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Introduction to Biomedical Imaging Alejandro Frangi, PhD Computational Imaging Lab Department of Information & Communication Technology Pompeu Fabra University www.cilab.upf.edu
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  • Introduction to Biomedical Imaging

    Alejandro Frangi, PhDComputational Imaging Lab

    Department of Information & Communication TechnologyPompeu Fabra University

    www.cilab.upf.edu

    http://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 () 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, = 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

    oB =

  • 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 (flip angle)

    1B dt =

  • 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 (180) 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 NxNy 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

    http://www.amershamhealth.com/http://www.cis.rit.edu/htbooks/mri/http://marr.bsee.swin.edu.au/~dtl/het408.htmlhttp://www.impactscan.org/http://www.isi.uu.nl/Education/MBT-MTI

    Introduction to Biomedical ImagingMagnetic Resonance ImagingFaster UnchangedSlower

    Introduction to Biomedical Imaging

    Alejandro Frangi, PhD

    Computational Imaging Lab

    Department of Information & Communication Technology

    Pompeu Fabra University

    www.cilab.upf.edu

    Magnetic Resonance Imaging

    Magnetic Resonance Imaging

    MRI 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

    Magnetic Resonance Imaging

    MRI 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 () 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

    Magnetic Resonance Imaging

    Precession

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

    The proportionality constant is known as gyro magnetic constant

    For hydrogen, = 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

    Magnetic Resonance Imaging

    Net magnetization

    The spins altogether form a net magnetization vector M

    M depends on the external field and the temperature

    Magnetic Resonance Imaging

    Resonance 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 (flip angle)

    Magnetic Resonance Imaging

    Situation before RF pulse

    Longitudinal vs. transverse magnetization

    After RF pulse only longitudinal magnetization (Mz)

    Mz is static and, hence, cannot produce induction signal

    Magnetic Resonance Imaging

    Situation 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)

    Magnetic Resonance Imaging

    Relaxation 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.

    @1.5TT1 [ms]T2 [ms]

    Fat26084

    WM920101

    GM79092

    Magnetic Resonance Imaging

    Why 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

    Magnetic Resonance Imaging

    Free 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)

    Magnetic Resonance Imaging

    Measurement 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

    Magnetic Resonance Imaging

    Spin Echo

    Magnetization is flipped to transverse plane

    through a RF pulse

    Dephasing due to local field inhomogeneities

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

    TE = echo time

    Spin rephasing

    First echo is recalled thus reconstructing the FID

    Magnetic Resonance Imaging

    MR 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

    Magnetic Resonance Imaging

    Image 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

    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

    Magnetic Resonance Imaging

    Spatial 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

    Magnetic Resonance Imaging

    Spatial 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

    Magnetic Resonance Imaging

    Spatial 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

    Magnetic Resonance Imaging

    Spatial 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 NxNy 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

    All spins have same precessional frequency

    Magnetic Resonance Imaging

    Spatial encoding

    Apply Phase Encoding Gradient

    Slower Unchanged Faster

    Magnetic Resonance Imaging

    Spatial encoding

    After Phase Encoding Gradient is turned off

    All spins have same frequency again, but different phase

    +90 0 -90

    Magnetic Resonance Imaging

    Spatial encoding

    Faster

    Unchanged

    Slower

    Apply Frequency Encoding Gradient

    Magnetic Resonance Imaging

    Spatial encoding

    Magnetic Resonance Imaging

    K-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)

    Magnetic Resonance Imaging

    K-space: interpretation

    K-space is the Fourier domain of the target image

    Trivial reconstruction: Inverse Fourier Transform

    Magnetic Resonance Imaging

    K-space: interpretation

    Duality between image and k space

    Field of View (FOV)

    Magnetic Resonance Imaging

    K-space: interpretation

    K-space allows to think in terms of frequency content

    Magnetic Resonance Imaging

    K-space: interpretation

    Low frequencies = image contrast

    Magnetic Resonance Imaging

    K-space: interpretation

    High frequencies = image details and edges

    Magnetic Resonance Imaging

    K-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

    Magnetic Resonance Imaging

    3D 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

    Magnetic Resonance Imaging

    Angiographgy

    Magnetic Resonance Imaging

    MR Scanners

    Magnetic Resonance Imaging

    MR Coils

    Brain coil

    Split head coil

    General purpose

    flex coil

    Torso coil

    Extremity coil

    Magnetic Resonance Imaging

    MR Scanner Console

    Magnetic Resonance Imaging

    MR Images

    Magnetic Resonance Imaging

    MR Images

    References & Acknowledgements

    References

    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

    o

    B

    w=g

    1

    Bdt

    q=g

    2

    /

    ()

    tT

    xyo

    MtMe

    -

    =

    1

    /

    ()(1)

    tT

    zo

    MtMe

    -

    =-