Hyperpolarized Nuclei for NMR Imaging and Spectroscopy - Lunds ...

calculating the field strength at which RS = β RC,
where β is an arbitrary
constant:
18
B
1
= κ
( VS
β) γ
0, trans
23
[22]
with a proportionality constant κ = 1.8·10 5 m 2 s –1 and V S given in m 3 . The
value of κ is based on σ = 5, µ = 1, ρ C = 1.678·10 –8 Ω m, † and a typical tis-
sue resistivity of ρ = 2 Ω m. ‡ From Table 2, it follows that the SNR of hy-
3 4
perpolarized substances will increase proportionally to B0 until the sample
noise regime is reached, and thereafter remain constant. This has important
implications for low-field imaging of polarized gases and liquids, which will
be discussed in the next section.
When RS >10 RC,
i.e., by setting β = 10 in Eq. [22], the noise contribution
from the coil will be negligible as compared with the sample noise.
Table 3 lists corresponding values of B0,trans for spheres with 40-, 20-, and 7cm
diameters, i.e., “body,” “head,” and “rat” dimensions, giving an estimate
how far the field strength may be reduced before the SNR of hyperpolarized
imaging agents begin to drop.
Table 3. Lower B 0 field limit for the regime where the SNR is independent of the
field strength. The calculations are valid for a solenoidal RF coil with length
and diameter equal to the sample diameter (∅).
Nucleus B 0,trans for a sphere
with 40-cm ∅ (mT)
B 0,trans for a sphere
with 20-cm ∅ (mT)
3 He 40 160 1000
13 C 120 480 4000
129 Xe 110 440 3600
B 0,trans for a sphere
with 7-cm ∅ (mT)
Hyperpolarized imaging can thus be performed at very low fields (mT
range) without loss of SNR. To date, several research groups have demonstrated
hyperpolarized gas imaging at field strengths between 2 mT and
† Resistivity of copper at 20°C (CRC Handbook of Chemistry and Physics, 83 ed. CRC Press,
Boca Raton, 2002).
‡ Many human tissues have a resistivity of ∼2-4 Ω m, e.g., muscle 1.71 Ω m, lung 1.57 Ω m;
however, fat has a value of 38.5 Ω m (Faes et al. 1999).