VII. Further Considerations
Hyperpolarization experiments are fundamentally different from those done with equilibrium polarization. In the case of ordinary polarization, multiple experiments can be conducted in order to gain further pieces of information about an experiment. In the case of hyperpolarization, once the polarization is lost it cannot be regained simply by waiting long enough. New methods are needed to utilize the available signal to the greatest advantage and extract information from the system as quickly as possible (40,41). Refocused INEPT sequences offer one route to the extraction of greater information.
Although the well known Zeeman polarization is generally the spin order of choice in an NMR experiment, other spin order types have been utilized. New experiments are currently being developed that utilize singlet spin order in varied ways so there is interest in being able to produce this spin order in many types of spin systems. Application of the spin order transfer algorithms described in the reverse sense would allow generation of singlet spin order when starting from Zeeman order.
magnitude of the gyromagnetic ratio. The other comes from the Faraday law which states that the voltage signal is proportional to the rate of change of the magnetic field so the higher precession of the larger gyromagnetic ratio gives a larger signal. For 13C, the sensitivity gain is approximately 16 and for 15N, the gain is approximately 100.
In MRI, the spatial resolution is proportional to the value of γ . This resolution is dependent upon the changes in frequency across a sample when a gradient is applied.
In any application, the size of the gradient is limited by the physical limitations of the system. In the medical applications typical to MRI use, the gradient magnitude and rate of change are limited by safety considerations.
The protons added initially by molecular addition in order to reach a high polarization on the heteronucleus are ripe for use by INEPT (19). Refocusing is desirable to bring the antiphase peaks into phase for maximum effect in the MRI environment where field homogeneity within biological tissue is difficult to achieve. Ideally, INEPT performed by transferring polarization from a single nucleus to a single nucleus will perfectly transfer the polarization. The efficiency when performed from one heteronucleus to multiple equivalent nuclei of another isotope is readily calculated (49), and with optimization can lead to a similar overall gain.
Since the protons added in heteronuclear PASADENA are inequivalent and couple together, the problem is more complicated than has been treated analytically. In general these two effects will lessen the utility of the technique, but it will still demonstrate advantage over heteronuclear detection in most cases. Since every
molecule is unique, mapping the expected result with different wait times is helpful as a guide to determine the appropriate wait times. For example, succinate in basic conditions (pH 13.3= ) with the coupling constants J12 =6.68 Hz, Hz, and Hz (36) would be expected to have average enhancement on the protons shown in Fig.
1S 6.32
J = −
2S 4.13 J =
51 as a percentage of the starting polarization on the 13C heteronucleus.
In this example, an advantageous initial wait (transfer time) would be about 60 ms and the second wait (refocusing time) would be about 70 ms to give an average polarization on the protons of about 25%. This is roughly half what is expected in the ideal case of equivalent protons reducing the sensitivity advantage of detecting on protons instead of carbon from 16 to 8, still an appreciable advantage. Experimentally, such a method has been shown to increase the overall sensitivity by 6.5 (48).
−20
−20
−20
−10 −10
−10
−10
−10
−10
−10
−10
−10
0 0 0 0 0
0 0
0 0
0 0
0 0
0
0
0
0000
0
0
0 10
10
10 10
10 10
10 20
20
first wait (ms)
second wait (ms)
0 20 40 60 80 100 120 140 160 180 200
0 20 40 60 80 100 120 140 160 180 200
Figure 51. Expected average polarization on the two protons of succinate from molecular addition of hydrogen to a deuterated precursor in base as a percentage of the starting polarization on the heteronucleus for guiding the choice of timing constants in a refocused INEPT experiment. Major contours are spaced every 10% and minor contours are spaced every 2%. This is an ideal calculation that
assumes the 4S I Iz 1z 2z order has relaxed to Zeeman polarization.
In cases where the chemical shift of the protons is sufficient, selective pulses can be used to restrict the transferred Zeeman spin order to one of the protons when the
molecule has been transferred to a high field for the experiment. This cannot be done for succinate, where the chemical shift difference is slight and only due to a secondary isotope effect from the single carbon label, but is useful for a number of demonstrated and proposed molecules. For TFPP, which has been demonstrated with an unselective refocused INEPT sequence (48), any of the three distinct protonated sites to which polarization transfer was observed could be chosen for selective transfer, since they are all separated by over 1 PPM. For choline labeled with 15N, which is also an attractive molecule for biological applications, nonselective refocused INEPT has been demonstrated with molecules hyperpolarized by DNP (77) and it is reasonable to expect that any of the protons that couple with the 15N could also be selectively polarized.
Selective polarization transfer has been demonstrated to the nine equivalent methyl protons by incorporating a single selective π pulse within the refocused INEPT sequence (49).