1Thomas Liu, BE280A, UCSD, Fall 2005Bioengineering 280APrinciples of Biomedical ImagingFall Quarter 2005MRI Lecture 4Thomas Liu, BE280A, UCSD, Fall 2005RF ExcitationFrom Levitt, Spin Dynamics, 20012Thomas Liu, BE280A, UCSD, Fall 2005RF ExcitationImage & caption: Nishimura, Fig. 3.2B1 radiofrequency field tuned toLarmor frequency and applied intransverse (xy) plane inducesnutation (at Larmor frequency) ofmagnetization vector as it tipsaway from the z-axis. - lab frame of referenceAt equilibrium, net magnetizaionis parallel to the main magneticfield. How do we tip themagnetization away fromequilibrium?http://www.eecs.umich.edu/%7Ednoll/BME516/Thomas Liu, BE280A, UCSD, Fall 2005Images & caption: Nishimura, Fig. 3.3a) Laboratory frame behavior of M b) Rotating frame behavior of Mhttp://www.eecs.umich.edu/%7Ednoll/BME516/3Thomas Liu, BE280A, UCSD, Fall 2005Nishimura 1996€ B1(t) = 2B1(t)cosωt( )i= B1(t) cosωt( )i − sinωt( )j( )+ B1(t) cosωt( )i + sinωt( )j( )Thomas Liu, BE280A, UCSD, Fall 2005€ Rotating Frame Bloch EquationdMrotdt= Mrot×γBeffBeff= Brot+ωrotγ; ωrot=00−ω 4Thomas Liu, BE280A, UCSD, Fall 2005€ Let Brot= B1(t)i + B0kBeff= Brot+ωrotγ= B1(t)i + B0−ωγ kIf ω=ω0=γB0Then Beff= B1(t)iThomas Liu, BE280A, UCSD, Fall 2005Nishimura 1996€ Flip angleθ=ω10τ∫(s)dswhereω1(t) =γB1(t)5Thomas Liu, BE280A, UCSD, Fall 2005Nishimura 1996Thomas Liu, BE280A, UCSD, Fall 2005Nishimura 19966Thomas Liu, BE280A, UCSD, Fall 2005Slice Selectionzslicefrect(f/W)W=γGzΔz/(2π)Δzsinc(Wt)Thomas Liu, BE280A, UCSD, Fall 2005€ Let Brot= B1(t)i + B0+γGzz( )kBeff= Brot+ωrotγ= B1(t)i + B0+γGzz −ωγ kIf ω=ω0Beff= B1(t)i +γGzz( )k7Thomas Liu, BE280A, UCSD, Fall 2005Nishimura 1996Thomas Liu, BE280A, UCSD, Fall 2005€ Small Tip Angle ApproximationMr(t,z) = jM0exp(− jω(z)t) exp(0t∫jω(z)s)ω1(s)dsFor symmetric pulse of length τMr(τ,z) = jM0exp(− jω(z)τ/2) exp(−τ/ 2τ/ 2∫j2πf (z)s)ω1(s +τ/2)ds = jM0exp(− jω(z)τ/2)Fω1(t +τ/2){ }f =− f (z )=−γ2πGzz8Thomas Liu, BE280A, UCSD, Fall 2005Nishimura 1996Thomas Liu, BE280A, UCSD, Fall 2005Nishimura
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