Nov 25 2008
In developing a model to explain the motion of atoms in a magnetic field, scientists have overcome a decades-old obstacle to understanding a key component of magnetic resonance.
This graphic depicts the quantum mechanical principle of super-adiabaticity, which was responsible for the behavior of atoms in some nuclear magnetic resonance experiments. If the trajectory of the atoms during an experiment were mapped on a globe, then the purpose of an adiabatic experiment is to move the atoms being studied from one point on the globe to another--slowly, and following a very carefully designed path (gray line). With super-adiabaticity, the atoms follow a different--sometimes, wildly different--path (orange line), but still end up at the right destination. Credit: Image courtesy of Philip Grandinetti, Ohio State University.
The new understanding may eventually lead to better control of magnetic resonance imaging (MRI) and higher resolution MRI diagnoses.
Collaborators at Ohio State University in Columbus and three institutions in France--the Centre National de la Recherche Scientifique, the Université d'Orléans, and the Université de Lyon--presented their findings in a paper that appears early online Nov. 25, 2008, in the Journal of Chemical Physics.
"This is very exciting work", said Tanja Pietraß, the program officer at the National Science Foundation who partially supported this project. "The fact that the researchers did not set out to work on this problem but more or less stumbled upon it and then used their ingenuity to solve it, demonstrates the importance of conducting basic research. In this case, the work may have a major impact on magnetic resonance imaging, positively affecting many peoples' lives."
The key breakthrough is a new understanding of a type of physical process called adiabaticity. Adiabatic processes are what physicists and engineers routinely use to control atoms in nuclear magnetic resonance (NMR) spectroscopy, and its better known sister, MRI. "An adiabatic process can be visualized as one where a system is 'held tightly'and slowly dragged by a controlling force from one state to the next," said chemist Philip Grandinetti of Ohio State. In MRI, magnetic energy holds the atoms in a patient's body in a steady state while radio waves are the controlling force that drags the atoms from one state to the next. "In a 'perfect' adiabatic process, the controlling force is moved infinitely slowly with the system's trajectory locked to the controlling force's trajectory," said Grandinetti.
Both NMR and MRI exploit a peculiar quantum mechanical property of subatomic particles called "spin". The nuclei of many atoms, most notably hydrogen, spin like tiny tops and possess a magnetic moment like a tiny bar magnet. In NMR and MRI the object under investigation--in medical applications, the patient--is placed inside a strong magnetic field that causes these tiny tops to align with the magnetic field and precess (or wobble, much like a child's top), in the direction of the gravitational field.
For MRI, the strong magnetic field needed for these techniques is generated inside the all too familiar tube that causes many patients claustrophobia, which can require sedation before a procedure. Once inside the magnet, each nucleus broadcasts its identity by emitting radio waves at its unique precession frequency, which depends on its interaction with surrounding atoms as well as the magnetic field strength.
The interaction with surrounding atoms is what makes NMR such a useful tool for chemists and biologists, allowing them to identify different chemical environments and molecular structures.
For MRI, it is the interaction of the nuclei with the magnetic field that is key, as magnetic field strength varies with location, enabling a researcher to code different parts of the body with different frequencies. Through the measurement of the atomic precession frequencies, an MRI radiologist can reconstruct a two-dimensional or three-dimensional image that accurately depicts the interior of a patient's body.
In performing such measurements, scientists often need to invert the nuclei so they are aligned against the magnetic field. Inverting the nuclei of people inside MRI scanners can reveal such things as cancer tumors, whose slightly different interaction with the nuclear spins can be used to detect their presence amid surrounding healthy tissue.
This is where adiabatic processes come into play. The inversions are often done "adiabatically", by subjecting the target to low power radio waves that sweep through a specific range of frequencies. If the sweep is performed slowly enough, then all the nuclei will ultimately be inverted.
"The confounding thing", says Grandinetti, "is that for decades adiabatic sweeps worked in many situations, even though the theory predicted that they should not have. To be fair, it wasn't clear that this discrepancy posed a real problem, and most people thought the conventional theoretical approach was doing a fine job in guiding them towards the optimum adiabatic process. It was only after we fully understood the reason for the discrepancy that we realized the conventional theoretical approach contained a flaw that might prevent the optimum adiabatic process from being discovered".
In the recent paper, Grandinetti and his colleagues solve this long-standing puzzle by introducing the concept of super-adiabaticity into the problem. Super-adiabaticity was first described in 1987 by Sir Michael Berry, a mathematical physicist at University of Bristol. When applied to magnetic resonance, it uncovers hidden behavior in the nuclear inversions that researchers had previously considered unrelated to adiabaticity.
Grandinetti and his colleagues describe a mathematical algorithm that can be used to predict the previously mysterious paths that the nuclei took on their way to the proper target state. This revelation, and the mathematical algorithm for its discovery, are particularly exciting as they open the door to new approaches for designing adiabatic processes in magnetic resonance as well as in other related fields.
One example is in a search for an MRI technique that does not require a patient to enter the confines of a large tube. Researchers are trying to exploit the stray fields of large magnets to do MRI, where the magnetic field is not contained only in the interior of a contraption but is leaking to the outside. The field becomes weaker as one moves further away from the center of the magnet, but researchers have been working on exploiting this natural non-uniformity as an aid to observe internal structures in objects.
"The problem is that these stray fields are highly inhomogeneous in nature, and to make up for this deficiency, researchers must control the dance of the spins in a way that compensates for this," said Grandinetti. "And this is exactly where the more precise control of superadiabaticity may prove to be a revolution in MRI. Who knows--may be a few years from now, you will be casually sitting next to the intimidating device, without the need for sedation?"
This work was funded by the National Science Foundation and CNRS and Le Studium in France.