June 16, Signal generation and gradient fields in MRI. Maximilian Oehm. Summary of physical fundamentals. Motivation. Complex representation

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1 in MRI of Signal in MRI June 16, 2015

2 in MRI Contents of 1 of

3 in MRI of of Magnetic field B e z (few T) Splits up energy levels N+ N N ++N 1ppm M = m V B No measurement in z-direction possible Precession around B ω L = γb z Images from O. Dössel: Bildgebende Verfahren in der Medizin

4 in MRI of of RF-Pulse (MHz, 100m) with ω = ω L flips magnetization π/2-pulse rotation by π/2 xy-plane π-pulse rotation by π negative z-direction Rotating M T signal in antenna Image from O. Dössel: Bildgebende Verfahren in der Medizin

5 in MRI of of Nuclei interact with environment (quantum theory) Spin-lattice interaction longitudinal relaxation (T 1 s) Spin-spin interaction transverse relaxation (T 2 10ms) T 1 T 2 interesting material property Environment B inhomogeneous different ω L dephasing

6 in MRI of of Dephasing faster decay (T 2 1ms) (FID) 1 T 2 = 1 T T 2 Want to measure T 2 spin-echo-technique Image from O. Dössel: Bildgebende Verfahren in der Medizin

7 in MRI of of Images from O. Dössel: Bildgebende Verfahren in der Medizin

8 Signal in MRI of &content[]=hcim

9 in MRI of

10 in MRI Magnetization as a complex number of Measure M T as imaginary number M T = M x +M y i Rotation phase exponential function M T = M T exp[ (ω 0t +φ)i] Mathematics easier at one instant of time M T phase

11 in MRI Quadrature detector of U R/I = U 1 sin/cos(ω 00 t) U 2 sin((ω 00 + ω)t +φ)) 1 = U 1 U 2 2 [cos/sin( ωt +φ) cos/sin((2ω 00 + ω)t +φ)] S(t) = U R +U I i = 1 2 U 1U 2 exp(( ωt +φ)i) Image from O. Dössel: Bildgebende Verfahren in der Medizin

12 in MRI Gradient of Add small B(x) = G x x e z ω(x) = γ(b 0 +xg x ) ω D (x) = γxg x Image from S. Webb: Webb s physics of medical

13 in MRI Simple technique of B y y Gz z No relaxation considered x

14 in MRI of Selective excitation Apply G z during π/2 pulse Idea: Excite slice, push rest out of resonance QT: T 2 decay for M T T 2 A(ω) = 1+(ω ω L ) 2 T2 2 Finite pulse additional frequencies ω D Solve Bloch equations for M y = M y0 : M T (t) = i γ M y0exp[iω D t] B T (ω D )

15 in MRI Selective excitation of Images from O. Dössel: Bildgebende Verfahren in der Medizin

16 in MRI of Images from O. Dössel: Bildgebende Verfahren in der Medizin

17 in MRI Phase encoding of G y G x y z S(t) = M T (k x,k y ) = M T (x,y)exp(ω(x)t)exp(φ(y))dydx M T (x,y)exp( ik x x)exp( ik y y)dydx x

18 in MRI of After π/2 pulse before measurement Apply G y for time T y Phase difference φ = γ G y y T y S(t) = k y = γg y T y Phase encoding M T0 (x,y) exp( iγg yt y y)dydx Control k y with G y T y. To resolve y: 1 y = γ π G y,maxt y

19 in MRI Frequency encoding of After phase encoding Apply G x while measuring S(t) M T (x,y) ω D = γg x x S(t) = M T0 (x,y) exp( iγg xxt)exp( ik y y)dydx k x = γg x t Measure multiple k x Bwidth of antenna for image size L x : bwidth = γg x L x

20 in MRI Cartesian 2D sequence k y of k x 90 G z G y G x measurement

21 in MRI Cartesian 2D sequence k y of k x 90 G z G y G x measurement

22 in MRI Example for a measurement of Image from O. Dössel: Bildgebende Verfahren in der Medizin

23 in MRI Surfing through k-space k y of G x T x G y T y k x 90 measurement G z G y G x

24 in MRI of Till now did not consider relaxation Disadvantages: Signal decays Decay damping Signal reduce error, measure k-space Advantages: Additional quantities differentiate tissues

25 in MRI of T 2 of M T = M T0 (x,y) exp( T E /T 2 (x,y)) Image from O. Dössel: Bildgebende Verfahren in der Medizin

26 in MRI of T 1 of M T = M T0 (x,y) (1 exp( T R /T 1 (x,y)) Image from O. Dössel: Bildgebende Verfahren in der Medizin

27 in MRI of Proton density T 1 -weighted T 2 -weighted T R long T R short T R long T E short T E short T E long Different parameters different contrast of different tissues Strong proton-density-, T 1 - T 2 -weight all possible images Image from S. Webb: Webb s physics of medical

28 in MRI Turbo-spin-echo sequence of Image from O. Dössel: Bildgebende Verfahren in der Medizin

29 in MRI EPI sequence of Image from O. Dössel: Bildgebende Verfahren in der Medizin

30 in MRI of Measure complex signal Imaging through sequence of gradient Selected excitation: push unwanted part out of resonance Phase frequency encoding: generate natural FT Inverse FT of signal image Can measure proton-density-, T 1 T 2 weighted images Fast MRI: Turbo-spin-echo EPI sequence

31 in MRI of Thank You For Your Attention!

32 in MRI Literature of DÖSSEL, O., Bildgebende Verfahren in der Medizin. Von der Technik zur medizinischen Anwendung, Berlin, Heidelberg: Springer, 2000 WEBB, S., Webb s physics of medical, 2nd edition, Boca Raton, London, New York: CRC Press, Taylor & Francis Group, 2012 MORNEBURG, H., Bildgebende Systeme für die medizinische Diagnostik, 3rd edition, München: Publicis MCD, 1995