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Basic principles and application in Medicine

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Title: Basic principles and application in Medicine


1
Nuclear magnetic resonance
  • Basic principles and application in Medicine

October, 2008
J.Brnjas-Kraljevic
2
6 October 2003 The Nobel Assembly at
Karolinska Institutet has today decided to award
The Nobel Prize in Physiology or Medicine for
2003 jointly to
Paul C Lauterbur and Peter Mansfield for their
discoveries concerning "magnetic resonance
imaging"
  • Paul Lauterbur (born 1929), Urbana, Illinois,
    USA, discovered the possibility to create a
    two-dimensional picture by introducing gradients
    in the magnetic field. By analysis of the
    characteristics of the emitted radio waves, he
    could determine their origin. This made it
    possible to build up two-dimensional pictures of
    structures that could not be visualized with
    other methods.
  • Peter Mansfield (born 1933), Nottingham, England,
    further developed the utilization of gradients in
    the magnetic field. He showed how the signals
    could be mathematically analyzed, which made it
    possible to develop a useful imaging technique.
    Mansfield also showed how extremely fast imaging
    could be achievable. This became technically
    possible within medicine a decade later.

3
Glossary
  • magnetic field field intensity tesla (T)
  • Earths magnetic field lt70 ?T in medicine
    0,5 3,0 T
  • homogeneous the same intensity in each space
    point
  • constant unchangeable intensity upon time
  • radiofrequent frequency of regular change of
    magnetic field intensity, in medicine 100 kHz
    10 GHz
  • field gradient regularity in the field
    intensity changes in linear dimensions of the
    space - (T/m) in medicine is better if more
    steep 30 mT/m (0,3 mT/cm)
  • pulse is the measure of energy transfer to the
    system time interval of RF-magnetic field that
    transferees the energy on spin system and induces
    excitation

4
  • nuclear spin intrinsic property of the material
    particle describes the magnetic property of
    nuclei with odd number of nucleons, in medicine
    nuclei with spin number ½ determines number of
    possible energy states in magnetic field if ½
    than two energy states
  • magnetic moment physical parameter - the
    measure of magnetic properties of nuclei with
    spin the base of NMR
  • resonance process of maximal energy transfer
    between two systems described by characteristic
    frequency
  • relaxation processes by which the excited
    system is after ending of perturbation returned
    to the ground energy state described by
    characteristic time

5
Magnetic Resonance
  • measured are magnetic properties of atomic nuclei
    in sample placed in the strong external magnetic
    field
  • - the changes in the state of the system are
    controlled

  • - resonant absorption
  • - the processes of returning to the equilibrium
    are followed

  • relaxation emission
  • if the structure of molecules is determined - it
    is spectroscopy method
  • in medical diagnostic - as spectroscopy (MRS) or
  • as imaging (MRI)

6
History
  • 1944. F.Bloch i E.Purcell nuclear magnetic
    resonance
  • 1971. R. Damadian differentiates T1 i T2 in
    tumors
  • 1973. P.Lauterbur the first MRI
  • 1975. R.Ernst distinguishing the signals by
    phase and frequency - presentation by Fourier
    transform the base of all modern MRI
  • 1977. P. Lauterbur independent by R.Damadian
    MRI of the whole body
  • P.Mansfield echo method (EPI) 5
    min/image today 5 s/image
  • 1986. NMR microscopy resolution 10 ?m in volume
    of 1 cm3
  • 1987. EPI method cardiac cycles in real time
  • C. Dumoulin angiography - MRA
    without contrast agents
  • 1993. functional MRI
  • 1995. spectroscopy in vivo
  • 1998. combination with other imaging methods
  • 2003. N.P. to P. Lauterbur and P. Mansfield

7
  • What is NMR ?
  • What is MRI?
  • What is fMRI?
  • What is looked at, what is seen, what is
    measured?
  • How is it measured?

8
We are interested in
cell
macromolecules and water
volume of heterogenic tissue
we measure
water molecules
water molecule
Hydrogen nucleus
Hydrogen atom
9
Interaction of the nuclear magnetic moment of
hydrogen and magnetic field
  • hydrogen nucleus has spin its magnetic
    properties are described by
  • magnetic moment, ?, and intrinsic magnetic
    field
  • in external magnetic field magnetic moment
    experience two possible states parallel or
    antiparallel to the field direction we talk
    about two possible states of energy
  • the volume of hydrogen placed outside the
    magnetic field magnets are randomly oriented
    in space volume is not magnetized

10
  • the same volume in the external magnetic field
    energy states occupancy is determined by
    Boltzmann,s distribution
  • there is more nuclei parallel to the field
    volume is magnetized
  • the top of single magnetic moment precesses in
    magnetic field with Larmor frequency, because of
    giromagnetic constant characteristic for the
    nucleus

11
homogeneous, constant magnetic field B0
It can be visualized like
no magnetic field
B0
M0
- randomly oriented magnetic moments - no
macroscopic magnetization
more magnetic moments are in the magnetic field
direction - macroscopic magnetization in the
direction of B0 field is measured
Very important nuclei, atoms or molecules are
not oriented, but magnetic moments!
12
  • ordered state of equilibrium system in the
    magnetic field is described by - macroscopic
    magnetization in the direction of the magnetic
    field
  • process of resonance will be realized by energy
    equal to the difference of the two states and it
    will promote more nuclei in the higher energy
    state resulting in change of amount and
    direction of macroscopic magnetization
  • this process is realized with the energy of
    radiofrequent magnetic field - frequency being
    characteristic for the observed nucleus
  • when the RF-field frequency is equal to
    Larmor-frequency of the nucleus the interaction
    of magnetic moment and the field changes the
    Boltzmann,s distribution
  • higher the difference of occupancy in the
    equilibrium more precise are the measurements of
    the resonance

13

Theory quantum physics
  • direction of the vector or the visualization
    of two possible energy states of magnetic moment
    in B0 field
  • difference in occupancy is bigger for the field
    of higher intensity
  • macroscopic magnetization is bigger for bigger
    difference

  • quant energy hn will be
    absorbed if DE hn

  • that is the value of the field where
    the signal is measured

14
Properties of the nucleus
biological abundance
abundance
0,63
0,0024
1/2
100
100
0,0004
100
0,015
1,11
1/2
0,094
1/2
natural abundance - fraction of isotope in the
element biological abundance fraction of the
element in the tissue
15
Resonance condition
  • states separation D E E1/2 - E-1/2
    depends on external magnetic field
  • by absorption of energy quant higher
    energy state
  • basic relation of magnetic resonance
  • ? ? B0
  • ? Larmor frequency

16
Radiofrequent magnetic field B1
  • resonance absorption of time dependent magnetic
    field energy

  • B1(t)B1maxis sin ?t
  • B1 is perpendicular to B0, and magnetic induction
    is 10-4 B0
  • B1 frequency Larmor frequency of atomic nucleus

B0
M0
B1
17
g B0
  • g const.
  • the same nuclei have different Larmor frequency
    if in different magnetic fields
  • if the inhomogeneity of the field is controlled
    the base of NMR as imaging method
  • B0 const.
  • different nuclei have different Larmor
    frequency, because g differ
  • in spectra their lines are separated

18
Relaxation
  • by end of excitation the system returns to the
    equilibrium state defined by Boltzmann
    distribution process of relaxation
  • two mechanisms of relaxation both are the
    source of information on dynamic properties of
    the system
  • in magnetic resonance - 4 basic parameters
  • - macroscopic magnetization,
  • - chemical shift,
  • - relaxation time T1,
  • - relaxation time T2

19
Quasiclassical model
  • nuclear magnetic moment bar magnet
  • B0 0 because of Brownian motion randomly
    oriented
  • B0 ? 0 - magnetic moments precess with Larmor
    frequency around field direction more are in
    Z, less in Z direction
  • phase of precession are different macroscopic
    magnetization is in magnetic field B0 direction
    no component in perpendicular plane
  • absorption of RF- field energy, forces the
    macroscopic magnetization to simultaneous
    precession about the axes of both fields
  • the motion is represented by spiral path from Z
    axis to XY plane and towards Z axis

20
Macroscopic magnetization
  • sample in B0 is magnetized
  • in the direction of magnetic field (axis Z)
    macroscopic magnetization M0 is measured -
    determined by
  • and has only longitudinal component
  • and expressed by measurable parameters

21
  • hence, macroscopic magnetization
  • increases with increasing magnetic field
    strength
  • good instruments work on higher fields
  • is inversely proportional with temperature
  • the best is to measure on law temperatures,
    unsuitable in medical applications
  • depends on density of nuclear spins of interest
  • in medicine hydrogen from water molecules
    (free or bound) and there is plenty of them in
    tissues or hydrogen in fat

22
Appearance of transversal magnetization
  • in equilibrium no transversal magnetization, Mxy,
    because of different precession phases of
    magnetic moments
  • the action of magnetic field B1 forces the
    equalization of the phases and the appearance of
    transversal magnetization
  • because of resonance energy absorption the
    longitudinal component is decreasing, Mz lt M0

z
B0
Mz
M0
y
B1
Mxy
x
23
  • in NMR experiment always transversal
    magnetization is measured as the induced
    electromotor force in detector coil
  • detector is placed in X-axis
  • amount of Mz i Mxy depends on length of field B1
    action. The angle of decline from Z is
  • the amount of energy transferred on the system by
    the radiofrequent field is named pulse

24
Characteristic pulses
  • ?/2 pulse
  • magnetization is rotated in Y-axis
  • ? pulse
  • magnetization is rotated in Z -axis

z
z
y
y
x
x
25
Chemical shift
  • observed nucleus is in B0 field not naked but in
    atom, so it feels local magnetic fields of
    surrounding electrons - mainly from own atom
  • Beff B0 - Bloc B0 (1- ?)
  • ? - shielding - depends on chemical composition
    of molecules of observed nuclei
  • effective field is always smaller than B0,
    because of diamagnetic effect of electron
  • weff g (B0 - Bloc)
  • hence, there is the shift in resonant frequency
    for the same nuclei in static magnetic field, but
    in different molecules
  • that is chemical shift, - defined by standard
    sample (ppm)

26
chemical shift in water and fat
  • difference in resonant frequency is only 1 kHz
    for 42 MHz, but enough to differ that two
    molecules
  • molecules are in the same static magnetic field
  • signal area is proportional to the number of
    resonating nuclei

27
w Dw g (B0 - Bloc)
  • intrinsic defined by chemical surrounding of
    the nucleus
  • induced defined by the surrounding of the
    molecule - solvent, pH, temperature, paramagnetic
    centers, secondary and tertiary structure in
    proteins, denaturation of proteins, different
    pathological processes
  • diagnostic value in spectroscopy in vivo

CH
CH3
CH3
CH2
CH2
CH
frekvencija/ Hz
28
Relaxation processes relaxation times
  • relaxation processes relies the energy in
    surrounding
  • decrease of system energy
  • interchange of energy among the observed nuclei
  • increase of entropy
  • both processes are determined by dynamic
    properties of the system
  • in biological systems tissue differ in relaxation
    parameters
  • processes are effective - signal of resonance is
    constantly measurable, despite the small
    difference in energy state abundance
  • processes of relaxation are random therefore
    described by exponential function with
    characteristic times
  • relaxation parameters
  • relaxation times T1 i T2

29
Spin-lattice relaxation - T1
  • energy absorbed in the spin-system is released
    into the local magnetic field induced by
    rotation of surrounding molecules
  • rotation is defined by correlation time
  • ?c 10-11 s for small molecule ?rot big
  • ?c 10-8 s for big molecule ?rot small ? ?
    (Larmor frequency)
  • in surrounding of big molecules the relaxation of
    the spin-system is faster ? T1 shorter
  • in plain water relaxation is slow ? T1 longer
  • T1 depends on temperature and viscosity of
    surrounding it is the measure of molecular
    motion
  • tissues have different T1

30
Determination of T1 - ? -t -?/2
  • applying ? pulse
  • longitudinal magnetization is changed from - M0
    to M0
  • T1 is determined from

M0(1-2e-1)
T1
31
  • applying ?/2 pulse
  • longitudinal magnetization increases from 0 to
    M0
  • T1 is determined from

32
Inversion recovery - IR
TI
signal
  • longitudinal magnetization is by 180 pulse
    turned into Z- direction and than returns to
    equilibrium value
  • by 90 pulse applied before completed relaxation
    the transversal magnetization is proportional to
    the amount of relaxed spins
  • in detector coil FID is induced
  • intensity of Fourier transform after one
    measurement is
  • S k r ( 1 - 2e-TI/T1 )
  • and after repetition
  • S k r ( 1 - 2e-TI/T1 e-TR/T1)
  • TR time of repetition
  • TI time between pulses

33
p/2 pulsa
  • magnetization is by 90o pulse rotated into XY
    plane
  • returns into equilibrium
  • in detector coil FID is measured
  • intensity of FT signal depends on time between
    pulses TR

34
T1 and T2
  • tissue T1 /s T2 /ms hydrogen density
  • CSF 0,8 - 20 110 - 2000 70 - 230
  • white matter 0,76 1,08 61 - 100 70 -
    90
  • gray matter 1,09 2,15 61 - 109 85 -
    125
  • membrane 0,5 2,2 50 - 165 5 - 44
  • muscle 0,95 1,82 20 - 67 45 - 90
  • fat 0,2 0,75 53 - 94 50 - 100

35
Spin-spin relaxation - T2
  • by termination of radiofrequency magnetic field
    action the magnetic moments interchange the
    energy
  • because of small inhomogeneities of magnetic
    field Larmor frequencies are different phases
    of precession starts to differ
  • transversal magnetization decreases exponentially
  • interchange of energy between spins is greater if
    the nuclei are closer and less movable - T2 is
    considerably shorter in solid state
  • tissues have different T2
  • for each nucleus in certain surrounding T2 ? T1

36
Determination of T2
  • applying ?/2 pulse
  • the disappearance of transversal magnetization is
    measured
  • T2 is determined from

37
Spin - Echo
  • to determine T2 most used method is spin-echo
    p/2, t, p
  • signal height depends on time between pulses (TE)
    and on repetition time (TR)

TE
38
How is spin-echo built
  • 90 pulse induces transversal magnetization
  • it diminishes - moments are dephasing because of
    different w - FID
  • after the time interval of t the 180 pulse
    along Y axis induces the phase coherence again
    after interval of 2t
  • this is the echo signal

39
Bloch equations
  • clasical presentation of macroscopic magnetic
    moment movement in
  • the magnetic fields
  • bases for T1 and T2 calculations

40
Relations of T1 and T2
  • in plain water T1 ? T2 3 s
  • tumor tissue has more water - T1 longer than for
    healthy tissues
  • in solid state T1 min - h T2 10-6 s
  • differences in relaxation times adequate for
    contrast enhancement in MRI
  • different sequences of pulses
  • necessary to repeat the sequence because the
    signals are very small
  • by good choice of field strength and sequence of
    pulses the contrast of the tissues can be amazing
    although the density of the observed tissues is
    practically the same

41
Contrasts in MRI
sl.10.
  • biological parameters are the relaxation times
  • T1 i T2 are main parameters for production of
    contrasts
  • by adjustment of time interval between pulses p i
    p/2
  • for measurements the interval producing the
    biggest difference between measured signals from
    different tissues is chosen
  • further improvement of contrasts by changing the
    intervals between sequences

T1B
T1A
T2B
T2A
42
T1 - source of contrasts
  • T1 difference source of contrast sequence ? - ?
    - ?/2
  • ? - pulse flips the magnetization in Z- direction
  • after time interval ?, Mz is greater for tissue
    with shorter T1
  • Mz,shortgt Mz,long
  • ?/2 pulse flips that component into XY - plane
  • Mxy,shortgt Mxy,long
  • in detector coil the measured signal (S)
  • S(Mxy,short) gt S(Mxy,long)
  • ? is chosen so to satisfy Mxy,short-Mxy,long
    max

43
T2 - source of contrasts
  • T2 difference - source of contrast sequence ?/2
    - ? - ?
  • - the appearance of spin echo (Hahn 1950)
  • ?/2 pulse flips the magnetization into XY- plain
  • after time interval ?, Mxy is bigger for tissue
    with longer T2
  • Mxy,longgt Mxy,short
  • ? pulse rephrases spins
  • after ? - signal of spin echo Sj dependent on
    t
  • in detection coil measured signal
  • Sj(Mxy,long) gt Sj(Mxy,short)
  • ? must satisfy Mxyd-Mxyk max

44
Contrast
T2
r
T1
tissue T1 /s T2 /ms hydrogen
density gray matter 1,09 2,15 61 -
109 85 - 125 white matter 0,76 1,08
61 - 100 70 - 90 CSF 0,8 - 20 110 - 2000
70 - 230 fat 0,2 0,75 53 - 94 50
- 100 muscle 0,95 1,82 20 - 67 45 -
90 skin 0,5 2,2 50 - 165 5 - 44
45
MR spectroscopy (MRS)
  • in medicine we use nuclei with magnetic moment -
    in characteristic molecules of tissues
  • spectral lines belong to chosen nuclei in
    different molecules or atomic groups
  • spectra display chemical shift for the small
    volume excited in the tissue
  • changes in the place and/or intensity of lines or
    the appearance of new lines point at metabolic
    and structural changes

46
Spectroscopy in vivo point resolved
spectroscopy - PRESS
  • with adequately chosen gradients of magnetic
    field B0 in X-, Y- and Z-direction we measure the
    signals from small volume
  • spectrum is display of chemical shifts
  • the concentration of single aminoacid can be
    determined
  • the structure of small volume is determined
  • in combination with imaging -fMRI

47
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48
Magnetic resonance instrument
  • constant and homogeneous magnetic field -
    electromagnet or superconductive magnet
  • in science - up to 14 T
  • in medicine up to 2,3 T
  • radiofrequent magnetic field - frequency 600 MHz,
    or 64 MHz - induced in coil
  • intensity of B1 is 10-4 B0
  • detection coil computer registration

RF generator
signal detector
B1
B0
U
49
Fourier transform
  • mathematical procedure - enables differentiation
    of frequencies
  • shortens the time of signal detection
  • enables huge number of repetition measurements
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