Boutis Group Magnetic Resonance Research Laboratory at Brooklyn College
Welcome to the Boutis NMR research group web page. Below you will find some information on the various projects that
the group members are engaged in.
SPIN DIFFUSION IN A RIGID SOLID
Spin diffusion, a term coined by Nicolas Bloembergen, is an early concept of magnetic resonance. The physics involves energy conserving flip-flops of pairs of dipolar coupled spins (driven by the dipolar Hamiltonian) that result in the spatial transport of spin coherence. While this kinametically simple process may be easy to understand in the limit of a few spins, the physics of spin diffusion and the determination of a spin diffusion coefficient is a multi body problem for large spin systems as the dipolar Hamiltonian contains a sum over all spins.
One's common intuition regarding diffusion, such as the canonical model of a gas diffusing freely through space, is to consider the dynamics as irreversible and random. Spin diffusion in a crystal lattice, however,
is different in that the Hamiltonian is known and thus the dynamics are deterministic and reversible. Rhim, Pines and Waugh demonstrated that the
time evolution of a many body system may be reversed, including spin diffusion, by applying a well-defined RF pulse sequence whose effective Hamiltonian may be
made equal to the dipolar Hamiltonian of the system scaled by a factor of -1/2. These pulse sequences serve as a fundamental building
block in the laboratory's experimental investigations of spin diffusion using pulsed gradient schemes.
One method for studying diffusion in magnetic resonance is to encode a spatial modulation of the magnetization in a sample, termed a grating, and then
measure the grating attenuation over time. The difficulty in measuring spin diffusion by these methods in a solid
is that the spin diffusion coefficient is very slow (order 10 ^-12 cm^2/s) and hence the displacement of coherence is typically very small over the time scale
of the spin-lattice relaxation time, T1. Given the slow diffusion coefficient and a typical time scale of approximately 100 seconds, the requirements for studying spin diffusion by these pulsed gradient schemes is that the wavelength of the
grating be on the order of one micrometer or less. In order to perform these measurements we require strong pulsed gradient field strengths that are not commercially available. An additional requirement is that we coherently control the spin system-we need to 'turn off' the dipolar interaction while encoding the grating. To do this we implement various RF pulse sequences based on a technique known as average Hamiltonian theory.
The laboratory is currently funded (with Vadim Oganesyan, College of Staten Island of CUNY) to investigate via theory, simulation and experiment the dynamics of spin diffusion in the short time, few spin regime. Students who are interested in this work should contact Dr. Oganesyan or Dr. Boutis.
EXPERIMENTAL STUDIES OF ELASTIN
The laboratory is currently performing a variety of experimental studies of Elastin, the principle protein component of the elastin fiber
found in vertebrate tissues. Elastin is truely one of the most remarkable biopolymers. The human aortic valve, composed of elastin, undergoes several billion stretch-strain cycles during our lifetimes and only fails once (or perhaps more than once
if you are lucky!). Our skin and lungs also owe their resilience to elastin. An underlying theme of the work relating to this
project is to investigate the complex correlated protein-water relationship in elastin and to use this information to better the understanding of the functional properties of this remarkable biopolymer. The laboratory is implementing various experimental techniques to pick away at this
complex problem ranging from conventional techniques to methods that require experimental hardware that is not commercially available.
Some recent experimental work we performed involved using homebuilt strong pulsed field gradients to study the tortuosity and surface
to volume ratio of water of elastin fibers. The experimental data provided a direct measurement of the molecular diffusion coefficients
of water in elastin over a time scale ranging from 1 ms to 20 ms. Shown in the figures below (left) are experimental data that
demonstrate that the diffusion coefficients are time dependent, which allowed for a measure of the surface to volume ratio
in bovine nuchal ligament elastin fibers. On the right, is an A. SEM image of a bovine nuchal ligament elastin fiber B. The same fiber crushed open under liquid nitrogen, highlighting the tortuosity of the fiber and C. Cartoon highlighting that diffusion is time dependent in a tortuous channel (moving from point A to point C may take longer in time than moving from A to point B, but the displacement is smaller).
More recently the group performed a deuterium double quantum filtered NMR experiment to study the anisotropic motion of water in
elastin. The essence of this experiment is that the deuterium nucleus has a quadrupolar interaction, which is only partially
averaged in anisotropic environments. The partial averaging of the quadrupolar interaction together with a well defined RF pulse
sequence allows for the creation of a double quantum coherence. The experiment allows for studying the degree of anisotropic motion by
measuring the time required for creating double quantum as well as the strength of the residual quadrupolar interaction. An additional parameter that may be extracted
from the experiment is the distribution of anisotropic environments. We recently studied the
DQF signal of deuterated water in bovine nuchal ligament elastin and probed the anisotropic motion of water ranging from 1ms
to 20ms. An example DQF signal from water in elastin is shown in the figure to the left. The data are fit to a theoretical curve that allows
one to extract the size of the residual quadrupolar interaction as well as the decay rate of the double quantum coherence.
The group is also engaged in a variety of other experiments to probe the complex structure-function relationship of elastin. Below is a list of some of our ongoing work:
Our work in the laboratory is currently funded under an NIH SC1 grant. Students who are interested in a related project should email me.
Exchange NMR studies
Investigations of elastin's structure as a function of mechanical deformation
Simulation/Experimental studies of short elastin mimetic peptides
AVERAGE HAMILTONIAN THEORY
Average Hamiltonian Theory (AHT) is a generalized quantum control scheme, developed by John Waugh in the late 1960's, for
coherently manipulating the dynamics of a quantum system. The idea is to perturb a quantum system via
an experimentally controllable time dependent perturbation (in NMR this is the Radio Frequency interaction), to
manipulate an otherwise time independent internal interaction (the dipolar interaction in a solid, for example). The technique
has been used in various facets of Nuclear Magnetic Resonance such as solid and liquid state NMR spectroscopy as
well as solid state NMR imaging. The control scheme
is not necesserily tied to Magnetic Resonance spectroscopy and imaging, but has been implemented in various paradigms of
quantum information processing as well. The basic concept of AHT can be understood by considering the figure below. The essence of any NMR experiment is to apply a series of RF pulses that coherently evolve the spin system from an initial state to some final state. The idea with AHT is that the series of pulses and/or free evolutions under any time independent internal Hamiltonian and time dependent RF pulse train may be described by a time independent effective Hamiltonian (or average Hamiltonian) that transforms the system from the state at t=0 to t=T.
The group has an ongoing interest in AHT and in enhancing pulse sequences via this control scheme. The Boutis group recently implemented this control scheme to develop and improve upon pulse sequences for spin I=1 quadrupolar
echo spectroscopy-a technique for measuring the broad quadrupolar spectra of a solid spin system. Information relating to these cycles may be found in the publications tab. We have compiled some concise notes on average Hamiltonian theory. If you would like them please send me an email at email@example.com.
NMR HARDWARE DEVELOPMENT
An ongoing interest of the laboratory is to develop and enhance NMR methodology. This typically involves hardware and pulse sequence development
and has proven to be a invaluable experience for students to learn the nuts and bolts of NMR. Below you will find some images of hardware undergraduates, graduate
students and postdoctoral research scientists have designed and built in the lab.