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The Special Interaction of Ionizing Radiation with Living Tissue

This chapter is arranged in four parts:
  1. Distinctive Characteristics of Ionizing Radiation, p.1
  2. Primary and Secondary Electrons, p.2
  3. Some Chemical Consequences:   Free Radicals, Scavengers, Altered Genetic Molecules, p.3
  4. Intra-Track and Inter-Track Carcinogenesis, p.6

          This chapter and the two other "auxiliary chapters" (Chapters 20 and 21) provide the support for certain points used in the proof that no safe dose of low-LET ionizing radiation exists -- either for acute exposure or for slow exposure -- with respect to human carcinogenesis.

1.   Distinctive Characteristics of Ionizing Radiation

          With respect to ionizing radiation, "dose" is a macroscopic concept describing the total energy deposited in tissue, and tissue-doses are expressed in energy-units per gram of irradiated tissue.

          The biologically important characteristics of low-LET radiation are that its energy is carried through tissue by high-speed electrons, and that the transfers of this energy occur along paths (tracks) in extremely localized or concentrated fashion.

          One need only consider the common fever in order to ponder the very high probability that the biological potency of ionizing radiation is related to its spatial concentration along tracks, rather than to its meager addition of energy to cells (Go81, pp.52-53). A dose of 400 cGy (400 rads) is equivalent in heat to only 4.184 x 10^-3 joules per gram of tissue -- enough to provoke a mini-fever of 0.001 degree Centigrade -- yet 400 cGy of ionizing radiation to the whole body, acutely delivered, will kill about half the humans exposed to it.

          Ionizing radiation as a toxic agent differs fundamentally from toxic substances, which can be introduced to a solution slowly and diluted to a lower and lower uniform concentration. By contrast, for low-LET radiations such as X-rays and beta particles, the minimal unit is the primary ionization track left by a single high-speed electron. The electron cannot be subdivided, and it cannot make its delivery of energy more gentle by diluting it evenly throughout the whole cell;   the initial transfer of energy occurs very abruptly and very close to the primary track, as we shall see in detail in Part 2 of this chapter.

Definition of "Particle Track" :

          Here it is useful to define "Particle Track," well-described by Kellerer, as follows (Kelle87, p.360):

          "A particle track is the random configuration of energy transfers produced by a charged particle and / or its secondaries." Kellerer adds the important information that the individual energy deposits may be either ionizations or excitations of molecules or atoms, and that the term "particle track" denotes the set of all transfers of energy produced by a charged particle and its secondaries, the secondaries being primarily electrons set in motion by the original charged particle. In the case of low-LET radiation, the initial charged particle creating the track is the electron itself.

Definition of the "Least Possible Disturbance" :

          Because the minimal event in dose-delivery of ionizing radiation is a single track, we can define the least possible disturbance to a single cell-nucleus:   It is the traversal of the nucleus by just one primary ionization track.

          This is not the same as an average of one primary ionization track per cell-nucleus. That average can be achieved by some nuclei in irradiated tissue having NO tracks through them, others having one track through them, and some having multiple tracks through them. At very low doses, when a gram of tissue is irradiated, not every nucleus is "hit" by a track. The nuclei which receive no track at all actually receive no dose at all, even though the tissue as a whole is called "exposed" at the macroscopic level. At the "microdosimetric level," however, wherever there is no track, there is no dose.

          Although we can, and will, speak of doses which correspond with fractional tracks -- say, 2.937 primary ionization tracks per nucleus, on the average -- fractional tracks exist only because an average has been computed. Fractional tracks do not exist. Either a track traverses a nucleus somewhere (one nuclear track) or it does not (zero nuclear track). We shall discuss the "off-center" traversals in Part 2.

          As we examine what is going on at the cellular level when tissue is exposed to low-LET exposure, it will become evident that the biologically important question for settling the threshold issue is not "What human studies exist at the lowest conceivable doses?", but rather, "What human studies exist which can address carcinogenesis (or its absence) when cell nuclei experience the least possible disturbance by ionizing radiation?"

2.   Primary and Secondary Electrons

          Gamma rays and X-rays are photons which injure cells and cell-nuclei by ejecting an electron from a molecule or atom and putting it into high-speed motion;   in Chapter 20, we will take account of the three ways in which such photons transfer their radiant energy to high-speed electrons. Beta particles, of course, are already high-speed electrons.

The Primary Electrons :

          Electrons in motion travel primarily in straight lines through human tissue, although occasionally one will suffer a major deflection and then travel in another straight line.

          The distance traveled (range) depends, of course, on an electron's initial energy;   ranges are tabulated in Chapter 20, Table 20-FG. At the energies which characterize the nine epidemiological studies in Table 21-A, the high-speed electron travels through more than one cell. The diameter of a typical human cell is about 14.2 micrometers or microns (Chapter 20).

          The key issue is that the interaction between ionizing radiation and living tissue occurs along the track of the electron, as described nicely by Freeman below (Free87b, p.278-279). Although Freeman is discussing effects of irradiating hydrocarbon liquids (instead of human tissue), the interactions will be very similar, since the interactions of electrons with matter are overwhelmingly determined by the average atomic number of the matter being traversed -- and the atomic numbers which characterize tissue and hydrocarbons are "in the same ballpark." We quote Freeman, with only the minor change of expressing all energies in MeV or eV:

          "The collision of a 0.6 MeV photon with a molecule usually causes an electron to be ejected with about half the initial photon energy. The ~0.3 MeV electron moves through the liquid losing energy in small bits (a few tens of electron-volts) and ionizes about 10^4 other molecules along its path. Thus, nearly all of the physical and chemical changes in the system are produced by the energetic electron and not by the initial photon. The kinetics of reactions induced by high-energy photons are therefore similar to those obtained if high-energy electrons are used as the primary radiation."

          As the primary electron transfers its energy bit by bit, of course it loses speed. When it is slower, the average distance decreases between consecutive transfers of energy, and the amount of energy transferred per unit of distance increases, on the average. In other words, its LET (Linear Energy Transfer, or amount of energy transferred per unit of path traveled) is constantly rising until its energy is too low for further ionization events.

          In both the low-LET and high-LET regions of a single primary electron track, random variations occur in the distance between consecutive energy-transfers and in the amount of energy imparted during consecutive transfers.

          All along its track, the primary electron is setting secondary electrons into motion, and they have their own tracks known as delta rays. Most delta rays are only a few nanometers long -- extremely short compared with the track of the primary electron. (There are 1,000 nanometers per micrometer.)

          The fate of the primary electron in creating further secondaries is a matter of statistical probabilities -- and independent of what has just happened before. The result is that the distribution of energy-transfer events is hardly ever the same for one primary electron as it is for another of the same initial energy. Therefore, when describing the various excited molecules, secondary electrons, and ions which result, analysts deal with the variation from one region to another by speaking in terms of probabilities.

Microzones and the Secondary Electrons :

          As the primary electron is creating its ionization track, it is setting secondary electrons into motion at irregular intervals. For example, a primary electron with an initial energy of about 300 KeV is producing secondary electrons at irregular intervals of a few hundred nanometers on the average (a few tenths of a micrometer). Freeman has described the energy-deposition events very carefully (Free87b, pp.278-281). Of course, the energy-deposition events creating the secondary electrons, with some several tens of electron volts of energy-loss for each deposition-event, reduce the energy of the primary electron.

          The amount of disturbance caused by a secondary electron depends on how much energy it acquired when it was ejected from its molecule by the primary electron. Freeman has suggested the following energy distributions per secondary-electron creation.

          About 75% of secondary electrons along a primary ionization track acquire enough energy to move away from their sibling ions, but not enough energy to remove an electron from another molecule. Where a single secondary electron is produced, the region is called a microzone of reactivity (Free87b, p.280). Secondary electrons of this class lose their excess energy by colliding with other molecules until they acquire the average energy of molecules in the vicinity;   they become "thermalized." Paretzke reports that the time-interval between ejection of the secondary electron to the time it is thermalized is of the order of 10^-11 to 10^-13 seconds (Par87, p.92, Fig.3.2).

          About 15% of secondary electrons acquire enough energy (~40 electron-volts) to remove an electron from one additional molecule. This second ionization occurs at an average distance of only 0.4 nanometer from the first ion. The two electrons scatter more or less randomly and become thermalized a few nanometers from the positive ions. When there are two such pairs of electrons and positive ions, the region is called a two-pair microzone.

          About 10% of secondary electrons acquire enough energy to remove electrons from two or more additional molecules -- sometimes from 10 or more other molecules. In a five-pair microzone, all the pairs would be produced within about one nanometer of each other, and within a time-interval of pico-seconds (trillionths of a second).

"Off-Center" Nuclear Traversals :

          When the Least Possible Disturbance to a cell-nucleus was defined in Part 1 as traversal by just one primary ionization track, the location of the track was deliberately left unspecified.

          Obviously, not all primary tracks which traverse a cell-nucleus go right through its full diameter. Although most tracks will be "off-center" (short chords, in the language of microdosimetry), one cannot assume that short chords menace a nucleus with fewer energy-transfers and with a lower chance of carcinogenic injury than do longer chords. When the primary electron is slow near the end of its track, and its LET has become high, an off-center track can pack more transfers of energy (more microzones of reactivity) into a nucleus than can a full-length chord when the electron's LET is still low. Thus, it would be biologically meaningless to introduce a distinction between off-center and central tracks, in the concept of the Least Possible Disturbance.

3.   Some Chemical Consequences:
      Free Radicals, Scavengers, and Altered Genetic Molecules

          Freeman remarks:   "The time scales of the reactions in an irradiated liquid divide naturally into two regimes: those that occur quickly within the individual reactive microzones and those of the species that diffuse away from the microzones, which occur at later times" (Free87b, p.281).

          Paretzke (Par87, p.92) refers to the first of these two regimes as the "physical stage," and the second regime as the "chemical stage." The times at which the various events in the "physical stage" occur are provided in his Figure 3.2 and are summarized below.

Events of the "Physical Stage" :

          A. The energy transfer to molecules in the irradiated medium occurs in times of the order of 10^-17 to 10^-16 seconds. Short times indeed.

          B. The energy transfer produces excited atoms or molecules -- with a large increment in energy -- which means these excited species are capable of undergoing a variety of unusual further reactions. The time scales for production of these excited molecules are between 10^-16 and 10^-11 seconds after the energy transfer has occurred.

          C. Dissociation, which represents break-up of excited molecules to produce a variety of species still possessing excess energy, occurs in time scales of the order of 10^-13 to 10^-11 seconds. Some of the dissociations are actually ionizations, productive of a positive atom-ion or molecule-ion plus an electron.

          D. Electrons produced in the ionizations of Step C interact by collision with atoms and molecules, with final reduction in energy of the electrons to the average energy of the species in the medium. This process is known as "thermalization", and occurs in time scales of the order of 10^-13 to 10^-11 seconds.

          E. The various events described in (A) through (D) are considered to be over by 10^-10 seconds after the initial energy transfer. Paretzke describes this time as the end of the physical stage and as the initial condition for the chemical stage of reactions. This is a time of one ten-billionth of a second.

Events of the "Chemical Stage" :

          Magee and Chatterjee provide a well-stated overview of the chemical stage (Magee87, p.171):

          "Radiation chemistry must always be considered in terms of track reactions. Energy is deposited by radiation in tracks and then follows a sequence of nonhomogeneous processes that create and transform reactive intermediates until final radiation chemical products are formed."

          Magee and Chatterjee (Magee87, pp.210-211) emphasize that the track reactions of the radiation's chemical stage are nonhomogeneous, because the reactive species which form the radiation's chemical products are created in tracks, rather than in a homogeneous solution. They state that the structure of the tracks is actually quite complicated, and that a large part of their effort involves the devising of reasonable track models.

          Their statement that the problem is quite complicated can be regarded as a massive understatement, especially for tissues, where we have nonhomogeneity of the cellular or nuclear medium itself, with structures such as chromosomes being present -- all over and above the nonhomeogeneity of the radiation tracks themselves.

          They confirm Paretzke's estimates of time scales with their statement (Magee87, pp.210-211) that "Our treatment of the track reactions begins at about 3 ps [three pico-seconds, or three trillionths of a second], at which time the chemical species are more or less thermalized following the initial deposition of energy at about 10^-16 s" [s = seconds].

Production of Free Radicals :

          Now we can examine the nature of some of those reactive intermediates and some of the final products, together with inspection of the time scales of the reactions which occur in an aqueous phase (cellular material is fundamentally based on an aqueous phase). Water itself is attacked in the earliest phase of the chemical reactions which develop. The transfer of energy to the water molecule excites the electrons of that molecule, to produce an excited water molecule, with much excess energy compared to its normal energy. The most probable event is an ionization, as follows:

        * (A)  :
        H O ---->  H O  plus e, 
         2          2

        where e  = electron.      

        The extremely reactive H O  molecule-ion undergoes 

   further reactions as follows:

        * (B)  :
        H O  plus H O ---->  H O  plus OH
         2         2          2

        Both H 0  and OH have an unpaired electron, so both

   species are "free radicals" and are themselves extremely 

        Magee and Chatterjee estimate that reaction (B) occurs

   in about 10    seconds, and converts all the H O  to H O and
                                                 2       3

   OH, on this time scale.

        The free "dry" electron reacts with water to produce a 

   hydrated electron, designated as e  (aqueous), on a time 
   scale of the order of 4 times 10    seconds.

        Above we stated that ionization is the "most probable" 

   event following energy-deposition from radiation, but other 

   reactions also occur, such as:

        * (C)  :

        H O (excited) ---->  H plus OH   and,

        * (D)  :

        H O (excited) ---->  H  plus O
         2                    2

        Note that H (hydrogen atoms), OH (hydroxyl radicals), 

   and O (oxygen atoms) are all themselves "free radicals," 

   possessing an unpaired electron, and they are extremely 

   reactive species which will interact with a variety of 

   chemicals in the aqueous medium.  For example:

        * (E)  :

        H O plus O  ---->  H O  , which is
         2                  2 2

        hydrogen peroxide.

          These various reactions account for the production of what Magee and Chatterjee regard as the major chemical entities produced, and these reactions are over well before "thermalization." So they are over well before 10^-11 seconds, following energy-deposition.

          Magee and Chatterjee suggest that by 10^-10 seconds after passage of a charged particle through a solution, we have the various highly reactive chemical species (described above) present in thermal equilibrium but far from chemical equilibrium, and they are present in a nonhomogeneous spatial distribution. These reactive species react with each other or diffuse away from each other. It is their suggestion that the reactive intermediate chemical species formed in one track react completely with each other and with constituents of the aqueous medium before they can diffuse far enough to encounter intermediates from another track.

          Since the reactive intermediates not only react with each other, but also react with constituents of the medium, it follows that the ultimate products depend upon what else is present in the medium. For example, in biological tissues oxygen is present, and hence reactions such as (F) and (G) occur:

        * (F)  :
         _                           _
        e  (aqueous) plus O  ---->  O   plus  H O
                           2         2         2

        In this reaction the hydrated electron converts oxygen

   molecules to the superoxide ion (which is O  ).

        * (G)  :
        H plus O  ----> HO
                2         2

        The product HO , is a free radical not previously 

   mentioned above.

          Magee and Chatterjee suggest that the host of reactions, between the initial radicals themselves and between the radicals and constituents of the solution, are pretty well completed to yield final products by times of the order of 10^-5 seconds following the initial energy-deposition event.

Action by "Scavengers" :

          The word "scavenger," which means any person, creature, or thing which removes impurities, refuse, or rubbish, is enormously useful in chemistry -- including radiation chemistry.

          Biological tissue is a water-based medium, in which are present numerous small molecules as well as large molecules (e.g., proteins), plus the structures such as chromosomes, which themselves contain DNA molecules, ribose-nucleic acids, and proteins. Any and all of these entities can act as scavengers for the various highly reactive radical intermediates which were formed in the early radiation reactions. Some products of such scavenging may be involved in the ultimate production of cancer.

Direct Action on Genetic Molecules :

          It would be a grave mistake for anyone to overlook the fact that genetic molecules (DNA, chromosomes) can suffer injury from direct interaction with a primary ionization track.

          Goodhead has pointed out that a variety of biochemical and other data would imply that diffusion-distances of radicals in cells are very small (less than a few nanometers) and, therefore, "that the only reasonable probability of multiple adjacent damage to DNA arises when a cluster [of radiation damage] is produced directly in, or very near the DNA" (Good88, p.238). Goodhead states further (p.238):

          "For low-LET radiations, approximately one-third of the energy deposition is via very low energy, < ~ 2 KeV electrons, which are known to have a relatively high RBE and a relatively high probability of producing localized clusters (of, say, > ~ 100 eV in the DNA), so this may well be the critical component of low-LET radiations."

          Such considerations echo the opening theme of this chapter:   In ways which no one yet fully fathoms, the spatial arrangement of energy-transfers along a track is important. Kellerer, one of the leading figures in the microdosimetry of ionizing radiation, points out that the effectiveness or menace of ionizing radiation is not "a mere function of the specific energy in the nucleus;   it depends in an insufficiently understood way on the spatial microdistribution of energy" (Kelle87, p.347).

          Other sources (see, for instance, Sies85 and Bav89) are also reporting that the specific geometry of the initial injury-site is crucial to the final outcome of subsequent molecular alterations. In other words, when microzones of energy-transfer (from the primary ionization track) occur directly upon or within the genetic molecules, the geometry of the particular site, the particular juxtaposition of components, the reduced mobility of reactive intermediates, possible transfers of energy along the molecule, and other such considerations (including altered chance of repair), can put such events into a very different class from interactions between genetic molecules and external free radicals in the medium.

          Some proponents of the safe-dose idea suggest a benign analogy between normal metabolism and ionizing radiation, by saying only that both of them produce free radicals in the medium. The comparison is misleading, if the important differences -- such as direct interaction of an ionization track with a genetic molecule -- are not mentioned.

"The Yalow Model" :

          Dr. Rosalyn Yalow (see Chapter 34) features free radicals in an article about "radiation phobia." She writes (Ya89, p.160-161):

          "The question as to whether there exists a threshold below which radiation effects in man do not occur should continue to be addressed. One can develop a tenable model that would be consistent with such a threshold. Since human beings are more than 75 % water, low-LET ionizing radiation is largely absorbed in the water resulting in the production of free radicals. Thus, many of the potential biochemical changes initiated in the cell and, in particular, damage to cellular DNA are probably a consequence of the action of the products of water radiolysis. If molecules which scavenge radicals and which are normally present in tissue greatly exceed in concentration the free radicals generated at low dose rates, there may well be no initiating event, i.e., damage to DNA. The threshold could be the dose rate at which the radiation-induced free radicals exceed the scavengers."

          We do not find the "Yalow Model" to be tenable or plausible as a safe-dose model:

          Not even a shoulder-to-shoulder "army" of other scavengers in the aqueous medium can protect the genetic molecules against direct interaction with an ionization track -- regardless of dose. The chance of direct interaction will be proportional to the number of tracks (that is, to the dose) right down to the lowest conceivable dose or dose-rate.

          Moreover, direct interactions may well be the important events in causing permanent alterations of genetic molecules (as pointed out by Goodhead above).

No Track, No Products :

          All of the events which occur because of the primary ionization track -- from the secondary electrons to all of their consequent products -- must be treated with the primary track itself as a single unit. If there were no primary track passing through a cell or cell-nucleus, none of the secondary events would occur. No track, no products.

          As we analyze the threshold issue, we must disregard any leakage of radiolytic products into an un-hit nucleus from the cytoplasm -- if such leakage occurs at all. No matter how low the dose or dose-rate, some nuclei necessarily experience direct hits and not just leakage. High-speed electrons traveling through tissue in straight lines do not know how to avoid the nuclei. Some nuclei necessarily continue to experience one primary ionization track until there is no tissue-dose at all.

A Reminder about Time Scales :

          We close this section on "the chemical stage" of radiation injury with a reminder:   While the damaging events from ionizing radiation do indeed occur in very short time-spans (small fractions of a second) and in close physical proximity to the initial energy-deposition events, there are very important events which follow. For example, DNA and chromosomal repairs -- and misrepairs -- go on for periods of the order of minutes to several hours after radiation damage (Chapter 18).

4.   Intra-Track and Inter-Track Carcinogenesis

          We can think of all the energy-transfers and consequent products along a single primary track as "intra-track" phenomena, to distinguish them from similar events which would occur elsewhere in the same cell or cell-nucleus as a result of the passage of a wholly separate primary electron.

          If there is any interaction of the products of one primary track with the products of another primary track, we would speak of "inter-track" phenomena.

          It is self-evident, from the nature of radiation tracks, that if track-phenomena are going to interact with each other, what matters is the nature of the interacting phenomena -- and it does not matter which track happened to produce them.

Single-Site and Multi-Site Lesions :

          Now let us examine the following premise:   A fully competent carcinogenic lesion may consist of an alteration at only one site in the nucleus, or it may also consist of alterations which occur at two (or more) separate sites in the nucleus and then interact to become carcinogenic. Let us call the first type of fully competent carcinogenic lesion `A'. For the second type, we will consider alterations at two sites, and call this type of lesion `B + C'. In terms of the diagrams:

The A1 Lesion :

          A1 illustrates the A type of lesion;   by itself, this single-site alteration, created by a single track, would be a fully competent carcinogenic lesion of the intra-track variety. The frequency with which A type lesions occur would be related to the number of tracks, or Dose^1.

The B1 + C1 Lesion :

          B1 + C1 illustrates a fully competent carcinogenic lesion, of the type which requires the interaction of sub-lesions B1 and Cl. This lesion, B1 + C1, is an intra-track lesion, because the B1 and C1 sub-lesions are both created by a single primary ionization track. The diagram shows that no other track is involved. Like the A type of lesion, the B1 + C1 lesion is the result of single-track action, and therefore its frequency would be related to the number of tracks, or Dose^1.

          The diagram does not indicate whether B1 and C1 are sub-lesions within the same molecule, or sub-lesions within two different molecules. (Both situations are possible.) The purpose of the diagram is to indicate that B1 and C1 are two lesions caused by the same primary track.

The B1 + C2 Lesion :

          B1 + C2 illustrates a fully competent carcinogenic lesion of the inter-track variety, because the B1 and C2 sub-lesions are created by different tracks. The frequency with which B1 + C2 lesions occur would be related to Tracks^2, or Dose^2.

Comparison of the Multi-Site Lesions :

          The orientation of a track relative to a genetic molecule is determined by chance -- the molecules are not stationary in the nucleus, the person is not stationary during occupational and environmental irradiation, and the tracks themselves are rarely coming from a single direction.

          Therefore, despite the visual suggestion by the diagrams that such orientation might differ between the two multi-site lesions (B1 + C1, versus B1 + C2), in fact the orientations and everything else about these two lesions can be identical -- except for the fact that one is an intra-track lesion and the other is an inter-track lesion.

          If these intra-track and inter-track multi-site lesions can be identical, it would be preposterous for anyone to suggest that only one could be carcinogenic and the other could be innocuous.

          Now, we return to the premise with which we started. Our purpose was to emphasize that -- even if interaction between multiple sites is sometimes or always involved in radiation carcinogenesis (which is by no means certain) -- intra-track carcinogenesis as well as inter-track carcinogenesis would occur.

The Capability of Single-Track Action :

          Before leaving the topic of intra-track carcinogenesis, it needs to be said that any lesion which can be inflicted in a nucleus by a pair of tracks, can also be inflicted by a single track acting alone.

          For instance, it is obvious that breaking a chromosome requires that two strands of DNA be broken. But this result does not require two separate ionization tracks. Events occurring along the same track can do it.

          A single track is also capable of inflicting damage on more than one chromosome. There is just no doubt that a single track can interact with more than one chromosome, as the track passes through the nucleus. Indeed, if a dozen chromosomes were ever in the same plane as the track and if they were lying across its trajectory, a single track could injure all twelve of them, in principle. Or if a single chromosome happened to be folded across the track's trajectory, a single track could interact with the same chromosome several times.

          Another example of capabilities involves the multi-pair microzone. It is true that a single track cannot intersect with itself and cannot superimpose two microzones upon each other, whereas a pair of tracks may sometimes intersect and produce (say) a 2-pair microzone and a 3-pair microzone in the same place. The result would be a 5-pair microzone -- and this is something which a single track produces on its own from time to time (see Part 2), without any help from another track.

          Lastly, we should mention again the possibility that sometimes carcinogenesis may be associated with multiple genetic injuries. And if so, such injuries can be inflicted by a single track. The earlier parts of this chapter leave no doubt that events at multiple, separate sites are certainly producible by a single track, acting alone.

          The bottom line from this discussion was stated in Chapter 18, Part 1:   "Single, primary ionization tracks, acting independently from each other, are never innocuous with respect to creating carcinogenic injuries in the cells which they traverse. Every track -- without help from any other track -- has a chance of inducing cancer by creating such injuries."

Linear-Quadratic Model of Dose-Response :

          In Chapter 18, we said that the statement quoted above is not controversial. Agreement about intra-track carcinogenesis is reflected in the Linear-Quadratic (LQ) model of dose-response which is almost universally used by the radiation community (see Chapter 22). In that model, the linear term (the L term) represents the relationship of intra-track events with Dose^1, and the quadratic term (the Q term) represents the relationship of inter-track events with Dose^2.

          It should be noted that the LQ model is fully consistent with our disproof of any safe dose or dose-rate. Indeed, the LQ model acknowledges that -- in the studies which we used in the disproof -- the probability is very high that the excess cancer which was observed all arose from single-track action (intra-track events). In the LQ model, intra-track events are overwhelmingly dominant at low doses and dose-rates. This is true when the LQ model has a concave-upward shape, and also when it has a concave-downward, supra-linear shape.

          The linear-quadratic model is examined in detail in Chapter 23.

Meaning of "Fully Competent Lesion" :

          The statement that intra-track lesions can be fully competent carcinogenic lesions should not be interpreted as a statement that every carcinogenic lesion becomes a clinically manifest cancer.

          A potential cancer may need assistance from promotional agents in order to reach a clinical stage, and may also have to evade a series of defenses by the body. But as far as radiation itself is concerned, a single primary ionization track has all the properties which make ionizing radiation a human carcinogen.

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