Electricity: measuring and testing – Particle precession resonance – Using a nuclear resonance spectrometer system
Reexamination Certificate
2002-02-04
2003-10-28
Gutierrez, Diego (Department: 2859)
Electricity: measuring and testing
Particle precession resonance
Using a nuclear resonance spectrometer system
Reexamination Certificate
active
06639405
ABSTRACT:
FIELD OF THE INVENTION
The present invention pertains to nuclear magnetic resonance (NMR) spectroscopy, and in particular to NMR apparatus for and methods of improving the quality of an NMR spectrum.
BACKGROUND OF THE INVENTION
The nuclei of many atoms possess non-zero angular momentum or spin. Where the nuclei have a net charge, the spin produces a magnetic moment. When a sample containing such nuclei is placed in a constant external magnetic field (e.g., B
0
in the z-direction), the net magnetic moments of the nuclei attempt to line up with the magnetic field. Some nuclei align themselves parallel to the magnetic field (i.e., in the positive z-direction), while others align themselves antiparallel to the magnetic field (i.e., in the negative z-direction). These two different orientations (“states”) of the nuclei have different energies, with the population difference being inversely related to the energy difference between the two states.
At equilibrium, more nuclei will be in the low-energy state than in the high-energy state. The individual magnetic moments, however, cannot perfectly line up with the external magnetic field, but rather are tilted at an angle and thus precess at an angle about the imposed magnetic field axis at a particular frequency, known as the Larmor frequency.
If an oscillating external magnetic field (typically, pulses of electromagnetic energy in the radio frequency (“rf”) range) is applied to the nuclei at the Larmor frequency, a resonance occurs, whereby the rf energy is absorbed due to the excess spin population of nuclei in the low energy state. This causes the magnetic moments in the lower energy state to flip to the higher energy state. Depending on the duration of the rf pulse, the populations of the two energy states will be perturbed from the equilibrium populations. When the oscillating magnetic field ceases, the precession of magnetic moments generates an electromagnetic signal that can be detected by a receiver coil appropriately arranged relative to the sample. The receiver coil converts the received signal into an electrical signal, which can then be analyzed. The populations of parallel and antiparallel nuclei return to an equilibrium state with a characteristic time period T
1
, known as the nuclear spin-lattice or longitudinal relaxation time.
Different nuclei precess at different frequencies. Accordingly, at a particular magnetic field strength, the nuclei will generally absorb energy at certain characteristic radio frequencies. Also, nuclei of the same nuclear species will absorb energy at shifted frequencies, depending upon their molecular environment. This shift, called the “chemical shift,” is characteristic of an atom's position in a given molecule. Plots of chemical shift (typically measured in parts-per-million or “ppm”) vs. signal strength (e.g., mV) reveal the energy absorption peaks (“resonances”) of the nuclei and provide a chemical analysis or “spectrum” of a given sample subject to NMR. In particular, NMR spectroscopy is used to characterize the structure and dynamics of proteins, nucleic acids, carbohydrates and their complexes, much in the way crystallography is used. NMR is also used in vivo to monitor and characterize living tissue, and in particular has been used to monitor defects in energy metabolism in animals. Details about NMR, including NMR spectroscopy, can be found in the book by S. Webb,
The Physics of Medical Imaging
, Institute of Physics Publishing, Ltd., 1992, Chapter 8.
A technique used in NMR to acquire a signal from the sample being measured is called the “spin echo” technique. After the initial rf pulse is turned off, the magnetic moments of the nuclei begin to once again precess in phase around the constant magnetic field B
0
. However, the individual magnetic moments begin to diverge as some nuclei precess faster and some precess slower than the central Larmor frequency. When the magnetic moments are first tipped by the rf pulse, a relatively strong signal or voltage is induced in the receiver coils. However, the signal gradually decreases due to energy exchange between spins (with a spin-spin relaxation time constant T
2
) and the dephasing of the spins, both of which are cumulatively characterized by a relaxation time T
2
*. This signal is called the “free induction decay” (FID).
A “spin echo” or subsequent representation of the FID can be generated by bringing the spins of the magnetic moments back into phase coherence by subjecting the sample to another rf pulse, called a “refocusing pulse.” For example, if, at a time &tgr; after the nuclear spins are tipped by a first rf pulse of appropriate frequency, magnitude, and duration (a 90° pulse), another electromagnetic signal of appropriate frequency, magnitude, and duration is applied to effect a 180° nutation of the nuclear spins (a 180° pulse), each individual spin is effectively rotated by 180° (in the rotating frame of reference). As a result, the phase becomes the negative of the phase accumulated before the 180° pulse in the former case. The magnetic moments that had been precessing faster than the central Larmor frequency, and thus “ahead” of the other magnetic moments before the 180° pulse, are now “behind” the slower magnetic moments. As the faster magnetic moments “catch-up” to the slower magnetic moments, a stronger and stronger signal is induced in the receiver coil until the faster magnetic moments pass the slower ones. The signal begins to fade as the magnetic moments spread out. In this manner, a so-called “spin echo” signal of the FID is generated. The peak amplitude of the spin echo depends upon the transverse or spin-spin relaxation time constant T
2
.
Ideally, the envelope of a spin-echo voltage signal is symmetrical in time. However, because of timing limitations between the initial rf excitation of the sample and the subsequent rf refocusing pulse, the initial portion of the spin-echo signal is generally not recoverable. Consequently, in practice, only a portion (e.g., half or slightly more than half) of the spin-echo signal can be used to obtain the associated NMR spectrum. The resulting spectrum is essentially a properly phased real component of the Fourier-transformed raw half spin-echo voltage signal. Since the imaginary part of the spectrum is more dispersive in terms of peak width, the NMR spectrum is often displayed in a real mode rather than the absolute value mode.
While this approach sometimes provides for an adequate spectrum, it is much preferred to have a spectrum with the highest possible signal to noise ratio (SNR) and spectral resolution, particularly for samples where the resonance peaks are closely spaced and the peak of tissue water needs to be suppressed. To date, NMR spectroscopists have had to use the half spin echo and accept the poor signal to noise ratio (SNR) and spectral resolution available from the half spin-echo signal.
Accordingly, there is need for a technique that could provide for high-resolution NMR spectra.
SUMMARY OF THE INVENTION
The present invention improves the quality of an NMR spectrum by acquiring more than half echo data and using an iterative numerical method to reconstruct the missing data points of the corresponding full symmetrical echo data.
A first aspect of the invention is a method of forming a high-resolution NMR spectrum. The method includes acquiring an initial partial spin-echo signal from a sample, the signal beginning at a time t=t
i
and having an echo-center portion. A low-resolution phase is then obtained from the echo-center portion, preferably by filtering the signal to isolate the echo-center and then Fourier-transforming the filtered signal. The partial spin-echo signal is then Fourier-transformed to obtain an initial spectrum having an initial phase. The phase of the initial spectrum is then replaced with the low-resolution phase to create a phase-constrained spectrum. The phase-constrained spectrum is then Fourier-transforming to obtain a reconstructed signal having data for time t<t
i
. The data in the reconstructed signal for time t>t
Chen Wei
Liu Haiying
Ugurbil Kamil
Gutierrez Diego
Regents of the University of Minnesota
Schwegman Lundberg Woessner & Kluth P.A.
Vargas Dixomara
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