Physics of particles - PTCOG

Physics of particles

H. Paganetti PhD Massachusetts General Hospital & Harvard Medical School

ideal

Depth

Do

se

Introduction

The ideal dose distribution

[J/kg] [Gy] Energy/Mass Dose: Energy deposited

e g

Z

Photoelectric

Effect Photon ejects electron

from an atom.

Compton

Effect Photons scattering

from atomic electrons.

f

g

e

q

g

’

Pair

Production Photons above twice

the electron rest mass

energy can create a

electron positron pair.

e+ g

e-

Z

Introduction

Dose deposition

Electrons

Introduction

Photons

ideal

Depth

Do

se

BEAM

Introduction

Also:

Modulation of intensities

Introduction

© INFN

• Photons – Charge: 0

– Indirect Ionization

• Electrons – Charge: -1

– Direct Ionization

– Mass: 512 keV

• Protons – Charge: +1

– Direct Ionization

– Mass: 2,000 • me

Introduction

Dose deposition

Protons Electrons

Introduction

The Bragg curve

depth [mm]

0 50 100 150 200 250 300

Do

se [

%]

0

20

40

60

80

100

120

Mono-energetic proton beam

Introduction

Photons

ideal

Protons

Depth

Do

se

BEAM

Beam energy controls the range

EXTRA DOSE

Introduction

depth [mm]

0 50 100 150 200 250 300

Do

se [

%]

0

20

40

60

80

100

120

• Distal distribution

Electromagnetic energy loss of protons

e

p p

–Ionization

–Excitation

Interaction probability

is proportional to

proton energy

Protons/Ions – Basic Physics


Bethe-Bloch equation

+--++-

-

G

Z

CLzzL

I

Tcmzcmrn

dx

dE eeee

2)(2)(22

)1(

2ln

22

2

1

2

22

max

22

2

222

0

I : mean excitation energy , material-dependent

δ : density correction

C : is the shell correction, important at low energies

Tmax : maximum energy transfer to an electron

L1 : Barkas correction (z3)

L2 : Bloch (z4) correction

G : Mott corrections


-dE

dx=

4pnk2Z2e4

mc2b 2ln

2mc2b 2

I (1- b 2 )- b 2

é

ëê

ù

ûú

Bethe [-Bloch] equation

= v/c


Dose = fluence × mass stopping power

N protons

area A

Δx

0

5

10

15

20

25

30

35

40

0 50 100 150 200 250 300

Energy (MeV)

Ran

ge (

cm

)

Eye treatments

Deep seated tumors

Typical treatments


Radiography depth [mm]

0 50 100 150 200 250 300

Do

se [

%]

0

20

40

60

80

100

120


© GSI

Protons

• Protons lose their energy in individual

collisions with electrons

• Protons with the same initial energy may have

slightly different ranges:

“Range straggling”


depth [mm]

0 50 100 150 200 250 300

Do

se [

%]

0

20

40

60

80

100

120

depth [mm]

0 50 100 150 200 250 300

Do

se [

%]

0

20

40

60

80

100

120


© H. Paganetti “Proton Therapy Physics” Taylor & Francis / CRC Press

Beam Range

100%

90%

80%

Electromagnetic energy loss of protons

• Lateral distribution

p’

p q

Proton Pencil Beam

Multiple Coulomb scattering (small angles)



• Protons are deflected in the electric field of

the nuclei. In general, multiple deflections will

occur

• For treatment planning related calculations a

purely Gaussian approximation is a good

approximation, except at the very end of the

range

Multiple Coulomb Scattering

200 MeV

160 MeV



0 50 100 150

4

3

2

1

0

s M

CS

[m

m]



Protons (148 MeV) 12C-ions (270 MeV/A)

Depth [mm]

80/20 Penumbra Comparison

0.00

0.25

0.50

0.75

1.00

15 cm 20 cm 25 cm

Normalization Depth

80 -

20 %

Dis

tan

ce (

cm

)

15 MV Photons

Protons

17 cm



20

40

60

80

100

Ø 2 mm

Ø 4 mm

Ø 6 mm

Ø 8 mm

Ø

Do

se

Depth


© A. Koehler (HCL)

g, n

p’

p p

p’

Elastic nuclear collision (large q) Nuclear interaction


Nuclear interactions of protons



• A certain fraction of protons have nuclear

interactions in tissue, mainly with 16O

(about 1% per cm of all protons)

• Nuclear interactions cause a decrease in primary

proton fluence

• Nuclear interactions lead to secondary particles

and thus to local and non-local dose deposition

(neutrons!)

• The dose from nuclear interactions is negligible in

the Bragg peak



Carbon (closed circles)

Oxygen (open circles)

© H. Paganetti “Proton Therapy Physics” Taylor & Francis / CRC Press


Total fluence

Primary fluence

Nuclear build-up


total energy

deposited

Contribution

in %

primary

protons

secondary

protons

alphas

&

recoils

Nuclear interactions of heavy ions

12C

Elastic nuclear collision (large q)

12C’

g, n

4He

Nuclear interaction (fragmentation)

12C




Fragmentation tails

© I. Pshenischnov





© I. Pshenischnov

Photons

ideal

Protons

Depth

Do

se

BEAM

Clinical dose distributions

Spread-out Bragg Peak

thickness

width



Multiple scattering angle and

energy loss for 160 MeV

protons traversing 1 g/cm2

of various materials

H i g h - D e n s i t y

S t r u c t u r e

B o d y

S u r f a c e

C r i t i c a l

S t r u c t u r e

T a r g e t

V o l u m e

B e a m

A p e r t u r e


Take Home Messages

• Heavy charged particles interact very

differently from photons (used in conventional

radiation therapy)

• The most important interactions are

ionization, Coulomb scattering, and non-

elastic nuclear interactions

• Heavy charged particle treatments are

associated with the reduction of the total

energy deposited in the patient by more than

a factor of 2

Physics of particles - PTCOG

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