Introduction to Biomedical Imaging - Unitat de ...afrangi/ibi/MagneticResonanceImaging.pdf · Introduction to Biomedical Imaging Magnetic Resonance Imaging MRI Principle ... Basics

Introduction to Biomedical Imaging

Alejandro Frangi, PhDComputational Imaging Lab

Department of Information & Communication TechnologyPompeu Fabra University

www.cilab.upf.edu

Introduction to Biomedical Imaging

Magnetic Resonance Imaging

Introduction to Biomedical Imaging

Magnetic Resonance ImagingMRI advantages

Superior soft-tissue contrast

– Depends on among others proton density, relaxation times

3D acquisitions possible

Free orientation of tomographic scan planes

No ionizing radiation

No iodinated contrast agent

Non-invasive

Imaging of anatomy/pathology and function

Introduction to Biomedical Imaging

Magnetic Resonance ImagingMRI Principle

Based upon: nuclear magnetic resonance

Resonance phenomenon of nuclear spins (magnetic moments of atomic nuclei) in a

strong external magnetic field

A rotating charge has an electromechanical momentum (μ) which has a direction

coincident with the rotation axis and a magnitude proportional to the angular

momentum of electrons and protons by the expression

The electromechanical momentum is known as nuclear spin

In the presence of an external magnetic field (B) all spins line up with it yielding a

net macroscopic moment (M); otherwise they are randomly distributed with no net

macroscopic momentum

Not all atoms have a zero spin. The spin is non-zero when the atom has an odd

number of protons or nucleons (p is odd or p+n is odd)

Practically speaking a spin can be seen as a kind of elemental magnet

Most important proton in the human body is Hydrogen

Introduction to Biomedical Imaging

Magnetic Resonance ImagingPrecession

Spins presses around the direction of the external field (Bo) at a frequency (Larmorfrequency) proportional to Bo

The proportionality constant is known as gyro magnetic constant

For hydrogen, γ = 42.58 MHz / T

From quantum mechanics it seems that only a limited number of spin states are possible (each with their own energy). E.g.: for H only ± 1/2

oBω = γ

Introduction to Biomedical Imaging

Magnetic Resonance ImagingNet magnetization

The spins altogether form a net magnetization vector M

M depends on the external field and the temperature

Introduction to Biomedical Imaging

Magnetic Resonance ImagingResonance phenomenon

Magnetization can be flipped toward the xy-plane by adding energy to the system by applying an RF pulse at the Larmor frequency

M-vector rotates toward the xy-plane over an angle θ (flip angle)

1B dtθ = γ∫

Introduction to Biomedical Imaging

Magnetic Resonance ImagingSituation before RF pulse

Longitudinal vs. transverse magnetization

After RF pulse only longitudinal magnetization (Mz)

Mz is static and, hence, cannot produce induction signal

Introduction to Biomedical Imaging

Magnetic Resonance ImagingSituation after RF pulse

RF perturbs the magnetization vector

Both longitudinal (Mz) and transverse (Mxy) components exist

Mxy component rotates at Larmor frequency

M is now time-varying and an induction signal can be measured with a receive coil (Free Induction Decay – FID)

Introduction to Biomedical Imaging

Magnetic Resonance ImagingRelaxation processes

The perturbation of the magnetization has a limited life-time

Relaxation returns M to its original (lower energy) state (exponentially)

Longitudinal relaxation increases Mz to M → T1 relaxation constant

Transverse relaxation reduces Mxy to zero → T2 relaxation constant

The increase of Mz can be slower than the decrease of Mxy

The nature of T1 and T2 relaxations is different!

T1 is related to spin-lattice interactions (between H protons and its surroundings)

T2 is related to spin-spin interactions (between protons themselves)

They depend on molecular structure, physical state (solid or liquid), temperature, external field strength, etc.

1/( ) (1 )t Tz oM t M e−= −

2/( ) t Txy oM t M e−=

@1.5T T1 [ms] T2 [ms]

Fat 260 84

WM 920 101

GM 790 92

Introduction to Biomedical Imaging

Magnetic Resonance ImagingWhy is MR becoming so important?

Provides nice contrast between soft tissues (vs. hard/soft tissue contrast in CT)

Each tissue has characteristic MR properties

T1, relaxation time for Mz

T2, relaxation time for Mxy

Proton density

This allows to obtain application-specific tissue-contrast by designing appropriate RF pulse sequences

Provides additional possibilities through flow-dependent phenomena or using saturation pulses

Introduction to Biomedical Imaging

Magnetic Resonance ImagingFree Induction Decay (FID)

RF pulse creates transverse magnetisation Mxy

Precession of transverse magnetisation at Larmor frequency

Amplitude of Mxy is initially dependent on proton density

Signal decays exponentially with time constant T2*

Signal can be measured using receive coil: Free Induction Decay (FID)

Introduction to Biomedical Imaging

Magnetic Resonance ImagingMeasurement Strategy

Free induction decay

Hard to measure (directly after the RF pulse)

Fast decay (T2*)

For imaging: echo techniques

Signal is recalled after some time (echo)

Two methods:

Spin echo techniques

Gradient (recalled) echo techniques

Introduction to Biomedical Imaging

Magnetic Resonance Imaging

Spin Echo

Magnetization is flipped to transverse plane

through a RF pulse

Dephasing due to local field inhomogeneities

Inversion pulse (180º) for spin refocusing at TE/2

TE = echo time

Spin rephasing

First echo is recalled thus reconstructing the FID

TE

Introduction to Biomedical Imaging

Magnetic Resonance ImagingMR image formation

Main scanner components

Magnet: constant main magnetic field Bo

Gradient coils: fields that vary in space

RF coils: for transmitting and receiving RF signals

Introduction to Biomedical Imaging

Magnetic Resonance ImagingImage formation

Static field gives a net magnetization

RF pulse excites nuclei and creates transverse magnetization

Spatial encoding of the signal using gradient fields

Echo read-out (using receive coil)

Reconstruction of image from measured echoes (mostly Fourier reconstruction)

Pulse sequence

Series of events in time: sequence

Pulse sequence contains components necessary to produce an MR image

Components: RF pulses, gradients, echo sampling

Nature and order of components determines kind of scan: sequence design

Spatial encoding

Slice selection

Frequency encoding

Phase encoding

Localization if based upon the fact that spins presses at the Larmor frequency, which depends on the local value of the magnetic field B

Introduction to Biomedical Imaging

Magnetic Resonance Imaging

Spatial encoding: slice selection

The excitation pulse can be selective or non selective

S: Only spins in a given slice are excited

NS: All spins covered by the transmit coil are excited

Thickness and location of slice are determined by the bandwidth of the RF pulse and gradient in direction of slice selection

Slice selection

Gradient field encodes space in frequency

Larmor frequency depends on local strength of magnetic field B: f ~ B

RF excitation pulse has finite bandwidth

Spins within a limited range of frequencies are excited: selective excitation

Slice thickness: determined by the shape of the pulse (bandwidth) and the gradient strength

Introduction to Biomedical Imaging

Magnetic Resonance ImagingSpatial encoding: slice selection

Gradient field causes dephasing within the slice

An inversion pulse is applied to achieve rephasing and thus yield maximal signal

Selection and rephasing lobes

Introduction to Biomedical Imaging

Magnetic Resonance ImagingSpatial encoding: frequency encoding (also read-out gradient)

By applying a gradient Gx along the x-direction, every position along the x-axis is associated with its own unique Larmor frequency: frequency encoding

The Fourier transform of the detected signal is a projection onto the x-axis

The amplitude of each frequency component is proportional to the summed signal in the y-direction for that x position

By repeated rotation and application of the read-out gradient, spatial information in more than one direction can be obtained

Lauterbur used this technique in combination with backprojection reconstruction to generate the first MR images

Introduction to Biomedical Imaging

Magnetic Resonance ImagingSpatial encoding: frequency encoding

Signal has now been encoded in slice (z) en frequency (x) directions

A third gradient is needed for full localization

Phase encoding gradient is kept on for a certain duration

Precession at different frequencies during that period of time gives different phases along the gradient direction: phase encoding

Introduction to Biomedical Imaging

Magnetic Resonance ImagingSpatial encoding: phase encoding

Combination of frequency and phase encoding gives spatial signal encoding in 2D plane

First step: phase encoding (y gradient)

– Between excitation and echo read-out

Second step: frequency encoding (x gradient)

– Gradient switched on during echo read out (a.k.a. read out gradient)

Image formation using Fourier transform on all acquired echo data

Data collection: sampling

With the frequency encoding gradient switched on (here: x-direction) Nx data points are sampled (digitized echo read-out)

Read out is performed for all Ny phase encoding steps:

– Ny phase encoding steps give Ny echos

Result Nx×Ny data points per slice: MATRIX

This signal matrix exists in so-called k-space

2D Fourier transform used to reconstruct an image from k-space

Introduction to Biomedical Imaging

All spins have same precessional frequency

Magnetic Resonance Imaging

Spatial encoding

Introduction to Biomedical Imaging

Apply Phase Encoding Gradient

Slower Unchanged Faster

Magnetic Resonance Imaging

Spatial encoding

Introduction to Biomedical Imaging

After Phase Encoding Gradient is turned offAll spins have same frequency again, but different phase

+90° 0° -90°

Magnetic Resonance Imaging

Spatial encoding

Introduction to Biomedical Imaging

App

ly F

requ

ency

Enc

odin

g G

radi

ent Faster

Unchanged

Slower

Magnetic Resonance Imaging

Spatial encoding

Introduction to Biomedical Imaging

Magnetic Resonance ImagingK-space

k-space contains raw scan data (sampled data points)

In 2D x-direction in k-space is frequency encoding: measured echoes

y-direction is phase encoding direction (gradient strength during phase encoding)

Introduction to Biomedical Imaging

Magnetic Resonance ImagingK-space: interpretation

K-space is the Fourier domain of the target image

Trivial reconstruction: Inverse Fourier Transform

Introduction to Biomedical Imaging

Magnetic Resonance ImagingK-space: interpretation

Duality between image and k space

Field of View (FOV)

Introduction to Biomedical Imaging

Magnetic Resonance ImagingK-space: interpretation

K-space allows to think in terms of frequency content

Introduction to Biomedical Imaging

Magnetic Resonance ImagingK-space: interpretation

Low frequencies = image contrast

Introduction to Biomedical Imaging

Magnetic Resonance ImagingK-space: interpretation

High frequencies = image details and edges

Introduction to Biomedical Imaging

Magnetic Resonance ImagingK-space filling strategies

By thinking in terms of frequency content one can devise non linear filling strategies which can have advantages in certain applications

Warning! These strategies may impose hardware constrains as the field gradients may need to switch very fast (slew rate limitations)

Standard Echo planar imaging (EPI)

Interleaved EPI Spiral Scanning

Introduction to Biomedical Imaging

Magnetic Resonance Imaging3D Imaging

Concept of spatial localization can be expanded to 3D by adding an extra phase encoding in the slice direction

Thick slab volume excitation is used

Introduction to Biomedical Imaging

Magnetic Resonance ImagingAngiographgy

Introduction to Biomedical Imaging

Magnetic Resonance ImagingMR Scanners

Introduction to Biomedical Imaging

Magnetic Resonance ImagingMR Coils

Brain coil Split head coilGeneral purposeflex coil

Torso coil Extremity coil

Introduction to Biomedical Imaging

Magnetic Resonance ImagingMR Scanner Console

Introduction to Biomedical Imaging

Magnetic Resonance ImagingMR Images

Introduction to Biomedical Imaging

Magnetic Resonance ImagingMR Images

Introduction to Biomedical Imaging

References & AcknowledgementsReferences

Amersham Health http://www.amershamhealth.com

Basics of MRI - Joseph P. Hornak http://www.cis.rit.edu/htbooks/mri/

Basic Principles of MR Imaging – Philips Medical Systems

Medical Imaging – D. Liley http://marr.bsee.swin.edu.au/~dtl/het408.html

Acknowledgements for some material used in these lectures

ImPACT http://www.impactscan.org

Magnetic Resonance Imaging – W. Bartels http://www.isi.uu.nl/Education/MBT-MTI