II. MRI Technology. B. Localized Information. Lorenz Mitschang Physikalisch-Technische Bundesanstalt, 29 th June 2009

Transcription

1 Magnetic Resonance Imaging II. MRI Technology A. Limitations to patial Infomation B. Localized Infomation Loenz Mitschang Physikalisch-Technische Bundesanstalt, 9 th June 009

2 A. Limitations to patial Infomation Michael Faaday Expeimental Reseaches in Electicity, London 1839

3 Electomagnetic Induction L E dl electomotive foce = d dt B d ate of change of magnetic flux U ind = dφ Φ dt negative sign indicates esistance to change Lenz s Rule

4 Basic Expeiment tansmit-eceive coil RF in signal out What signal do we get fom the voxel?

5 Pinciple of Recipocity, ignal Intensity The emf induced in a RF pobe by magnetic moment M fom a voxel ΔV at a specific position is detemined by the magnetic field amplitude B 1 at that position i when unit cuent flows though the coil, d Δ U ( B M ) ind = 1 dt B 1X cos ωt M = M sin ωt ; B1 = B1Y ; B1X = B1Y = 0 B 1Z 0 Bt maximum signal amplitude ΔUU ωm ind max 0 B t

6 Noise Noise ae stochastic ti fluctuations ti of induced dvoltage geneated dby themal motion of chages and cuents Nyquist, mean quadatic voltage U n = 4kfTR k, Boltzmann s constant f, spectal bandwidth T C, coil tempeatu R C, coil esistance T, sample/body tempeatue R, sample/body esistance signal/noise fom ΔV TR = T R + U ind max T R 1 C3 C 13 coil sample/body ωm0bt U N 4kf TCR C + T n ( R )

7 ample / Body Resistance ample in tansmiteceive cicuit causes eney loss Joule heating esistance=mean powedissipation / (mean cuent) Unit ac of fequency ω geneates B 1 which 1 R it E induces E in sample/body of conductivity σ σ = sample B 1 cos(ωt) B 1 homogeneous in small voxel ΔV dv ω E = 1 ( ) R = σω B1 dv 4 sample θ B 1 geomety facto fo coil and object

8 Coil Resistance hindeed d motion of electons in lattice of the conducto confined to skin on the suface of the coil ( skin effect ) effective coil esistance single laye solenoid L, conducte length P, conducto cicumfence μ μ 0, pemeability ρ(t C ), esistivity η=5, coection to skin-effect fo tight winding R C = ωμ μ 0 ρ ( T ) C L η 13 P P conducto cicumfence geomety facto fo coil θ C

9 Themal Equilibium Magnetization, total /N Boltzmann distibution of population of enegy levels geneates excess magnetization in themal equilibium 0 = Nγ h I(I 1)B 0 / 3kT M + Cuie law fo ambient T N, numbe of spins in ΔV γ, gyomagnetic atio I, spin quantum numbe B 0, Zeeman field stength h, Planck constant Total /N fom voxel ΔV N T C T ω ωμ Nγ h μ 0 ρθ I(I + 1) C + T σω θ 6 B t k 3 f

10 /N in NMR and MRI tandad conditions (oom tempeatue, 1 Tesla, 1 Lite physiological saline solution, solenoid, ) in vito NMR 1 H, /N~1: N~ mm 3 wate: N= in vivo MRI small sample, ~cm 3 : R C >>R lage object: R C <<R 7 / 4 ω NγI(I + 1) ~ T C T ωnγi(i + 1) ~ N N 3/ T /N inceases fast with Lamo fequency o high Zeeman field Cooling electonics hl helps ignal aveaging, heteonuclea labelling, only wate can be easonably measued Resolution limited it to ~ 1 mm 3 Resticted expeiment time, no labelling possible,

11 Hypepolaization Non-themal initial polaization may lift the limitations of MRI, /N~M 0 Dynamic nuclea polaization γ γ 660, T 1.1 K Cuie law! e / 1H p Paahydogen induced polaization ( + + ) 1 H in singlet state 100% Lase polaization Nuclea spins of 19 Xe, 3 He gain excess magnetization ~0% by collisions with optically excited Ions

12 B. Localized Infomation suface coil: high /N (small θ ), inhomogeneous, poo localization elaxation behavio: N 3, numbe of voxels T 1, longitudinal elaxation time T *, (T * ), tansvese (effective) elaxation time τ, duation of expeiment individual sampling τ ~ N 3 T 1 ~ 36 h at T 1 = 0.5 s, N=64 line wise sampling τ ~ N T 1 ~ 1/h plane wise sampling τ ~ N T 1 ~ 1/min o ~ 1/h at esolution N=56 elective excitation of the magnetization in a plane of the object.

13 Field changes linealy with position ( ) = B + G B 0 Zeeman Field Gadients Lamo fequency changes accodingly ω ( ) = γ B0 + γ G x-gadient y-gadient z-gadient Local pecession by gadient offset in otating fame: t k-space ik ( ) ( ) ( t) k() t = G( t' ) dt' M, t M,0 e γ 0 = Linea coelation of esonance/pecession fequency and spatial position

14 elective Excitation Tansvese magnetization in otating fame afte pulse of length τ, amplitude B 1 along x-axis in small flip angle appoximation M (, τ ) γ M ( ) B1 ( t ) τ γ G t 0 e dt 0 slice pofile = FT of pulse shape Gadient stength to excite slice of width ΔZ by RF pulse of bandwidth BW G = BW γδz

15 Gadient along one diection (1D): M = sample Encoding of patial Dimension ik () ( ) ( t) t M,0 e dv P() e ik ( t) = d Pojection of Magnetization along is FT of ignal as function of k. N signal samples at Δk = γg Δt Total spatial dimension esolution: FOV = patial esolution (technically): FOV/N π / Δ k and fom Nyquist Theoem: field of view Independent gadients along two diections x, y (D): ( k, k ) M ( x, y) ik ( ) ik M = e x t x y (t)y x y dxdy sampling D k-space with gadient-echo sequence

16 Relaxation times weighted local magnetization Image Contast M ( x, y) = ρ( x, y) e T e T 1 e T T1 T e white matte light, Gey matte dak T = 450 ms contast invesion white matte dak, gey matte light T = 3.3 s T

17 MR Imaging = localized detemination of MR paametes which need medical intepetation so, let s pactice