MRI System Block Diagram

RFamp

spectrometer

r.f.coil gradient coil

Xamp

Yamp

Zamp

Principle of Gradient Coil

Bz

xBz

z

Isotope Spin %age I abundance MHz/T

1H 1/2 99.985 42.5752H 1 0.015 6.5313C 1/2 1.108 10.7114N 1 99.63 3.07815N 1/2 0.37 4.3217O 5/2 0.037 5.7719F 1/2 100 40.0823Na 3/2 100 11.2731P 1/2 100 17.25

Common NMR Active Nuclei

Alignment of Spins in a Magnetic Field

spin

magnetic moment

B0 field

M

M=0

Energy in a Magnetic Field(Zeeman Splitting, Spin ½)

E+1/2= B0/2 E-1/2= +B0/2P+1/2= 0. 5000049 P-1/2= 0.4999951

1.5T, T=310K, P(E)exp(E/kT)

mI = +½ mI = ½

Larmor Frequency

E+1/2= B0/2 E-1/2= +B0/2

Allowed transitions E = B0

= 0

mI = ½

mI = +½

0 = B0

Quantum Mechanical Description(Spin ½ Case)

> = a½½> + a+½+½>

I=½, 2I+1 Zeeman splittingsmI = ½

mI = +½

Mz = <Iz> = a+½2 a½2

Mxy = <Ix+ iIy>

Coupling with a B1 Field

B0

B1

Birdcage coil

A

time

Spin ExcitationM M

M

rotating frame

laboratory frame

Free Induction Decay

FT

FT

frequency

frequency

time

time

M

Free Induction DecayM

M

M

90

90

90

small positive shim mis-set

medium positive shim mis-set

large positive shim mis-set

Free Induction DecayM

M

M

90

90

90

small negative shim mis-set

medium negative shim mis-set

large negative shim mis-set

Product Operators

Mx Mx

My Mycos + Mzsin

Mz Mzcos Mysin

x

x

x

Mx Mycos Mzsin

My My

Mz Mzcos + Mxsin

y

y

y

Mx Mxcost + Mysin t t

My Mycost Mxsin t t

Mz Mz

t

r.f.

freeprecession x

yz

Bloch Equations

dMz(t) = [Mz(t) M0]dt T1

dMxy(t) = Mxy(t)dt T2

Mz

Mxy

Mz Mz

Mxy Mxy

T1 Relaxation

Mz(t) = M0 + {Mz(0) M0}exp(-t/T1)

Mz Mz

t t

saturation–recovery

inversion–recovery

dMz(t) = [Mz(t) M0]dt T1

M0 M0

Mz(0) = 0 Mz(0) = M0

Spin EchoM

M

M180

180

18090

90

90

small positive shim mis-set

medium positive shim mis-set

large positive shim mis-set

Spin EchoM

M

M180

180

18090

90

90

small negative shim mis-set

medium negative shim mis-set

large negative shim mis-set

T2 Relaxation

Mxy(t) = Mxy(0) exp(t/T2)

Mxy

t

dMxy(t) = Mxy(t)dt T2

Slice Selection

0

0time

time

frequency

frequency

FT

FT

Slice Selection

0time frequency

G