2011-10-24 fmh-physik-kurs psi englisch(tony) · 2018-02-22 · 0 5 10 15 20 25 30 0.0 0.5 1.0 1.5...

Dr. Stephan Dr. Stephan KlKl ööck ck Head of Department for Medical PhysicsHead of Department for Medical Physics

(Interpreted by Tony Lomax)(Interpreted by Tony Lomax)

Basic physicsBasic physics24.24. OctoberOctober 2011 at PSI2011 at PSI

Overview of presentationOverview of presentation

1. Fundamentals of atoms and matter1. Fundamentals of atoms and matter

2. Fundamentals of Radiation2. Fundamentals of Radiation

3. Interactions of radiation with matter3. Interactions of radiation with matter

On November 8th 1895, Wilhelm Conrad Röntgen observed that ‘rays’ from a cathode ray-generator turned photographic

films black

Discovery of X-rays which resulted in first Nobel Price in 1901

Famous physicists 1Famous physicists 1

Albert Einstein (1879 - 1955, 3rd degree expert at the federal patent office in Berne) revolutionized modern physics, including

the first description of the photo-electric effect

Famous physicists 2Famous physicists 2

Macroscopic ViewMacroscopic ViewHow can we describe such a complex systemHow can we describe such a complex system……??

Microscopic ViewMicroscopic ViewHow can we describe such a complex systemHow can we describe such a complex system……??

Modern descriptors: Modern descriptors: Standardized Quantities and SI Standardized Quantities and SI -- UnitesUnites

cdLuminous Intensity Iv

molAmount of Substance n

KThermodynamic Temperature T

AElectric Current I

sTime t

kgMass m

mLength l

SystémeInternational d`Unités (SI)

Modern descriptors:Modern descriptors:Derived Quantities and UnitsDerived Quantities and Units

Energydose D

Voltage U

Electric Charge Q

Energy E

GyJ/Kg (m2 / s2)

Vm2 * kg / A * s3

Cs * A

Jm2 * kg / s2

1 eV = 1 Q e * 1 V = 1.6022 x 10-12 J(kinetic energy of an electron afterpassing an accelaration field of 1V)

For example:

Thomson‘s Model�Uniform mass distribution�Uniform charge distribution

Rutherford‘s Model�Concentration of mass

and charge in the nucleus�Negatively charged

electrons are forming a spherical cloud

Microscopic View Microscopic View -- Descriptions of the atomDescriptions of the atom

Bohr‘s Model of the Hydrogen Atom

�Combination of Rutherford‘s model and Planck‘s Idea of quantitized nature of radiation processes

�Electrons populate orbits without loosing energy despite being constantly accelerated

�The angular momentum of electrons in an allowed orbit is quantitized

�Emission of radiation occurs only when an electron transits from one orbit to another


Shellmodelof 56Ba


Categorisation of matter (elements)

From: http://From: http:// atom.kaeri.re.kratom.kaeri.re.kr //

Microscopic View Microscopic View -- Description of matterDescription of matter

Particles making up an atom :

�Z Protons

�N Neutrons

�Z Electrons

Atomic weight: A = Z + N

Protons and neutrons are known as nucleons

NAZ X

Microscopic View Microscopic View -- Description of matterDescription of matter

From: http://From: http:// atom.kaeri.re.kratom.kaeri.re.kr //

Microscopic View Microscopic View -- Description of matterDescription of matterE

lem

ents

Isotopes (increasing atomic weight (A))

Classification of RadiationClassification of Radiation

� Particle radiation� Electrons, protons, alpha-particles, neutrons, …

� Electromagnetic radiation� X-rays, Gamma rays, …

�Non-ionising radiation� Ultrasound, lasers, etc

Types of radiation

Emitted X-ray

Excitation

Relaxation

Scatter

Scatter δ

Scatter

Ionisation

Electron interactions with shell electrons

Radiation sources Radiation sources –– XX--ray productionray production

Elastic scattering Excitation Ionisation

+ + +

Emitted X-ray

Scatter

Electron interactions with nuclei


Elastic scattering Bremstrahlung Nuclear interactions

+ +

Scatter

Emitted X-ray

n

p

Electron lost from beam

Secondary particles

Radiation sources Radiation sources –– XX--ray productionray productionTypical X-ray spectrum

Bremstrahlungcontinuum

Characteristic energy for L-K shell transitions

Characteristic energy for M/N-

K shell transitions

� Bremsstrahlung- Due to electron-nucleus Coulomb interactions

� Characteristic radiation- Due to electronic transitions from atomic shells with

higher energy to lower energy-shells- Occurs after electron excitation or ionisation-

processes

Radiation sources Radiation sources –– XX--ray productionray productionCharacteristics of the X-ray spectrum

� Loss of energy/particles due to collisions- Electrons (energy loss)

- Nuclei (particle loss)

� Loss of energy due to electromagnetic (radiative) inte ractions (including Bresmstrahlung)

- Predominant effect for energy loss for all particles

- Bremstrahlung only important for electrons

� Finite range of particles- Dependent on initial energy- Dependent on ‚stopping power‘ of material

Electron (particle) energy losses and range


Collision-stopping power

E.g. stopping powers for Electrons


Radiativestopping power

X-ray generation is relatively inefficient

X-ray tube and electronic Scheme


X-ray tubes (detail)


Diagnostics (~100KeV)

Therapy (Orthovoltage ~500-600 KeV)


β– - DecayThe spontaneous decay of a neutron into a proton and an electron (+ an anti-neutrino!)

_

υ++⇒−epn

Radiation sources Radiation sources –– RadioRadio --isotopesisotopesExamples of radioactive decay mechanisms

_

1 υ++⇒−

+ eYX AZ

AZ

β+ - DecayThe spontaneous decay of a proton into a neutron and a positron (+ a neutrino!)

υ++⇒+enp

υ++⇒+

− eYX AZ

AZ 1

α42

42 +⇒

−− YX A

ZAZ

α - DecayThe spontaneous emission from a high-Z nucleus of an alpha particle

Quantity/ Unit:

Decay results in an exponential decrease of radioactivity within the sample

teA ⋅−⋅= λ0A

2/10

0 A2

A Te ⋅−⋅= λ

A Bq1(decay event) / s

Radiation sources Radiation sources –– RadioRadio --isotopesisotopesRadioactivity

T1/2 is called the ‘half-life’of the radioisotope (the

time it takes for activity to decay by one half)

The most important radioactivity for radiotherapy…

From: http://en.wikipedia.org/wiki/File:Cobalt-60_Decay_Scheme.svg

Radiation sources Radiation sources –– RadioRadio --isotopesisotopesThe decay scheme of Co-60

� β- decays which leave the nucleus in an excited state

� Nucleus then ‘relaxes’to the final decay product (60-NI) through two stages

� For first ‘relaxation’ a photon of 1.17MeV is emitted

� For the second a photon of 1.33 MeV

60Co-Gamma emission spectrum

The energy of both is higher than typically acheivable with X-ray tubes

Hence historical and continued application in radiotherapy….

From:http://de.wikipedia.org/wiki/Gammaspektroskopie

E = 1.17 MeVE = 1.33 MeV

Radiation sources Radiation sources –– RadioRadio --isotopesisotopes

Classification of RadiationClassification of Radiation

� Direct ionisation (charged particles)

�electrons, protons, alpha-particles etc.

� Indirect ionisation (uncharged radiation) �X-rays, gamma rays, ...

Interactions effects

� Elastic Scattering- Thomson, Rayleigh, …

� Inelastic scattering - Compton scattering

� Absorption by orbiting electrons- photoelectric effect , triple production

� Absorption by the nucleus or the resulting coulomb field- pair production , photo-destruction

Note – Indirect ionising radiations have no maximum range…!

Indirect ionisation (uncharged radiation) Indirect ionisation (uncharged radiation)

Attenuation of (uncharged) radiation beams

Attenuation of electromagnetic radiation in matter through scatter and absorption leads to exponential decrease of

intensity

Absorber

„Intensity“

Indirect ionisation (uncharged radiation)Indirect ionisation (uncharged radiation)

Penetration

No maximum range…!

deI ⋅−⋅= µ0I

2/10

0 I2

I de ⋅−⋅= µ

Indirect ionisation (uncharged radiation)Indirect ionisation (uncharged radiation)Attenuation of (uncharged) radiation beams

Like radioactive decay, the non-deterministic effects of attenuation can be described statistically…

d1/2 is called the ‘half-thickness’ of the material

(the thickness of the material which reduces beam intensity (I) to half

its original intensity)

Where µ is called the ‘Linear attenuation coefficient’ of the traversed material

Linear attenuation coefficient is the probability (per unit path length) that a photon will have an interaction with the absorber

It is dependent on the attenuation coefficients for three main processes� τ τ τ τ −−−− Photoelectric effect (nuclear absorption)

� κ κ κ κ −−−− Pair production (electron absorption)

� σσσσ −−−− Compton scattering (inelastic scattering)

κστµ ++=

Indirect ionisation (uncharged radiation)Indirect ionisation (uncharged radiation)Attenuation of (uncharged) radiation beams

The Photoelectric Effect (The Photoelectric Effect ( ττττττττ))


The removal of a inner shell electron by the direct interaction of a photon and loss of photon

� Steep decrease of ττττ with increasing energy � Strong dependency on absorber‘s Z� Linear density dependency much less important than Z

relation.

−− +=⋅ ebind

ekin EEh ν

ρτ ⋅∝3

3

E

Z

The Photoelectric Effect (The Photoelectric Effect ( ττττ))


� Energy dynamics

� Attenuation coefficient

Compton scattering (Compton scattering ( σσ))


Removal of a loosely bound outer shell electron and scattering of photon

'νν ⋅++=⋅ −− hEEh ebind

ekin

ρσ ⋅∝A

Z

� Z/A for different elements approximately constant (0.4-0.5) � Linear relationship with density

� Energy dynamics


Compton scatteringCompton scattering


Pair production (Pair production ( κκκκ))Indirect ionisation (uncharged radiation)Indirect ionisation (uncharged radiation)

The spontaneous conversion (in the neighbourhood of the nucleus) of a photon into an electron and positron

−++− ++=⋅ /02 ee

kinekin EEEh ν

)lg( νρκ ⋅⋅⋅∝ hZ

� Energy threshold at: 2*me*c2 = 1.22 MeV� Overwhelms Compton scattering (σ/ρ = κ/ρ) at energies

>25 MeV in water

Pair productionPair production


� Energy dynamics


� All contributions to the total attenuation coefficient are density-dependant

� Formalism of mass attenuation coefficient

ρµµ /=m

cm2 / gMass attenuation coefficient µm

cm-1Linear attenuation coefficient µ

Mass attenuation coefficientMass attenuation coefficient




σ (Compton scattering)

τ (Photo electric)

κ (Pair production)

µm (Total)

Energy fluence rate

(Amount of energy crossing a unit area per unit time)

tA

EΨ

dd

d

⋅=

MeV / cm2 * sEnergy fluence rate Ψ

Energy Energy fluencefluence rate for photon beamsrate for photon beams

Photon beamsPhoton beams

Settings for U/R are standardized, so the produkt of I*tdefines the dose/blackness on a film

IΨ ∝ 2≈∝ UΨ

tIR

UtΨD ⋅⋅∝⋅∝

2

2

mA * s„Exposure“



The inverse square law

2

1

RΨ ∝



Photons

Depthdosecurves:6 & 15 MV, FS 2x2 & 40x40

Electron build-up effect (skin sparing)

Characteristics of therapeutic beamsCharacteristics of therapeutic beams

6 MV

15 MV

Photons:

Profiles:6 & 15 MeV, FS 2x2 & 40x40


Shallow depths

Deep depths

Photon fieldwith wedge:

Profiles:6 MeV, Lead wedge (60°), FS 3x3 & 40x15


Electrons:

Depthdosecurves :6, 9, 12, 15, 18, 22 MeV, FS 2 round & 25x25


Finite range!


Protons:

Depthdosecurves :100MeV-210MeV, 3x3mm pencil beams

0 5 10 15 20 25 300.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

Dos

e [a

rbitr

ary

units

]

Depth [cm]

210MeV 200MeV 190MeV 180MeV 170MeV 160MeV 150MeV 140MeV 130MeV 120MeV 110MeV 100MeV

Finite range!

X-ray radiographs

Density-distribution

Nuclear medicine

Radiopharmaceutical concentration

Medical use of radiationMedical use of radiation

DiagnosticsDiagnostics


DiagnosticsDiagnostics


RadiotherapyRadiotherapy

Good Bye and Good Good Bye and Good LuckLuck

LiteratureLiterature ::

� Dosimetrie ionisierender Strahlung, H. Reich, B.G. Teubner, Stuttgart, 1990

� Strahlenphysik, Dosimetrie und Strahlenschutz in zweiBänden, B.G. Teubner, Stuttgart, 1992 (Bd.1) & 1997 (Bd. 2)

� Radiation Oncology Physics: A Handbook for Teachers and Students. E.B. Podgorsak, IAEA-Publication, 2005 (available via internet)

� http://de.wikipedia.org/wiki/Hauptseite

2011-10-24 fmh-physik-kurs psi englisch(tony) · 2018-02-22 · 0 5 10 15 20 25 30 0.0 0.5 1.0 1.5...

Documents