Medical Image Analysis Medical Imaging Modalities Figures come from the textbook: Medical Image...

Medical Image AnalysisMedical Image AnalysisMedical Imaging Modalities

Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

Anatomical or structural◦X-ray radiology, X-ray mammography,

X-ray CT, ultrasound, Magnetic Resonance Imaging

Functional or metabolic◦Functional MRI, (Single Photon

Emission Computed Tomography) SPECT, (Positron Emission Tomography) PET, fluorescence imaging


X-ray ImagingX-ray Imaging


Figure comes from the Wikipedia, www.wikipedia.org.


39 P50N K

LO

N

Ejected Electron

Incident Electron

X-ray Photon

Figure 4.1. Atomic structure of a tungsten atom. An incident electron with energy greater than K-shell binding energy is shown interacting with a K-shell electron for the emission of an X-ray photon.

X-ray ImagingX-ray ImagingTungsten

◦K-shell binding energy level: 69.5 keV◦L-shell binding energy level: 10.2 keV◦An emision of X-ray photon of 59.3 keV

X-ray generation◦Electrons are released by the source

cathode and are accelerated toward the target anode in a vacuum under the potential difference ranging from 20,000 to 150,000 volts


X-ray 2-D Projection X-ray 2-D Projection ImagingImagingDiagnostic radiology

◦2-D projection of the three-dimensional anatomical structure of the human body

◦Localized sum of attenuation coefficients of material: air, blood, tissue, bone

◦Film or 2-D array of detectorsDigital radiographic system

◦Use scintillation crystals optically coupled with photomultiplier



X-ray Source

X-ray ScreenFilmX-ray Screen

3-D Object orPatient

2-D ProjectionImage

Anti-scatter Grid

Figure 4.2. (a). A schematic diagram of a 2-D X-ray film-screen radiography system. A 2-D projection image of the 3-D object is shown at the bottom. (b). X-ray radiographic image of a normal male chest.

X-ray 2-D Projection X-ray 2-D Projection ImagingImagingScattering

◦Create artifacts and artificial structures

Reduce scattering◦Anti-scattered grids and collimators


X-ray MammographyX-ray MammographyTarget material

◦Molybdenum: K-, L-, M-shell binding energies levels are 20, 2.8, 0.5 keV. The characteristic X-ray radiation is around 17 keV.

◦Phodium: K-, L-, M-shell binding energies levels are 23, 3.4, 0.6 keV. The characteristic X-ray radiation is around 20 keV.

A small focal spot of the order of 0.1mm



X-ray Source

X-ray ScreenFilmX-ray Screen

CompressedBreast

MovingAnti-scatter Grid

CompressionDevice

Figure 4.3. A film-screen X-ray mammography imaging system.


Figure 4.4. X-ray film-screen mammography image of a normal breast.

X-ray Computed X-ray Computed TomographyTomography3-D


dxzyx

inout ezxyIzxyI),,(

),;(),;(


y

x

zX-Y Slices

Figure 4.5. 3-D object representation as a stack of 2-D x-y slices.


x

z

y

Iin(x; y,z)Iout(x; y,z)

(x,y; z)

11

22 92

15

12 42 52 62 72 82

Figure 4.6. Source-Detector pair based translation method to scan a selected 2-D slice of a 3-D object to give a projection along the y-direction.


Figure 4.7: The translate-rotate parallel-beam geometry of first generation CT scanners.

X-ray Computed X-ray Computed TomographyTomographyGenerations

◦First: an X-ray source-detector pair that was translated in parallel-beam geometry

◦Second: a fan-beam geometry with a divergent X-ray source and a linear array of detectors. Use translation to cover the object and rotation to obtain additional views


Generations◦Third: a fan-beam geometry with a

divergent X-ray source and an arc of detectors. Without translation. Additional views are obtained by simultaneous rotation of the X-ray source and detector assembly. “Rotate only”

◦ Fourth: use a detector ring around the object. The X-ray source provides a divergent fan-beam of radiation to cover the object



Figure 4.8. The first generation X-ray CT scanner


Ring of Detectors

Source

SourceRotation Path

X-rays

Object

Figure 4.9. The fourth generation X-ray CT scanner geometry.


Figure 4.10. X-ray CT image of a selected slice of cardiac cavity of a cadaver.


Figure 4.11. The pathological image of the selected slice shown with the X-ray CT image in Figure 4.10

Magnetic Resonance Magnetic Resonance ImagingImagingNuclear magnetic resonance

◦The selected nuclei of the matter of the object

◦Blood flow and oxygenation◦Different parameters: weighted,

weighted, Spin-density◦Advance: MR Spectroscopy and

Functional MRI◦Fast signal acquisition of the order of

a fraction of a secondFigures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

1T 2T


Figure 4.12. MR images of a selected cross-section that are obtained simultaneously using a specific imaging technique. The images show (from left to right), respectively, the T1-weighted, T-2 weighted and the Spin-Density property of the hydrogen protons present in the brain.

Magnetic Resonance Magnetic Resonance ImagingImaging1H: high sensitivity and vast

occurrence in organic compounds13C: the key component of all

organic15N: a key component of proteins

and DNA19F: high relative sensitivity31P: frequent occurrence in organic

compounds and moderate relative sensitivity

Adapted from the Wikipedia, www.wikipedia.org.

MR SpectroscopyMR Spectroscopy



Functional MRIFunctional MRI



MRI PrinciplesMRI Principles : spin-lattice relaxation time : spin-spin relaxation time : the spin density


1T

2T

MRI PrinciplesMRI Principles

1. Great web sites1. Simulations from BIGS - Lernhilfe

für Physik und Technik2. http://www.cis.rit.edu/class/

schp730/bmri/bmri.htm


MRI PrinciplesMRI PrinciplesSpin

◦A fundamental property of nuclei with odd atomic numbers is the possession of angular moment

Magnetic moment◦The charged protons create a

magnetic field around them and thus act like tiny magnets


MRI PrinciplesMRI Principles : the spin angular moment : the magnetic moment : a gyromagnetic ratio, MHz/T

A hydrogen atom◦ :42.58 MHz/T


J

J


NN

SS

JJ

JJ

Figure 4.13. Left: A tiny magnet representation of a charged proton with angular moment, J. Right: A symbolic representation of a charged proton with angular moment, J and a magnetic moment, μ.

MRI PrinciplesMRI PrinciplesPrecession of a spinning proton

◦The interaction between the magnetic moment of nuclei with the external magnetic field

◦Spin quantum number of a spinning proton: ½

◦The energy level of nuclei aligning themselves along the external magnetic field is lower than the energy level of nuclei aligned against the external magnetic field



Figure 4.14 (a) A symbolic representation of a proton with precession that is experienced by the spinning proton when it is subjected to an external magnetic field. (b) The random orientation of protons in matter with the net zero vector in both longitudinal and transverse directions.


MRI PrinciplesMRI PrinciplesEquation of motion for isolated

spin

Solution:

J

kHHdt

Jd

00

kHdt

d

0

00 H


Longitudinal Vector OX at the transverse position X

Net LongitudinalVector: Zero

Net TransverseVector: Zero

Net LongitudinalVector: Zero

Net TransverseVector: Zero


Lower Energy

Level

Higher Energy

Level

S

N

H

Lower Energy

Level

Higher Energy

Level

S

N

H0

Figure 4.15 (a). Nuclei aligned under thermal equilibrium in the presence of an external magnetic field. (b). A non-zero net longitudinal vector and a zero transverse vector provided by the nuclei precessing in the presence of an external magnetic field.


Non-zero Net Longitudinal Vector

x

y

z

x

y

zH0

Net Zero Transverse Vector

MRI PrinciplesMRI PrinciplesThe precession frequency

◦Depends on the type of nuclei with a specific gyromagnetic ratio and the intensity of the external magnetic field

◦This is the frequency on which the nuclei can receive the Radio Frequency (RF) energy to change their states for exhibiting nuclear magnetic resonance

◦The excited nuclei return to the thermal equilibrium through a process of relaxation emitting energy at the same precession frequency

MRI PrinciplesMRI Principles90-degree pulse

◦Upon receiving the energy at the Larmor frequency, the transverse vector also changes as nuclei start to precess in phase

◦Form a net non-zero transverse vector that rotates in the x-y plane perpendicular to the direction of the external magnetic field



S

N

S

N x

y

z

Figure 4.16. The 90-degree pulse causing nuclei to precess in phase with the longitudinal vector shifted clockwise by 90-degrees as a result of the absorption of RF energy at the Larmor frequency.

MRI PrinciplesMRI Principles180-degree pulse

◦If enough energy is supplied, the longitudinal vector can be completely flipped over with a 180-degree clockwise shidf in the direction against the external magnetic field



S

N

S

N

x

y

z

Figure 4.17. The 180-degree pulse causing nuclei to precess in phase with the longitudinal vector shifted clockwise by 180-degrees as a result of the absorption of RF energy at the Larmor frequency.

MRI PrinciplesMRI PrinciplesRelaxation

◦The energy emitted during the relaxation process induces an electrical signal in a RF coil tuned at the Larmor frequency

◦The free induction decay of the electromagnetic signal in the PF coil is the basic signal that is used to create MR images

◦The nuclear excitation forces the net longitudinal and transverse magnetization vectors to move


MRI PrinciplesMRI PrinciplesA stationary magnetization

vector

The total response of the spin system


N

nnM

1

1

0

2

)(

T

kMM

T

jMiMHM

dt

Md zzyx


Dephasing

RF Pulse

Random Phase (Zero Transverse Vector)

In Phase Spin

Relaxation

Figure 4.18. The transverse relaxation process of spinning nuclei.

MRI PrinciplesMRI PrinciplesThe longitudinal and transverse

magnetization vectors with respect to the relaxation times

where


tiTtyxyx eeMtM 02/

,, )0()(

11 //0 )0()1()( Ttz

Ttzz eMeMtM

piyxyx eMM 0)0()0( ',',


t

t

Mx,y (t)

Mz (t)

Figure 4.19. (a) Transverse and (b) longitudinal magnetization relaxation after the RF pulse.

MRI PrinciplesMRI PrinciplesThe RF pulse causes nuclear

excitation changing the longitudinal and transverse magnetization vectors

After the RF pulse is turned off, the excited nuclei go through the relaxation phase emitting the absorbed energy at the same Larmor frequency that can be detected as an electrical signal, called the Free Induction Decay (FID)


MRI PrinciplesMRI PrinciplesThe NMR spin-echo signal (FID

signal)


dxdydzezyxMS zyxizyx

zyx )(0 ),,(),,(

zyxzyxi

zyx dddeSMzyx zyx )(0 ),,(),,(

MR InstrumentationMR InstrumentationThe stationary external magnetic

field◦Provided by a large superconducting

magnet with a typical strength of 0.5 T to 1.5 T

◦Housing of gradient coils◦Good field homogeneity, typically on

the order of 10-50 parts per million◦A set of shim coils to compensate for

the field inhomogeneity Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.


Gradient Coils

Magnet

Gradient Coils

RFCoils

PatientPlatform

MonitorMonitor Data-Acquisition

System

Figure 4.20. A general schematic diagram of a MR imaging system.

MR InstrumentationMR InstrumentationAn RF coil

◦To transmit time-varying RF pulses◦To receive the radio frequency

emissions during the nuclear relaxation phase

◦Free Induction Decay (FID) in the RF coil


MR Pulse SequencesMR Pulse SequencesNMR signal

◦The frequency and the phaseSpatial encoding in MR imaging

◦Frequency encoding and phase encoding



x

z

y

y

xx

y

z

z

Sagital

Coronal

Axial

Figure 4.21 (a). Three-dimensional object coordinate system with axial, sagittal and coronal image views. (b): From top left to bottom right: Axial, coronal and sagittal MR images of a human brain.

MR Pulse SequencesMR Pulse Sequences


Z Gradient

90 RF Pulse(Slice Selection)

X Gradient

Phase-Encoding(x-scan selection)

Z Gradient

180 RF Pulse(Slice Echo Formation)

Y Gradient

Frequency Encoding(Read-Out Pulse)

Figure 4.22. (a): Three-dimensional spatial encoding for spin-echo MR pulse sequence. (b): A linear gradient field for frequency encoding. (c). A step function based gradient field for phase encoding.


Varying Spatially DependentLarmor Frequency

S

N

S

N

Linear Gradient

Precessing Nuclei

External Magnet

Positive PhaseChange

Negative PhaseChange

Phase -EncodingGradientStep

MR Pulse SequencesMR Pulse SequencesThe phase-encoding gradient

◦Applied in steps with repeated cycles◦If 256 steps are to be applied in the

phase-encoding gradient, the readout cycle is repeated 256 times, each time with a specific amount of phase-encoding gradient


Spin Echo ImagingSpin Echo Imaging :

◦Between the application of the 90 degree pulse and the formation of echo (rephasing of nuclei

:◦Between the 90 degree pulse and

180 degree pulse


ET

2/ET


RF Energy: 90 Deg Pulse

Zero Net Vector:Random Phase

RelaxationDephasing


Echo -Formation


Zero Net Vector:Random Phase

In Phase

Rephasing

Echo -Formation

In Phase

Figure 4.23. The transverse relaxation and echo formation of the spin echo MR pulse sequence.

Spin Echo ImagingSpin Echo ImagingK-space

◦The placement of raw frequency data collected through the pulse sequences in a multi-dimensional space

◦By taking the inverse Fourier transform of the k-space data, an image about the object can be reconstructed in the spatial domain

◦The NMR signals collected as frequency-encoded echoes can be placed as horizontal lines in the corresponding 2-D k-space


Spin Echo ImagingSpin Echo Imaging : the cycle repetition time weighted

◦A long and a long weighted

◦A short and a shortSpin-density

◦A long and a short


RT

2T

RT ET

1T

RT ET

RT ET


90 deg RF pulse

180 deg RF pulse

Gz: Slice Selection Frequency EncodingGradient

Gx: Phase EncodingGradient

Gy: Readout Frequency EncodingGradient

TE /2

TE /2

TE

RF pulseTransmitter

NMRRF FIDSignal

Figure 4.24. A spin echo pulse sequence for MR imaging.

Spin Echo ImagingSpin Echo Imaging

The effective transverse relaxation time from the field inhomogeneities


12 1),,(),,( 0T

T

T

T RE

eezyxzyx

2

11

2*

2

H

TT

Spin Echo ImagingSpin Echo ImagingThe effective transverse

relaxation time from a spatial encoding gradient


2

11*

2**

2

Gd

TT

Echo Planar ImagingEcho Planar ImagingA single-shot fast-scanning

methodSpiral Echo Planar Imaging (SEPI)

◦where

)(1

)( tdt

dtG xx

)(1

)( tdt

dtG yy

tttx cos)(

ttty sin)(


90 deg RF pulse

90 deg RF pulse


Gx: OscillatingGradient

Gy: Readout Gradient

RF pulseTransmitter

NMRRF FIDSignal

Figure 4.25. A single shot EPI pulse sequence.


gy

gx

x

y

Figure 4.26. The k-space representation of the EPI scan trajectory.


x

y

SEPI Trajectory

Data SamplingPoints

Figure 4.27. The spiral scan trajectory of SEPI pulse sequence in the k-space.


90 deg RF pulse

180 deg RF pulse


Gx Gradient

Gy Gradient

TE /2

TE /2

TE

RF pulseTransmitter

NMRRF FIDSignal

TD

Figure 4.28. The SEPI pulse sequence


Figure 4.29. MR images of a human brain acquired through SEPI pulse sequence.

Gradient Echo ImagingGradient Echo ImagingFast low angle shot (FLASH) imaging

◦Utilize low-flip angle RF pulses to create multiple echoes in repeated cycles to collect the data required for image reconstruction

◦A low-flip angle (as low as 20 degrees)◦The readout gradient is inverted to re-

phase nuclei leading to the gradient echo during the data acquisition

◦The entire pulse sequence time is much shorter than the spin echo pulse sequence



Low Flip Angle RF pulse


RF pulseTransmitter


Gy: Readout Frequency EncodingGradient TE

NMRRF FIDSignal

Figure 4.30. The FLASH pulse sequence for fast MR imaging.

Flow ImagingFlow ImagingTracking flow

◦Diffusion (incoherent flow) and perfusion (partially coherent flow)

◦The FID signal generated in the RF receiver coil by the moving nuclei and velocity-dependent factors

MR angiography



90 deg RF pulse

180 deg (selective)RF pulse




TE /2

TE

RF pulseTransmitter

NMRRF FIDSignal

Figure 4.31. A flow imaging pulse sequence with spin echo.


Figure 4.32: Left: A proton density image of a human brain. Right: The corresponding perfusion image.


90 degree RF pulse


RF pulseTransmitter



TE NMRRF FIDSignal

Next 90 degree RF pulse

TR

Figure 4.33. Gradient echo based MR pulse sequence for 3-D MR volume angiography.


Figure 4.34. An MR angiography image.

Nuclear Medicine Imaging Nuclear Medicine Imaging ModalitiesModalitiesRadioactivity decay

Half-life of a radionuclide decay


teNtN )0()(

693.0

halfT

Nuclear Medicine Imaging Nuclear Medicine Imaging ModalitiesModalitiesThe radioactivity of a

radionuclide◦The average decay rate

◦Curie (CI) disintegrations per second

(dps)

◦Becquerel (Bq) One dpsFigures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

Ndt

dN

10107.3

Single Photon Emission Single Photon Emission Computed TomographyComputed TomographyRadioisotope

◦The radioisotopes are injected in the body through administration of radiopharmaceutical drugs that metabolize with the tissue

Gamma rays◦The gamma rays from the tissue pass

through the body and are captured by the detectors surrounding the body to acquire raw data for defining projections


Single Photon Emission Single Photon Emission Computed TomographyComputed TomographyRadionuclides

◦Thallium ◦Technetium◦Iodine◦Gallium

Gamma ray◦Decay by emitting gamma rays with

photon energy ranging from 135 keV to 511 keV

Attenuation xd eII

0


Object EmittingGamma Photons

Scintillation Detector Arrays Coupled with

Photomultiplier Tubes

Figure 4.35. A schematic diagram of detector arrays of SPECT scanner surrounding the patient area.

Single Photon Emission Single Photon Emission Computed TomographyComputed TomographyScintillation detector

◦Barium fluoride◦Cesium iodide◦Bismuth germinate BGO

Photomultiplier tube



Figure 4.36. A 99Tc SPECT image of a human brain

Single Photon Emission Single Photon Emission Computed TomographyComputed TomographyAttenuation and scattering

◦Photoelectric absorption and Compton scattering

Poor in structural information◦Attenuation and scattering

Assessment of metastases or characterization of a tumor

Lower cost than PET


Positron Emission Positron Emission TomographyTomographyConcept

◦Simultaneous detection of two 511keV energy photons traveling in the opposite direction

Radionuclides◦Decay by emitting positive charged

particles called positrons◦Fluorine 18-F◦Oxygen 15-O◦Nitrogen 13-N◦Carbon 11-C


Object EmittingPositrons

Scintillation Detector Arrays

Point of Positron Emission

Point of Positron Annihilation

Position Dependent Photomultiplier Tubes

CoincidenceDetection

SystemComputer

Display

Detector Ring

Figure 4.37. A schemtaic diaggram of PET scanner.

Positron Emission Positron Emission TomographyTomographyAfter emission

◦Travel typically for 1-3 mm, losing some of its kinetic energy

◦The annihilation of the positron with the electron

◦Cause the formation of two gamma photons with 511keV traveling in opposite directions

◦Coincidence detection◦The point of emission of a positron is

different from the point of annihilation with an electron

Positron Emission Positron Emission TomographyTomographyRadiopharmaceutical

◦Fluorodeoxyglucose (FDG)◦Resolution and sensitivity of PET

imaging is significantly better than SPECT



Figure 4.38: Serial images of a human brain with FDG PET imaging.

Ultrasound ImagingUltrasound ImagingDiagnostic imaging

◦Anatomical structures, blood flow measurements and tissue characterization

◦Safety, portability, low-cost



Ultrasound ImagingUltrasound ImagingVelocity

Relative intensity in dB

Shorter waves◦Better imaging resolution

Frequencies: 2 MHz to 5 MHz are common

c

2

110log10I

I

Reflection and Reflection and TransmissionTransmissionAcoustic impedance


cZ 0

21

122,1 ZZ

ZZR

21

22,1

2

ZZ

ZT


x1 x2 x3

I0

R0

T1,2

T3,4

T2,3

T4,3

T3,2

T5,4

Z1

Z2Z3

Z4 Z5

T2,1

Figure 4.39. A path of a reflected sound wave in a multilayered structure.

RefractionRefractionSnell’s law


1

2sinsinc

cit


Piezoelectric crystal

Acoustic absorbers

Blockers

ImagingObject

Transmitter/Receiver

Circuit

ControlCircuit

PulseGeneration and

Timing

Data-Acquisition Analog to

Digital Converter

Computer Imaging Storage and Processing

Display

Figure 4.40. A schematic diagram of a conventional ultrasound imaging system.

Ultrasound ImagingUltrasound ImagingA-mode

◦Records the amplitude of returning echoes from the tissue boundaries with respect to time

◦Perpendicular incident angle◦Basic method


Ultrasound ImagingUltrasound ImagingM-mode

◦Variations in signal amplitude due to object motion

◦X-axis represents the time, while the y-axis indicates the distance of the echo from the transducer



Figure 4.41. M-Mode display of mitral valve leaflet of a beating heart.

Ultrasound ImagingUltrasound ImagingB-mode

◦Two-dimensional images representing the changes in acoustic impedance of the tissue



Figure 4.42. The “B-Mode” image of a beating heart with mitral stenosis.

Ultrasound ImagingUltrasound ImagingDoppler ultrasound imaging


c

cos2 ffdoppler


Figure 4.43. A Doppler image of the mitral valve area of a beating heart. Figures 4.4.3-5 are taken from the website http://www2.umdnj.edu/~shindler/ms.html.

Medical Image Analysis Medical Imaging Modalities Figures come from the textbook: Medical Image...

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