Basic principles and application in MedicineBasic principles and application in Medicine

October, 2008 J.Brnjas-Kraljević

6 October 20036 October 2003The Nobel Assembly at Karolinska Institutet has today decided to award The Nobel Prize in Physiology or has today decided to award The Nobel Prize in Physiology or Medicine for 2003 jointly toMedicine for 2003 jointly to Paul C Lauterbur Paul C Lauterbur and and Peter MansfieldPeter Mansfieldfor their discoveries concerningfor their discoveries concerning "magnetic resonance imaging" "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.

GlossaryGlossary

magnetic field – field intensity – tesla (T) Earths magnetic field <70 T – in medicine 0,5 – 3,0 T homogeneoushomogeneous – the same intensity in each space point

constantconstant – unchangeable intensity upon time radiofrequentradiofrequent – frequency of regular change of

magnetic field intensity, in medicine 100 kHz – 10 GHz field gradientfield 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)

pulsepulse – 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

nuclear spinnuclear 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 momentmagnetic moment – physical parameter - the measure of magnetic properties of nuclei with spin; the base of NMR

resonanceresonance – process of maximal energy transfer between

two systems – described by characteristic frequencycharacteristic frequency relaxationrelaxation – processes by which the excited system is

after ending of perturbation returned to the ground energy state – described by characteristic timecharacteristic time

Magnetic ResonanceMagnetic 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

- resonantresonant absorptionabsorption - the processes of returning to the equilibrium are followed – relaxationrelaxation emissionemission

if the structure of molecules is determined - it is spectroscopy methodspectroscopy method

in medical diagnostic - as spectroscopyspectroscopy (MRS) or as imagingimaging (MRI)

HistoryHistory 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

What is NMR ?What is NMR ? What is MRI?What is MRI? What is fMRI?What is fMRI? What is looked at, what is seen, what is What is looked at, what is seen, what is

measured?measured? How is it measured?How is it measured?

We are interestedWe are interested inin

wwe measuree measure

cell macromoleculesand water

watermolecules

watermolecule Hydrogen

atomHydroge

n nucleus

volume of

heterogenic tissue

Interaction of the Interaction of the nuclear magnetic moment of nuclear magnetic moment of

hydrogenhydrogenand magnetic fieldand magnetic field

hydrogen nucleus has spin – its magnetic properties are described by

magnetic moment,magnetic moment, , , and intrinsic magnetic field

in external magnetic field magnetic moment experience two possible states: parallelparallel or antiparallelantiparallel 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

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

kT

E

eN

N

21

21

0B

B0M0

nono magnetic field magnetic field

- randomly oriented magnetic moments - no macroscopic macroscopic magnetizationmagnetization

homogeneous, constant homogeneous, constant magnetic field Bmagnetic field B00

more magnetic moments are in the magnetic field direction - macroscopic magnetizationmacroscopic magnetization in the direction of B0 field is measured

Very important: nuclei, atoms or molecules are not oriented, but magnetic moments!

It can be visualized like:

ordered state of equilibrium system in the magnetic field is described by - macroscopic magnetizationmacroscopic magnetization in the direction of the magnetic field

process of resonance 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

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 magnetizationmacroscopic magnetization is bigger for bigger difference

quant energy h will be absorbed if E =

h

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

Theory – quantum physicsTheory – quantum physics

nucleus number of

protons  neutrons

spin    / MHz/T

11HH 1  0  1/2 99,98   42,58 2H 1  1 1 0,015   6,54 31P 0 1    17,25 23Na 2 1  3/2 11,27 14N 1  1   1 3,08 13C 0 1    10,71 19F  0 1    40,08 

1/2

1/2

100

1,11

100 0,015

0,0004

0,0024

0,094

abundance biologicalabundance

1/2 100

0,63

Properties of the nucleusProperties of the nucleus

natural abundance - fraction of isotope in the elementbiological abundance – fraction of the element in the tissue

Resonance conditionResonance condition

states separation: E = E E = E+1/2+1/2 - E - E-1/2 -1/2 depends on external magnetic field

by absorption of energy quant higher energy state

basic relation of magnetic resonance

= = B B00

– Larmor frequency

02

hE B

02

hEh B

Radiofrequent magnetic field Radiofrequent magnetic field BB11 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

BB11

B0

M0

= = cconst.onst. 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

BB0 0 = const.= const. different nuclei have

different Larmor frequency, because differ

in spectra their lines are separated

BB00

by end of excitation the system returns to the equilibrium state defined by Boltzmann distribution – process of relaxationprocess 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

RelaxationRelaxation

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

QuasiclassicalQuasiclassical modelmodel

Macroscopic Macroscopic magnetizationmagnetization

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:

)(1 2121

11

N

izi

N

iziV

02

222

0 BkT12

IhNM

2121 NNN

hencehence, , macroscopic magnetizationmacroscopic 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

Appearance of transversal magnetization

in equilibrium no transversal magnetization,transversal magnetization, MMxyxy, 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 < M0

Mz M0

Mxy

z

x

y

B0

B1

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

tB max1

Characteristic pulsesCharacteristic pulses

/2 pulse

magnetization is rotated in Y-axis

pulse

magnetization is rotated in Z -axis

max12

2

Bt

z

x

y

z

x

y

max1Bt

Chemical shiftChemical 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

BBeff eff = B= B00 - B - Blocloc = B = B00 (1- (1- )) - shielding - depends on chemical composition of molecules

of observed nuclei effective field is always smaller than B0, because of

diamagnetic effect of electron

effeff = = (B(B0 0 - B- Blocloc)) 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)

dtans

measdtans

610

chemical shift in water and fatchemical 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 fieldsignal area is proportional to the number of resonating nuclei

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 spectroscopy in vivoin vivo

BB0 0 - B- Blolocc))

CHCH2

CH3

frekvencija/ Hz

CH

CH2

CH3

Relaxation processes –Relaxation processes – relaxation times 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

Spin-lattice relaxation - TSpin-lattice relaxation - T11

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

TT1 1 depends on temperature and viscosity of surrounding – it is the depends on temperature and viscosity of surrounding – it is the measure of molecular motionmeasure of molecular motion

tissues have different Ttissues have different T11

kT

a

3

4 3

c

Determination of TDetermination of T11 - - ---

/2/2 applying pulse longitudinal magnetization is changed from - M0 to + M0 :

T1 is determined from

1210

Tt

z eMtM

T1

M0(1-2e-1)

e

MMTM z

001 2)(

applying /2 pulse longitudinal magnetization increases from 0 to +M0

T1 is determined from

110

Tt

z eMtM

e

MMTM z

001 )(

Inversion recovery - IRInversion recovery - IR

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 = S = kk r ( 1 - 2e r ( 1 - 2e-TI/T1-TI/T1 ) ) and after repetition

S = S = kk r ( 1 - 2e r ( 1 - 2e-TI/T1-TI/T1 + e + e-TR/T1-TR/T1) ) TR – time of repetitionTI – time between pulses

TI

signal

//22 pulsa 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

11 T

TR

ekS

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

Spin-spin relaxation - TSpin-spin relaxation - T22

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 Ttissues have different T22

for each nucleus in certain surrounding T2 T1

Determination of TDetermination of T22

applying /2 pulse the disappearance of transversal magnetization is

measured

T2 is determined from

20

Tt

xy eMtM

e

MTM xy

02 )(

Spin - EchoSpin - Echo

to determine T2 most used method is spin-echo: //2,2,

signal height depends on time between pulses (TE) and on repetition time (TR)

211 TTE

TTR

eekS

TE

How is spin-echo builtHow is spin-echo built

90° pulse induces transversal magnetization

it diminishes - moments are dephasing because of different - FID

after the time interval of the 180° pulse along Y –axis induces the phase coherence again after interval of 2 this is the echo signal

Bloch equationsBloch equations clasical presentation of macroscopic magnetic moment movement in

the magnetic fields

bases for T1 and T2 calculations

Relations ofRelations of T T11 and and TT22

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

Contrasts in MRIContrasts in MRI

biological parameters are the relaxation times

T1 i T2 are main parameters for production of contrasts

by adjustment of time interval between pulses i /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

T1

A

T1

B

T2BT2A

sl.10.

TT1 1 - - source of contrastssource of contrasts

T1 difference source of contrast: sequence - - - - /2/2 - pulse flips the magnetization in Z- direction after time interval , Mz is greater for tissue with shorter T1

Mz,short> Mz,long /2 pulse flips that component into XY - plane:

Mxy,short> Mxy,long in detector coil the measured signal (S):

S(Mxy,short) > S(Mxy,long) is chosen so to satisfy Mxy,short-Mxy,long = max

TT2 2 - - source of contrastssource of contrasts

T2 difference - source of contrast: sequence /2/2 - - - -

- 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,long> Mxy,short pulse rephrases spins after - signal of spin echo – SSj j dependent on in detection coil measured signal:

Sj(Mxy,long) > Sj(Mxy,short)

must satisfy Mxyd-Mxyk= max

kj eS ~

ContrastContrast

T2T1

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

MR spectroscopy (MRSMR 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

Spectroscopy Spectroscopy in vivoin vivopoint resolved spectroscopy - - PRESSPRESS

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

Magnetic resonance Magnetic resonance instrumentinstrument

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

U

RF generator

signal

detector

B0

B1

Fourier transformFourier transform

mathematical procedure - enables differentiation of frequenciesshortens the time of signal detection enables huge number of repetition measurements