NMR imaging

Mikael JensenAssociate professor

Dept. Mathematics and Physics

Royal Veterinary and Agricultural University

April 2002

• Non-destructive • Dynamic• In-vivo

• or

• Destructive• Static• Once in a lifetime

Why imaging

Medical use

•Røntgen

•Ultralyd

•Termografi

Veterinary use

Penetrating radiation

• X-rays (20-200 keV)• Gamma (80-511 keV)• Radiofreqency 63

MHz• Light(near infra-red)• Ultrasound

X-ray

• Show differences in electron density

• Small inherent contrast in soft tissue

• Many photons means good S/N ratio

• Good geometric resolution

• Planar ( projections )

• Can be used for tomography ( CT-scan)

• Uses ionizing radiation

Radio-isotopes (gamma radiation)

• Function more than anatomy

• Totally dependent on nature of tracer

• Few photons, high contrast

• Poor gometric resolution

• Uses ionizing radiation

Ultrasound

• Shows differences in sound velocity and density*

• Tissue borderlines

• Air-filled cavities creates shadows

• Real-time

• Cheap and safe

• Interactive* Egentlig: Forskel i akustisk impedans !

NMR – imaging (MRI)

• No ionising radiation

• Large inherent contrast in soft tissue

• Can demonstrate both anatomy and function

• Good geometrical resolution

• Expensive

• Restricted acces to patient during exam

Very good web introduction to MRI

http://www.cis.rit.edu/htbooks/mri/inside.htm

Go and read it !

NMR imagingFrequency= γ B

For protons γ= 42 MHz / Tesla

Wawelength at 1 Tesla ?Wawelength = c/f = 7 meter !

?

x

y

Bo

External magnetic field necessary for NMR

z

By convention we choose z axis along Bo

N

S

We need nuclei with magnetic moment for NMR

Could be Hydrogen in water (protons)

Nuclei 

Unpaired Protons 

Unpaired Neutrons 

Net Spin 

(MHz/T) 

1H 1  0  1/2  42.58 

2H 1  1  1  6.54 

31P 0  1  1/2  17.25 

23Na 0 1  3/2  11.27 

14N 1  1  1  3.08 

13C 0  1  1/2  10.71 

19F  0  1  1/2  40.08 

Larmor condition

When the energy of the photon matches the energy difference between the two spin states an absorption of energy occurs.  In the NMR experiment, the frequency of the photon is in the radio frequency (RF) range. In NMR spectroscopy,  is between 60 and 800 MHz for hydrogen nuclei. In clinical MRI,  is typically between 15 and 80 MHz for hydrogen imaging.

E = h  B  E = h  f

f = B (Larmor condition)

(proton)= 42 MHz/ Tesla

Boltzman StatisticsAt room temperature, the number of spins in the lower energy level, N+, slightly outnumbers the number in the upper level, N-. Boltzmann statistics tells us that

N-/N+ = e-E/kT.

E is the energy difference between the spin states; k is Boltzmann's constant, 1.3805x10-23 J/Kelvin; and T is the temperature in Kelvin.

1.000.000 1.000.001

The time constant which describes how MZ returns to its

equilibrium value is called the spin lattice relaxation time (T1).

The equation governing this behavior as a function of the time t after its displacement is:

Mz = Mo ( 1 - e-t/T1 ) 

T1 relaxation

T2 relaksation

The time constant which describes the return to equilibrium of the transverse magnetization, MXY, is called the spin-spin

relaxation time, T2.

MXY =MXYo e-t/T2

Bloch equations

Free induction decay (“FID”)

90o

Short RF pulse at Larmor frequency

Detected RF signal from nuclei

Fourier transform af FID

tid

frekvens(sted)

F

F-1

NMR in organic chemistry

CH3CH2OHAlso known asEthanol

Frequency alias ”chemical shift”

1951

1991

MRI imaging is ”broadband”

•In chemical NMR typical resolution (linewidth) is 0.1 ppm•Chemical shifts are of the order of 1- 10 ppm

•In imaging we have inhogeneous magnetic fields•In imaging we use frequncy to encode spatial position•Typical space coding 100 Hz/mm or 500 ppm/mm

f f

Pulsewidth and flipangle

pw 2pw 3pw

90o 180o 270o

Spin echo

90o 180o

TE/2 TE/2

Gradient in magnetic field

B = Bo + Gx x

Bo = 1,5 T

Gx = 25 mT /cm

Frequency coding df/dx = Gx γ =1 kHz /cm = 100 Hz/mm

Gradient

FFT

time f

Imaging of one slice

Gzz

x

y

Slice selected echo

90o

180o

Gz

Only signal from slice

Normally chosen as z-direction

Read-out gradient90o

180o

Gz

Gx

Phase encoding gradient90o

180o

Gz

Gx

Gy

Repeat this, and you got the image

n repetitions

2D FFT

n

m data points

m

Another way to do imagingSelect one slice ! Do many experiments with different directions of readout gradient

Back projection

Filtered back projection

Radon transformation ( MRI, CT, PET, Spect ….)S.R. Deans, S. RoderickThe Radon Transform and Some of its Applications.Wilwy, New York1983

Slice selective MRI by back projection

Many values

Many values

Repeat formany angles

Multi slice imaging

Inversion recovery imaging

MRI hardware

Magnet

0.015 – 0.3 Tesla Resistive0.5 – 3 Tesla Superconducting

B0

Gradients

Safety

•Static magnetic field•No metal objects•Shielding•B < 3 Tesla

•RF power deposition•Deposited power < 4 W / Kg•No hot spots•B < 3 Tesla (f < 130 MHz )

Images!

Lumbar spine MRINormal Prolaps Malignancy ?

Liver

                                                                                      

                                          

Arrows point to multiple lesions in the liver demonstrating metastases.

Tværsnit af rygmarv hos rotte

Hjernen af en stær (in vivo)

Good image archives:

NORTHEAST WISCONSIN MRI CENTERMR IMAGES

http://www.newmri.com/humanbo2.htm

RADIOLOGIC ANATOMY BROWSER™

http://rad.usuhs.mil/rad/iong/homepage.html

End of lecture

Bloch Purcell Lauterbur