magnetic resonance imaging - epileptologieepileptologie-bonn.de/.../slambertz_mribasics.pdf · 1...
TRANSCRIPT
1
Magnetic Resonance Imaging
-the basics-
Sonja Lambertz
What is MRI?
2
medical imaging technique based on NMR
Introduction: the hydrogen atom
● 1 electron
● nucleus: 1 proton
remember: total nuclear spin
𝐼 = 𝐼 𝑖 + 𝐿𝑖𝑖
intrinsic spin: 𝐼𝑝 =1
2
● total nuclear spin of hydrogen: ½
3
4
Introduction: magnetic moment
● magnetic moment:
𝜇𝐼=𝛾𝐼 𝜇𝐼,𝑧 = ±1
2𝛾ℏ
𝛾: gyromagnetic ratio (material dependant)
γ∗ =γ
2π𝑀𝐻𝑧 𝑇
nucleus
Introduction: in a magnetic field
● Larmor frequency
𝜔0 = 𝛾𝐵0
𝜔0 ∝ MHz
● Zeeman-effect
𝐸 = −𝜇𝑧 ∙ 𝐵0
∆𝐸 = 𝛾ℏ𝐵0
7
𝜇𝑧 = −1
2𝛾ℏ
𝜇𝑧 = +1
2𝛾ℏ
Introduction: magnetization
● excess of nuclei parallel to 𝐵0:
𝑁−
𝑁+ = 𝑒 Δ𝐸/𝑘𝑇
𝑁−
𝑁+ 𝐵0 = 1 T, 𝑇 = 37°C ∝ 6,6𝑝𝑝𝑚
• causes net magnetization:
𝑀 = 𝑑𝜇
𝑑𝑉 𝑀𝑧 =
𝑁−−𝑁+ 𝜇𝑧
𝑉
𝑀𝑧 𝐵0 = 1T, 𝑇 = 37°C = 3 ∙ 10−3 A m
𝑀𝑥,𝑦 = 0 8
nuclear magnetic resonance
● apply RF-field in x-y-direction 𝐵𝑇 ∝ 1mT:
𝐵𝑥 = 𝐵𝑇 cos𝜔𝑇𝑡
𝐵𝑦 = 𝐵𝑇 sin𝜔𝑇𝑡
𝐵𝑧 = 𝐵0
● resonance condition 𝜔𝑇 = 𝜔0:
− magnetic moment forced out of equilibrium postition
10
nuclear magnetic resonance
applet:
http://www.drcmr.dk/BlochSimulator/
11
nuclear magnetic resonance
● rotating frame moving with 𝜔0 around 𝐵0:
13
No RF-Field With RF-Field
𝜔𝑇 = 𝛾𝐵𝑇
nuclear magnetic resonance
● length of pulse defines angle:
●
𝜋
2-pulse: flips 𝑀 into x-y-plane
𝜏𝜋2 ∝ 300μs 𝐵𝑇 ∝ 10−5T
14
𝜔𝑇 =𝑑𝛼
𝑑𝑡
𝛼 = 𝛾𝐵𝑇𝜏
Free Induction Decay
16
● transverse magnetization decays after RF-pulse
spin-lattice-relaxation
● longitudinal magnetization 𝑀𝑧 recovers
𝑀𝑍 𝑡 = 𝑀𝑧,𝑒𝑞 − 𝑀𝑧,𝑒𝑞 −𝑀𝑧 0 𝑒−𝑡/𝑇1
17
spin-spin-relaxation
● transverse magnetization 𝑀𝑇 decays due to
random, temporary spin-spin-interaction:
slows down speeds up
18
spin-spin-relaxation
● decay of transverse magnetization 𝑀𝑇
𝑀𝑇 𝑡 = 𝑀𝑇 0 𝑒−𝑡/𝑇2
19
𝑇2∗-decay
● in reality: transverse magnetization 𝑀𝑇 decays
with time 𝑇2∗, faster than 𝑇2:
1
𝑇2∗ =
1
𝑇2+
1
𝑇2𝑖
● additional 𝑇2𝑖 caused by inhomogenities.
𝑀𝑇 𝑡 = 𝑀𝑇 0 𝑒−𝑡/𝑻𝟐∗
20
Spin Echo
● rephasing of the spins using a 180°-pulse
22
TE=echo time
measuring 𝑇1
● use inversion recovery:
23
𝑀𝑧 𝑡 = 𝑀𝑧 0 1 − 2𝑒−𝑡/𝑇1
measuring 𝑇1
24
weighted MRIs
𝑻𝟏 𝑻𝟐 relative
proton
density
distilled water 3 s 3 s 1.0
cerebro spinal fluid 3 s 300 ms 1.0
gray matter 1.2 s 60-80 ms 0.98
white matter 800 ms 45 ms 0.80
fat 150 ms 35 ms 1.0
25
weighted MRIs
𝑇1-weighted 𝑇2-weighted proton density
weighted
26
conclusion
● static magnetic field aligns spins
● net magnetization
● transverse RF-field induces nutation of
magnetization, if 𝜔0 = 𝜔𝑇
● measurable magnetization in transverse plane
● material dependant relaxation times 𝑇1, 𝑇2 and
proton density give contrast
27
sources
● “MRI Scanner” Image from "Colour & Form Study." Colourful Language. N.p., n.d. Web. 26 Apr.
2013. <http://eleanormaclure.wordpress.com/2012/08/07/colour-form-study/>.
● “Knie MR” Image from "Magnetresonanztomographie." Wikipedia. Wikimedia Foundation, 20
Apr. 2013. Web. 26 Apr. 2013. <http://de.wikipedia.org/wiki/Magnetresonanztomographie>.
● “Nuclear Spin” Image from "Nuclear Magnetic Resonance." IMAIOS. N.p., n.d. Web. 26 Apr.
2013. <http://www.imaios.com/en/e-Courses/e-MRI/NMR>.
● “Guy in MRI” Image from "Open Air MRI and Diagnostic Imaging." Center In Amarillo Texas.
N.p., n.d. Web. 26 Apr. 2013.
<http://sites.securemgr.com/folder14715/index.cfm?fuseaction=browse>.
● “Zeeman Splitting” Image from "ThomasPomorski.com." ThomasPomorski.com. N.p., n.d. Web.
26 Apr. 2013. <http://www.personal.psu.edu/tzp124/assign6.html>.
● “Flip angle”, “FID” Images from "BME/EECS 516 Home Page." BME/EECS 516 Home Page.
N.p., n.d. Web. 26 Apr. 2013. <http://web.eecs.umich.edu/~dnoll/BME516/>.
● “Spin Echo”, “T2measurement” Images from Nuclear Magnetic Resonance. RWTH Aachen,
Feb. 2011. Web. 26 Apr. 2013. <http://institut2a.physik.rwth-
aachen.de/de/lehre/praktikum/Anleitungen/FK14-NMR_20110207.pdf>.
29
sources
● "DRCMR." Bloch Simulator for Education in MRI and NMR. N.p., n.d. Web. 28 Apr. 2013.
<http://www.drcmr.dk/bloch>.
● "BME/EECS 516 Home Page." BME/EECS 516 Home Page. N.p., n.d. Web. 28 Apr. 2013.
<http://web.eecs.umich.edu/~dnoll/BME516/>.
● Lehnertz, Klaus Prof. Dr. "Magnetresonanztomographie/Magnetic Resonance Imaging." Uni
Bonn. 2013. Lecture.
● Dossel, Olaf. Bildgebende Verfahren in der Medizin: Von der Technik zur medizinischen
Anwendung. Berlin: Springer, 2000. Print.
● Demtroder, Wolfgang. Atome, Molekule Und Festko rper: Berlin: Springer, 2005. Print.
● Demtroder, Wolfgang. Kern-, Teilchen- Und Astrophysik: Berlin: Springer, 2010. Print.
● "Nuclear Magnetic Resonance." IMAIOS. N.p., n.d. Web. 28 Apr. 2013.
<http://www.imaios.com/en/e-Courses/e-MRI/NMR>.
30
Bloch equations
𝑑𝑀𝑥′
𝑑𝑡= −
1
𝑇2∗𝑀𝑥
′ + 𝜔0 −𝜔𝑇 𝑀𝑦′ − 𝜔𝐹 sin𝜓𝑀𝑧
′
𝑑𝑀𝑦′
𝑑𝑡= − 𝜔0 −𝜔𝑇 𝑀𝑥
′ −1
𝑇2∗𝑀𝑦
′ +𝜔𝐹 sin𝜓𝑀𝑧′
𝑑𝑀𝑧′
𝑑𝑡= +𝜔𝐹 sin𝜓𝑀𝑥
′ −𝜔𝐹 cos𝜓𝑀𝑦′ −
1
𝑇1𝑀𝑧
′ −𝑀𝑧0′
31