| Overview: This one-day course will explore the physical methods
and mathematical models that underlie nearly all research and development in MRI
and MR spectroscopy. Specific topics include:
Quantum mechanical and semi-classical models of the proton dynamics;
Spin density and equations for coupled spin systems;
Intra- and intermolecular multiple quantum coherence;
Physical mechanisms of hyperpolarization;
Quantum-mechanical description of the spin-RF coil interaction;
RF field equations and reciprocity laws at all field strengths;
Quantum mechanical and classical descriptions of T1,
T2 and
other contrast mechanisms;
Mathematical models for susceptibility contrast;
Tissue models to explain MRI contrast;
Chemical and physical principles of contrast agent design;
Mathematical description of dynamic equilibrium magnetization in fast sequences;
Description of echo formation and contrast using spin phase diagrams;
Principles of manipulation of magnetization phase for applications; and
Models and equations for RF pulse design.
Educational Objectives:
Upon completion of this course, participants should be able to:
Starting from first principles in quantum mechanics, describe and derive the
equations for spin and magnetization dynamics, and explain the semi-classical
limits of the quantum mechanical model;
Describe the spin density formalism used to model the dynamics of coupled spin
systems, and the application of this formalism to understand experiments in MR
spectroscopy, as well as experiments that reveal residual intra- and
inter-molecular dipolar interactions of water in tissues;
Describe the quantum mechanical and semi-classical theory of relaxation, and the
mechanisms of relaxation of protons that can result in generation of image
contrast;
Describe the physical tissue models needed to understand image contrast from
relaxation parameters, magnetization phase, microscopic susceptibility, the
action of contrast agents, and generally from cellular structure on the
miscroscopic (< 100 nanometers) and mesoscopic (1-100 micron) scale; and
Describe the mathematical models used in deriving new pulse sequences and RF
pulse modulation. Specifically, describe how spin phase diagrams are used to
understand dynamic equilibrium in short tr sequences, and how these diagrams are
used for developing new sequences with new contrast dependencies. Describe the
different mathematical models used for RF pulse design, and their relative
advantages and disadvantages.Audience Description:
The course is designed for Ph.D. candidates and recent graduates in physics,
chemistry, applied mathematics, and engineering. It is also well suited to
established MR scientists who seeks a more quantitative understanding of the
physics and mathematical foundations of MRI. The individual who will benefit
most will have a graduate education MR physics, chemistry, applied mathematics,
or engineering. An individual with several years of direct MRI experience, but
without prior formal physics and mathematics training will also benefit.
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