biomedical imaging i

BMI I FS05 – Class 1 “X-Ray Physics” Slide 1

Biomedical Imaging IBiomedical Imaging I

Class 1 – X-Ray Imaging I: Background and Physics

9/14/05

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BackgroundBackground

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IntroductionIntroduction

Aim of medical imaging:

Creating images of internal structures (and functions) in a living (human) organism

Preferably non (or minimally) destructive / noninvasive

Diagnostic implications

Achieved by using the capability of various forms of energy to penetrate and interact with matter.

Historic starting point:

W. K. Röntgen’s discovery of the X rays experimenting with a cathode ray tube and fluorescent screen/photographic film (1895, 1901 first Nobel award in physics).

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Discovery of x-raysDiscovery of x-rays

X-ray history on the web:

http://www.xray.hmc.psu.edu/rci/centennial.html

Physical Institute, University of Würzburg, Germany.

Wilhelm Konrad Wilhelm Konrad RRööntgen (1845-1923)ntgen (1845-1923)

(photographed in 1896)(photographed in 1896)

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Discovery of x-raysDiscovery of x-rays

Cover of Original Publication: "A New Kind of Rays"

Wilhelm Konrad Wilhelm Konrad RRööntgen (1845-1923)ntgen (1845-1923)

(photographed in 1896)(photographed in 1896)

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First x-ray imagesFirst x-ray images

Radiograph of the hand of Albert von Kolliker, made at the conclusion of Roentgen's lecture and demonstration at the Würzburg Physical-Medical Society on 23 January 1896.

The famous radiograph made by Roentgen on 22 December 1895, and sent to physicist Franz Exner in Vienna. This is traditionally known as "the first X-ray picture" and "the radiograph of Mrs. Roentgen's hand. "

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Early x-ray setupEarly x-ray setup

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X-rays in clinical useX-rays in clinical use

Dr. Edwin Frost (1866-1935) is credited with making the first diagnostic radiograph in the U.S. at Dartmouth on 3 February 1896.

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X-rays in clinical useX-rays in clinical use

E. Haschek and 0. Lindenthal produce first contrast-enhanced radiograph of veins in hand (Vienna, January 1896).

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X-ray dangersX-ray dangers

Mihran Kassabian (1870-1910) meticulously noted and photographed his hands during progressive necroses and serial amputations.

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X-ray publicationsX-ray publications

In May of 1897, Heber Robarts, M.D., of St. Louis, launched the American X-ray Journal.

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X-ray imaging principleX-ray imaging principle

X-ray imaging background, foundations:

(History)

X-rays

Atomic structure

Important x-ray-matter interactions

X-ray instrumentation / applications:

Generation of x-ray

Detection of x-ray

Specific applications

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Physical foundationsPhysical foundations

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Atom and electronic transitionsAtom and electronic transitions

Electrons (-) are organized in shells around nucleus (+)

Higher shell (greater shell radius) = higher electronic energy

Electronic transitions between shells require or release energy

+

-

--

n = 1

n = 2

n = 3

E = h = E3 - E2

E = h = E2 - E1

Absorption

Emission

Excitation

Relaxation

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Complex AtomsComplex Atoms

Number of protons Z: Atomic number (determines element)

Number of neutrons N: Neutron number

Number of protons + neutrons Am = Z + N: Mass numberNa

22

11

-

-

-

-

--

- -

--

-+

+

+

+ ++

+ +

+

K-shell (n=1, strongly bound)

L-shell (n=2)

M-shell (n=3, weakly bound)

...

Valence electron

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Energy schemeEnergy scheme

Binding energy (BE): energy binding electron to atom

Ionization energy IK,L,… BE: amount of energy needed to remove electron from atom

BE counted in negative units of electron volts (eV)

At infinity, BE 0. Continuum

Zero

K

L

M

N

E

Binding energy for 53I: -33.2 keV (K), -4.3 keV (L), -0.6 keV (M)

BE for valence electrons: ~ -10 eV (H: -13.6 eV)

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Wave vs. particle interpretationWave vs. particle interpretation

X-ray as electromagnetic wave:

Frequency = 1/T [s-1 = Hz]

Wavelength [m]

Propagation at speed of light c = inverse relationship of and

X-ray as particle (photon):

Stream of weightless, neutral particles moving at speed of light

Each photon carries energy:

Radiation intensity I [W/cm2]:

2 2

number of photons photon energyPower W Energy J

Area cm Time Area cm Time Areapn E h

h

n

AEp h hc/

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Electromagnetic spectrumElectromagnetic spectrum

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X-rays characteristicsX-rays characteristics

EM radiation at wavelengths 0.1 – 100 keV (10 – 0.01 nm)

Diagnostic Range ~1-100 keV

Ionization energy for valence electrons < ~10 eV X-rays is ionizing radiation (harmful)

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Energy unitsEnergy units

SI unit: 1 Joule [J] = 1 Nm = 1 kg m2 s-2

Electron volt [eV]: The potential energy of one elementary charge gained/lost (e = 1.610-19 C) when crossing a potential difference of 1V:

1 eV = 1.610-19 C 1 V = 1.610-19 [A s V] = 1.610-19 J

100 keV = 105 1.610-19 J = 1.610-14 J = 16 fJ (… per photon)

+

-

1V

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X-Ray Interaction with MatterX-Ray Interaction with Matter

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Interaction Processes Interaction Processes

Absorption: photon is destroyed and its entire energy is transferred to the target

Scattering: photon is deflected and might or might not transfer portion of its energy to the target (inelastic & elastic scattering, respectively)

Each interaction removes photon from beam path, thereby decreasing the beam intensity

target detector

beam path

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X-Rays in a Homogeneous TargetX-Rays in a Homogeneous Target

Consider the relative change in intensity dI across small distance dx:

dI is proportional to: – I dx

t n linear attenuation coefficient

dIdI I dx I

dx

x

dx

I0 Id

Target

I I - dI

l0

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Exponential Law of AbsorptionExponential Law of Absorption

Integration over entire target length:

The exponential law of absorption:

0 0

00

0

ln ln ln

dI l

I

dd

ld

dIdx

I

II I l l

I

Ie

I

0xI x I e

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Linear attenuation coefficientLinear attenuation coefficient

Linear attenuation coefficient [cm-1] depends on photon energy and material absorption spectra

Half value layer HVL = the thickness after which intensity is reduced to half of the initial value:

Mass-attenuation coefficient / [cm2/g] independent of physical state of material

HVL0 HVL 0.52

ln 2 HVL

ln 2 0.693HVL

xII x e

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Physical interaction processesPhysical interaction processes

Relevant interaction processes and their individual coefficients:

Photoelectric absorption

Compton scattering

linear absorption coefficient is the sum of individual absorption and scattering coefficients

= pecs

Coefficients = pecs are proportional to the interaction probabilities

(also: “cross-section” [ and, respectively]) of each process.

Questions:

• What are the mechanisms for the different interaction processes?

• What do they depend on?

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Photoelectric absorptionPhotoelectric absorption

The photon knocks an electron out of one of the inner shells of a target atom. The electron is excited into the continuum; the photon is destroyed in the process.

Possible for a given shell only if photon energy Ep exceeds ionizing energy for the shell:

Kinetic energy of electron Ke according to energy conservation:

-

--

-

--- -

--

-

Ep = h

Ke

KLM

Continuum0

IK

IL

IM

IN

E

Ep IK, L, M,...

Ke= Ep IK, L, M,...

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Photoelectric absorptionPhotoelectric absorption

Photoelectric absorption process is most likely – i.e. the cross section is largest – for Ep IK, L, M,... (resonance)

Photoelectric absorption cross section decreases strongly with photon energy ( Ep

-3) as photon energy increases relative to IK, L, M,...

Photoelectric absorption cross section increases strongly with Z (~ Z3) because I Z

Photoelectric absorption in K shell usually dominates

Photoelectric absorption depends on:

Z – The atomic number of the element

E – The radiation (photon) energy

3

3p

Z

E

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Compton scatteringCompton scattering

The x-ray photon interacts with one of the weakly bound electrons of the atom. This electron can be considered free because Ex-ray 1-100 keV >> Ee,b few eV.

Inelastic scattering process:

x

y

px

y

'p

e

2;

1 (1 cos ) 511p p p

p p ee

E E EE E E

m c

keV

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Compton cross-section Compton cross-section

Compton scattering cross-section decreases with photon energy

Compton scattering cross-section increases with electron density e[electrons/cm3]

Weak dependence (increase) on Z

Compton scattering depends on:

E – The radiation (photon) energy

– The electron density

1eE

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Compton scattering angular distributionCompton scattering angular distribution

Likelihood of a photon to be scattered into a certain direction depends on photon energy Ep:

Low Ep high “backscatter” probability (~180)

High Ep high “forward scatter” probability (peaked distribution,~ 0)

incidentphotons

180

0

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Cross section examples ICross section examples I

PE: Photoelectric absorption

S: Compton scatter

PR: Pair production (for E > 2MeV, not

relevant for medical imaging)

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Cross section examples IICross section examples II

/[

cm2 /

g]

Z = 6 Z = 53 Z = 82

Legend:

: Photoelectric absorption: Compton scatter: Pair production

Not discussed in detail in lecture:

r: Raleigh scattertr: Triplett productiontr: mass energy transfer coeff.tr: photoelectric energy transfer coeff.en: mass energy absorption coeff.

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Attenuation coefficient dependenciesAttenuation coefficient dependencies

Legend:

: photoelectric cross-sect. @ Z = 6(C): photoelectric cross-sect. @ Z = 64 (Gd): Compton cross-sect. @ Z = 6(C): Compton cross-sect. @ Z = 64 (Gd) : photoelectric cross-sect. @ 20 keV: photoelectric cross-sect. @ 60 keV: Compton cross-sect. @ 20 keV: Compton cross-sect. @ 60 keV

Z3/4

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Contribution of interactionsContribution of interactions

Z (tissue) < 10E (diagnostic x-ray) < 10…100 keV

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X-ray contrastX-ray contrast

Soft tissue components: Z < 10

Bone: 20Ca

Air filled spaces

I

x

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X-ray contrast examplesX-ray contrast examples