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Variable Rate Selective Excitation Radio Frequency Pulse in Magnetic Resonance Imaging

Stephen Stoyan. Variable Rate Selective Excitation Radio Frequency Pulse in Magnetic Resonance Imaging. MRI Background Model Results Future Work. Overview. MRI Background: Basics of MRI. Radio Frequency (rf) pulses excite the sample

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Variable Rate Selective Excitation Radio Frequency Pulse in Magnetic Resonance Imaging

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  1. Stephen Stoyan Variable Rate Selective Excitation Radio Frequency Pulse in Magnetic Resonance Imaging

  2. MRI Background Model Results Future Work Overview

  3. MRI Background: Basics of MRI Radio Frequency (rf) pulses excite the sample Field gradients spatial encode the sample Large uniform static rf coil receives a signal external magnetic field Signal: Amplified Digitized Fourier-Transformed

  4. Nuclei with odd atomic weight and/or odd atomic number posses an angular momentum. Any electrically charged particle which moves creates a magnetic field called a magnetic moment. An ensemble of nuclei produce a ‘spin system.’ When an external magnetic field is applied the magnetic moments align in the direction of the field. MRI Background: Magnetization

  5. MRI Background: Magnetization • Magnetization is the net vector quantity of the magnetic moments of each nuclei in a given unit volume or voxel. • Given an external magnetic field, magnetic moment vectors rotate around the axis of the field. • This secondary spin is termed, Precession.

  6. MRI Background: Precession • The speed of proton precession is referred as, Precessional Frequency. • Stronger magnetic fields constitute higher precessional frequencies. • The frequency at which the nucleus will absorb energy is described in the Larmor equation.

  7. The equation for torque on a magnetic moment due to an external magnetic field, Making the substitution into , Proton interactions Spin-lattice interactions: A magnetic moments minimum energy state is in the direction of the external magnetic field. Spin-spin interactions: Magnetic moments experience local fields of their neighbours and the applied field. MRI Background: Interactions

  8. MRI Background: Bloch Equation • Combining proton interactions into equation produces the Bloch equation, where,

  9. Model: General rf Pulse • In processing an image a precise radio frequency (rf) pulse is applied in combination with a synchronized gradient. • An rf pulse at the Larmor frequency excites a voxel of protons into the transverse plane. • Gradients produce time-altering magnetic fields of linear-varying magnitude.

  10. The Variable Rate Selective Excitation (VERSE) rf pulse is a transverse excitation with a fraction of the field strength. By decreasing the duration of each sample and uniformly distributing signal amplitude, the VERSE pulse reduces SAR (Specific Absorption Rate). Subsequently our objective becomes, Model: VERSE Pulse

  11. The gradient is set to have linear-varying magnitude. represents the transverse plane at a particular position depending on its specific coordinate value. Model: Gradient

  12. Model: Coordinate Positions • Set and restrict to be a finite subset of , then partition the constraint into coordinate position values and . : Coordinate positions that are “in” the slice. : Coordinate positions that are “outside” of the slice.

  13. Magnetization vectors in will be tipped by an angle of . Magnetization vectors in will not be tipped and remain at the initial magnetization value. Model: Sin and Sout

  14. Model: Rotating Frame of Reference • The main super-conducting magnet, , induces a rotating frame of reference.

  15. Model: Coordinate Positions • Now external magnetization is a function of coordinate positions . • and are independent of . • The same notation must be incorporated into net magnetization.

  16. Since VERSE pulses have short sampling times there is no proton interactions, hence, from the Bloch equation: Model: Bloch Equation

  17. Slew rate or gradient-echo rise time, identifies how fast a magnetic gradient field can be ramped to different field strengths. For our problem we bound gradient and slew rate, . Model: Gradient and Slew Rate

  18. The semi-infinite nonlinear optimization problem, Model: Optimization Problem

  19. Results: Initializations • 5 Slice Problem:

  20. Results:

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  28. Use 5 slices to interpolate 15 slices. Add spin-lattice and spin-spin proton interactions. Add rotation into the equations. Investigate other variations of VERSE pulses. Test on MRI machine. Future Work

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