Nuclear Magnetic Resonance Imaging

Type of physical science: Classical physics

Field of study: Electromagnetism

Nuclear magnetic resonance imaging, or NMRI (MRI), is a technique that produces cross-sectional and three-dimensional images of organic and inorganic materials, employing the phenomena of nuclear magnetic resonance (NMR) to visualize the spatial distribution of hydrogen or other nuclei innate in or injected into the material in question.

Overview

All inorganic and organic materials contain nuclei composed of protons and neutrons. Atomic nuclei containing an odd number of protons, neutrons, or both have a nuclear spin and an associated nuclear magnetic momentum, or moment. Spinning nuclei in a magnetic field respond like a spinning gyroscope precessing about the local potential field direction. Since odd-numbered nuclei have a net positive electrical charge, their magnetic moment arises from their intrinsic spin via the basic relation μ = γJ, where μ is the magnetic moment, J is the angular momentum of the spinning nuclei in the nuclear model of Niels Bohr and Arnold Sommerfeld, and γ is a fundamental constant known as the gyromagnetic ratio. Because the magnetic energy of nuclei can assume only discrete quantized values, only specific energy states are permitted, corresponding to spin alignments of nuclei—either parallel (up) or antiparallel (down)—with respect to the direction of an imposed magnetic field. Transitions between these magnetic energy levels result from applying an electromagnetic pulse whose frequency matches the resonant frequency. This phenomenon is known as nuclear magnetic resonance (NMR). The resonant frequency, also called the Larmor frequency, is given by the equation ω = γB, where ω is the angular frequency of the nuclei in question and B is the applied magnetic field strength. The total fraction of magnetized nuclei in a given sample depends on thermal agitation and the strength of the applied magnetic field.

Perhaps the most basic NMR experiment applies what is termed a π/2 pulse to a sample in equilibrium by means of a radio-frequency coil whose axis is perpendicular to the direction of the applied magnetic field. When the magnetization state of a sample is thus disturbed by the radio-frequency pulse, it returns to its original equilibrium condition with a characteristic time constant T₁, known as the spin-lattice relaxation time. The NMR signal itself also decays with a characteristic time constant T₂, known as the spin-spin relaxation time, reflecting the strength of innate local nuclear-spin interactions. This basic NMR technique is a method to elicit and distinguish preferentially T₂ behavior in a net NMR time series, encompassing different proportions of T₁ and T₂ contributions.

In standard NMR spectroscopy, a small sample is placed between the poles of an electromagnet with a uniform and controllable field. A number of coils connected to an electromagnetic frequency oscillator surround the sample. A sweep circuit is then employed to measure the strength of the magnetic field in a smooth and continuous fashion. A short, intense radio-frequency pulse is then applied to the sample. When the Larmor resonant frequency of a sample is reached by the sweep signal, a corresponding signal induced in a second receiver coil is detected and further amplified. Resonant frequencies in the strong magnetic fields required—typically equal to or greater than one tesla—are typically in the one- to fifty-megahertz radio-frequency band. The resulting NMR waveform is a superposition of signals from the radio-decay signals of many precessing nuclei, which decay exponentially with different characteristic time constants.

In addition to examining NMR waveforms as signals in time, by computing the Fourier transform of these generally complicated waveforms, it is possible to produce a graph showing the amplitude strength of radio-frequency contributions over specific sweep frequencies from single free-induction decay (FID) measurements. The Fourier transform of a decaying radio-frequency signal from a precessing nucleus closely approximates a Gaussian bell-shaped spectral line; the reciprocal of its width is the relaxation time. Because the energy separation between up and down spin orientations of nuclei in a sample is proportional to the magnetic-field strength, resonance frequencies for a given nucleus can be selected and varied at will merely by varying the applied magnetic field. This permits NMR spectroscopy to choose convenient resonant frequencies that are optimal for recording and processing by specific hardware, software, and application requirements.

Because the resonant frequencies of common nuclei, such as hydrogen in water molecules, are well known and radio-frequency absorption spectra accurately represent the total water molecules at a given location, two-dimensional geometric planes of nuclear spins at right angles to the direction of the applied magnetic field will be a one-dimensional projection, on one coordinate axis, of the three-dimensional planes of nuclei in the sample perpendicular to this direction.

Direct T₁ imaging is a primary source of tissue contrast in NMR imaging methods as applied to biology, chemistry, and medicine. A variety of sequences for transmitting radio-frequency pulses to target nuclei have been specifically devised to exploit this contrast, resulting from different T₁ values. In one method, known as the T₁ inversion recovery method, net sample magnetization is first inverted and then analyzed at a later time interval. As in many imaging methods, successful image formation in NMR depends on the signal-to-noise (SNR) ratio, which is itself a strong function of the thermal and electromagnetic state of the material being imaged, as well as magnetic-field strength and uniformity.

Another class of NMR images or parameter maps is obtained by measuring and processing other NMR parameters in addition to T₁ and T₂. Several methods exist to measure the flow velocity of moving nuclear spins observed from FID signals. An important further class of NMR images results from what is called the chemical-shift effect. Because two identical nuclei, respectively isolated and in contact with adjacent molecular forces, have slightly but measurably different resonant frequencies, the shift from the true (isolated nuclei) to the observed (net nuclei) frequency is termed the chemical shift. Chemical-shift NMR imaging is experimentally measured with spatially changing gradient radio-frequency pulses, which yield information on the type and structure of specific molecules present in a sample.

In two-dimensional NMR spectroscopy, the magnitude of resonant spin frequencies is measured and displayed on a cathode-ray tube after Fourier transform signal processing of decay times. The data is plotted against two different frequency scales, one direct (FID measurements) and the other indirect (numerous recordings of one-dimensional spectra on an incremented delay). NMR imaging methods arose as an effort to produce spatially localized NMR spectra, such as from specific organs or tissue sections. The specific imaging method, imaged parameters, and particularly image-reconstruction methods have major consequences for ultimate NMR imaging quality. The varieties of mathematical techniques for image reconstruction, considered experimentally, employ angular variations of the above magnetic-field gradients.

Another class of imaging methods, called Fourier integration imaging, uses perpendicular field gradients that are applied sequentially and vary in time or position. The original multiple-angle projection reconstruction, from American biochemist Paul Lauterbur's work, is similar to techniques used in x-ray tomographic reconstruction. A single NMR slice is not sufficient to produce an accurate and comprehensive two-dimensional image. Lauterbur's imaging method rotates the magnetic-field gradient in a series of small angular displacements to obtain for each angular step a project slice or view from the FID signal. After a sufficient number of slices have been obtained, the image is reconstructed by the mathematical signal-processing technique of back projection, also known as the line-integral projection technique. The desired two-dimensional image of precessing nuclei is given as the integral sum of the data to be projected with what is called the projection filter.

Although computationally implemented by a wide variety of mathematical algorithms, back projection basically sums corresponding values of projections for each point in the angular image plane. Many scientists liken back projection to optically determining the location and shape of an object placed inside a shaded lamp by tracing the object's contours at different angular locations around the lampshade and then tracing or projecting optical rays back to their common geometric intersection.

In back-projection reconstruction, final image accuracy and fidelity depend on the total number of individual back projections recorded. In addition to lengthy measurements for all projections, Lauterbur's original approach has been generally proved oversensitive to errors arising from small motions of the sample and fluctuations in the magnetic field. Subsequently, a more efficient imaging method was proposed, employing two-dimensional Fourier transform signal processing. In two-dimensional NMR imaging, one or more magnetic-field gradients are added to resolve the three-dimensional distribution of nuclear spins into their respective Fourier domain components.

In what is called the direct Fourier transform imaging method, the measured FID or spin-echo signal is defined by the double (over both x and y dimensions) integral summing over the two-dimensional magnetic-spin density to be imaged and an exponential basis or filter function defined in terms of the magnetic field gradients in the x and y directions. This formula underscores the important fact that the NMR signal measured in the x and y directions is itself the two-dimensional inverse Fourier transform of the actual spin density. As a result, the spin density can be obtained by taking the two-dimensional Fourier transform of the measured signal. Such Fourier transform imaging methods have generally simpler data collection and are notably faster, as they require no back projection.

Applications

Appropriately designed and applied, radio-frequency pulses in NMR can provide further increases in the contrast between healthy and malignant tissues. Lauterbur employed the technique of back-projection reconstruction to give the first adequately resolved means for generating two-dimensional maps or pictures of the density and relaxation times of precessing protons in biological and human-tissue samples. Many diseases can be directly associated with increased water concentration in given tissues, in turn increasing T₁ relaxation times. The full range of applications encompassed by magnetic resonance imaging (MRI) is suggested by some of the names for the topic: in vivo proton density mapping; water-dependent decay time imaging; and various types of NMR spectroscopy, including organ specific, chemical specific, and chemical shift.

Because MRI is noninvasive, has high spatial and temporal resolution, has great sensitivity and information content for target nuclei, does not use ionizing radiation, and is capable of providing images of the distribution of a wide variety of NMR-measurable parameters characteristic of different chemical conditions, it is commonplace in hospitals and similar facilities. MRI is the preferred imaging technique for neurological imaging, as it provides better contrast than other common techniques, such as x-ray computed tomography (CT), and is often used in conjunction with other imaging techniques, such as CT and positron emission tomography (PET).

In addition to the nearly ubiquitous hydrogen nucleus/proton, there have been successful attempts to use MRI to image a number of alternative nuclei, including carbon 13, fluoride 19, potassium 31, and sodium 23, the latter two of which naturally occur at high levels in the human body. Fluorine and lithium can be externally administered and imaged in the vascular and liver systems and the brain, respectively. Potassium NMR spectra have provided detailed images of chemical processes in tissues involving metabolites and energy-conversion processes.

Applications of NMR imaging outside the biomedical sciences include the study of diffusion and reaction kinetics in physical and solid-state chemistry and the nondestructive evaluation of spatially inhomogeneous engineering materials. NMR has also proved useful in the petroleum industry for purposes of petroleum and natural-gas exploration, where it can be used to study the pores in rock and sedimentary strata and identify any fluids they may contain, and in oil refineries, where it has been used to analyze crude-oil samples in much less time than conventional laboratory methods.

Context

In 1932, the Dutch physicist C. J. Gorter theoretically proposed that when atoms or molecules are subjected to strong magnetic fields, Zeeman-type energy transitions can be induced between different nuclear spin energy states. After work on military radar systems at the Massachusetts Institute of Technology's Lincoln Laboratories during World War II, Edward Mills Purcell of Harvard University experimentally confirmed magnetic resonance in solids, almost simultaneously with Felix Bloch's work at Stanford University with liquids. In 1951, following the previous year's discovery by the German physicist Otto Hahn that NMR spin echoes could be used to measure flow velocities in moving liquids, French physicist Pierre Gabillard was the first to note that spatial localization of specific nuclei was possible using NMR. After 1956, these techniques began to be widely supported and adopted through the National Institutes of Health.

In 1959, Latvian émigré and electrical engineer Vsevolod Kudravcev developed a method for displaying the embryo inside a quail egg on a television screen using NMR. After further experiments in 1961, Kudravcev noted that magnetic fields of high uniformity could be used to localize the NMR response from very specific tissue volumes of interest using both static and alternating field gradients. Because his studies were never published in a scientific journal, however, it was not until the development of larger and more uniform electromagnets in the late 1960s that biomedical interest in NMR was revived. In 1968, James Langham built a low-field NMR instrument capable of yielding good signals, distinguishing water from fat in an entire mouse. Armenian engineer Raymond Damadian filed the first US patent in 1972 and published the first brief account of the potential scope of NMR in 1974. Damadian emphasized his discovery of abnormal T₁ values from faster-growing cancer tissues. A Japanese patent filed in 1973 was described in 1976 as having apparatus similar to that of Kudravcev. Sequential radio-frequency signals displayed in the form of real-time images from various parts of the human body were first published by Peter Mansfield and Andrew Maudsley in 1976 and Damadian et al. in 1978.

Because the simple, low-resolution methods took many hours to implement, considerable interest arose in faster NMR imaging methods. In addition to L. Jeener's 1971 proposals for two-dimensional NMR spectroscopy, the classic paper by Lauterbur in Nature in 1973 first detailed the use of back-projection reconstruction for generating two-dimensional images of proton density and relaxation times. In 1975, Anil Kumar and others proposed a new, more efficient method of NMR imaging using the two-dimensional Fourier transform, the possibilities of which had been recognized in part by R. R. Ernst and Philip W. Anderson in 1966.

Although development of NMR spectroscopy and in vivo imaging had largely occurred separately, in 1978, the British electronics firm EMI announced its first NMR images of the human brain from a commercial system using projection reconstruction. These successes led to large-scale industrial interest, and highly expensive automated imaging systems were rapidly acquired by hospitals beginning in the early 1980s.

Principal terms

FREE-INDUCTION DECAY: the radio-frequency signal emitted from NMR by precession of transversely magnetized nuclei after excitation

IMAGE RECONSTRUCTION: the specific mathematical models or procedures that define which kind of parameter map or distribution will be computed from tomographically surveyed data

NUCLEAR MAGNETIC RESONANCE: the phenomenon exhibited by the magnetic spin systems formed by nuclei of certain atoms whereby nuclei absorb energy at specific natural (resonant) frequencies when subjected to alternating magnetic fields

RESOLUTION: spatially, the ability to distinguish clearly according to some criterion two or more closely separated objects; temporally, the discrimination of two or more nearly simultaneous events

SIGNAL-TO-NOISE RATIO: the ratio of the desired amplitude or energy from a signal to that from unwanted noise

SPIN ECHO: the radio-frequency signal produced by the 90-degree or 180-degree radio-frequency energizing pulses in NMR, measured by the decay constant T2 and returning after the last radio-frequency excitation pulse, whose amplitude indicates the number of protons or nuclear specie and their mutual phase and whose frequency indicates local magnetic field strength

SPIN-LATTICE RELAXATION TIME: the time constant that measures the precession of nuclear spins proceeding toward thermal equilibrium defined by other adjacent particles in atomic/molecular lattices, measured by the decay constant T1

ZEUGMATOGRAPHY: the original NMR imaging method; refers to the linkage (zeugma meaning "joining together" in Greek) between the spatial position of target nuclei in a sample and their Larmor resonant frequency, as determined from their NMR radio-frequency emissions in the presence of linear magnetic-field gradients

Bibliography

Apperley, David C., Robin K. Harris, and Paul Hodgkinson. Solid State NMR: Basic Principles & Practice. Highland Park: Momentum, 2012. Print.

Carbajo, Rodrigo J., and José L. Neira. NMR for Chemists and Biologists. Dordrecht: Springer, 2013. Print.

Chen, C. N., and D. I. Hoult. Biomedical Magnetic Resonance Technology. New York: Hilger, 1989. Print. Provides a unique guide to almost all prototypal and commercial NMR equipment envisioned and used in laboratory and clinical applications. Covers the various types of ancillary microcomputer and data processing/display equipment and contains some performance comparisons. Features many photographs and diagrams to illustrate NMR imaging techniques.

Eubanks, B. A. Magnetic Resonance Imaging: An Introduction to Theory and Methods. Philadelphia: Lippincott, 1991. Print. Written for chemists, physicists, engineers, physicians, and others who need to know the basic conceptual background, operational principles, and jargon of NMR spectroscopy and two- and three-dimensional imaging.

Findeisen, Matthias, and Stefan Berger. 50 and More Essential NMR Experiments. Weinheim: Wiley, 2014. Print.

Gladden, Lynn F., Michal Lutecki, and James McGregor. "Nuclear Magnetic Resonance Spectroscopy." Characterization of Solid Materials and Heterogeneous Catalysts: From Structure to Surface Reactivity. Ed. Michel Che and Jacques C. Védrine. Vol. 1. Weinheim: Wiley, 2012. Print.

Paudler, William W. Nuclear Magnetic Resonance: General Concepts and Applications. New York: Wiley, 1987. Print. Focuses specifically on the basic atomic and molecular physics of nuclear magnetic resonance. Includes valuable details on radio-frequency signals, magnetic fields, and signal-to-noise ratio. Contains a summary of typical experiment measurement procedures.

Pettegrew, Jay W., ed. NMR: Principles and Applications to Biomedical Research. New York: Springer, 1989. Print. Contains much biological as well as chemistry-physics information on in vivo NMR spectroscopy and imaging for specific organs, tissues, and organisms. Includes sections on NMR image contrast enhancement.

Swenberg, Charles E., and James J. Conklin, eds. Imaging Techniques in Biology and Medicine. San Diego: Academic, 1988. Print. A nearly self-contained resource, not only for a quick look at NMR but also for x-ray, ultrasonic, radiometric, and other methods of clinical and research imaging. Brief but clear descriptions of the principles, applications, requirements, and general performance of each imaging technique. Includes discussion of imaging limits for each technology.

Valk, J., C. MacLean, and P. R. Algra. Basic Principles of Nuclear Magnetic Resonance Imaging. New York: Elsevier, 1985. Print. Designed to serve as a means of self-study as well as a supplement to chemistry and biomedical textbooks. Illustrates basic theoretical principles through simple graphics and provides carefully selected examples that are actually encountered in clinical and research situations.

Wade, Glen. Handbook of Digital Imaging Techniques and Technology. New York: McGraw, 1989. Print. Written primarily for undergraduate engineers and physicists, with a minimum of mathematics and many diagrams and illustrations. A fundamental reference for Fourier, back-projection, and other algebraic methods and algorithms for one-, two-, and three-dimensional imaging. Useful coverage of the computer and signal-to-noise ratio requirements and comparative performance of different imaging methods applied to the test cases.

Wolf, Gerald L., and Carol Popp. NMR: A Primer of Medical Imaging. Thorofare: Slack, 1984. Print. Features a simplified discussion of existing commercial systems for NMR imaging of human tissue. Well illustrated, with NMR images from representative medical cases histories, including some discussion of medical diagnosis. Well referenced.

Young, Stewart W. Nuclear Magnetic Resonance Imaging: Basic Principles. New York: Raven, 1984. Print. Reviews core physical concepts using the Bohr-Sommerfeld atom and nuclear-spin model. Requires little technical background. Graphically illustrates basic concepts of resonance, magnetic moment, and the Boltzmann constant as related to practical imaging-system requirements.

Zandvoort, Henk. Models of Scientific Development and the Case of Nuclear Magnetic Resonance. Norwell: Kluwer, 1987. Print. Examines in great detail the historical background and chronological development of the physics and imaging technologies and the applications of nuclear magnetic resonance. Compares the discovery and development of NMR with other discoveries in quantum mechanics and related areas of atomic/nuclear physics.

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