HL Chemistry - Option A :

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16 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

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MAGNETIC RESONANCE IMAGING

HL Chemistry
-

Option A :


Modern Analytical Chemistry

Overview of MRI


1) Put subject into large magnetic field


2) Transmit radio waves into subject [2~10 ms]


3) Turn off radio wave transmitter


4) Receive radio waves re
-
transmitted by subject
0


5) Convert measured RF data to image

Many factors contribute to MR
imaging


Quantum properties of nuclear spins


Radio frequency (RF) excitation properties


Tissue relaxation properties


Magnetic field strength and gradients


Timing of gradients, RF pulses, and signal
detection

MRI uses a combination of Magnetic
and Electromagnetic Fields


NMR measures
magnetization

of atomic nuclei in the presence
of magnetic fields


Magnetization can be manipulated by manipulating the
magnetic fields (this is how we get images)


Static

magnetic fields don’t change (< 0.1 ppm / hr):


The main field is static and (nearly) homogeneous


RF

(radio frequency) fields are electromagnetic fields that
oscillate at radio frequencies (tens of millions of times per
second)


Gradient

magnetic fields change gradually over space and can
change quickly over time (thousands of times per second)


Radio Frequency Fields



RF electromagnetic fields are used to manipulate the
magnetization of specific types of atoms



This is because some atomic nuclei are sensitive to
magnetic fields and their magnetic properties are tuned to
particular RF frequencies



Externally applied RF waves can be transmitted into a
subject to perturb those nuclei



Perturbed nuclei will generate RF signals at the same
frequency


these can be detected coming out of the subject


MRI

X
-
Ray, CT

Electromagnetic Radiation Energy

What kinds of nuclei can be used for NMR?


Nucleus needs to have 2 properties:


Spin


charge


Nuclei are made of protons and neutrons


Both have spin ½


Protons have charge


Pairs of spins tend to cancel, so only atoms with
an odd number of protons or neutrons have spin


Good MR nuclei are
1
H,
13
C,
19
F,
23
Na,
31
P

Hydrogen atoms are best for MRI


Biological tissues are predominantly
12
C,
16
O,
1
H,
and
14
N


Hydrogen atom is the only major species that is
MR sensitive


Hydrogen is the most abundant atom in the body


The majority of hydrogen is in water (H
2
O)


Essentially all MRI is hydrogen (proton) imaging

Nuclear Magnetic Resonance Visible Nuclei

Why do protons interact with a
magnetic field?


Moving (spinning) charged particle
generates its own little magnetic field


Spinning particles with mass have angular
momentum

A Single Proton

+

+

+

There is electric charge

on the surface of the
proton, thus creating a
small current loop and
generating magnetic
moment
m
.

The proton also
has mass which
generates an

angular
momentum

J

when it is
spinning.

J

m

Thus proton “magnet” differs from the magnetic bar in that it

also possesses angular momentum caused by spinning.

Angular Momentum

J

= m
w
=m
v
r

m

v

r

J



m

=
g

J



g

is the gyromagnetic ratio

g

is a constant for a given nucleus

The magnetic moment and angular
momentum are vectors lying along the
spin axis



Magnetic field
B

and magnetization
M

are
vectors
:



Quantities with direction as well as size



Drawn as arrows ....................................



Another example: velocity is a vector (speed is its size)


Vector operations:


dot product AB cos
q


cross product AB sin
q


Magnetic field exerts torque to line magnets up in a
given direction



direction of alignment is direction of
B



torque proportional to size of
B

[units=
Tesla, Gauss=
10

4

T]


Vectors and Fields

How do protons interact with a
magnetic field?


Moving (spinning) charged particle
generates its own little magnetic field


Such particles will tend to line up with external
magnetic field lines (think of iron filings
around a magnet)


Spinning particles with mass have angular
momentum


Angular momentum resists attempts to change
the spin orientation (think of a gyroscope)

Net Magnetization

Bo

M

T
B
c
M
o

Net magnetization


Small
B
0

produces small net magnetization
M


Larger
B
0

produces larger net magnetization
M
,
lined up with
B
0


Thermal motions

try to randomize alignment of
proton magnets


At room temperature, the population ratio of anti
-
parallel versus parallel protons is roughly 100,000
to 100,006 per Tesla of
B
0

The Energy Difference Between

the Two Alignment States


D

E = 2
m
z

B
o


D

E


h

n




n  g
/2
p B
o


known as Larmor frequency


g
/2
p
= 42.57 MHz / Tesla for proton

Resonance frequencies of common nuclei

To measure magnetization we
must perturb it


Need to apply energy to tip protons out of
alignment


aligned with magnetic field is lowest energy


aligned opposite magnetic field is next lowest
energy state


Amount of energy needed depends on
nucleus and applied field strength (Larmor
frequency)


The Effect of Irradiation to the Spin
System

Lower

Higher

Spin System After Irradiation



If
M

is not parallel to
B
, then it precesses clockwise around

the direction of
B.


“Normal” (
fully relaxed
)

situation has
M

parallel to
B
, and
therefore does not precess


Precession

This is like a gyroscope

Derivation of precession frequency

This says that the precession frequency is the

SAME as the larmor frequency



=
m

×

B
o



= d
J

/ dt

J =
m
/
g


d
m
⽤琠㴠
g

(
m

×

B
o
)

m
(t) = (
m
xo
cos
g
B
o
t +
m
yo
sin
g
B
o
t)
x

+ (
m
yo
cos
g
B
o
t
-

m
xo
sin
g
B
o
t)
y

+
m
zo
z


RF Coil: Transmitting
B1

Field


To tip spins in the static
B
0

field we apply (transmit)
a magnetic field
B
1

that fluctuates at the precession
frequency and points perpendicular to
B
0

(how do we
achieve this?


by making a coil)



The effect of the tiny
B
1

is


to cause
M

to spiral away


from the direction of the


static
B
0

field



B
1

10

4

Tesla



If
B
1

frequency is not close to


resonance,
B
1

has no effect

NMR signal decays in time


T1 relaxation


Flipped nuclei realign with the magnetic
field


T2 relaxation


Flipped nuclei start off all spinning
together, but quickly become incoherent (out of phase)


T2* relaxation


Disturbances in magnetic field (magnetic
susceptibility) increase rate of spin coherence T2
relaxation


NMR signal is a combination of the total number of nuclei
(proton density),
minus

the T1 relaxation and T2 relaxation
components

Different tissues have different
relaxation times

Relaxation times are important
for generating image contrast


T1
-

Gray/White matter


T2
-

Tissue CSF


T2*
-

Susceptibility (functional MRI)

MRI Scanner

Things needed for a typical MRI scanner


Strong magnetic field, usually from
superconducting magnets.


RadioFrequency coils and sub
-
system.


Gradient coils and sub
-
system.


Shimming coils and sub
-
system.


Computer(s) that coordinate all sub
-
systems.

MRI scanner components

Diagram of a MRI Scanner System

1.
Magnet

-

The patient/subject is placed in a magnet which creates a uniform magnetic field in order to
align the hydrogen nuclei (protons) of water and fat.

2.
Gradient Amplifiers

-

Introduce precise changes in the magnetic field in order to localize the image slice
and to phase
-
encode Fourier space. There are three, one for each axis: x, y, and z.

3.
RF Transmitter

-

Sends radio waves whose energy equals the Larmor frequency of the nuclear spin

4.
A
-
D converter

-

Takes the signal received from the RF amplifier and converts it into a digital signal,
which is then sent to the computer to be viewed as an image.

5.
RF Amplifier

-

Amplifies the NMR signal from the patient. Taken from the RF coils, and is then relayed
to the A
-
D converter.

6.
Computer

-

Basically runs the show. It tells what to transmit, at what frequency, and reconstructs the
digital signal into an image.


More Detailed Diagram

MRI System

Gradient Coil Construct


Gradients impart a ‘linear’ and
predictable variation within the
‘bore’ of the magnet to create
spatial (frequency and phase)
encoding in the sample



Left


a photo of a gradient ‘set’
and the diagrams of the coil
winding orientations

A

B

RF coils

Image taken with a surface
coil

Phased
-
Array Coil


Litz Coil



Using NMR signals for imaging


Need to prolong and amplify the
decaying signal


Need to know the spatial location of the
tissue generating the signal

The decaying NMR signal can be
recovered by realigning spins

Spin Echo

Imaging

Gradient Echo

Imaging

Spatial location is identified by using
spatially varying magnetic fields

Proton resonance with

uniform magnetic field

Proton resonance with

axial field gradient

It is actually spatial frequency, not
physical location, that is scanned



Gradients cause spins to spread out and realign at


different times



Bands of tissue with uniform spacing will realign


together



MRI scanning systematically samples the strength


of the signal at different spatial frequencies

Horizontal sampling (Kx)

Vertical sampling (Ky)

MRI scanner collects spatial
frequency data (in k
-
space)

Horizontal spatial frequency density

Vertical

spatial

frequency

density

A 2
-
dimensional Fourier transform
mathematically converts from spatial
frequency to reconstructed MRI images

The versatility of MRI arises from the
different types of tissue contrast that can
be generated by manipulating parameters


TR


adjusting the time between acquisitions affects T1
relaxation


TE


adjusting the time between refocusing pulses
affects T2 and T2* relaxations


Timing of gradients affects sampling


Additional gradient pulses before the RF pulse can
enhance specific tissue properties


Chemical agents can further enhance image contrast