Solutions of the Bloch equations for MRT

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Discussion Overview

The discussion revolves around the Bloch equations and their solutions, particularly in the context of magnetic resonance techniques. Participants explore the conditions under which certain equations are valid and their relationship to free precession and magnetization components as observed by a detector coil.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions whether specific equations are special solutions of the Bloch equations and seeks clarification on the conditions for their validity.
  • Another participant confirms that the equations in question represent free precession when no RF is being transmitted.
  • A follow-up inquiry seeks to confirm the validity of the equations after a 90° excitation pulse, which is affirmed by another participant.
  • There is a discussion about the lower three solutions being related to the magnetization component from the perspective of the detector coil, with a participant seeking confirmation on this point.
  • Clarifications are made regarding the assumptions of the solutions, including that spins are on-resonance and the longitudinal magnetization being zero immediately after a 90° RF pulse.

Areas of Agreement / Disagreement

Participants generally agree on the relationship between the equations and the Bloch equations, as well as the conditions under which they hold. However, there are nuances regarding the assumptions made in the solutions that remain open for further discussion.

Contextual Notes

Limitations include assumptions about resonance and initial conditions, which may affect the applicability of the discussed solutions. The discussion does not resolve all aspects of these assumptions.

Derbyshire
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Hello all,

I have a question about the relationship between
1691101354726.png

1691101337116.png

resp.
1691101317270.png


and the Bloch equations
1691101375370.png
.

Are these upper equations special solutions of the Bloch equations? If yes, under what condition(s) do the solutions hold?

Thanks in advance for helpful support!
 
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Yes, those are the free precession equations. They apply when there is no RF being transmitted.
 
Thank you. So the upper 5 equations are valid e.g. after the end of a 90° excitation pulse as long as no further RF pulse is irradiated?
 
Derbyshire said:
Thank you. So the upper 5 equations are valid e.g. after the end of a 90° excitation pulse as long as no further RF pulse is irradiated?
Yes, that is right
 
Thanks Dale,

one more question: i assume that the lower three solutions are the magnetization component from "view" of the detector coil, right?
 
Thanks!
 

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