The Future of Imaging

On a November afternoon in 1865, Wilhelm Röntgen, a young physics professor in Würzburg, Bavaria, captured the first ever X-ray image: a skeletal picture of his wife’s hand. In the hundred-plus years that have passed since Röntgen’s discovery of X-rays, scientists have discovered several different methods to image the body. One of the most useful imaging techniques is magnetic resonance imaging (MRI). MRI, unlike X-ray radiography, can render high-contrast images of soft tissues, such as the brain, heart, and even tumors, in stunning detail. With the development of a wide array of powerful MRI-based techniques like 3D imaging, the need for faster and more efficient ways of implementing MRI increases. A team of researchers led by Todd Constable, Professor of Diagnostic Radiology, Biomedical Engineering and Neurosurgery at Yale, has developed a novel way of improving the efficiency of MRI using magnetic field gradients with nonlinear geometries.

A 3D MRI image of the Circle of Willis and other cerebral arteries. Souce: New Zealand Brain Research Institute.

The Basics of MRI

MRI depends on a property of protons known as spin, analogous to angular momentum in classical physics. Nuclei with a non-zero spin, such as hydrogen nuclei, have a magnetic moment that can interact with magnetic fields. Our tissues are full of hydrogen atoms, especially in the form of fat and water. An MRI machine applies a powerful magnetic field (typical MRIs can have fields several thousand times as strong as the Earth’s), causing a small fraction of these protons to preferentially orient themselves so that their magnetic moments are parallel to the external field, just as the arrow of a magnetic compass will align itself with the Earth’s magnetic field.

Unlike the compass, however, which always points toward the north pole, hydrogen atoms can orient their magnetic moments in two possible ways: a lower energy state in which the magnetic moments are oriented parallel to the field, or a higher energy state in which they are antiparallel to the field. If a hydrogen atom in the lower energy state absorbs a photon with just the right amount of energy, it can reverse its orientation and flip into the higher energy state. The energy required depends on the strength of the magnetic field; at field strengths typically found in MRIs, the protons are excited by photons in the radio frequency range. When pulses of radio waves are applied in an MRI machine, some of the hydrogen atoms will absorb the radiation and flip, returning to their original state after the pulse disappears. As the protons relax, they release energy in the form of electromagnetic radiation, like a radio signal that can be received by an antenna. Receiver coils in the machine can detect this signal, called the free induction delay. By analyzing characteristics of the signal that vary in different tissues, such as the relaxation rate, the MRI machine can determine what kind of tissue the signal originated from.

Using a combination of pulse sequences with many contrast differences, it is possible to gain a surprising amount of information about the sample, such as whether a tumor is malignant or not. However, this process requires time, as MRI exams using multiple pulse sequences typically take about an hour to complete. During this time, patients must remain completely still in the cramped tunnel of the MRI machine, surrounded by the clatter of electromagnetic coils turning on and off. The experience is frequently unpleasant, but as MRI techniques improve in efficiency, hour-long scans could become a thing of the past.

The 2D image of phase and frequency values can be transformed into the final image through the use of a special mathematical technique known as a Fourier Transform. Image courtesy of Professor Todd Constable, Department of Radiology.

Parallel Imaging

One major innovation in MRI efficiency has been the development of parallel imaging, which uses several smaller receiver coils in lieu of a single larger coil. Parallel arrays of coils allow data to be collected from multiple places simultaneously. But more importantly, they allow for a limited amount of spatial localization. Each coil has a small area of sensitivity, so some information about where a signal originated can actually be determined just by looking at which coils picked up the signal.

Until recently, most advances in parallel imaging were the result of increasing the number of coils in parallel, with machines now being able to orchestrate up to 128 coils in tandem. Unfortunately, the gain in efficiency from increasing coil numbers experiences diminishing returns due to factors like cost and inductive effects between the coils. So instead of focusing on coil number, Constable’s team sought a new approach. Conventional MRIs use linear magnetic field gradients to encode spatial information. However, the receiving coils in an MRI are usually oriented in a circle around the sample. Constable’s team asked if a radial magnetic field gradient might be better able to complement the geometry of the receiving coils than a linear gradient.

The Problem of Spatial Localization

To understand why MRIs use magnetic field gradients, we have to ask the question: how can we construct a 2D image of the sample from a series of MRI signals? In other words, can we encode spatial information about the hydrogen atoms in a form that can be retrieved from a MRI signal? The conventional solution to this problem is to encode spatial information by applying series of linear magnetic field gradients, i.e. magnetic fields that vary in intensity along a coordinate axis.

The first gradient, called the slice-selecting gradient, allows a two-dimensional slice of the 3D space to be isolated for imaging. In the slice-selecting gradient, the magnetic field increases in intensity along the z-axis. As the strength of the magnetic field goes up along the z-axis, the difference in energy between the low and high energy states of the protons will also change, and the protons will be excited at higher resonance frequencies. If we apply a radio pulse containing only a few frequencies, then only the hydrogen atoms with resonance frequencies will absorb that energy and give off an MRI signal. Since the resonance frequency of a hydrogen atom is dependent on its location along the z-axis, a two-dimensional slice can be sampled from the 3D space by applying radio pulses with selective frequencies.

Once we have the 2D slice, the other two gradients, which vary along the x- and y-coordinates, are also applied using electromagnetic pulses. Like the slice-selecting gradient, these gradients allow hydrogen atoms to be localized in the x- and y-coordinates by causing two properties of the hydrogen atoms, the phase angle and resonance frequency, to vary along each respective axis. These two properties can be decoded from the MRI signal. By applying a series of these phase and frequency encoding gradients pulses and measuring the signal that results from each one, a 2D matrix with rows of phase elements and columns of frequency elements can be generated. A mathematical technique called an inverse Fourier transform is then used to reconstruct the final image from this data.

O-Space and Null Space Imaging

Instead of using the linear phase and frequency encoding gradients, Constable’s team decided to encode spatial information with a combination of parallel receiver coils and radial magnetic gradients centered at different places around the sample circumference. Radial localization is provided by the field gradient and angular localization is provided by the array of receiver coils. The center placements form an O-like shape in the plane of the image, giving the technique its name: O-space imaging.

The center of the radial gradients is offset using a superposition of linear and radial gradients. Image courtesy of Professor Todd Constable, Department of Radiology.

Constable’s team designed their technique so that the phase encoding gradient was no longer required. This innovation makes the technique faster than conventional methods because the phase encoding gradient step is the most time-intensive step of MRI imaging. After multiple acquisitions at different center placements, the MRI machine returns a map of isofrequency contours in concentric circles, like a topographical map, but demarcating outlines of equal resonance frequencies rather than altitude. A transform analogous to the Fourier transform is applied to produce a projection of the image along concentric rings, which can be transformed into the final image using sophisticated mathematical techniques that account for the geometry of the field gradients used for spatial encoding.

Constable and his team have successfully created MRI machines that can create radial magnetic field gradients, and preliminary studies of O-space imaging have shown that the technique can retrieve useful images with far less data than comparable methods. O-space imaging can reduce the amount of sampling required during an MRI scan by factors of up to sixteen-fold under optimal conditions, drastically cutting the amount of time needed to run an MRI scan.

Future Research Goals

Now Constable’s team is pursuing two different goals with their research. First, they are working in partnership with Siemens to create commercial MRI machines that can use O-space imaging. Second, they are examining if the concept of O-space imaging can be generalized to even more novel geometric field gradients. In this regard, they are working on forming a set of customized magnetic field gradients that are specifically designed to complement the geometry of any arrangement of coils. Using a mathematical method that focuses on finding the null space of the receiver coil array, or the areas least well characterized by their areas of sensitivity, Constable and his team are discovering magnetic field gradients with even more unusual shapes based on spherical harmonics. These shapes have the potential for even more efficient spatial encoding properties.

This work is in the early stages and new hardware must be built to fully test the approach, but the preliminary results to date are promising. The technology being developed in Constable’s lab could one day be an integral part of the MRI machines of the future, helping them climb new heights in speed and functionality.

About the Author
SOONWOOK “WOOKIE” HONG is a junior in Pierson College. He has worked in Professor Wolin’s Lab studying noncoding RNAs in salmonella strains.

The author would like to thank Professor Todd Constable for taking the time to share his research.

Further Reading
Stockmann, Jason P., Pelin Aksit Ciris, Gigi Galiana, Leo Tam, and R. Todd Constable. “O-space Imaging: Highly Efficient Parallel Imaging Using Second-order Nonlinear Fields as Encoding Gradients with No Phase Encoding.” Magnetic Resonance in Medicine (2010). Print.
Hornak, J. (2005, May 10). The Basics of MRI. Retrieved November 16, 2011, from
J.W. Akitt, NMR and Chemistry, An Introduction to the Fourier Transform – Multinuclear Era. Chapman and Hall, London, 1983.