Introduction to Radiobiology Lesson 1 · Edoardo Milotti - Radiobiology 9 R&D TECHNICAL REPORT P3-080/TR 29 Figure 2.4 Schematic annealing spectra for graphite irradiated at various

Introduction to RadiobiologyLesson 1

Master of Advanced Studies in Medical Physics A.Y. 2018-19

Edoardo MilottiPhysics Dept. – University of Trieste

Edoardo Milotti - Radiobiology 2

Radiation damages all kinds of human tissues – both healthy and diseased – as well as other materials

An area of ulceration on the hand, caused by exposure to radiation therapy


Aim of radiotherapy: destroy cancer cells, limit damage to healthy tissues

The purpose of these lessons is twofold:

1. gain a basic knowledge of the phenomenology of radiation damage to tissues

2. understand the optimization of therapy, based on the concept of maximum damage to cancer cells, minimum damage to healthy tissues


Tissues are difficult, material science is easy, so let’s start with materials. Consider graphite in nuclear reactors

The Windscale (Sellafield) nuclear power plant, where the worst nuclear accident in the UK took place in 1957. The accident was due to uncontrolled energy release from the graphite in the reactor.


Nuclear reactors and the Wigner EffectThe Windscale accident was due to uncontrolled energy release from graphite in the nuclear reactor.

• Wigner energy occurs in graphite under neutron irradiation because atoms are displaced from their normal lattice positions into configurations of higher potential energy (on average this corresponds to ~ 25 eV per displaced atom).

Graphite unit cell

Edoardo Milotti - Radiobiology 6R&D TECHNICAL REPORT P3-080/TR

27

Figure 2.2 The structure of graphite and the formation of interstitials (from Simmons 1965 and Kelly 1981)

The hexagonal structure of graphite

a

b

a

b

A single

Di-interstitial (C2)

(C2)2 interstitials

Equilibrium positions of di-interstitials


R&D TECHNICAL REPORT P3-080/TR

26

Vacant Lattice sites X Displaced atoms Figure 2.1 Distribution of displaced atoms and vacant lattice sites (from Simmons 1965)

Primary knock-on atom

Fast neutron

• Fast neutrons undergo a series of collisions and produce displacement cascades

• A 1 MeV neutron produces on average about 900 displacements

• Not all displacements produce defects, as a displaced C can fill a vacancy

• The interstial atom-vacancy pairs are called Frenkel defects


• The quantity of accumulated stored energy is a function of fast neutron flux, irradiation time, and temperature.

• The higher the irradiation temperature, the lower is the amount of “stored” energy. In all cases, a saturation point may be achieved in terms of the total amount of stored energy for long periods of irradiation.

• The maximum amount of stored energy ever found in a graphite sample is ~2,700 J/g, which if all released at once could theoretically lead to a temperature rise of approximately 1500 °C assuming adiabatic conditions.

• The Wigner effect has been known for a long time, and in reactors that use graphite as a moderator there are established procedures to periodically release the stored energy with annealing cycles.



29

Figure 2.4 Schematic annealing spectra for graphite irradiated at various temperatures (from Simmons 1965)

- 2 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0

A n n e a l i n g t e m p e r a t u r e ( ° C )

Ene

rgy

rele

ase

with

tem

pera

ture

I r r a d i a t i o n t e m p e r a t u r e - 1 9 5 ° C

- 2 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0


Ene

rgy

rele

ase

with

tem

pera

ture

I r r a d i a t i o n t e m p e r a t u r e 3 0 ° C

- 2 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0


Ene

rgy

rele

ase

with

tem

pera

ture

I r r a d i a t i o n t e m p e r a t u r e 2 0 0 ° C


29

Figure 2.4 Schematic annealing spectra for graphite irradiated at various temperatures (from Simmons 1965)

- 2 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0


Ener

gy r

elea

se w

ith te

mpe

ratu

re

I r r a d i a t i o n t e m p e r a t u r e - 1 9 5 ° C

- 2 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0


Ener

gy r

elea

se w

ith te

mpe

ratu

re

I r r a d i a t i o n t e m p e r a t u r e 3 0 ° C

- 2 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0


Ener

gy r

elea

se w

ith te

mpe

ratu

re

I r r a d i a t i o n t e m p e r a t u r e 2 0 0 ° C

Energy released by irradiated graphite as temperature increases


Radiation damage in materials-428- Journal of the Korean Physical Society, Vol. 51, No. 1, July 2007

Fig. 3. Typical pictures of etched track pits caused by twodi↵erent particles. (a) 5.4-MeV ↵ particles (b) ⇠0.9-MeVprotons.

polyester, and di↵erent target thicknesses between 1 µmand 50 µm were used to generate proton with di↵erentenergies.

The Thomson parabola spectrometer is based uponthe superposition of an electric field and a magnetic fieldand can be used to analyze the kinetic energy and thecharge of particles at various the positions. An electricfield of E = 1.5 kV and a magnetic field of B = 8.47 kGinside a gap of 5 mm was applied along a 5-cm length.The pinhole of 400 µm was installed in front of the TPSto improve the energy resolution of the spectrum, anda CR39 detector was placed 15 mm away from the endof the TPS. This setup enbled us to investigate the de-pendences of the energies, the incident angles, and thecharges of the particles on di↵erent etching conditions.

IV. RESUTLS AND DISCUSSION

Figure 3 presents pictures of typical etched track pitscaesed by 5.4-MeV alpha particles and ⇠0.9-MeV pro-tons etched at 70 �C in 6N NaOH for 6 hours. Sincealpha particles are emitted in random directions from asurface of �35 mm diameter coated by 210Po, their trackpits are randomly cluttered with various shapes. A roundshape indicates normal incidence on the detector surfacewhile an elliptical shape corresponds to oblique incidencetoward the direction of the major axis. The measured de-tection e�ciency was about 40 % in our case. In contrastto the 210Po source, the shapes of etched track pits ofprotons generated by using a 10-TW laser were almostround, which meant most of the protons were incidentperpendicular to the detector surface.

The bulk etch rate was measured by using the weightloss method. Its mean value for a 6-hour etching 70 �C in6N NaOH is 1.396 µm/h, which is slightly greater thanother measurements [11]. The optimal etching conditiondepends on the energies and the kinds of particles. Inthe case of our experiments using a 10-TW laser sys-tem, a few MeVor less protons are the main source to beoptimized.

A TPS produces di↵erent particle trajectories, de-pending on the energy, the mass and the charge of ions,so di↵erent parabolic traces are recorded in the nucleartrack detector for protons and other ions. A horizontal

Fig. 4. Typical spectrogram taken with protons and ionsin a CR39 detector after a Thomson Parabolic Spectrometer.

displacement of tracks in the plastic detector correspondsto a decrease in the particle energy, and a verticle direc-tion is related to the charge-to-mass ratio, Z/m. Fig-ure 4 presents a typical spectrogram taken with protonsand ions generated by high-intensity laser irradiation ofa 13-µm polyester target. When the detector was prop-erly etched, all traces taken with protons and ions wereclearly distiguishable and countable. We can see fromFigure 4 that tracks for 0.1-MeV protons are deformeddue to over-etching, but they are still countable usingthe program ImageJ [12].

Four plastics were placed 15 mm behind the TPS andwere exposed to protons and light ions produced by usinga 6-µm polyester film target. After etching the four de-tectors in the same container for 3, 6, 9 and 12 hours, re-spectively, we measured the depth, H and the diameter,D, of a track pit at di↵erent positions (which is relatedto the energy) as shown in Figure 5. If a good spectrumof protons is to be obtained, the visibility and the count-ability over a wide energy range are important. Afterpassing the optimal etching time, tracks are over-etchedso that a deep V -shaped track becomes more rounded,wider, and shallower with the etching time. From thesedata, we can observe the development of track pits withetching time and the dependence of the track etch rateon the energy of the protons. The accuracy of measuredtrack etch rate is limited by the resolution of the micro-scope and the etching condition. A deeper track depthenhances the contrast ratio, and a size of ⇠10 µm can beresolved using the Omax microscope. The track depthwas the deepest for a 6-hour etching over the etchingenergy range (see Figure 5(a)) with countable sizes of7.5 ⇠ 9 µm (see Figure 5(b)). With increasing the etch-ing time, the absolute variation of the etch rate ratioand the diameter were reduced (see Figure 5(c)). Thetrack depths etched for 9 and 12 hours were shallowerthan that etched for 6 hours while their diameters werelarges. These results indicate that the tracks are over-etched after 6 hours. Furthermore, less background [13]

Radiation damage in CR-39 plastic

CR-39 dosimeter


Radiation damage to plastic scintillators


Radiation damage to human tissues is different from damage in inert material

1. Damage mechanisms are different

2. Cells and tissues have (limited) self-repair capabilities

In these lessons we are going to learn about both topics


RadiationEffectsDamage - 1 - K. E. Holbert

RADIATION EFFECTS AND DAMAGE The detrimental consequences of radiation are referred to as radiation damage. To understand the effects of radiation, one must first be familiar with the radiations and their interaction mechanisms. Further, the fundamental characteristics of the material(s) being irradiated must also be understood. A brief summary of the characteristics of radiation is first presented below. This is followed by a general discussion of the effects of radiation, along with some specific examples, with an emphasis toward the ionizing effects.

1. Ionizing Radiations The radiations of concern here include charged particles such as electrons (beta particles), protons, alphas and fission fragment ions, and the neutral radiations including photons (gamma and X rays) and neutrons. Table I compares some key characteristics of the radiations, including charge, mass, and range in air. For a kinetic energy of 1 MeV, the electron is relativistic (0.94c). For the same energy, the heavier particles are slower, stopped easier and deposit their entire energy over a shorter distance. The passage of radiation through tissue is depicted in Figure 1.

Table I: Comparison of Ionizing Radiation

Radiation (EK = 1 MeV)

Characteristic Alpha (α) Proton (p) Beta (β) or

Electron (e) Photon

(γ or X ray) Neutron (n)

Symbol +242 Heorα +11

1 Horp βore01− γ00 n1

0 Charge +2 +1 –1 neutral neutral Ionization Direct Direct Direct Indirect Indirect Mass (amu) 4.001506 1.007276 0.00054858 — 1.008665 Velocity (cm/sec) 6.944×108 1.38×109 2.82×1010 c=2.998×1010 1.38×109 Speed of Light 2.3% 4.6% 94.1% 100% 4.6% Range in Air 0.56 cm 1.81 cm 319 cm 82,000 cm* 39,250 cm* * range based on a 99.9% reduction

Alpha particle: easily stopped least penetrating

Beta particle: very much smallermore penetrating

Gamma ray and X-ray:pure energy with no massmost penetrating

� neutral atom/moleculez ion

Figure 1. Radiation paths in tissue.

Ionizing radiation


Alpha particle (He nucleus)easily stopped, small penetration, very damaging

Beta particle (electron)longer penetration, less ionization, less damaging

Gamma ray and X-raylocalized ionization, less damaging


Energy loss by ionization/excitation – dE/dx






The Bragg peak

Bragg curve of 5.49 MeV alpha particles in air. This radiation is produced from the initial decay of radon (222Rn). Stopping power (which is essentially identical to LET) is plotted here versus particle range.

(Adapted from the Wikipedia article http://en.wikipedia.org/wiki/Linear_energy_transfer)

x(E) =

Z E0

E

��dx

dE

�� dE

��dE

dx

��



(adapted from http://en.wikipedia.org/wiki/Bragg_peak and http://en.wikipedia.org/wiki/Proton_therapy )

http://en.wikipedia.org/wiki/Bragg_peak

http://en.wikipedia.org/wiki/Proton_therapy


Stopping power or LET (Linear Energy Transfer)?

Same definition

BUT ...

Stopping power includes only the ionization losses of individual charged particles.

LET is the energy released in tissues per unit track length per particle by a beam of

particles, and includes secondary particles as well.

In contrast to the stopping power, which has a typical unit of MeV/cm, the unit reserved for the LET is keV/µm.

dE

dx


Alpha particle (He nucleus)easily stopped, small penetration, very damaging

Beta particle (electron)longer penetration, less damaging (more excitation, fewer secondaries)

Gamma ray and X-raylocalized ionization, less damaging

+ - + - - + + - + - + + - + + - + - + -- - + + - + - + + - ++ -+-- + - + + - - + - + - - + - + - + - ++ + - - + - + - - + -- +- +


Stopping power vs. LET

An ionizing particle produces ion/electron pairs along the track and loses energy, and the Bethe formula gives the mean energy loss per unit length. Stopping power includes all losses, also those due to radiation not absorbed in tissue.

+-+

-

-+

+-

-+

LET includes only the energy absorbed in tissue. The strict definition of LET does not include neutral particles, however it can be extended to include photons as well. Photons, produce ion/electron pairs only when they are absorbed; in this case the mean energy loss per unit length is the average due to secondary charged particles kicked off by the absorbed photon.

The secondary particles interact in turn and produce “tubes” of excited and ionized molecules.


Typical LET values (in tissue or tissue-like material)


Track structure (example, low-energy electrons)



from M. R. Kia , and H. Noshad, Phys. Plasmas 23, 053120 (2016)


electrons in water

Ionizationsexcitations


α particles



Carbon ions



For indirect action of x rays the chain of events from the absorption of the incident photon to the final biological damage is as follows:

Incident x-ray photon

Fast electron or positron

Ion radical

Free radical

Breakage of bonds

Biological effect

Typical time scale involved in these 5 steps:

• (1) The physics of the processtakes of the order of 10-15 s.

• (2) The ion radicals have a lifetimeof the order of 10-10 s.

• (3) The free radicals have a lifetimeof the order of 10-5 s.

• (4) The step between the breakageof bonds and the biological effectmay take hours, days or years.

Water radiolysis and production of ROS (Reactive Oxygen Species)


Molecular oxygen and the superoxide anion

Oxygen molecule: double bond ”hides” the electrons

Superoxide anion: added electron forces the other atom to display an unpaired electron.


Hund's rule: for a given electronconfiguration the term with themaximum multiplicity has the lowestenergy. In the case of oxygen, theunpaired electrons (triplet state) fitthe rule.

This also fits with the behavior ofoxygen, which, when liquid, isparamagnetic.

However, three different states areactually possible, two with pairedelectrons.

Singlet oxygen is common, an easyway to produce it is by mixinghydrogen peroxide with sodiumhypochlorite. It has a residualparamagnetism associated with theorbital angular momentum.

singlet oxygen

triplet oxygen

Reactivity of molecular oxygen: "triplet oxygen" and "singlet oxygen"


Simple explanation of the reactivity of "singlet oxygen"

Atom A Atom B

Bond with paired electrons

Here it is difficult to insert an oxygen molecule with unpaired spins, but it is easy to insert singlet oxygen. Thus higher reaction rates for singlet oxygen than triplet oxygen!


The superoxide anion is highly reactive and toxic

• Human cells use the superoxide anion to kill bacteria.

• The enzymes of the complex NADPH oxidase (NOX) produce superoxide.

• The absence of NADPH oxidase leads to the chronic granulomatous diseases.

• The superoxide anion is toxic to human cells, and this requires mechanisms to get rid of it, like the enzyme superoxide dismutase.


Main types of ROS (Reactive Oxygen Species)

Electron structures of common reactive oxygen species. Each structure is providedwith its name and chemical formula. The • designates an unpaired electron.

This involves mostly the ionization

and the excitation of water molecules


Physical stage (time < 10-15 s)

3. Mechanisms of water radiolysis

The radiolysis of water is usually divided in three more or less overlapping stages: physical (<10‐15 s), physico‐chemical stage (∼10‐15‐10‐12 s) and non‐homogeneous chemical stage (∼10‐12‐10‐6 s). Although this time division is controversial, it gives a convenient way to describe the mechanisms involved in water radiolysis. 3.1 Physical stage (<10‐15 s)

The physical stage is the absorption of ionizing radiation by matter. The main consequences are the ionization and excitation of water molecules. An ionization event is the removal of an electron from the water molecule: (3) Similarly, an excitation is the transfer of an electron from a fundamental state to an excited state: (4) There are several molecular orbitals and excitation levels in the water molecule. The description of these states is beyond the scope of this text and is not necessary for the discussion that follows. 3.2 Physico‐chemical stage (∼10‐15‐10‐12 s)

The ionized and excited molecules created during the physical stage are highly unstable. During this stage, lasting ∼10‐12 s, the ionized and excited water molecules dissipate their energy by energy transfer to neighboring molecules and bond rupture. The sequence of events of the physico‐chemical stage is, in fact, not well characterized experimentally. However, some important physico‐chemical stage events worth mentioning: proton transfer to a neighboring molecule, dissociation of excited water molecule and electron thermalization and solvatation. The proton transfer to a neighboring water molecule is very important, because it leads to the

production of an .OH radical*:

+•+• +→+ OHOHOHOH 322 (5)

*In chemistry, a radical (also referred to as free radical) is an atom, molecule or ion with at least one unpaired electron. The unpaired electron usually cause them to be highly chemically reactive. The radical site is usually

noted by putting a dot on the atom (ex.: .OH)






+•+• +→+ OHOHOHOH 322 (5)



The ionized and excited molecules produced in the physical stage are highly unstable, and they transfer their energy by dissipating it on neighboring molecules and by breaking chemical bonds.

Proton transfer to a neighboring water molecule leads to the production of

·OH radicals (i.e., an ion with an unpaired electron; radicals are usually quite reactive).


Physico-chemical stage (time ≈ 10-15 s – 10-12 s)






+•+• +→+ OHOHOHOH 322 (5)



There are several pathways for the dissociation or the deexcitation of the excited water molecule


Physico-chemical stage (time ≈ 10-15 s – 10-12 s) /ctd.

They are several channels for the dissociation of an excited water molecule:

OHHOH *

2•• +→

(6a)

)D(OHOH 1

2*

2 +→

(6b)

)P(OH2OH 3*

2 +→ •

(6c)

Where O(1D) and O(3P) are the singlet and triplet state of the atomic oxygen, respectively. The excited water molecule can also return to its fundamental state without dissociation (by heat loss):

OHOH 2*

2 → (7)

Most secondary electrons have low energy6, but some of them may have energy in the keV or even in the MeV range. These electrons lose their energy into medium by doing further ionization, excitations until they eventually reach thermal equilibrium with the liquid. The electron, which is negatively charged, interacts with the dipoles of the surrounding water molecules and becomes trapped in a state called « trapped electron ». Finally, this electron becomes a « hydrated electron », which behaves like chemical specie. This rapid sequence of events can be written as follows:

−−−− →→→ aqtrth eeee (8)

The hydrated (or solvated) electron is of great importance in water radiolysis. However, its

existence has been proposed only in the 1950’s and it was observed experimentally in the 1960’s. 3.3 Non‐homogeneous chemical stage (∼10‐12‐10‐6 s)

At the end of the physico‐chemical stage, the species H., .OH, H2, H2O2 are created in very high concentration in the spurs. Other species such as O(3P) may also be present, in small quantity. They diffuse in the medium and eventually encounter chemical species created in other spurs, which gives them the opportunity to react. In general, the radical species (such as H., .OH and e‐aq) react in ∼1 μs to form the molecular species H2 and H2O2. For example, H2O2 is formed by the reaction .OH+.OH→H2O2. Another important reaction is H.+ .OH→ H2O, which forms back water.

Many reactions are known to occur in pure, irradiated liquid water; the most important are given in the following table.

atomic oxygen, singlet state

atomic oxygen, triplet state


OHHOH *

2•• +→

(6a)

)D(OHOH 1

2*

2 +→

(6b)

)P(OH2OH 3*

2 +→ •

(6c)


OHOH 2*

2 → (7)







thermal de-excitation


... a note on atomic oxygen ... (from Footie et al. (eds.) "Active Oxygen in Chemistry", Chapman & Hall, 1995

Atomic oxygen, which is atomic number 8, has a total of eight electrons. Using theconcept of atomic orbitals and the Pauli exclusion principle to fill these orbitals withelectrons, the placement of these eight electrons in the atomic orbitals of O isrepresented by the electronic configuration 1s22s22p4.

Since the 2p orbitals are only partially filled, there are three different ways toarrange the electrons in the 2px 2py and 2pz orbitals. Hund's rule, which states thatthe ground-state configuration corresponds to an orbital occupancy that gives thehighest multiplicity, can be used to rule out either the second or the thirdconfigurations in the figure as the ground state, because each of these configurationhas a multiplicity of 1 as compared to a multiplicity of 3 for the first configuration.


The ground state of atomic oxygen therefore has two unpaired electrons, and isdesignated as the 3P ("triplet P") state.

Of the two remaining configurations, the second is lower in energy based on Hund'ssecond rule which states that, if the multiplicity is the same, the configuration with thehighest total orbital angular momentum (L) will have the lower energy. Because thesecond configuration has the higher L value, it is lower in energy. This configuration isthe first excited state of atomic oxygen, designated as the 1D ("singlet D") state. The thirdconfiguration is the second excited state, designated 1S.

Secondary electrons also behave as a new individual species and they become hydrated


Physico-chemical stage (time ≈ 10-15 s – 10-12 s) /ctd.


OHHOH *

2•• +→

(6a)

)D(OHOH 1

2*

2 +→

(6b)

)P(OH2OH 3*

2 +→ •

(6c)


OHOH 2*

2 → (7)







At the end of the physico-chemical stage, the species H·, ·OH, H2, H2O2 are created in very high concentration in the spurs.

Other species such as O(3P) may also be present in small quantity. They diffuse in the medium and eventually encounter chemical species created in other spurs, which gives them the opportunity to react.

In general, the radicals such as H·, ·OH and e-aq react in ∼1 μs to form the molecular species H2 and H2O2. For example, H2O2 is formed by the reaction

·OH + ·OH → H2O2

Another important reaction is H· + ·OH → H2O, which forms water.


Non-homogeneous chemical stage (time ≈ 10-12 s – 10-6 s)


Chemical reactions table

Reactions

H.+H.→H2 .OH+.OH→H2O2 H2O2+e

‐aq→OH‐+.OH H++O2

.‐ →HO2.

H.+.OH→H2O .OH+H2O2→HO2

.+H2O H2O2+OH‐→HO2

‐+H2O H++HO2‐→H2O2

H.+H2O2→H2O+.OH .OH+H2→H.+H2O H2O2+O(

3P)→HO2.+.OH H++O.‐→.OH

H.+e‐aq→H2+OH‐ .OH+e‐aq→OH‐ H2O2+O

.‐→HO2.+OH‐ OH‐+HO2

.→O2.‐+H2O

H.+OH‐→H2O+e‐aq

.OH+OH‐→O.‐+H2O H2+O(3P)→H.+.OH OH‐+O(3P)→HO2

‐ H.+O2 →HO2

. .OH+HO2.→O2+H2O H2+O

.‐→H.+OH‐ HO2.+O(3P)→O2+

.OH H.+HO2

.→H2O2 .OH+O2

.‐→O2+OH‐ e‐aq+e

‐aq→H2+2OH

‐. HO2.+HO2

.→ H2O2+O2 H.+O2

.‐→HO2‐ .OH+HO2

‐→HO2.+OH‐ e‐aq+H

+→H. HO2.+O2

.‐→ HO2‐+O2

H.+O(3P) →.OH .OH+O(3P)→HO2. e‐aq+O2→O2

.‐ HO2‐+O(3P)→O2

.‐+.OH H.+O.‐→OH‐ .OH+O.‐→HO2

‐ e‐aq+HO2.→HO2

‐ O(3P)+O(3P)→O2

At the end of the non‐homogeneous chemical stage, the following equation for the radiolysis of water can be written: (9) 3.3.1 Yields of radiolytic species

The radiolytic yield of the species X, noted G(X), is defined as:

energy deposited eV 100destroyed)(or created species ofNumber G(X) =

(10)

The units of the radiolytic yields are molec./100 eV. In SI units, 1 molec./100 eV ≈ 0.10364

μmol/J. An equivalent definition of G(X) is G(X)=(1/ρ)(d[X]/dD), where ρ is the density of the irradiated medium, [X] is the concentration of X and D is the dose. It is usually obtained by using the slope of the graph [X] vs D at origin. If D=It, where I is the dose‐rate and t is the time, we can write G(X)=(1/ρI)(d[X]/dt).

The yield of the radiolytic species at the end of spur expansion, at ∼10‐6 s, is called primary yield and is noted GX. In pure liquid water, the primary yields of the principal radiolytic species are (in molec./100 eV)13: 50.2G

aqe =− ; 56.0G H =• ; 7.0G22OH = ; 45.0G

2H = ; 50.2G OH =•

(11)

Experimentally, the yield values can be obtained by pulsed‐radiolysis.

The end result of the radiolysis of water leads to radiochemical species

Chemical reactions table

Reactions

H.+H.→H2 .OH+.OH→H2O2 H2O2+e

‐aq→OH‐+.OH H++O2

.‐ →HO2.

H.+.OH→H2O .OH+H2O2→HO2

.+H2O H2O2+OH‐→HO2

‐+H2O H++HO2‐→H2O2

H.+H2O2→H2O+.OH .OH+H2→H.+H2O H2O2+O(

3P)→HO2.+.OH H++O.‐→.OH

H.+e‐aq→H2+OH‐ .OH+e‐aq→OH‐ H2O2+O

.‐→HO2.+OH‐ OH‐+HO2

.→O2.‐+H2O

H.+OH‐→H2O+e‐aq

.OH+OH‐→O.‐+H2O H2+O(3P)→H.+.OH OH‐+O(3P)→HO2

‐ H.+O2 →HO2

. .OH+HO2.→O2+H2O H2+O

.‐→H.+OH‐ HO2.+O(3P)→O2+

.OH H.+HO2

.→H2O2 .OH+O2

.‐→O2+OH‐ e‐aq+e

‐aq→H2+2OH

‐. HO2.+HO2

.→ H2O2+O2 H.+O2

.‐→HO2‐ .OH+HO2

‐→HO2.+OH‐ e‐aq+H

+→H. HO2.+O2

.‐→ HO2‐+O2

H.+O(3P) →.OH .OH+O(3P)→HO2. e‐aq+O2→O2

.‐ HO2‐+O(3P)→O2

.‐+.OH H.+O.‐→OH‐ .OH+O.‐→HO2

‐ e‐aq+HO2.→HO2

‐ O(3P)+O(3P)→O2

At the end of the non‐homogeneous chemical stage, the following equation for the radiolysis of water can be written: (9) 3.3.1 Yields of radiolytic species

The radiolytic yield of the species X, noted G(X), is defined as:

energy deposited eV 100destroyed)(or created species ofNumber G(X) =

(10)

The units of the radiolytic yields are molec./100 eV. In SI units, 1 molec./100 eV ≈ 0.10364

μmol/J. An equivalent definition of G(X) is G(X)=(1/ρ)(d[X]/dD), where ρ is the density of the irradiated medium, [X] is the concentration of X and D is the dose. It is usually obtained by using the slope of the graph [X] vs D at origin. If D=It, where I is the dose‐rate and t is the time, we can write G(X)=(1/ρI)(d[X]/dt).

The yield of the radiolytic species at the end of spur expansion, at ∼10‐6 s, is called primary yield and is noted GX. In pure liquid water, the primary yields of the principal radiolytic species are (in molec./100 eV)13: 50.2G

aqe =− ; 56.0G H =• ; 7.0G22OH = ; 45.0G

2H = ; 50.2G OH =•

(11)

Experimentally, the yield values can be obtained by pulsed‐radiolysis.


Time-dependent cross sections of the nonhomogeneous spatial distributions of the mainradiolytic species (eaq, .OH, H., H2, and H2O2) in liquid water exposed to 24-MeV 4He2+ ions from 1 ps to 10 µs.

Adapted from I. Plante and J.-P. Jay-Gerin: “Monte-Carlo step-by-step simulation of the early stages of liquid water radiolysis: 3D visualization of the initial radiation track structure and its subsequent chemical development”, Journal of Physics: Conference Series 56 (2006) 153-155


13.4 Examples of Calculated Charged-Particle Tracks in Water 403

Fig. 13.1 Chemical development of a 4-keVelectron track in liquid water, calculated byMonte Carlo simulation. Each dot in thesestereo views gives the location of one of theactive radiolytic species, OH, H3O+, e–

aq, or H,at the times shown. Note structure of trackwith spurs, or clusters of species, at early

times. After 10–7 s, remaining species continueto diffuse further apart, with relatively fewadditional chemical reactions. (Courtesy OakRidge National Laboratory, operated by MartinMarietta Energy Systems, Inc., for theDepartment of Energy.)

schemes (13.4)–(13.10) can thus be used to carry out the chemical development ofa track.

Three examples of calculated electron tracks at 10–12 s in liquid water were shownin Fig. 6.5. The upper left-hand panel in Fig. 13.1 presents a stereoscopic view ofanother such track, for a 4-keV electron, starting at the origin in the upward direc-tion. Each dot represents the location of one of the active radiolytic species, OH,H3O+, e–

aq, or H, shown in Table 13.2, at 10–12 s. There are 924 species present ini-tially. The electron stops in the upper region of the panel, where its higher linearenergy transfer (LET) is evidenced by the increased density of dots. The occurrenceof species in clusters, or spurs, along the electron’s path is seen. As discussed inSection 6.7, this important phenomenon for the subsequent chemical action of ion-izing radiation is a result of the particular shape and universality of the energy-lossspectrum for charged particles (Fig. 5.3). The passage of time and the chemical

Chemical development of a 4-keV electron track in liquid water, calculated by Monte Carlo simulation. Each dot in these stereo views gives the location of one of the active radiolytic species, OH, H3O+, e–aq, or H, at the times shown. Note structure of track with spurs, or clusters of species, at early times. After 10–7 s, remaining species continue to diffuse further apart, with relatively few additional chemical reactions. (Adapted from James E. Turner: “Atoms, Radiation, and Radiation Protection, 3rd ed.” Wiley 2007)





























Track of a 300 MeV 12C6+ ion, from ~10-12 to ~10-6 s, front viewEach dot represents a radiolytic species. The changes in color indicate chemical reactions.

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Track of a 300 MeV 12C6+ ion, from ~10-12 to ~10-6 s, side viewEach dot represents a radiolytic species. The changes in color indicate chemical reactions.

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G value: number of a given species produced per 100 eV of energy loss by the original charged particle and its secondaries, on the average, when it stops in the water.

Table extracted from Turner: “Atoms, Radiation, and Radiation Protection”



Table extracted from Turner: “Atoms, Radiation, and Radiation Protection”


Exercise:

If a 20-keV electron stops in water and an average of 352 molecules of H2O2 are produced, what is the G value for H2O2 for electrons of this energy?



Exercise:

If a 20-keV electron stops in water and an average of 352 molecules of H2O2 are produced, what is the G value for H2O2 for electrons of this energy?

Answer:

20 keV/100 eV = 200 therefore G = 352/200 = 1.76



Electrons, protons, and alpha particles all produce the same species in local track regions at 10-15 s: H2O+, H2O∗, and subexcitation electrons.

The chemical differences that result at later times are presumably due to the different spatial patterns of initial energy deposition that the particles have.


13.5 Chemical Yields in Water 407

Table 13.3 G Values (Number per 100 eV) for Various Species inWater at 0.28 µs for Electrons at Several Energies

Electron Energy (eV)

Species 100 200 500 750 1000 5000 10,000 20,000

OH 1.17 0.72 0.46 0.39 0.39 0.74 1.05 1.10H3O+ 4.97 5.01 4.88 4.97 4.86 5.03 5.19 5.13e–

aq 1.87 1.44 0.82 0.71 0.62 0.89 1.18 1.13H 2.52 2.12 1.96 1.91 1.96 1.93 1.90 1.99H2 0.74 0.86 0.99 0.95 0.93 0.84 0.81 0.80H2O2 1.84 2.04 2.04 2.00 1.97 1.86 1.81 1.80Fe3+ 17.9 15.5 12.7 12.3 12.6 12.9 13.9 14.1

the other species, such as H2O2 and H2, increase with time. As mentioned earlier,by about 10–6 s the reactive species remaining in a track have moved so far apartthat additional reactions are unlikely. As functions of time, therefore, the G valueschange little after 10–6 s.

Calculated yields for the principal species produced by electrons of various ini-tial energies are given in Table 13.3. The G values are determined by averaging theproduct yields over the entire tracks of a number of electrons at each energy. [Thelast line, for Fe3+, applies to the Fricke dosimeter (Section 10.6). The measuredG value for the Fricke dosimeter for tritium beta rays (average energy 5.6 keV),is 12.9.] The table indicates how subsequent changes induced by radiation can bepartially understood on the basis of track structure—an important objective in ra-diation chemistry and radiation biology. One sees that the G values for the fourreactive species (the first four lines) are smallest for electrons in the energy range750–1000 eV. In other words, the intratrack chemical reactions go most nearly tocompletion for electrons at these initial energies. At lower energies, the number ofinitial reactants at 10–12 s is smaller and diffusion is more favorable compared withreaction. At higher energies, the LET is less and the reactants at 10–12 s are morespread out than at 750–1000 eV, and thus have a smaller probability of subsequentlyreacting.

Similar calculations have been carried out for the track segments of protons andalpha particles. The results are shown in Table 13.4. As in Fig. 7.1, pairs of ionshave the same speed, and so the alpha particles have four times the LET of theprotons in each case. Several findings can be pointed out. First, for either type ofparticle, the LET is smaller at the higher energies and hence the initial density ofreactants at 10–12 s is smaller. Therefore, the efficiency of the chemical developmentof the track should get progressively smaller at the higher energies. This decreasedefficiency is reflected in the increasing G values for the reactant species in the firstfour lines (more are left at 10–7 s) and in the decreasing G values for the reactionproducts in the fifth and sixth lines (fewer are produced). Second, at a given velocity,the reaction efficiency is considerably greater in the track of an alpha particle thanin the track of a proton. Third, comparison of Tables 13.3 and 13.4 shows some


Homework

A 50 cm3 sample of water is given a dose of 50 mGy from 10-keV electrons.

If the yield of H2O2 is G = 1.81 per 100 eV, how many molecules of H2O2 are produced in the sample?


The radiolysis of water is known to damage metal pipes, but how do the radiolytic species act in cells and organisms?

• Radiobiology is a branch of science which combines basic principles of physics and biology and is concerned with the action of ionizing radiation on biological tissues and living organisms.

• Ionizing radiation acts at the molecular and cellular level, while in this Master’s course we are interested in the medical issues: in this Radiobiology course we try to understand how the action of radiation at the microscopic level affects human health


Next step, study the effects of ionizing radiation on individual cells.

To this end we need to know cells first.

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