[CR]: [CR] is the whole blood GBCR concentration, and R
20*
is R
2* 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 r
2*s
are much larger than plasma relaxivities and exhibit almost no r
2*
variation between different GBCR chelates. In addition, the vast majority of signal
dephasing is reversible by spin echo (SE;
i.e.,
R
2 << R
2′ [≡ R
2* - R
2]).
The large r
2* 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 [CR
e]
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 + D
c}
B0 +
Ic,
where D
c 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 (D
e) is equal to $$$\chi_e/3$$$. The D
i
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 (P
W) 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 μm
2/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 D
i,
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 R
2* and Sim R
2. Similarly, Sim R
2e* and Sim R
2e
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 R
2ʹ agrees remarkably well with the
in vitro experimental R
2ʹ (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 R
2* that is mainly irreversible (
i.e., the reversible component Sim R
2eʹ
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 D
i 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 P
W = 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 R
20 (R
2 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
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