Lima J.J.Pedroso, de (ed.). Nuclear Medicine Physics

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488 Nuclear Medicine Physics

8.11.3 Ionizing Radiation, Ionization Mechanisms, and Biological Action

For a better understanding of damage resulting from ionizing radiation action

on DNA, which is organized into chromosomes in the cell, we will ﬁrst brieﬂy

recall the cellular division cycle.

Thecycle of celldivision insomatic cells isdivided intotwo parts: interphase

and mitosis.

During the interphase part, which occupies most of the duration of the

cellular division cycle, the amount of cellular DNA is duplicated as a result

of synthesis of replicas of existing chromosomes.

Interphase is divided into three parts: G1 (ﬁrst intermediary stage), where

synthesis of numerous proteins occurs; S (synthesis), during which a new

copy of the entire molecule of DNA is produced, before cell division; and G2

(second intermediary stage), during which the integrity of the chromosome

is tested. The process of synthesis S is separated from mitosis by intermediary

stages G1 and G2, during which normal activity of the cell is maintained.

Mitosis, which lasts from 1 to 2 h, is the process of cell division and includes

notonly the divisionof thenucleus butalso thatof the cytoplasm(cytokinesis).

The duration of G1 determines the frequency of cell division, ranging from

hours to more than a hundred days, depending on the type of cells.

The synthesis S lasts about 8 h, and G2 lasts about 4 h.

Mitosis, in turn, is divided into four parts: the prophase (P), during which

the nuclear membrane disappears; the metaphase (M), during which the

mitotic spindle is formed and where chromosomes ﬁt in; the anaphase (A),

during which the chromosomes migrate over the spindle to opposite parts

in the cell; and telophase (T), in which nuclear and cell membranes reappear,

contributing to the emergence of two separate cells.

Cell sensitivity to radiation varies during the different phases of the cell

cycle. The cells of mammals are more resistant to radiation at the end of the

S phase and more sensitive toward the end of G2 and mitosis.

The probability that a given molecule will be affected by direct action

increases with its dimensions.

At a molecular level, the biological effects of radiation, direct and indirect,

are rare events, random and independent of each other, and are, thus, covered

by Poisson statistics.

It should be noted that, while accepting that DNA is a critical target for the

effects that involve changes in the integrity of the processes on cell division,

there is no evidence of an exclusive involvement of this molecule.

The cells, after irradiation, may die trying to start the process of cell divi-

sion. They can divide, causing aberrant forms. They may be unable to divide,

though physiologically functioning, behaving similar to normal cells and

keeping alive for long periods. The cells can divide as apparently normal ones

till a generation of sterile daughter cells occurs. They may, ultimately, divide

normally or with minor changes in division, such as cycles with different

times from normal [38].

Dosimetry and Biological Effects of Radiation 489

Although it is known today that target theory is not entirely appropriate

to explain what happens in a system as complex as a cell, its contribution is

important for the study of the situation in which the mechanisms of recovery

do not alter the initial damage in a signiﬁcant way.

Directly ionizing radiations, with high LET (α particles, heavy ions, and

neutrons),produce most of their biological damage by directaction. However,

for any type of radiation and, in particular, with ionizing energy photons, a

strong probability of interaction with water molecules occurs, leading to the

production of ions, radicals, and other chemically reactive structures.

The processes leading to the initial cellular damage take place in times from

−17

to 10

−5

s. Possible further steps in the chain of events after irradiation,

which occur on a time scale from minutes to decades, are damage repair;

cellular death; and genetic, somatic, or teratogenic effects.

As a ﬁrst approach in the development of models to simulate the effects

of ionizing radiation, biological tissues can be considered as dilute solutions

(suspensions) resulting from the large amount of water in their composition.

Indirect effects are, consequently, to be expected.

For a radiation ﬁeld with a given ﬂuence, the probability that a particular

target (molecule or structure) will be on the path of radiation and be affected

bydirectaction increaseswith the increaseof thetargetdimensions. DNAwith

molecular mass of 6–8×10

u and a main role in cellular life is, obviously, a

critical target.

There is strong circumstantial evidence to indicate that DNAis the principal

target for the biological effects of radiation, including cell death, mutation,

and carcinogenesis. This has been observed and scored as a function of dose

in experiments where the DNA was denatured and the supporting structure

stripped away.

DNA is a large molecule that presents the well-known double helix

structure, as seen in Figure 8.29.

Nucleotides, the two long chains on DNA molecule, consist of deoxyribose

(S) and phosphates (P) that wind around each other in a spiral. The two long

intertwined strands are held together by the bases, which form cross links

between the long strands in the same manner as the treads in a stepladder.

There are four different bases, two purines: adenine (A) and guanine (G), and

two pyrimidines: cytosine (C) and thymine (T).

The base cross-links are formed when two of these bases, one of which is

attached to each long strand, join together. The cross-linked bonds arespeciﬁc,

with adenine exclusively coupling with thymine (A–T) and cytosine coupling

only with guanine (C–G). The bits of information are coded in triplets of

various combinations of A–T and C–G cross links, and the sequence of these

triplets determines the genetic information contained in a DNA molecule

(Figure 8.29b).

Cells in the human body can be divided into two very general groups:

somatic and germinative cells. The latter are the direct agents for species

reproduction, and the former consist of all the remaining ones. Each normal

490 Nuclear Medicine Physics

(a) (b)

SCGS

FIGURE 8.29

DNAdouble helix structure.The nucleotides, the strands ofthe doublehelix, consist of alternating

deoxyribose (S) and phosphate (P) units. Two pairs of complementary bases, adenine (A) and

thymine (T), and guanine (G) and cytosine (C), link the two nucleotide chains.

cell contains a complete set of chromosomes that consists of DNA and has

the templates for human beings. In humans, cells contain 23 pairs of chro-

mosomes. Germinative cells (spermatic cells and ovules) contain 23 single

chromosomes, one half that is in somatic cells.

Genetic information can be altered by many different chemical and phys-

ical agents, called mutagens, which disrupt the sequence of bases in a DNA

molecule Figure 8.30a. The breaks in an intact DNA molecule, produced by

the action of ionizing radiation, can be of several different types and have

different biological consequences with regard to an eventual cellular death or

another type of damage. We can classify the damage:

1. One single-strand break (Figure 8.30b).

2. Double breaks with the ruptures well apart (Figure 8.30c).

3. Breaks close to each other, in different strands (Figure 8.30d).

If the information content of a somatic cell is altered, as is schemati-

cally represented in Figure 8.31, then its descendents may show some sort

of an abnormality. If this altered information occurs in a germ cell that is

subsequently fertilized, then the new individual may carry a genetic defect

or a mutation.

A mutation resulting from alterations, such as those schematically shown

in Figure 8.31a–e (base elimination, base substitution, hydrogen bond

Dosimetry and Biological Effects of Radiation 491

DNA intact

(a)

(b)

(c)

(d)

Break in a single strand Two opposite breaks

Two strand breaks well apart

FIGURE 8.30

Single- and double-strand breaks in DNA molecule. (a) Intact DNA molecule. (b) One single-

strand break. (c) Double break with the ruptures well apart; the repair efﬁciently occurs. (d)

Breaks close to each other in different strands.

break, single-strand break, and double-strand break, respectively), is called

a point mutation, because it results from damage to one point on one

gene.

In intact DNA, however, single-strand breaks are of little biological conse-

quence as far as a cell killing is concerned, because they are readily repaired,

(a)

(d)

(e)

Base

deletion

Single strand

break

Double strand

break

SG CS

(b)

(c)

Base

substitution

DNA molecule

SG CS

Hydrogen

bond

disruption

FIGURE 8.31

Mechanisms of DNA damage by radiation: (a) Base deletion. (b) Base substitution. (c) Hydrogen

bond disruption. (d) Single-strand break. (e) Double-strand break.

492 Nuclear Medicine Physics

over the course of a few hours, with the opposite strand being used as a

template (Figure 8.30b).

However, if the repair is incorrect, it may result in a mutation.

If both strands of the DNA are broken and the breaks are well separated

(Figure 8.30c), again repair readily occurs, as the two breaks are separately

handled.In contrast, ifthe breakson thetwo strandsareoppositeeach other, or

separated by only a few base pairs (Figures 8.30d and 8.31e), this may lead to a

double-strand break. Most of the important biological effects of ionizing radi-

ations are a direct consequence of the rejoining of two double-strand breaks.

When a double-strand break occurs, permanent genetic damage can arise

in the next cellular division in the form of chromosomal aberrations. In most

of these double-strand breaks, the fragments reunite with the original conﬁg-

uration, and the only result may be a point mutation at the site of the original

break. In a small fraction of breaks, however, the broken pieces do not reunite,

thereby giving rise to an aberration.

If this happens and one of the broken fragments is lost, the daughter cell

does not receive the genetic information contained in the lost fragment when

the cell divides. Another serious consequence after chromosomal breakage,

especially if two or more chromosomes are broken, is the interchange of the

fragments among the broken chromosomes and the production of aberrant

chromosomes. Cells with such aberrant chromosomes usually have impaired

reproductive capacity as well as other functions, with serious consequences

in the next mitosis. Several forms of abnormal chromosomes are known,

depending on where the damage occurred along the strand and how the

damaged pieces connected or failed to connect to other chromosome frag-

ments. Many of these chromosomal abnormalities are lethal: the cell either

fails to complete mitosis the next time it tries to divide or fails within the next

few divisions. Other abnormalities allow the cell to continue to divide, but

they may contribute to the multistep process that sometimes leads to cancer

many cell generations later.

Figure 8.32 illustrates two ways in which breaks in two separate chro-

mosomes may rejoin. In the upper half of the ﬁgure, translocation occurs,

generating abnormal chromosomes. Translocation, in general, is not lethal

but may generate cells that will probably be active in cancer promotion.

In the lower half of the ﬁgure, the two broken chromosomes rejoin in such

a way that a dicentric and two acentric fragments are formed. This exchange

type aberration is lethal to the cell; the fragment with no centromere will

be lost during cell division, whereas the aberrant chromosome with two

centromeres will make a normal mitosis impossible.

In mammalian cells, the DNA double-strand breaks are mainly repaired by

a junction of nonhomologous terminal parts.

Nonrepaired or badly repaireddamage in phases before replication (G0-G1)

can lead to chromosome aberrations.

Damage of nonrepaired or not well repaired in phases posterior to replica-

tion (end of S and G2) can lead to aberrations in chromatides.

Dosimetry and Biological Effects of Radiation 493

Dicentric +

fragments

Translocation

Breaks in two

separate

chromatids

FIGURE 8.32

Chromosome aberrations. Translocation is, in general, not lethal but may release an oncogene.

Dicentric fragments are generally not viable.

Aberrations resulting from asymmetric transpositions (dicentric and rings)

are generally lethal.

Aberrations resulting from symmetric transpositions (translocations and

eliminations) resulting from badly repaired DNA damage can lead to car-

cinogenesis.

The available techniques to study DNA double-strand breaks are not

sensitive enough to be used as biological dosimeters in case of radiation

accidents.

Cell survival is evaluated through cell clustering capacity. The inability of

cells to make colonies in cultures in vitro is considered cellular death (repro-

ductive death), and cellular survival is evaluated by the existence of this

capacity.

Suspensions of isolated normal nonirradiated cells, sown in a geliﬁed nutri-

ent culture medium, at a large fraction, give rise after 1–2 weeks of incubation

to macroscopically visible colonies that can be ﬁxed, dyed, and counted.

∗

clustering efﬁciency is deﬁned by the ratio between the number of clusters

observed and the initial number of cells in plaque.

†

This same operation carried out with cells after irradiation with ionizing

radiation shows a decrease in the clustering efﬁciency. The evaluation of

effects is performed using pedigree analysis.

∗

Isolated, normal cells after tripsinization are clonogenic.

†

Clustering efﬁciency varies with cellular lines and cell density.

494 Nuclear Medicine Physics

8.12 Mathematical Models of Cellular Survival in Ionizing

Radiation Fields

Several mathematical equations have been proposed to describe the loss of

reproductive capacity observed in experiments with cells in culture irradiated

with ionizing radiation.

Cell survival curves are graphical representations of the fraction of survival

cells (S) as a function of the absorbed dose. Survival curves show different

shapes for different cells and for different types of radiation.

Certain types of radiation-sensitive cells, such as hematopoietic stem cells,

show linear survival curves, on a log-linear scale. This proﬁle is also a general

rule for cells irradiated with high LET radiation (Figure 8.33, curve 1)

Cells irradiated with low LET radiation show survival curves that either

present a variable dimension shoulder followed by a steep falloff (Figure 8.33,

curve 2) or have no shoulder (nonlinear with slope increasing with dose)

(Figure 8.33, curve 3). It is generally possible to obtain equations that ﬁt these

curves.

The inactivation of individual biological structures by ionization radiation

is one of the accepted postulates in the development of models for the action

of radiation on living matter.

At the level of the events that occur in cell sensitive zones by direct or

indirect action of radiation, the eventual biological effects of radiation result

–3

–2

–1

α-particle

3,8 Mev

X-rays

240 kVp

Neutrons

15 Mev

24 810

Absorbed dose (Gy)

FIGURE 8.33

Survival curves are linear for radiation of high TLE (1) or present the shapes (2) and (3) for low

TLE.

Dosimetry and Biological Effects of Radiation 495

from discrete energy transfer, corresponding to rare events (hits),

∗

which are

random and independent of each other. To be damaged, a cell needs to be hit

at least once, but a great deal of possibilities can be considered.

These processes are subjected to Poisson statistics, as they result from their

own characteristics.

Two distinct approaches have been used to develop cell survival equations:

one based on target theory, with several possible models, and a second one

assuming a linear-quadratic model.

8.12.1 Multiple Target Models (Target Theory Models)

8.12.1.1 One Sensitive Region n Hits

Assuming that the conditions of Poisson statistics are valid, let us suppose

that the average number of hits in a speciﬁc sensitive region of a cell in a

population, in a ﬁeld of radiation, is m. The probability that a particular cell

receives n hits in its sensitive region is

P(n) =

−m

. (8.110)

Obviously, mis proportionalto thedose D and m = aD wherea isa constant.

P(n) =

(aD)

−aD

. (8.111)

If n is also the number of hits necessary to inactivate the cell, all the cells

receiving less than n hits will survive. Then the survival probability is

P(n) = P(0) + P(1) +P(2) +···+P(n −1). (8.112)

If N is the number of surviving cells after dose D and N

is the initial

number of cells in the irradiated sample, then the probability of surviving

can be written:

= P(0) +P(1) + P(2) +···+P(n −1). (8.113)

∗

The number of atoms/cc tissue is about 10

, a value that is much bigger than the number of

atoms hit by radiation.

496 Nuclear Medicine Physics

Applying Equation 8.111 to the terms on the right-hand side of Equation

8.113, it comes

N = N

−aD

(1 +aD +

(aD)

+···+

(aD)

n−1

(n −1)!

), (8.114)

N = N

−aD

n−1



k=0

(aD)

. (8.115)

If n = 1, then

N = N

−aD

. (8.116)

Equation 8.116 is a decreasing exponential function, which is the simplest

case of cellular survival. It is seen in cases of irradiation of isolated cells in

vivo or in culture (bacteria, animal cells, etc.) for high LET radiation. In this

case, the data can be ﬁtted by a straight line in a semilogarithmic plot. The

constant a has the dimensions of the reciprocal of absorbed dose. Substituting

a = 1/D

, Equation 8.116 can be written as

S =

= e

−D/D

, (8.117)

where S is the fraction of surviving cells for dose D.

= 1/ais the mean lethal dose, that is, the average dose receivedby the cell

population, assuming a potentially inﬁnite life and that death is exclusively

due to radiation. D

is proportional to the resistance of cells to radiation, and

1/D

increases when the radio-sensitivity increases. D

is also the dose that

reduces the initial population by the factor 1/e = 0.37.

The semilog representation Equation 8.117 is a straight line with slope −a,

the negative reverse of the mean lethal dose D

, which fully characterizes the

process.

In the present case, where inactivation occurs with just one hit, D

is also the

dose that correspondsto one hit per sensitive region (average value). The total

number of hits equals the number of sensitive regions, that is, of irradiated

cells. D

varies from a few Gy in mammalian systems to values of the order

of thousands Gy in virus.

The mean lethal dose D

is also used, and t is the dose for which S = 0.5.

It is easily shown that

= 0.693/D

(8.118)

Assuming that the hits correspond to ionization processes and that w is the

ionization mean energy, for an absorbed dose D, the mean energy delivered

in the sensitive region of volume V and speciﬁc mass ρ is DVρ.

For dose, D

Vρ = w.

Dosimetry and Biological Effects of Radiation 497

Then, the volume of the sensitive region is

V = w/D

ρ (8.119)

Values of V for tissues and cells are known. For mammalian tissues, V is of

the order of 10

−23

An accurate value of w can be difﬁcult to know, as it depends on the LET of

the radiation and on the different interaction cross sections with the atoms of

the medium.

When the ions produced are well separated in the medium and we have the

situation of cellular death with a single hit, then a possible model for studying

the process is the ionization in a gas with an atomic number identical to that of

the tissue or suspension irradiated. This is the case of air and some biological

tissues that have w ≈ 34 eV.

When the situation of cells with a single sensitive region and a single hit,

as in the case of Equation 8.116, is analyzed, the same result can be obtained

starting from the equation

dN =−aNdD (8.120)

that is, the simple observation that the number of hits dN, that is supposed

to occur for dose dD, increases when N and dD increases.

8.12.1.2 Multiple Sublethal Sensitive Zones/One-Hit Model

Most mammalian cells have several sensitive zones. We can postulate that

for cellular death to occur, all the sensitive zones have to be hit (sublethal

sensitive zones). Additionally, we assume that sensitive zones are inactivated

with a single hit.

The probability that a sensitive zone is not struck is given by the survival

equation for one zone one hit (Equation 8.117). The inverse probability to this

one, that is, the probability that the zone is hit, is then

p = 1 −e

−aD

. (8.121)

If the cell has h sensitive zones, the probability of these being struck is



1 −e

−aD



. (8.122)

The survival probability of an irradiated cell with h sensitive zones is the

inverse probability to p

, that is,

= 1 −



1 −e

−aD



. (8.123)