Introduction au génie biomédical - Montefiore Institute · GBI001.1 University of Liège! JGV 1/05/10 Introduction au génie biomédical! GBI0 001! ... Nobel P. in Physics, 1901#

University of Liège!GBI001.1 JGV 1/05/10

Introduction au génie biomédical!GBI0 001!

Imagerie médicale!

Prof. Jacques Verly!Departement dʼElectricité, Electronique et Informatique!

(Institut Montefiore)!


WHY MEDICAL IMAGING IS SUCH AN EXCITING FIELD FOR ENGINEERS!

« Que ferait aujourdʼhui la neurochirurgie sans ingénieur? »!Par le Prof. Brotchi (ULB)-FABI-TELEVIE 2006!

Didier Martin, CHU, Liège


OVERVIEW OF IMAGING MODALITIES!


MEDICAL IMAGING MODALITIES!

• Main!– Ionizing radiation!

• X-ray transmission!• Radionuclide emission!

– Nonionizing radiation!• Nuclear magnetic resonance!• Ultrasound!

• Others!– Biomagnetic imaging!– Neutron and charged-particle transmission!– Electrical current source!– Electrical conductivity!– Light-photon absorption imaging!– Thermal imaging!– Optical coherence tomography!


• Ionizing radiation!– X-ray transmission!

• Projection radiography!• Conventional tomography!• Computed tomography (CT)!

– Radionuclide emission!• Projection (Gamma camera)!• Single-photon emission computed tomography

(SPECT)!• Positron-emission tomography (PET)!

MAIN MEDICAL-IMAGING MODALITIES (1)!


• Nonionizing radiation!– Nuclear magnetic resonance (NMR)!

• Magnetic resonance imaging (MRI):Structural & functional!

• MR spectroscopy (MRS) and ! chemical shift imaging!• Diffusion tensor imaging (DTI)!

– Ultrasound!

MAIN MEDICAL-IMAGING MODALITIES (2)!


EXAMPLE MEDICAL IMAGES!

X-ray CT Angiography PET

MRI DTI Ultrasound


EXAMPLE MEDICAL IMAGING EQUIPMENT!


PHYSICS OF IONIZING RADIATION!


STRUCTURE OF ATOMS (1)!


• Atomic number (Z) = nbr of protons!• Atomic mass (A) = nbr of nucleons (protons + neutrons)!• Example: Uranium 238!

! ! ! !

! ! (Z can be dropped since determined by U)!

• Isotope or nuclide!! ! Example: isotopes of Hydrogen!

Hydrogen (1H) ! Deuterium (2H)! Tritium (3H)!

STRUCTURE OF ATOMS (2)!

+ + N + N N


RADIOACTIVE DECAY, RADIONUCLIDES, AND RADIOACTIVE MATERIALS!

• Depending upon ratio of neutrons to protons, nuclides are stable or unstable!

• All elements with Z≥83 (Bismuth) and/or A≥201 are unstable!

• Over time, nucleus of unstable nuclides undergoes radioactive decay, i.e.!– May transmutes to another nucleus, e.g. Ra → Rn!– Emits ionizing radiation!

• α: Helium nuclei!! β: negatrons or positrons* !• γ: pure electromagnetic radiation (like X-rays)!

• Nuclides that undergo such decay are called radionuclides!

• Any material that contains measurable amounts of radionuclides is called a radioactive material!

* Only for artificially-produced radionuclides!


DECAY OF RADIONUCLIDES!

Decay occurs randomly, but a collection of radionuclides !decays exponentially at a rate specific to the radionuclide!

Half-life, T1/2

235U: 1.41 x 108 years 18F: 109.77 minutes

Activity (decays/s)

N0

0.5 N0

T1/2 = 0.693 λ

t


WHAT IS IONIZING (OR PENETRATING) RADIATION ?!

• Ionizing radiation consists of charged and/or neutral "particles" that create ion-pairs in target material!

• An ion-pair is a pair of oppositely-charged ions held together by Coulomb attraction without formation of a covalent bond!

• An ion-pair results from the ejection of one or more orbital electrons!

• An ion-pair behaves as one unit!

• Examples: α-particles, X-rays, γ-rays!


ELECTROMAGNETIC WAVE SPECTRUM!


SOURCES OF IONIZING RADIATION!

• Natural!– Terrestrial: natural radioactivity (mostly 232Th, 235U, 238U )!– Extraterrestrial: cosmic rays (principally protons)!

• Man-made!– X-rays (since 1895)!– Artificial radioactivity!

• Unavoidable by-product of nuclear reactions!• Deliberately-produced by particle accelerators!

– Industrial applications!– Medical applications (e.g. 18F)!


NEGATRONS AND POSITRONS!

• Negatrons and positrons* originate from nucleus!

• Negatrons are electrons!

• Positrons are like electrons, but have a positive charge!

Negatrons are (negatively-charged) electrons from nucleus (β-, e(-))Positrons are positively-charged electrons from nucleus (β+, e+)!

*Only for artificially-produced radio nuclides!


HISTORY OF IONIZING RADIATION (1)!

1803 1895 1896 1897

Dalton proposes

chemical theory of atoms (indivisible)#

Roentgen discovers

X-rays#

Becquerel studies

fluo. & phospho. materials (U salts)#

Thomson discovers electron#

John DALTON

(1766-1844)#

Wilhelm Conrad ROENTGEN (1845-1923)

Nobel P. in Physics, 1901#

Antoine Henri BECQUEREL (1852-1908)


Joseph John (J.J.)THOMSON (1856-1940)


Photos: http://nobelprize.org/


HISTORY OF IONIZING RADIATION (2)!

1897 1898 1911 1913

Marie Curie investigates

source of radiation in Uranium#

M. & P. Curie discover radium#

Rutherford discovers

atom made of + nucleus & - electrons#

Bohrdevelops

planetary view of atom#

Marie CURIE

(1867-1934) Nobel P. in Physics, 1903

Pierre CURIE

(1854-1906)Nobel P. in Physics, 1903#

ErnestRUTHERFORD

(1871-1937)Nobel P. in Chemistry, 1908#

Niels Henrik David BOHR

(1885-1962)Nobel P. in Physics, 1922#



RADIONUCLIDES OF NATURE!


RADIONUCLIDES OF NUCLEAR MEDICINE!


MASS AND ENERGY (1)!

• Gram-atomic mass (or mole) = mass in grams of an isotope numerically equal to its atomic mass (A)!

• Every mole contains same number of atoms: Avogadroʼs number (NA) =!

• Atomic mass unit (amu) = 1/12 mass of !• Mass of one atom of !• Mass of one amu = !• Mass of electron of rest = !


MASS AND ENERGY (2)!

• Mass and energy are linked by !• Energy is often expressed in electron-volts

with !• Energy of 1 amu = !• Energy of rest-mass of electron = !


ALPHA (α) DECAY (1)!

Too many protons causing excessive repulsive force → a Helium nucleus is emitted!

http://library.thinkquest.org/3471/radiation_types_body.html


ALPHA (α) DECAY (2)!

• Example α decay!

• α-emission occurs only if!! ! Mass (Parent) > mass (Daughter) + mass (α-particule)!

• Mass difference Δm gives radiation energy via E = Δm c2!

• For above example!

! E = [226.025406 amu – (222.017574 + 4.002603) amu] x 931.502 MeV/amu!! ! ! ! i.e. E = 4.87 MeV!

Parent# Daughter α-emission

Conservation of mass (A) Conservation of charge (Z)


BETA (β) DECAY: (A) NEGATRON (β-) EMISSION (1)!

too high

→ neutron converts to proton and emits an electron!


Nbr of neutrons!Nbr of protons!


• Negatrons are (negatively-charged) electrons from nucleus!

• Example β- decay!

• Following decay, nucleus is left in excited energy state!

• Subsequent decay to lower energy state produces a (single) γ photon (without change in A or Z) !

BETA (β) DECAY: (A) NEGATRON (β-) EMISSION (2)!

E = (14.003242 amu – 14.003074 amu) x 931.502 MeV/amu i.e. E = 0.156 MeV

Too high for electron → partly carried by (Fermi, 1930)


NEUTRINO ( )!

• Neutrino = "little neutral one"!• Existence postulated by Fermi in 1930!• Zero electrical charge!• Resting mass smaller than that of electron!• Interacts very weakly with matter → difficult to

detect!• Only detected experimentally in 1950!• Antineutrino ( ) in antiparticule to neutrino!• When a particle collides with its antiparticle,

they annihilate and release electromagnetic radiation, e.g. γ-rays!


BETA (β) DECAY: (B) POSITRON (β+) EMISSION (1)!

too small

→ proton converts to neutron and emits a positron!


Nbr of neutrons!Nbr of protons!


BETA (β) DECAY: (B) POSITRON (β+) EMISSION (2)!

• Positrons are positively-charged "electrons" from nucleus!

• Example β+ decay!

• Positron quickly recombines with an electron from surrounding material, producing a pair of γ photons!

• Occurs only in artificially-produced nuclides, e.g. 18F!


GAMMA (γ) RADIATION!

• Pure electromagnetic radiation (like X-rays)!• Single-photon emission (used in Gamma camera &

SPECT)!– Transition of nucleus from excited energy state to lower-

energy state!• Decay following β- emission, e.g. 131I!

– Electron capture (EC) or K capture!• Can occur with β+, e.g. 52Fe!

– Isomeric transition (IT), e.g. 99mTc (Isomer)!• Only produces γ!

• Two-photon emission (used in PET)!– Generally occurs with (short-lived) β+, e.g. 18F!

(at 180° and 0.511 MeV*)

* Corresponds to rest mass of electron


INTERACTION OF IONIZING RADIATION WITH MATTER (“ABSORBER”)!

• Charged particles (p, α, β-, β+, e, …) – In general: many small energy transfers resulting in

ionization – β+ is short-lived and quickly recombines with e

• Neutral "particles" (n, X, γ, …) – In general: largely-unimpeded travel, then one-time

large energy transfer – Neutrons (n) – Photons (X, γ)

• Photoelectric effect (E < 0.2 MeV) • Rayleigh scattering • Compton scattering (0.2 ≤ E < 5 MeV) • Pair production* (E ≥ 1.2 MeV)

(opposite of annihilation)#


INTERACTION OF PHOTONS WITH MATTER (“ABSORBER”)!

Another form of interaction is pair production!


"ATTENUATION" OF IONIZING RADIATION BY MATTER!

• Charged particles!– Rate of loss of energy (dE/dx) given by Bethe-Block (or

stopping-power) equation!– Uniform loss rate along particle track!

• β emission in water: 2 MeV cm-1!– Stopping distance ("range″)!

• 10 MeV α particle in water: 1 cm!• Neutral “particles”!

– Microscopically: cross-section σ!– Macroscopically: linear attenuation coefficient, μ

(probability of one interaction per unit length)!– Mean free path (1/μ):!

• 1 MeV γ photon in Pb: 1.3 cm!


IMAGING BY X-RAY TRANSMISSION!


BASIC PRODUCTION AND DETECTION OF X-RAYS!


X-RAYS WERE DISCOVERED IN 1895 BY ROENTGEN!

Wilhelm Conrad ROENTGEN!

(1845-1923)!First Nobel Prize Winner, 1901!


THE THREE FUNDAMENTAL TECHNIQUES OF X-RAY TRANSMISSION IMAGING!

Projection radiography Conventional tomography

Computerized tomography (CT)


MAIN INTERACTION OF X-RAYS WITH MATTER:IONIZATION!

• Ionization: formation of ion pairs!• Binding energy: 13.6 Z2 for K-shell electron!• Photoelectric effect: process by which photon knocks off

electron!• Coulomb interaction: process by which e knocks off e!• A 50 KeV X-ray photon will ionize ~2000 atoms in air!• Photoelectric effect and Coulomb interactions are mostly

responsible for attenuation, stopping, and damage!

Visible (500 nm) 2.48 eV X-ray ~70 KeV γ-ray ~1 MeV


BEERʼS LAW FOR RADIATION ATTENUATION!

(Nonlinear attenuation)

University of Liège!

EXAMPLE OF ATTENUATION AND CONTRAST!CALCULATION!

" PATIENT "

LUNG (~AIR)

LUNG LUNG

LUNG

LUNG LUNG

CHEST CHEST

CHEST CHEST

chest

chest chest

chest RIB RIB

RIB RIB

tumor

tumor

35cm

3 3

3 3 3

3

29

29

13 13

13 13

1.5 1.5 1.5 1.5

1.5 1.5 1.5 1.5

0.14

0.14

0.14 0.05

0.4 0.4

I0

X-ray I

µ (cm-1) 24%

24%

55%


HOUNSFIELD SCALE FOR ABSORPTION COEFFICIENTS!


THE OBJECT TO BE IMAGED MUST BE VIEWED AS A 2D OR 3D FUNCTION!

f(x,y) f(x,y,z)

Nature of ‘‘ f ’’ varies with modalities: - Linear attenuation coefficient for X-ray CT - Spin density for MRI


LINE INTEGRALS AND PROJECTIONS!

Shown in 2D but generalizable to 3D

and even ND

Line integral along l


FUNDAMENTAL PROBLEM:2D IMAGE RECONSTRUCTION FROM PROJECTIONS!

p Є(-∞,∞)!

y

x

f(x,y)

p l Φ

2D function p(p,Φ)

is the Radon transform of f(x,y)

(Rf)(p,Φ)=RADON{f(x,y)}

(Radon, 1917)

Amazingly, it is possible to recover f(x,y) from all p(p,Φ)’s!


AS A STARTER, LET US LOOK ATCIRCULARLY-SYMMETRIC OBJECTS!

Radon transform!reduces to!

Abel transform !!


THE ABEL TRANSFORM (AT)!

Can we invert the Abel transform?


THE MODIFIED ABEL TRANSFORM (MAT)!

1. Change of variables!

AT

2. Definitions!

Can we invert the Modified Abel Transform?!

MAT


LTI-SYSTEM INTERPRETATION OFMODIFIED ABEL TRANSFORM!

(anticausal! )


1D FOURIER TRANSFORM (FT)!

IN SIGNAL PROCESSING COURSE!

FT

FT-1

FT

FT-1

FT


INVERTING THE MAT!

FT


LTI-SYSTEM INTERPRETATION OF MAT AND INVERSE MAT!

MAT INVERSE MAT


FINALLY … INVERTING THE AT!

1. Change of variables!

2. Definitions!

(Same as before)#

MAT-1 AT-1


THE ABEL TRANSFORM AND ITS INVERSE!

There are tables of AT pairs (just as for FTʼs)!

Example:!

AT

AT


FROM ABEL TO RADON!

• The AT and its inverse are the key to understanding image reconstruction from projections for circularly-symmetric objects!

• The existence of AT-1 is reassuring and gives hopes that one can reconstruct arbitrary objects from their projections!

• The RT generalizes the AT to arbitrary objects!

• Amazingly, the RT also has an inverse !!

• The fundamental result for understanding most of image reconstruction from projections is the projection-slice theorem!


KEY INITIAL CONTRIBUTORS TO IMAGE RECONSTRUCTION FROM PROJECTIONS!

1917 1956 1963 1968

Radon proposes

a backprojection method#

Bracewell proposes

projection-slice theorem#

Cormackpublishes

a first paper#

Hounsfield files

patent for CT scanner#

Johann RADON

(1887-1956)#

Ronald Newbold BRACEWELL (1921-2007 )

Allan M.CORMACK(1924-1998)

Nobel P. in Physiology or Medicine, 1979#

Godfrey N.HOUNSFIELD (1919-2004)

Nobel P. in Physiology or Medicine, 1979#



2D FOURIER TRANSFORM (FT)!

Most theorems and properties of 1D FT!extend to 2D FT!

2D FT

2D FT-1

FT


2D FOURIER TRANSFORMIN POLAR COORDINATES!

x

y

r θ

v

u Φ

ρ (x,y) (u,v)


ROTATING f(x,y) ROTATES F(u,v):(1) PROOF!

Rotation by α#

x

y

x

y

α FT

FT


ROTATING f(x,y) ROTATES F(u,v):(2) ILLUSTRATION!

FT

FT


! KEY 2D PROJECTION-SLICE RELATION FOR f(x,y) AND F(u,v)!

f(x,y)


2D PROJECTION-SLICE THEOREM:Due to R.N. Bracewell, 1956, in radioastronomy!


2D PROJECTION-SLICE THEOREM(FOR ARBITRARY OBJECTS)!

2D FT f(x,y) F(u,v)

p(x’,Φ) P(u’,Φ) 1D FT

PROJECT (RADON TRANSFORM)

SLICE (SET v’=0)


2D PROJECTION-SLICE THEOREMFOR CIRCULARLY-SYMMETRIC OBJECTS!

HANKEL TRANSFORM f(r) F(ρ)

p(x) P(u) 1D FT

PROJECT (ABEL TRANSFORM) same !

f(r)

p(x) F(ρ)

AT

FT

HT


HISTORY OF IMAGE RECONSTRUCTION FROM PROJECTIONS (1)!

1917:! Radon develops a filtered backprojection method for gravitation equations!

1956:! Bracewell develops projection-slice theorem for reconstructing microwave images of the sun

1961:! Oldendorf develops a reconstruction method based on backprojection!

1963:! Cormack publishes his 1st fundamental paper on reconstruction (2nd in 1964)

1967:! Hounsfield (an engineer) envisions possibility of reconstructing an image from X-ray attenuation measurements at several angles!


HISTORY OF IMAGE RECONSTRUCTION FROM PROJECTIONS (2)!

1968:! DeRosier and Klug solve reconstruction problem in electron microscopy!

1968:! Hounsfield and EMI file patent!1971:! EMI unveils 1st CT-scanner prototype!1972:! EMI ships 1st commercial CT-scanner!1972:! Hounsfieldʼs patent is published!1973:! Hounsfield publish his fundamental paper in

British J. of Radiology!1976:! EMI commercializes 1st CT-scanner!1979:! Cormack & Hounsfield share Nobel Prize in

Physiology or Medicine!


THE FOUR GENERATIONS OF SCANNING GANTRY DESIGNS!


IMAGING BY RADIONUCLIDE EMISSION!


IMAGING BY RADIONUCLIDE EMISSION INVOLVES THREE DISTINCT TASKS!

• Design, production, and administration of clinically-useful radionuclides (aka radioactive tracers or radiopharmaceutical), e.g. 18F.!

• Design and use of instruments for locating (i.e. "imaging") these tracers and following their temporal evolution in body!

• Determination of relations between tracers and physiology!


THREE MAIN TECHNIQUES FOR MEASURING RADIOACTIVITY!

• Photography (X-ray film)!• Ionization (effective for α, but not for γ)!• Luminescence (effective for α, β, γ)!

– Basis for widely-used scintillation detectors!– Used in Gamma camera, SPECT, and PET!


THE THREE FUNDAMENTAL TECHNIQUES OF RADIONUCLIDE EMISSION IMAGING!

• Projection (Gamma camera)!• Emission computed tomography (ECT)!

– Single-photon emission computed tomography (SPECT)!

– Positron emission tomography (PET)!


GAMMA CAMERA (1)!

• Detects γ-radiation via luminescence!• Developped by Hal Anger in the late 50ʼs!• Called!

– Scintillation camera or!– Gamma camera or!– Anger camera!

• Reflected, at the time, the convergence of nuclear physics, electronics, optics, and data processing in a clinical setting!


GAMMA CAMERA (2)!


GAMMA CAMERA (3)!


SINGLE-PHOTON EMISSION COMPUTED TOMOGRAPHY (SPECT)!


POSITRON EMISSION TOMOGRAPHY (PET)!


NEXT TIME …!

• Magnetic resonance imaging (MRI)!• Image-guided surgery!• Image segmentation!• Image registration!


ACKNOWLEDGMENTS!

Many thanks to the following people for helping putting this presentation together:!

Lara VigneronBenoît JaspartSophie le Maire Philippe Ries!

Documents

Introduction au génie biomédical - Montefiore Institute · GBI001.1 University of Liège! JGV 1/05/10 Introduction au génie biomédical! GBI0 001! ... Nobel P. in Physics, 1901#