lecture3_nmr_parameters

lecture3_nmr_parameters - Todays Lecture 3) Mon, Oct 6:...

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A. S. Edison University of Florida 2009 Today’s Lecture 3) Mon, Oct 6: Introduction to NMR Parameters a. Review of Bloch equations b. Chemical shift—BMRB database c. J coupling—Karplus equation d. T1 e. T2
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A. S. Edison University of Florida 2009 Bloch Equations 1 0 T ) ( ) ( ) ( ) ( ) ( ) ( M t M t B t M t B t M dt t dM z r x y r y x z - - - = γ y-axis pulse x-axis pulse 2 T ) ( ) ( ) ( ) ( ) ( t M t M t B t M dt t dM y x r x z y - + = γ x-axis pulse 2 T ) ( ) ( ) ( ) ( ) ( t M t B t M t M dt t dM x r y z y x - - - = y-axis pulse In the Bloch equations, magnetic fields along the x and y axes create B 1 fields or pulses. These are typically applied for short durations, and the length of time the pulse is turned on is adjusted to give a desired rotation (such as 90 or 180 degrees).
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A. S. Edison University of Florida 2009 RF Pulses 1 0 T ) ( ) ( ) ( ) ( ) ( ) ( M t M t B t M t B t M dt t dM z r x y r y x z - - - = γ y-axis pulse x-axis pulse In our simulation of the Bloch equations, we showed that for protons ( γ =2 π *26.7*10 7 Hz/T) and a B 1 field of 9.3*10 -5 T, it takes 40 μ s to rotate the magnetization one time around the x or y axis. The relationship between “rf field strength” and pulse length is simply: ) 360 ( 1 2 1 o PW B = π
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A. S. Edison University of Florida 2009 What range of frequencies can be covered with a given rf pulse? This says that a 40 μ s 360 0 pulse will create an effective field strength ( γ B 1 /2 π ) of 25000 Hz. This relationship can also be understood from the Heisenberg Uncertainty Principle: h p x x 2245 or h 2245 t E 1 2245 τ ϖ or This tells us that we can only know the frequency of a 40 μ s pulse to within about 25000 Hz. Thus, ALL frequencies in this range are effected (but not all equally!). ) 360 ( 1 2 1 o PW B = π γ
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University of Florida 2009 What range of frequencies can be covered with a given rf pulse? Since a wide range of frequencies can be covered by a pulse, do they all behave the same? NO γ B 1 ϖ γ B 1 eff A frequency ∆ϖ from the center (carrier) rf frequency will actually experience an effective field strength given by 2 2 1 1 ) ( ) ( ϖ γ + = Β εφφ The rotation axis will also be tilted at the angle ϕ . This can cause problems! However, if γ B 1 is much larger than ∆ϖ , the problems are minimal. This is why we like short pulses. φ
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lecture3_nmr_parameters - Todays Lecture 3) Mon, Oct 6:...

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