Notes on Modern Physics and Ionizing Radiation

VI. Radiation Damage and Dose Measurement

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This chapter begins with an overview of the mechanisms of damage by ionizing radiation and the techniques that have been used to study them. Then we consider the standard physical measures of radiation dose and their biological significance.

A. Biochemistry

Studies of radiation damage involve various methods of evaluation, depending on the nature of the radiation and of the sample (Herbert and Tolbert, 1976; Powell and Martel, 1977). The crudest, but perhaps the most compelling criterion for living organisms is simply whether they continue to live and reproduce without mutations. In the case of a structural member of a nuclear reactor, changes in strength or corrosion resistance are of great concern. A single protein, for example the digestive enzyme alpha-chymotrypsin (abbreviated alpha CT in the following), that has been crystallized from a solution containing about ten other chemical species in significant concentrations, constitutes a system that is much simpler than a living cell, but yet complicated enough to be interesting.

The biologically and medically significant effects of radiation can be divided according to the classes of structures ultimately affected: membranes; proteins, both structural and enzymatic; the various RNA's; and the genetic DNA. Membrane and protein damage may kill promptly, while DNA damage may cause problems only for offspring, or may cause cancer after many years. An investigation of radiation damage to a crystallized enzyme has several appealing features. In addition to the simplicity of the system and the ability of the method to display changes on a very small scale, there are reasons to believe that the results may be of general interest. The inter-molecular forces that hold the crystal together are very weak (protein crystals are notoriously fragile), and protein crystals are typically half to one quarter water. The environment of the individual molecules is therefore similar to the cellular interior. A note of caution must be sounded, though, since large fragments created by irradiation will not be able to migrate freely through the crystal, and so may re-attach themselves, a "healing" process that would probably be much reduced both in solution, and also in the interior of a living cell.

When a beam of X-rays strikes, for example, a protein crystal, the energy that is delivered to the crystal or its surroundings may directly break intra-molecular bonds and it may also create chemically active fragments ("free radicals") which can in turn attack the molecules of the crystal. Some of the energy may be expected to break the inter-molecular bonds, disordering the crystal without destroying molecules. Other energy will go into vibrations and other excitations, dissipating throughout the crystal without breaking bonds. It is unlikely, because of the wide range in the strengths of the intra-molecular bonds (from less than 0.1 eV to more than 4 eV), that all of the bonds in a crystal will be equally susceptible to radiation damage.

Much study of radiation damage is organized around the concept of "free radicals," referred to briefly above. Free radicals can be defined as covalently bound groups of atoms (or single atoms) which have at least one unpaired electron, and which are free to move within the sample. Their presence in an irradiated specimen is demonstrated by electron paramagnetic resonance (Gräslund, et al, 1973). Their involvement in the radiation damage process in solution is demonstrated by adding to the solution other chemicals known to combine readily with free radicals ("scavengers"; Meyers, 1973; Demopoulos, 1973).

The net effect of the addition of a scavenger results from the balance among several competing effects.

  1. The scavenger, S, may itself be degraded by the radiation, forming one or more new species of free radical, S*. The S* may directly attack the sample molecules, in which case the "scavenger" has sensitized the sample to the radiation.

  2. There may be reactions of S or S* with free radicals that would otherwise have attacked the sample, thereby protecting it from the radiation (true scavenging).

  3. S or S* may react with free radicals or other components of the solution that would otherwise have acted as true scavengers; in this case, again, S sensitizes the sample to the radiation.

The balance among these three classes of effects of the addition of the species S to solutions of the sample will depend on the concentrations and diffusion speeds of the several reactants present (Rotlevi, 1973).

A particularly interesting example of the use of a scavenger in the study of free radical radiation damage is presented by V. Kasche (1974), whose results raise doubts about the precise similarity of crystalline and solution cases. Kasche demonstrates that the immobilization of individual alpha-chymotrypsin (alpha CT) molecules reverses the sign of the effect of dissolved oxygen on the rate of radiation damage. To be precise, he found that "Oxygen ... sensitizes the radiation-induced deactivation of immobilized alpha-chymotrypsin, but protects the free enzyme in solution." His experiments were carried out at pH 7, approximately the value for peak biochemical activity of alpha CT, not at pH 4, the condition for crystallization. The alpha CT molecules were immobilized by covalent bonding to suspended Sepharose, a beaded preparation of the poly-saccharide agarose. This bonding has been demonstrated to have little effect on the enzymatic activity (Kasche, 1973; Kasche, et al, 1971). The radiation used was Co-60 gamma rays (whose photon energy is approximately equal 1 MeV, two orders of magnitude larger than CuK radiation). Within experimental error, the residual specific enzymatic activity was exponentially related to dose.

Kasche argues that the destruction of immobilized alpha CT requires radicals to diffuse into that small volume fraction containing the enzyme, a process during which the radicals are subject to termination reactions with the solvent and other radicals. At high enough oxygen concentrations, "all of the aqueous electron and proton radicals react with oxygen, the rate of radical recombination decreases considerably, and more radicals, .OH , .O2, and .H2) should be able to react with immobilized enzyme molecules."

On this basis we see that variations in the environment of the enzyme can be expected to alter the relative amounts of the various radiation-induced free radicals attacking it. In turn, this will alter the frequencies of damage at the various sites in the molecule attacked by each of the radicals. Nonetheless, if a site is observed to be damaged preferentially under one set of conditions, it can be regarded as specifically vulnerable in general, even though it may escape attack in certain environments.

Sagan (1989) and Wolff (1989) address the possibility of beneficial effects of low levels of radiation. For example, it is conceivable that the body might "overproduce" free radical scavengers in response to low dosage levels of ionizing radiation. If that happens, of course, there would be health benefits, as free radicals caused by a variety of mechanisms would be prevented from having their full damaging effects.

There have been at least two probes used to demonstrate specific radiation damage effects, i.e., departures from the randomness assumed in the methods of correcting crystal diffraction data for radiation damage. Blake and Phillips (1962) took partial myoglobin diffraction data sets, from which they made maps of the electron-density projected along one crystal axis. Their repeated measurements displayed systematic shifts of the electron density with increasing dose, although they could not associate them with specific parts of the known molecular structure.

Baumeister, et al (1976) used infrared spectroscopy to study the irradiation of tripalmitin model membranes with 100 keV electrons. The spectra were analyzed to measure the vibrations associated with groups of bonds, involving C, H, O, and residues along the hydrocarbon chain. The results clearly demonstrate that the C-C bonds of the backbone are much less sensitive to the radiation than the others studied, and that there is some variation among the others. Although C-C bonds in general may be relatively immune to the effects of the radiation, there may be certain classes which are more frequently attacked.

B. Physical Dose Measures

Physically based measures of irradiation include "absorbed dose" and "exposure." Exposure refers to the radiation incident upon the object, while absorbed dose refers to the actual interaction of that radiation within the object. Absorbed dose can be measured in terms of

As discussed by Cember (see Table 5.1, p. 114, and p. 151) the energy required to create an ion-pair does depend on the material, but is typically around 35 eV, so there is a rough correlation between energy- and charge-based measures.

Definitions of a number of important units of measurement are provided in the table below. Although the caloric heating is rarely of primary interest with ionizing radiation, the most common units of absorbed dose are the rad and Gray.

For externally originating radiation, it is commonly appropriate to measure the exposure, the radiation incident on the sample, in terms of the ionization produced in air when that radiation passes through it. The unit of measure is the Roentgen, defined in the table. The charge in question is the total on all the ions of one sign created by the radiation directly or indirectly (by the secondary radiation created by its passage through the air). For a variety of reasons the Roentgen is a useful unit of exposure only for radiation whose quanta have energies up to about 3 MeV; above that level it is customary to specify the strength of the incident radiation field, the exposure, in terms of Joules per square meter or Joules per square centimeter. (Exposure rates would therefore be measured in Watts per square meter or per square centimeter.)

An exposure to radiation of 1 Roentgen will produce an absorbed dose of nearly 1 rad for air and muscle at nearly all energies of the incident quanta. For photons, that rough equality holds from 10 keV to over 100 MeV. As shown by Cember (Fig. 6.6, from O. Glassen), the rough equality of dose in rads and exposure in Roentgens, holds also for bone and fat above 200 keV. Below that energy, bone absorbs over 4 rads and fat less than half a rad for the same 1 Roentgen exposure. It is for this reason that diagnostic X-ray machines are operated to give the bulk of their photons between 20 keV and 100 keV, providing contrast between tissue types.

Measures of dose and exposure are typically predicated on the assumption known as "reciprocity," that a doubled rate of irradiation for half the time duration will produce the same effects. The healing mechanisms of living organisms can be saturated, so it seems very unlikely that reciprocity will hold over all dose rates, but it is likely to be a good approximation at the moderate and higher rates where acute injury short of immediate death is likely.

The following definitions are based primarily on the CRC Handbook of Chemistry and Physics, 66th Ed., "Definitions" section, page F-65 and following, "Units" section, page F-241 and following, and on section 18.1 of Medical Physics by Cameron and Skofronik.

Becquerel (Bq)
A unit of activity of a radioactive source. 1 Bq = 1 decay/sec.

Curie (Ci)
A unit of activity of a radioactive source. 1 Ci = 37 Gigabecquerel.

Gray (Gy)
A unit of absorbed dose of ionizing radiation. The dose is 1 Gray when the density of the total energy absorbed, in any medium from any type of ionizing radiation, is 1 Joule/kg. The dose can be expected to vary from point to point within the irradiated object.

A unit of absorbed dose of ionizing radiation. 1 rad = 10 milligray.

Relative biological effectiveness (RBE)
The biological effectiveness of any type or energy of ionizing radiation in producing a specific damage (e.g., leukemia, anemia, cataracts, carcinogenesis, shortening of life span, etc.), relative to 250 kVp X-rays; (exposure in rem) = RBE * (exposure in rep). (See below for the definition of the "rep"; see Chapter VII for a discussion of kVp.) The numerical value of the RBE depends on radiation type, the quantum energy, and the specific type of damage. The data available by conscionable means (!) do not usually permit many significant figures. The RBE is sometimes described as the product of a "Quality Factor" Q and other multiplying factors N.

Roentgen (R)
A unit of exposure to ionizing radiation. That quantity of X- or gamma-radiation such that the associated corpuscular emission per 0.001293 g of dry air (equals 1 cc at STP) produces, in air, ions carrying 1 esu of quantity of electricity of any one sign; alternatively, 258 microcoulombs/kg.

Roentgen equivalent man (REM)
That amount of ionizing radiation of any type which produces the same damage to humans as 1 roentgen of 250 kVp X-radiation.

Roentgen equivalent physical (REP)
That amount of ionizing radiation of any type which results in the absorption of energy at the point in question in soft tissue to the extent of 93 ergs/g. It is approximately equal to 1 roentgen of 250 kVp X-radiation in soft tissue, or 0.93 rads, or 9.3 milligray.

Sievert (Sv)
Dose equivalent; dimensionally J/kg, but calculated as the product of the physical absorbed dose in Gy and the Relative Biological Effectiveness.

C. Biological Effects

People typically survive exposure to moderate doses of radiation, with symptoms whose severity and duration depend on the dose. Extensive experiments have not, of course, been performed(!), but the available information on human susceptibility to toxic effects of ionizing radiation can be summarized as follows:

LD sup 50 sub 30

The lethal dose for 50 % of the exposed population to die within 30 days of exposure is about 4.5 Gy = 450 rads, for whole body exposure. Some organs and tissues are more sensitive to radiation, and some less. Death of the person may result from the overall insult to the body or from the destruction of a vital organ. Acute exposure (high rate over a short or medium time) and chronic exposure (low rate sustained for a long time) at equal total doses may or may not produce the same effects.

Since death of the organism can be expected only if one or more vital organs suffer too large a fraction of their cells dying at once, it is interesting to consider the lethal dose per cell. The diameter of one cell is about 0.1 mm, so its volume is about 1 picoliter. Taking the density as essentially 1 g per cubic centimeter = 1 kg/liter, we say immediately that the mass of a cell is about 1 nanogram = 1 pico(kg). Hence the lethal dose corresponds to an energy, E = 4.5 picoJ/cell = 28 MeV/cell.

If 10 percent of this energy goes to breaking bonds, how many bonds will that be? Using 2 eV, half the C-C single bond strength, as typical, 1,400,000 bonds must be broken per cell in order to kill. This indicates clearly that most of the structure of the cell is not vital on a molecule by molecule basis, an observation that comes as no surprise to any biologist.

Langlois, et al (1987) provide an analysis of data from Japanese atomic bomb survivors that indicates a strong correlation between dose and a specific type of somatic cell mutation. Dose-response studies of the bomb survivors are complicated by the difficulty of obtaining precise estimates of the dose inflicted upon each individual. The dose estimates are based on each individual's statements (recorded some time after the war) as to his or her location when the bomb exploded (for direct exposures), and subsequent travels and treatment (when evacuated, when bathed, etc.; for exposure from fallout). These dose estimates are much more reliable for averages of groups of people than for single individuals. A significant correlation exists between estimated dose and variant frequency (mutation rate). For individuals, there is a lot of scatter, but for groups of 10 the relationship is convincingly linear. (See Fig. 2 of the paper, in which doses are expressed in centigrays.)

Jean L. Mark reports that humans appear to be appreciably less sensitive than mice to radiation, as measured by genetic damage in offspring. The dose required to double the "naturally occurring rate" seems to be roughly 200 rem, based on recent work with the survivors of the Hiroshima and Nagasaki bombs.

D. Contamination and Irradiation

We will now consider at length the fourth of the following four scenarios for radiation damage to people: first, external radiation sources, such as X-ray generators, second, surface physical contamination, such as dust containing radioactive materials, third, internal physical radioactive sources, such as "radium needles," fourth, internal chemical contamination, in which the radioactive materials are in a chemical form that influences their "trajectory" through the body. For some materials, the elemental form is itself chemically significant (e.g., iodine and calcium). We must consider the nature of the damage to be expected and the degree of self-cleansing or self-shielding that may be expected.

There are two types of damage that internal radioactive materials may produce: first, the radiation produced may be expected to exhibit the usual sort of destructiveness. Second, many radioactive species are heavy metals, and are therefore chemically toxic, even at extremely low concentrations. In either context we need to consider the balance between damage and removal of the material.

Consider a graph of the rate of removal of a substance (in moles/sec) vs the concentration (in moles/l) of that substance within the relevant tissue (perhaps the circulating blood). Such a graph will typically exhibit a portion passing linearly through the origin and in theory may exhibit at high concentration a leveling off, or saturation. If the concentration is so high that the removal mechanisms have saturated, the graph of concentration vs time can be expected to exhibit a linear decline (constant total rate of removal). On the other hand, if the concentration is low, the rate of removal will decline as the concentration is reduced, hence the graph will head downward at a decreasing slope, flattening out. The mathematics is exactly parallel to that of radioactive decay: during this final phase of removal, the concentration will decline exponentially with time. (Saturation is not typically observed for non-lethal doses.)

This exponential removal law applies to any chemical species at low concentration. If you are concerned with radioactive decay of a contaminant, then you must also consider the "removal" by decay in two ways. First, after it decays it is no longer the original substance, so there is less of that material present. (A complete anaylsis must address the possible radioactive or chemical toxicity of the post-decay, or "daughter" material; we return to this issue below.) Thus, the concentration of the original material will decline faster if it decays and is being removed by the body, than it would if it were decaying in vitro. Second, the damage done to the body results only from the decay that occurs within the body. Calculating the amount of material that will be excreted prior to its decay is an elementary exercise in calculus, provided that the original concentration is so low that the removal is following an exponential law. In that case, the effect is to produce an exponential reduction in concentration with time, with an overall "effective half-life" calculated from the "biological half-life" and the "radioactive half-life," as follows:

equation graphic

This equation just says that the total rate of removal is the sum of the rates of removal by biological action and by decay.

The biological half-life can be dramatically reduced, thereby reducing the radiation injury to the patient, by the administration of appropriate drugs. In particular, REAC/TS (1987) reports that actinides (in general, atomic number, Z, between 90 and 103, inclusive, but see below for exceptions) can be removed from soft tissue before migration to bone, through the administration of gram quantities of Zn-DTPA or Ca-DTPA, salts of diethylenetriamine-pentaacetic acid. This chelation agent binds to the heavy metal atom and is then excreted by the kidneys. Uranium and neptunium (Z=92 and Z=93) should NOT be chelated because the complex is unstable and renal damage occurs. As of 1987, the use of DTPA salts for this purpose is as an FDA approved "Investigative New Drug" sponsored by the Department of Energy and administered by the Medical and Health Sciences Division of the Oak Ridge Associated Universities.

Equation 1 does not apply in the case of concentrations high enough to induce full or even partial saturation of the body's removal mechanisms. If the removal mechanism is completely saturated, so that the rate of removal in moles/sec is constant, then the calculation requires only slightly more elaborate use of calculus. At intermediate concentrations, however, there is not likely to be any simple algebraic expression for the rate of removal as a function of concentration, and therefore almost surely no simple algebraic expression for the concentration as a function of time nor for the total amount removed before decay.

There are two additional features of internal contamination that we need to examine: first, the insult to the organism will depend on the chemistry of the contaminant as well as its radioactivity. If there is no particular affinity of the contaminant for any one organ or system, then the radiation and its damage will be diffused over the whole body, and the dose to each organ will be lower. On the other hand, such materials as iodine and strontium exhibit strong specific tropism, for thyroid and bone respectively (in any of their isotopes, radioactive or not). The radiation will therefore be concentrated and the dose to the selected organ will be higher, perhaps even reducing the functioning of that organ so much as to be life-threatening for the organism.

Second, the decay products may themselves be hazardous (by radioactivity, or chemical toxicity, or both). Their removal mechanisms or target organs may differ from those of the original material. The heavy element radioactive species all have similar chemistry (they are large transition metals), but the fission fragments and other light elements will typically have decay products with notably different chemistry (see Chapter I). The mean life of the decay products, if they are radioactive, may not permit migration to the target organ indicated by the chemistry. The total radiation dose must be evaluated with the inclusion of the entire decay chain, bearing in mind the lifetimes, chemical affinity, removal pathways, radiation types, and quantum energies (including any X-radiation, either from atomic electron re-alignment or from beta particle secondary bremsstrahlung).

An interesting example of the analysis of experimental data is the determination of the half-lives of two different, independently decaying isotopes. This problems arises when natural silver is exposed to neutron radiation, because there are two naturally occurring isotopes (Ag-107 and Ag-109) each of which can capture a neutron to form a radioactive nucleus (Ag-108 and Ag-110). Their half-lives are 2.42 minutes and 24.4 seconds, respectively [Weast, 1984]. A conventional analysis fails to yield a straight line on the semi-log plot, because of the mixture. The useful technique is one of successively more accurate approximations.

First, one examines the data at later times when the shorter half-life material will be mostly gone. Based on that data, one extrapolates backwards through t=0 to determine the portion of the activity due to the longer half-life material at each intervening time. The excess of the activity above that level is presumed due to the decay of the shorter half-life material. The logarithm of that excess is then plotted against time, a straight line fit performed, and the resulting rate (due to the shorter life material) subtracted from the total observed rate to obtain a second approximation to the decay rate for the longer life material. After a few cycles through this analysis, one will have stable values for the two decay rates, and therefore also for their half-lives. This technique proves useful only if one has large number of observations, at different times, during both the early period when there is significant activity from the shorter life material and the later period when only the longer life material remains. Even then, it will not yield good results in cases where the two half-lives are too close in value.

Similar complexities of analysis will occur with short decay chains, in which the daughter nucleus itself decays to a granddaughter nucleus. The mathematical analysis will involve cases that depend on the initial amounts and relative half-lives of the radioactive species involved. Many of these cases can be described roughly as "double exponential decay," comparable to that observed with neutron activated silver samples.

E. Radiation Dosimetry

Any technique that can be used to measure radiation, rather than just detect its presence (as Geiger counters do) can be adapted to dosimetry. A variety of situations call for the measurement of radiation doses, but they may be grouped into two main classes: personnel monitoring, intended to protect individuals who work with radioactive materials or radiation producing machinery, and site monitoring, intended to protect workers and passersby who might be exposed to radiation from specific sources. The same range of techniques can be applied to both groups, but different methods may be optimum.

Radiation dosimeters are typically used so as to provide measurements of the dose over a specific time interval, for example, monthly film badges. The typical intended use is to detect lapses in technique, or broken equipment, that would, over time, produce excessive exposures. Therefore, convenience (so that workers will actually wear the devices) tends to dominate over precision in the engineering of the dosimeters.

It is important that workers understand the limitations of the dosimeter, since incorrect positioning can readily lead to falsely low readings. Film badges, for example, are typically much more sensitive to radiation from the front than from the back, because the plastic holder and clip absorb radiation, and they will be calibrated for direct exposure, not when shielded by being inside a pocket, even though facing out. Another distinction that needs to be made is that different dosimeters will be sensitive to different types of radiation, or for a given type of radiation, only to a limited range of quantum energies. Thus soft X-rays might damage a person's skin significantly, without being accurately detectable through the light-shielding paper wrapper of a film badge.

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Dick Piccard revised this file ( on December 30, 2004.

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