Radiation therapy is based on the exposure of malign Radiation therapy is based on the exposure of malign tumor cells to significant but well localized doses of radiation to tumor cells to significant but well localized doses of radiation to destroy the tumor cells. The goal is to maximize the dose at destroy the tumor cells. The goal is to maximize the dose at the tumor location while minimizing the exposure of the the tumor location while minimizing the exposure of the surrounding body tissue.surrounding body tissue.

Radiation therapy can be Radiation therapy can be performed by using external radiation performed by using external radiation sources (charged particle exposure by sources (charged particle exposure by accelerator beams, neutron exposure by accelerator beams, neutron exposure by reactor beams - reactor beams - EXTERNAL BEAM EXTERNAL BEAM THERAPY) THERAPY) or by using internal radiation or by using internal radiation sources (long-lived radioactive sources sources (long-lived radioactive sources in close vicinity of the tumor in close vicinity of the tumor - - BRACHYTHERAPY).BRACHYTHERAPY).

Both approaches (EXTERNAL BEAM THERAPY and Both approaches (EXTERNAL BEAM THERAPY and BRACHYTHERAPYBRACHYTHERAPY) require careful treatment planning since the ) require careful treatment planning since the radiation therapy is technically difficult and potentially dangerous. radiation therapy is technically difficult and potentially dangerous.

The most important parameters The most important parameters for treatment planning and dose for treatment planning and dose calculations are:calculations are:

• energy loss of radiation energy loss of radiation

• stopping power of radiation (LET)stopping power of radiation (LET)

• range and scatter of radiationrange and scatter of radiation

• dose and isodose of radiationdose and isodose of radiation

These parameters need to be carefully studied for planning the These parameters need to be carefully studied for planning the radiation treatment to maximize the damage for the tumor while minimizing radiation treatment to maximize the damage for the tumor while minimizing the potential damage to the normal body tissue. An insufficient amount of the potential damage to the normal body tissue. An insufficient amount of radiation dose does not kill the tumor, while too much of a dose may radiation dose does not kill the tumor, while too much of a dose may produce serious complications in the normal tissue, may in fact be produce serious complications in the normal tissue, may in fact be carcinerouscarcinerous ..

The energy loss of the radiation defines the " linear energy transfer“ The energy loss of the radiation defines the " linear energy transfer“ (LET see section on biological effects of radiation) and therefore the (LET see section on biological effects of radiation) and therefore the absorbed dose absorbed dose D. D. The solid line indicates the probability for destroying the The solid line indicates the probability for destroying the tumor cells as a function of dose. The dashed line corresponds to the tumor cells as a function of dose. The dashed line corresponds to the probability of causing cancer as a function of dose. A reduction of dose from probability of causing cancer as a function of dose. A reduction of dose from 50 Gy to 45 Gy (5% reduction) lowers the chances of cure significantly from 50 Gy to 45 Gy (5% reduction) lowers the chances of cure significantly from 65% to 15%. On the other hand an increase of dose by 5% to 60 Gy may kill 65% to 15%. On the other hand an increase of dose by 5% to 60 Gy may kill all the cancer cells but increases the risk of complications from 10% to 80%.all the cancer cells but increases the risk of complications from 10% to 80%.

ENERGY LOSS OF PARTICLE RADIATION IN MATTERENERGY LOSS OF PARTICLE RADIATION IN MATTER

Energy loss and dose are correlated with each other and Energy loss and dose are correlated with each other and help to formulate the interaction of internal and external radiation help to formulate the interaction of internal and external radiation with matter to predict the affectivity of the radiation treatment and with matter to predict the affectivity of the radiation treatment and the possible damage to adjacent body tissue.the possible damage to adjacent body tissue.

Radiation treatment is based on different kind of radiation Radiation treatment is based on different kind of radiation and depends on the different kind of interaction between the and depends on the different kind of interaction between the radiation and matter (body tissue).radiation and matter (body tissue).

• • interaction by collision with nuclei in material (short range forces) interaction by collision with nuclei in material (short range forces)

1. Light charged particles (electrons)1. Light charged particles (electrons)

• • excitation and ionization of atoms in absorber material (atomic effects)excitation and ionization of atoms in absorber material (atomic effects)

• • interaction with electrons in material (collision, scatter)interaction with electrons in material (collision, scatter)

• • deceleration by Coulomb interaction (Bremsstrahlung)deceleration by Coulomb interaction (Bremsstrahlung)

2. Heavy charged particles (Z>1)2. Heavy charged particles (Z>1)

• • excitation and ionization of atoms in absorber material (atomic effects)excitation and ionization of atoms in absorber material (atomic effects)

• • Coulomb interaction with nuclei in material (collision, scatter) Coulomb interaction with nuclei in material (collision, scatter) (long range forces)(long range forces)

3. Neutron radiation3. Neutron radiation

Each interaction process leads to a certain amount of Each interaction process leads to a certain amount of energy loss, since a fraction of the kinetic energy of the energy loss, since a fraction of the kinetic energy of the incoming particle is transferred to the body material by incoming particle is transferred to the body material by scattering, excitation, ionization or radiation loss. scattering, excitation, ionization or radiation loss.

The interaction between radiation particles and The interaction between radiation particles and absorber material determines the energy loss of the particles absorber material determines the energy loss of the particles and therefore the range of the particles in the absorber material.and therefore the range of the particles in the absorber material.

The sum over all energy loss events along the trajectory The sum over all energy loss events along the trajectory of the particle yields the total energy loss.of the particle yields the total energy loss.

Electrons are light mass particles, electrons are Electrons are light mass particles, electrons are therefore scattered easily in all directions due to their therefore scattered easily in all directions due to their interactions with the atomic electrons of the absorber interactions with the atomic electrons of the absorber material. This results into more energy loss per scattering material. This results into more energy loss per scattering event.event.

The multiple scattering results in a very limited spatial The multiple scattering results in a very limited spatial resolution of the electron beam within the absorber material.resolution of the electron beam within the absorber material.

The energy loss of the electrons is dominated by The energy loss of the electrons is dominated by excitation and ionization effects (dE/dx)excitation and ionization effects (dE/dx)excexc and by bremsstrahlung and by bremsstrahlung

losses (dE/dx)losses (dE/dx)radrad,,

the energy loss components depend sensitively on the charge the energy loss components depend sensitively on the charge number number ZZ and the average ionization potential I and the average ionization potential I 11.5 11.5Z Z [eV] of the [eV] of the absorber material, the number density N, the relativistic velocity of absorber material, the number density N, the relativistic velocity of the electrons v ( the electrons v ( = v/c ) = v/c ) with mass mwith mass m00..

First term is proportional to First term is proportional to ZZ::

Second term is proportional to Second term is proportional to ZZ22 and energy and energy EE::

The ratio between these two components The ratio between these two components depends on the energy of the electron beam depends on the energy of the electron beam E E and the and the charge charge Z Z of the absorber material.of the absorber material.

EXAMPLEEXAMPLEfor Pb with Z=82, for for Pb with Z=82, for E E 8.5 MeV radiative losses dominate. 8.5 MeV radiative losses dominate.

Because of the strong interaction with the absorber material, Because of the strong interaction with the absorber material, electrons experience immediate energy loss and the intensity drops electrons experience immediate energy loss and the intensity drops rapidly. This limits the range rapidly. This limits the range R(E) R(E) of the electron beam in the material:of the electron beam in the material:

Body tissue is typically low Body tissue is typically low Z Z material and the material and the range can be approximated by a simple expression:range can be approximated by a simple expression:

EXAMPLEEXAMPLE

The range of 100 keV and 1.0 MeV electrons in muscle The range of 100 keV and 1.0 MeV electrons in muscle tissue is 1.33tissue is 1.331010-2-2 g/cm g/cm22 and 0.412 g/cm and 0.412 g/cm22, respectively., respectively.

andand

For heavy ions the electron loss is described by the Bethe For heavy ions the electron loss is described by the Bethe formula in terms of the number density formula in terms of the number density N N and charge number and charge number Z Z of the of the absorber material and the charge number absorber material and the charge number zz, mass m, mass m00, and velocity , and velocity v v

of the projectiles.of the projectiles.

the average ionization potential is I the average ionization potential is I 11.5 11.5Z Z [eV].[eV].

The energy loss is used to calculate the stopping power for the The energy loss is used to calculate the stopping power for the projectiles in the material and their range. The stopping power is defined as projectiles in the material and their range. The stopping power is defined as the energy loss per distance: the energy loss per distance:

or as energy loss per distance and number density (or density):or as energy loss per distance and number density (or density):

The stopping power is proportional to The stopping power is proportional to ZZ22, , it increases it increases rapidly at low energies, reaches a maximum and decreases rapidly at low energies, reaches a maximum and decreases gradually with increasing energy.gradually with increasing energy.

The stopping power allows to calculate the range of the The stopping power allows to calculate the range of the heavy particles in the absorber material.heavy particles in the absorber material.

(Note, heavy particles are less scattered than electrons due to (Note, heavy particles are less scattered than electrons due to their heavy masses and the beam shows significantly better their heavy masses and the beam shows significantly better spatial resolution.)spatial resolution.)

Because of the specific energy dependence of the energy loss Because of the specific energy dependence of the energy loss (or stopping power curve) incoming high energy particles experience (or stopping power curve) incoming high energy particles experience only little energy loss only little energy loss dE/dx, dE/dx, but the energy loss maximizes when but the energy loss maximizes when particles have slowed down to energies which correspond with the peak particles have slowed down to energies which correspond with the peak of the energy loss curve. The energy of the particles (with an initial of the energy loss curve. The energy of the particles (with an initial energy energy EEi i ) ) at a certain depth at a certain depth d d can be derived by:can be derived by:

The position The position ddmaxmax of maximum energy loss can be directly of maximum energy loss can be directly

calculated from the initial energy and the stopping power of the calculated from the initial energy and the stopping power of the projectiles in the absorber material.projectiles in the absorber material.

for protons the energy loss maximizes at energies around for protons the energy loss maximizes at energies around E ( d ) E ( d ) 100 100 keV, keV, for for -particles around 1 MeV.-particles around 1 MeV.

Due to interaction with the body material the projectiles Due to interaction with the body material the projectiles scatter and the beam widens as a function of depth. This effect is scatter and the beam widens as a function of depth. This effect is called angle straggling.called angle straggling.

The angle straggling is more pronounced for electron The angle straggling is more pronounced for electron beams due to the large momentum transfer. For beam particles beams due to the large momentum transfer. For beam particles (single charge) with momentum (single charge) with momentum p p and velocity and velocity v, v, angle straggling in angle straggling in a target with number density a target with number density NN and charge number and charge number Z Z over a over a thickness thickness d d is described by:is described by:

with e as elementary charge. Because of the substantially smaller mass of with e as elementary charge. Because of the substantially smaller mass of electrons the angle straggling range is significantly larger than for protons and electrons the angle straggling range is significantly larger than for protons and heavier particles. Angle straggling results in an increase of the bombarded area heavier particles. Angle straggling results in an increase of the bombarded area with depth. It defines the isodose profile during the radiation procedure.with depth. It defines the isodose profile during the radiation procedure.

INTERACTION OF INTERACTION OF -RAYS WITH MATTER-RAYS WITH MATTER

Energy loss effects for Energy loss effects for and X-ray radiation are characterized by and X-ray radiation are characterized by

• photo effectphoto effect

• Compton scatteringCompton scattering

• pair productionpair production

Photons interact with matter by photo absorption which Photons interact with matter by photo absorption which causes excitation or ionization of atoms. Only photons of well defined causes excitation or ionization of atoms. Only photons of well defined energies corresponding to the excitation energies in the atoms are energies corresponding to the excitation energies in the atoms are absorbed for excitation processes.absorbed for excitation processes.

The probability for photoelectric absorption The probability for photoelectric absorption determines determines the attenuation of the the attenuation of the -radiation due to photoeffect:-radiation due to photoeffect:

with with n n 4.5 depending on the photon energy 4.5 depending on the photon energy EE and Z the and Z the

charge number of the absorber material. As higher Z as better charge number of the absorber material. As higher Z as better the absorption probability. The photo effect dominates at low the absorption probability. The photo effect dominates at low energies.energies.

The Compton scattering represents scattering of photons of The Compton scattering represents scattering of photons of energy energy = h = h;; with electrons in the absorber material. This causes with electrons in the absorber material. This causes the photon to be deflected from its original path by a certain angle the photon to be deflected from its original path by a certain angle and to transfer part of its energy to the electron recoil.and to transfer part of its energy to the electron recoil.

The new photon energy is described by:The new photon energy is described by:

with a maximum energy transfer ofwith a maximum energy transfer of

The probability for the scattering per unit distance is the The probability for the scattering per unit distance is the attenuation coefficient attenuation coefficient which can be expressed in terms of the which can be expressed in terms of the charge number charge number Z Z of the material, the number density of the material, the number density N, N, and the and the Compton collision cross section per atom Compton collision cross section per atom CC::

The attenuation coefficient is directly proportional to the The attenuation coefficient is directly proportional to the charge number charge number Z.Z.

The third absorption (attenuation) process is pair The third absorption (attenuation) process is pair production and takes place at energies production and takes place at energies EE 1.022 MeV. 1.022 MeV.

While interacting with the Coulomb field of a nucleus or While interacting with the Coulomb field of a nucleus or electron, the energy of the photon is converted to the electron, the energy of the photon is converted to the formation of an electron positron pair.formation of an electron positron pair.

The probability for pair production is expressed in The probability for pair production is expressed in terms of the attenuation coefficient terms of the attenuation coefficient kk,,

with with = = rr0022/137 (r/137 (r00 is the electron radius) and the function is the electron radius) and the function P P which which

depends on the photon energy. The attenuation coefficient for pair depends on the photon energy. The attenuation coefficient for pair production is basically proportional to production is basically proportional to ZZ22..

The total attenuation coefficient The total attenuation coefficient depends on the photon depends on the photon energy energy E E and the charge number and the charge number Z Z of the absorber material:of the absorber material:

The total attenuation coefficient effects the The total attenuation coefficient effects the intensity loss of the photons in an absorber of thickness intensity loss of the photons in an absorber of thickness t t as discussed before.as discussed before.

The attenuation coefficient is closely related to the The attenuation coefficient is closely related to the energy transfer and energy absorption coefficient for energy transfer and energy absorption coefficient for - and X-ray - and X-ray radiation in materials. The energy transfer coefficient radiation in materials. The energy transfer coefficient tr tr // in a in a

material of density material of density is defined by:is defined by:

taking into account the energy losses taking into account the energy losses (the average emitted (the average emitted fluorescence energy) and fluorescence energy) and EEavgavg (average kinetic energy of the (average kinetic energy of the

electron recoils) and 2mcelectron recoils) and 2mc22 (rest energy of the electron positron pair). (rest energy of the electron positron pair).

The energy absorption coefficient The energy absorption coefficient en en // describes the describes the

energy losses to Bremsstrahlung and is expressed by,energy losses to Bremsstrahlung and is expressed by,

with with g g as a function of photon energy and mass number.as a function of photon energy and mass number.

The energy loss of a monoenergetic photon beam of The energy loss of a monoenergetic photon beam of initial flux initial flux 00 (photons/m(photons/m22) is:) is:

The energy loss The energy loss dE/dx dE/dx for a monoenergetic beam for a monoenergetic beam EE = = hh is is

therefore proportional to the transfer and absorption coefficientstherefore proportional to the transfer and absorption coefficients

forfor

For high initial energies the coefficients are large which For high initial energies the coefficients are large which translates into a maximum of energy loss at smaller depths which translates into a maximum of energy loss at smaller depths which decreases gradually with the decrease of the absorption coefficient decreases gradually with the decrease of the absorption coefficient towards lower energies.towards lower energies.