MR TRACKING METHODS Dr. Dan Gamliel, Dept. of Medical Physics, Ariel University Center in Samaria

MR TRACKING METHODS

Dr. Dan Gamliel, Dept. of Medical Physics,

Ariel University Center in Samaria

Overview

• Nuclear Magnetic Resonance (NMR)

• Magnetic Resonance Imaging (MRI)

• Magnetic Resonance Motion Effects

• Magnetic Resonance Tracking Methods

The NMR method • Nuclear Magnetism

• Macroscopic magnet: collection of magnetic moments

• single magnetic moment: electric current loop

• nuclear or electronic magnetic moment: from (orbital + spin) angular momentum

• non-zero nuclear moment: with Pauli principle - usually odd number of nucleons

1H , 13C, 17O , 23Na , 31P , …

(non-zero spin)

The NMR method• magnetic moment in external field

• Classically:Energy term of magnetic moment in external magnetic field:

Larmor Precession of magnetic moment around direction of external field

)cos( BU

Bdt

d

The NMR method• magnetic moment in external field

• Quantum mechanically:Splitting of energy levels

For S = ½ (e.g., 1H nucleus):

Each type of nucleus has its value(= = Zeeman frequency)

Longitudinal projection of spin angular momentum

“spin” = nuclear magnetic moment

00 2

1

2

1BhhE

The NMR method• Effect of time dependent transversal field

• Static (constant) magnetic field: B0 = B0 z Generates net magnetization along Z - parallel to static field (longitudinal direction)

• Time dependent magnetic field:B1 = B1 cos( t) x (transversal = perpendicular to static field)

• Effect of time dependent field: Excitation of transitions between energy levels of static field – rotates some spins from Z direction to XY plane (or to the –Z direction)

The NMR method

• The resonance phenomenon

• For static field, transition (or precession) frequency is B0 (typical: 107 – 108 Hz)

• For time dependent field, strength (amplitude) is equivalent to B1 (typical: 103 Hz)

• The excitation is effective only if | (close to resonance)

1

01

201

20

)(

)(

T

MMMM

dt

d

T

MMMM

dt

d

T

MMM

dt

d

zyz

yxzy

xyx

Classical Bloch equations:

precession and decay

The NMR method

• The energies

Transition frequencies

for a single atom:

• Nuclear or electronic processes rays, X rays)

~ 1018 - 1020 Hz

• Chemical processes – electronic transitions (visible – UV): ~ 1014 – 1017 Hz

• Nuclear magnetic transitions (NMR): ~ 107 – 109 Hz

(RF - radio frequencies - range)

The NMR method• The importance of resonance

• Net magnetization depends on population difference between “parallel” and “anti-parallel” • The population difference depends on the Boltzmann factor for the energy difference• At room temperature:

exp(- h / kT) ~ 10-5

- very small net magnetization (paramagnetic) in the strong static magnetic field

- For a sufficient signal: need- resonance effect- a large (macroscopic) sample

The NMR method• Modes of operation

• CW (continuous wave) (frequency domain):

- Constant static field (constant resonance value)

- “sweep” over oscillation frequency of the time-dependent field

- Measure signal for each oscillation frequency :

resonance peak at

• Pulsed operation (time domain experiment):

- Constant static field (constant resonance value)

- Operating the time-dependent field for a short time, exactly needed to rotate magnetization from the Z axis to the XY plane - Measure the signal for many time values do a Fourier transform from t to get the same resonance graph !

NMR method

• Relaxation of magnetization

After time dependent field stops operating: spins return gradually to original state

• Thermal equilibrium (final) relaxation – for longitudinal magnetization

- T1 time constant

Earlier change – signal decay:• Loss of coherence – for transversal magnetization - T2 time constant (partial relaxation)• T2 with field inhomogeneity

– T2* time constant

The NMR method

• the change in magnetization due to relaxation

Transversal magnetization decays as MXY ~ exp(- t / T2 )

Longitudinal magnetization recovers as MZ ~ M0 (1 – exp(- t / T1 )

The NMR method• The resonance graph (CW or pulsed method)

Time domain signal (pulsed method):Mx + iMy ~ exp{-i(t – t / T2 }

The peak of the frequency domain graph: at

2

1

T

The width at half the peak height:

NMR pulse sequences

• Typical experiments (pulsed method)

Overall structure of pulse sequence:

Preparation – e.g. inversion

Excitation – cause change of state

Evolution – e.g. refocusing or other pulses

Detection – measurement of signal (as a function of time)

Data processing (Fourier transform)

NMR pulse sequences

• Typical experiments (pulsed method)

Essential steps:

• Excitation (by an RF “90º pulse”– rotating magnetization)

• Measurement of signal as a function of time

• Fourier transform of signal from time to frequency

Some additional options (with many possible combinations):

• Refocus Mxy (by an RF “180º pulse”) – to undo T2* decay - “spin echo” experiment

• Invert Mz (by an RF “180º pulse”)

• Add a changeable time interval before another pulse

NMR pulse sequences

• Typical results (spectrum: signal vs. frequency)

This is the spectrum of a sample containing two types of chemical groups – in each group the hydrogen nucleus has a different resonance frequency.

In addition, interactions between spins cause splitting of each resonance to several spectral lines

NMR Experimental system

• Superconducting magnet

(cooling – liquid nitrogen, liquid helium)

• Transmitter/ receiver

• Spectrometer

NMR

• Main applications

• Main nucleus: 1H (water, lipids, …)

• Study chemical structure by:

- chemical environment of atom

- interactions between atomic nuclei

• Study dynamic processes involving spins:

- diffusion processes

- exchange processes

• Study details of structure and processes by special pulse sequences

The MR Imaging (MRI) method• Transmission of NMR frequencies in body

• X-ray images of human body are possible because X-rays are (partly) transmitted through the human body

• Also RF waves are partly transmitted through the body ! - The following graph shows absorption of electromagnetic radiation in the human body – as a function of wavelength

The MRI method• Background – other medical imaging modalities

• Optical images (visible light): reflection and diffraction

good resolution in diffraction (short wavelength)

high contrast (absorption differences)

• X-ray images: transmission and diffraction

good resolution in CT (beam collimation)

contrast: absorption differences and contrast materials

• Nuclear medicine: emission from radionuclide

low resolution, low contrast

very good functional information

The MRI method• Problems for NMR imaging

Needed: • spatial resolution • contrast

Problem for resolution:• In optical images: resolution ~ wavelength (very short) – but NMR wavelength ~ 1 meter !• In X-ray images: resolution ~ focusing of beam – difficult for NMR wavelength

Problem for contrast:• Water density in body – similar in different tissues

The MRI method• Solution for spatial resolution

Spatial dependence of resonance frequency by modification of “static” magnetic field:

B0 Bz = B0 + Gz (t) z + Gy (t) y + Gx (t) x }

• During excitation pulse: slice selectionGz z-dependent excitation resonance

• During signal readout (sampling): frequency encoding Gx x-dependent readout resonance

(many time points for resolution)• Between excitation and readout: phase encoding

Gy y-dependent added phase (many repetitions of sequence with different phase)

TE

TR

The MRI method• Basic pulse sequence

• Excitation, field gradients, signal readout with two time parameters:

TE, TR

• initial dephase in view axis – for (k-space) symmetry around echo

The MRI method• Solution for image contrast

• TE (Time to Echo) = time from excitation to (refocusing moment of) readout

= time for decay of signal -

determines contrast by T2 differences between tissues

• TR (Time to Repeat) = time from excitation to next excitation

= time for return of magnetization to equilibrium -

determines contrast by T1 differences between tissues

• Relative density of 1H (“proton density”) – minor contrast factor, useful in some applications


Some typical values (times in ms):

Tissue T1 (0.5 T) T1 (1.5 T) T2 proton density

grey matter 680 1130 100 10.6 %

white matter 450 720 90 10.6 %

skeletal muscle 560 1180 34 9.3 %

liver 360 720 60 9.7 %

Blood 200 1200 30(v)-250(a)

Fat 200 260 60 9.6 %

tumors (longer) (longer)


Signal amplitude vs. time for two tissues with different T2 values

Recovery of MZ after excitation for two tissues with different T1 values

The MRI method• Useful timing combinations for image contrast

1. short TE, long TR (TE << T2 and TR >> T1 ): little decay, "full relaxation" - "proton density" contrast -

signal increases with spin density

2. long TE, long TR (TE ~ T2 and TR >> T1 ): much decay, "full relaxation" - T2 contrast

signal increases with T2

3. short TE, short TR (TE << T2 and TR ~ T1 ): little decay, little relaxation - T1 contrast signal decreases when T1 increases

(Note: T2* replaces T2 where appropriate)

• Advantages:- Non-ionizing radiation (unlike CT and NM)- Many different contrasts available (various pulse

sequences - T1, T2, spin density, static tissue, blood vessels, …)

- No limitation on imaging plane (same as in CT)- Both anatomic and (more limited) functional information

The MRI method• Clinical utility

• MRI systemSuperconducting magnetGradientsTransmit/receive system + coils


• Some images:


• Top left:

T1 contrast

(useful to distinguish tumors)

• Top right:

T2 contrast

(anatomic detail)

• Some images (Joseph Hornak – online course):


• Measured signal (in “k-space”) – without relaxation:

• Reconstructed image (spin density) – without relaxation:

The MRI method• Measured signal and image reconstruction

dydxeeyxkkS ykixkiyx

yx 22,,

yx

ykixkiyx dkdkeekkSyx yx 22,,

tGk xx 2

yy Gk2

MRI techniques (examples):• Standard (grad. echo, spin echo): ~ 100 – 1000 s• Fast (fast spin echo, FLASH, etc.): ~ 50 s • Very fast (EPI, single shot FSE etc.) ~ 0.1 s – 0.5 s

Internal motion in body (examples):• Respiratory cycle ~ 2 – 4 s• Cardiac cycle ~ 1 s• Gastro peristaltic motion cycle ~ 10 - 20 s• blood velocity ~ 0.1 - 1 m/s

The MRI method• Time scales in imaging and in internal motion

Some motion effects:

• Some spins feel only early part of “imaging sequence”• Some spins feel only late part of “imaging sequence”

• Some spins acquire a time dependent phase, reconstructed as a “change in position“. Example:

x(t) = x0 + v t (time dependent phase)

MR Motion Effects• Phase change due to motion

dtGtvdtGxdtGx xxx

222 0

Some ways of avoiding motion artifacts:

• Change gradient pattern in pulse sequence to compensate for common motion effects (blood motion)

• Cardiac/peripheral (ECG) gating• Respiratory gating (bellows)• Breathholding• Fast pulse sequence• Tagging (e.g. cardiac)• Dynamic correction using “navigator”

• Spatial “suppression” of moving region in image

MR Motion Effects• Avoiding motion artifacts

MR Tracking MethodsThe need for tracking a position

• Compare stages in time change in anatomic structure

• Interventional procedure:

- imaging while operation is being carried out

- follow position of instrument (e.g. needle)

- follow changes in anatomic region

MR Tracking MethodsUsing External Markers

• External Markers:

markers seen in MR image, placed in known positions

reference points for position of special object (e.g. needle)

reference points for position of relevant anatomic region

employs simple and accurate calculations

enables directing treatment to desired location

requires: “static” region


• Scan for locating external markers:

Fast, short TE (gradient echo type)

geometrical information used for operation

example:

locating ultrasound transducer during

Focused UltraSound ablation of tissue


• A possible way to monitor (with MRI) temperature of ablated region:

Chemical shift (change in resonance frequency) depends on temperature

temperature difference off-resonance difference

phase difference:

B t

temperature mapping

MR Tracking MethodsUsing Navigator Pulse Sequence

• For a “dynamic” region (large motion – mainly breathing):

must follow region dynamically

• Navigator Pulse Sequence:

Sequence generates partial image data (e.g. a straight line)

– to mark a specific anatomic structure (e.g. diaphragm)

reference for position of relevant region (e.g. liver)


• Using reference image:• Take a reference image(s)• Check correlation of specific image with a reference image• Check cross- correlation between images

• Using a navigator sequence:• Run a reference navigator• Run navigators between some of the repetitions of the main

pulse sequence• Check correlation between reference navigator and a current

navigator, correct current image


• (Commercial sequence)

• The Cardiac Navigator feature combines a cardiac gated, 3D Fast GRE or 3D FIESTA sequence with a navigator pulse that tracks the motion of the diaphragm. By placing the navigator tracker pulse over the right hemi-diaphragm, the acquisition is synchronized to the end-expiration respiratory phase of the patient thus minimizing respiratory ghosting artifacts.

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MR TRACKING METHODS Dr. Dan Gamliel, Dept. of Medical Physics, Ariel University Center in Samaria