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Quantification in Hyperpolarized NMR Arnab Dey, and Narayanan Chandrakumar J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b00142 • Publication Date (Web): 12 Feb 2016 Downloaded from http://pubs.acs.org on February 13, 2016

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The Journal of Physical Chemistry Letters

Quantification in Hyperpolarized NMR Arnab Dey and Narayanan Chandrakumar* MRI-MRS Centre, Department of Chemistry, Indian Institute of Technology-Madras Chennai-600036, Tamil Nadu, India AUTHOR INFORMATION Corresponding Author *

To whom correspondence should be addressed. Address: MRI-MRS Centre, Department of

Chemistry, Indian Institute of Technology-Madras, Chennai-600036, Tamil Nadu, India. Fax: (+) 91-2257-4202, E-mail: [email protected]; [email protected]

1 ACS Paragon Plus Environment


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ABSTRACT

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Quantitative aspects of hyperpolarized NMR are analyzed in the present work

and it is shown theoretically and experimentally that measured ‘apparent’ signal enhancements could deviate significantly from real enhancements of polarization. Expressions are given as a function of spin count to deduce real enhancements from measured ‘apparent’ enhancements, and vice versa. While the findings are of particular relevance to high field work employing highQ probes, and to analytical applications of hyperpolarized NMR whose objective is the measurement of spin count, our experiments demonstrate their significance even for low and moderate field work with probes of moderate Q-factor.

TOC GRAPHICS


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Hyperpolarized NMR is currently witnessing vigorous research activity and renewed popularity, as it seeks to address the Achilles heel of NMR, viz., poor sensitivity, without seriously compromising its core strength, viz., high resolution. This opens up a number of chemical applications. Perhaps the earliest polarization enhancement technique in NMR was Dynamic Nuclear Polarization (DNP)1-3 otherwise known as the Overhauser Effect (OE, or ODNP), and related techniques in the solid state, including the Solid Effect (SE).4 It was subsequently shown that hyperpolarization could be achieved by suitable techniques that harness the high spin order in parahydrogen, yielding parahydrogen induced polarization (PHIP).5-10 More recently, PHIP has received a significant boost by the avoidance of a chemical reaction across a multiple bond as originally required, relying instead on a catalyst to bind both parahydrogen and the ‘substrate’ species of interest, accomplishing polarization transfer by spin exchange, and NMR signal enhancement in the bulk phase by subsequent chemical exchange; this technique is termed Signal Amplification By Reversible Exchange (SABRE).11-13 While signal enhancement was often the prime motivation in early ODNP studies (which were performed in continuous wave (cw) NMR mode), quantitative measurements for elucidation of the mechanism of the Overhauser effect resulted in the recognition that continuous wave ODNP studies reveal a peculiar effect which results in the deviation of the measured (or ‘apparent’) enhancement from its real value.14-16 In this report, we argue that this effect could play a vital role in the time domain measurements typical of modern hyperpolarized NMR as well, including ODNP, as well as SABRE / PHIP. We give a quantitative relation between the apparent and real enhancement factors, which would aid quantitative analysis based on hyperpolarized NMR spectra. We also demonstrate this effect experimentally in pulsed mode at a moderately low NMR frequency.



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The basic phenomenon that gives rise to ‘false’ enhancements may be termed the Qenhancement effect.14-16 It is to be noted especially that this is a fundamental effect that is unrelated to questions of sample transfer, arising as it does from the fact that the probe circuit quality factor Q changes with the sample polarization. In simple terms, the NMR probe which houses the sample under investigation has a quality factor Q that is governed by the coil inductance L0 and effective serial resistance R0. Near the resonance condition, this is changed substantially by the NMR characteristics of the sample, viz., the radiofrequency susceptibility χ of the spin ensemble, and leads to measurable – even strong – effects under conditions of high spin polarization, especially for high-Q probes and high frequency measurements. The effect may be modeled in a straightforward manner, the NMR coil impedance Z being given in SI units by:

1

Z  i0L0[1(0 )]  R0  i0L0[1( '(0 ) i "(0 ))]  R0

Here i is the unit imaginary, is the filling factor, and  is the angular frequency at which resonance occurs (ie, Hz). The contribution of the real part of the spin susceptibility ′ being zero on resonance, we find for the coil impedance on resonance:

Z i0L0 0L0"(0) R0

 2

For the quality factor of the NMR probe, we thus find that it changes from Q = L0/R0 far off resonance to Q′ = L0/[L0+R0] on resonance. We may write the measured signal S in terms of the transverse nuclear spin magnetization M, quality factor Q′ and proportionality constant a as:

S  aQ ' M ~ aQ '  "(0 )

 3


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Given a ‘real’ signal enhancement factor Ar, which is proportional to the polarization enhancement P = ()/, and invoking the well-known relation between the rf susceptibility and the d.c. or Curie susceptibility,17 we find the relation between the real enhancement Ar and the measured apparent enhancement Aa:

[1  Q   B ( A r  1 ) ] 1  Aa Ar



4 

1 1 (1  A a Q   B )  Ar A a (1  Q   B )



5 



6 

N  2  B  4kT

2



0



1 2

In Eq. (6), which is valid for a spin-1/2 ensemble, the symbols have their usual significance; in particular,

B represents the imaginary part of the rf susceptibility under Boltzmann conditions,

represents the linewidth in Hz and N, the spin count in the sample. The expression for the apparent enhancement Aa (Eq. (4)) in particular clearly demonstrates that in general it deviates more strongly from the real enhancement Ar for larger values of the basic NMR coil Q-factor, larger filling factors, larger rf susceptibility (arising for example from higher spin count, higher spectrometer frequency or smaller linewidth), and finally, for larger magnitude of the real enhancement. It may be noted that the high temperature approximation implicit in the above expression for the rf susceptibility is well and truly valid for room temperature measurements at 600 MHz, even with an enhancement factor of magnitude 1000.



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In order to experimentally demonstrate the significance of Q-enhancement effects on hyperpolarized NMR we have performed 1H-ODNP experiments on benzene at a 1H NMR frequency of 14.6 MHz with different polarizing radicals, the microwave ESR irradiation being at X-band. We have measured Aa of benzene with different radicals at the same concentration as a function of microwave power level. We infer the ultimate enhancements at complete ESR saturation, Aa,

as well as Ar,, by plotting the inverse enhancement (apparent or real,

respectively, the latter calculated using Eqs. 5 and 6), vs. the inverse of relative power and extrapolating to infinite microwave power. The ultimate-ultimate enhancement, defined as the ultimate enhancement divided by the leakage factor f is then calculated. [f is the ratio of the longitudinal relaxation time of the spins with and without the radical, subtracted from unity.]

Table 1. Apparent and Real ultimate Enhancement and ultimate-ultimate enhancement values of benzene with different radicals of same concentration (20 mM) Sample

Radical

Apparent Ultimate Enhancement, Aa,

Real Leakage Apparent Ultimate Factor Ultimateenhancement, (f) Ultimate enhancement Ar,

Real UltimateUltimate enhancement, U∞

Benzene Galvinoxyl 259

158.7

0.80

323.7

198.4

Benzene BDPA

204

134.2

0.68



197.4

Benzene TEMPO

337.8

183.8

0.88



208.9

Typical values of some of the relevant experimental parameters used in arriving at the calculated quantities in Table 1 are summarized in the Experimental section. It is clear that the apparent ultimate-ultimate enhancement values of all systems measured at X-band and tabulated in Table


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1 are unrealistically close to – and even exceed – the dipolar limit of 329.1. It is thus clear that corrections for the Q-enhancement effect are very significant even at such a low 1H NMR frequency, sample volume and Q-factor of the probe. The expected value of U may be evaluated on the Hubbard model18 from a plot of the coupling parameter  (which is the ratio of cross-relaxation and auto-relaxation rates) vs. electron resonance frequency employing the correlation time 4.064 × 1011 s19-20; at 9.6 GHz the coupling parameter is calculated to be 0.3, which implies a theoretical value of U = 197.5 (see Supplementary Information). It is to be noted that the maximum deviation of the corrected experimental U values from the theoretical value derived as discussed above is about 6 %, as against the corresponding apparent values, which deviate by as much as 94%. It may also be pointed out that enhancements have been calculated from the experimental spectra based on the peak integrals, which are independent of any linewidth differences between the equilibrium and enhanced signals; in practice in our experiments the enhanced signals show a maximum line narrowing of ca. 5%, in keeping with trends known from early cw work.14



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Figure 1. Plot of reciprocal real enhancement (Ar) vs. reciprocal relative microwave power (P); system: C6H6/TEMPO; Fitting Equation:



1 1 1  c P 1  Ar Ar ,

 where c is a constant.

To assess the significance of the Q-enhancement effect in the context of high frequency NMR with probes of high Q-factor as commonly used for solution state work, we take typical values of the relevant quantities and tabulate below for hyperpolarized 1H NMR the apparent enhancement for a given negative real enhancement, as a function of the spin count in the sample. We have employed a Q-factor of 400, which is typical of current generation commercial probes especially for solution state NMR, a filling factor  of 0.7, a spectral linewidth  of 1 Hz and a sample volume of 0.5 ml, the spectrometer frequency being 600 MHz, and the temperature, 298.2 K. With this fairly typical set of parameters, and at a real enhancement factor of 100, which is a moderate polarization enhancement, we note that the deviation of the apparent (ie, measured) enhancement from the real value is well over 10% already at a spin count of 220 nmol (ie,


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1.31017 spins), deviating ever more strongly and even changing sign at higher spin counts (see Table 2). The behavior of the apparent enhancement factors over 8 decades of the spin count starting from 1011 spins is plotted in Figures 2 and 3, for given negative and positive real enhancements.

Figure 2. Plot of inverse apparent enhancement (Aa1) vs. spin count (real enhancement Ar = 100). The dashed line extension indicates the fixed value of Ar1.

Figure 3. Plot of inverse apparent enhancement (Aa1) vs. spin count (real enhancement, Ar = 100). The dashed line extension indicates the fixed value of Ar1



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Table 2. Apparent enhancement Aa vs. Spin Count for Ar = 100 Spin Concentration

Spin Count

Real enhancement, Ar

Apparent enhancement, Aa

1 nM

3.0115  1011

100

100.00002

10 nM

3.0115  1012

100

100.00024

100 nM

3.0115  1013

100

100.00242

1 μM

3.0115  1014

100

100.02422

10 μM

3.0115  1015

100

100.24275

100 μM

3.0115  1016

100

102.48176

1 mM

3.0115  1017

100

131.95503

10 mM

3.0115  1018

100

+70.34027

100 mM

3.0115  1019

100

+4.30726

1M

3.0115  1020

100

+0.41465

10 M

3.0115  1021

100

+0.04131

100 M

3.0115  1022

100

+0.00413

EXPERIMENTAL SECTION: Experiments were carried out on a solution state DNP system with coil-in-the-cavity configuration (Bruker MD4 resonator), with Bruker ELEXSYS and Avance III electronics for microwave and RF excitation and detection respectively, including a mutual trigger arrangement, and a Bruker wide air gap 10 electromagnet with 2.7 kW power supply. We have performed several ODNP experiments with different types of radicals at the same concentration at a 1H NMR frequency of 14.6 MHz and room temperature (298 K); the Q- factor was 80, sample volume was 70 µl, the benzene proton spin count being 2.84 × 1021, with a filling factor  of 0.43 (being the ratio of the sample volume to the active volume of the coil); the


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spectral linewidth of the 1H signal of benzene was about 28 Hz. Leakage factor is calculated by measuring the T1 of benzene with and without the radical, and subtracting the ratio from unity. In summary, while the quantitative deviations between measured (‘apparent’) and real enhancements are a function of the actual set of NMR experiment parameters relevant to a given study – in particular, the spectrometer frequency and spectral linewidth, the Q-factor, filling factor, spin count, temperature and the real polarization enhancement – our results clearly establish the significance of these Q-enhancement corrections both in hyperpolarized NMR spectroscopy and imaging, and highlight the need to take them explicitly into account in interpreting hyperpolarized NMR data, especially in analytical applications of hyperpolarized NMR whose objective is the measurement of spin count. ACKNOWLEDGMENTS: A.D gratefully acknowledges Indian Institute of Technology Madras for award of a teaching assistantship. N.C acknowledges the Department of Science and Technology, India for a spectrometer grant, and for award of the J.C. Bose National Fellowship. Supporting Information Available: Derivation of relation between the Real Enhancement (Ar) and the measured Apparent Enhancement (Aa). Two additional plots of reciprocal real enhancement vs. reciprocal relative microwave power for: (i) C6H6/BDPA; (ii) C6H6/Galvinoxyl; and also three additional Tables which list: (i) real enhancements for a given negative apparent enhancement; (ii) real enhancements for a given positive apparent enhancement; and (iii) apparent enhancements for a given positive real enhancement, all as a function of spin count.



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