Estimating the Impact of Low Level Radiation

Is radiation more dangerous than the official estimates, or less? We will use mathematical modeling to evaluate estimates of low level radiation impact.

Part 1 Written 2000

Formatted 2010



Part 1: Interpolating the Curves

In studying health, we frequently test using very high doses then interpolate linearly to make assumptions about lower exposures. There is no easy and ethical means of measuring all exposure levels. So we interpolate from available data.


linear extrapolation

But the real effect might not follow the cause linearly. This will lead to very poor estimates.

With radiation, some things are considered logarithmic rather than linear. Both the linear model and the logarithmic model may be inaccurate for predicting the effects of low exposures to radiation.


If one observes the DC current output of an ion chamber, or photo-multiplier tube, one will notice that the current output follows square root relationship to the input radiation.


Over a range of about a decade and a half the square root curve follows closely to the log curve which is normally used to plot radiation's intensity.

Might this imply that the square root curve would be a better choice for plotting radiation, or even a better model for understanding the effects of radiation?


Related pages at this site


  So why does current have a square root relation to radiation? The answer shows up in communication theory and simple circuit theory. Radiation produces a random series of ionizations that a detector reads as electrical pulses. A communication theory text will show that random impulse noise has a power spectrum that contains a DC part. From circuit theory, power has a known relationship to current:
P= I2R or I = sqrt(P/R).

Current from the detector acts as the square root of the incoming power or radiation intensity.

This all seems to raise a few questions:

  • Since power has a square relationship to both the ionization pulses in and the current out, would using square root curves be a more natural model for radiation metering?
  • Which is the best model for the impact of radiation for any given material such as living tissues: number of ionizations, power absorbed, current generated, power within a certain spectrum range or, other?

Without knowing the answer to the second question, valid interpolations from large doses to small doses of radiation can not be made. Our models for the health impacts of low level radiation may be contain significant errors. Which model is best for interpolations? For circuits, the square root model is the best. But what model is best for living flesh? To answer that we must determine how the energy is absorbed by the flesh.

The discussion above only considers possible nonlinear effects of the radiation. No consideration is given to the probable nonlinear characteristics of human flesh and other absorbing materials.

Since I first made the observation that radiation has nonlinear characteristics I have read two sets of articles regarding the health effects of radiation.

  1. Research done on cells in laboratory environments show greater damage resulting from low level radiation than the "linear no threshold model" would imply.
  2. Research done on living organisms, including human epidemiological studies, that show that low level radiation may be non-harmful, and possibly even beneficial.
This page was motivated when I observed that the current from a radiation detector followed a square root curve. Traditional meters use logarithmic scales. I wondered why the standard had not been made square root the natural output of the detector. I also wondered whether the effects of radiation also followed the square root curve. See more considerations below in Part 2.

Part 2: What are the Sources of the Non-linearities

In many branches of science we reduce complex multidimensional concepts to simple linear measurements. This makes measurement and communication easier, but removes critical information. Unfortunately, this reduction may remove the very information that we actually want to know. Radiation is composed of many dimensions. Each of these dimensions may have nonlinear aspects. We will briefly review these major dimensions.

Many Types of Radiation
We use the words radiation and radioactivity to cover a broad range of emissions. Usually, we use the term radiation to mean ionizing radiation, but sometimes we use the term to refer to electromagnetic radiation. Each type of radiation has its own distinct energy and way of interacting. We frequently use the same sensors to detect the presence of many of them. But, each can have a different impact on living tissue.

Name alternate description action
Alpha particles: ionized helium nucleus Will not penetrate skin, but will ionize the first molecule it encounters.
Beta particles: fast moving electrons Can penetrate a little and ionize molecules they hit.
X-rays high energy electromagnetic radiation Highly penetrating, may ionize or pass right through with minimal effect
Neutrons:   Can enter and alter atomic nuclei
Antimatter:   Very reactive. Will alter, transmute first matter it encounters
Radionuclides: radioactive elements - atoms that emit alpha, beta, or gamma rays Have both chemical and radiation effects.
Non-ionizing radiation electromagnetic spectrum Includes microwaves, radiowaves, and light

Many Dimensions of Effects
Just as there a many types of radiation, radiation can have many different effects on materials such as living tissues. Each of these effects will have different health impacts with quite different nonlinear curves.

  • Heating: Radiation will heat the tissues that absorb it. A large dose will cause burning. A mild dose some heating. A background dose will cause no observable variations from normal temperatures. For example, turning on the lights in a room cause no observable temperature change for your body. Standing in the bright sun will make you sweat and tan. Staying in tropical sun can cause serious burning even with relatively short exposures. From this example, we recognize that the health impact depends on time. The same dose that is harmful over a short time may actually be good for you over a longer time.
  • Current generation: Radiation can create electrical currents in the materials it hits. This is how solar cells work. It is the basis of the discussion in part one. As shown, the effect is known to be nonlinear. How such currents might affect living tissues is not well studied.
  • Ionization: Nuclear radiation is also called ionizing radiation. It can ionize, break apart, molecules that it hits. Those molecules become altered. Altered molecules in living tissues will no longer function in the cells as they should. Each cell contains billions of molecules. Ionizing certain molecules will just interfere with the cell temporarily, altering others may cause cell death, and altering DNA may cause mutations that reproduce and spread in future cells. Some of these changes may lead to cancer or birth defects.
  • Chemical bonding: Radionuclides are chemical elements so they can deposit in the body the same as any other chemical or poison. This depositing can have unusual delayed effects. For example, the thyroid absorbs iodine. When the iodine decays it emits beta and gamma radiation. The radiation will ionize surrounding molecules. After the decay the thyroid no longer has iodine where it needs iodine, it now has xenon which it doesn't need. The transmutation iodine to xenon will alter the molecules in which it was bonded. Thus, radionuclides have both radiation and chemical impacts on living tissues.
  • Resonance: Tissues may absorb non-ionizing radiation through resonance. The best known example is the microwave which heats by vibrating molecules of water and some organic molecules. Although resonance effects have not been highly studied there is evidence that some electromagnetic frequencies change the speeds at which specific biological reactions occur and may alter brain waves.

Each of these effects is most likely nonlinear For heating a specific dose spread out over a long time has much less impact than the same dose over a short time. Doses do not add up. For some of the other effects a specific dose over a long might have a greater effect than the same dose over a short time. There is no easy means to determine the impact of long term exposures.

Many Dimensions of Absorption

Ionizing radiation, neutrons, and radioactive elements are each absorbed differently by different materials. Thus, the definition of a radioactive field is not constant or easy to define. The measure of the radioactive field is totally dependent on which material it is passing through and what type of radiation it is. Thus, the same radiation passing through the air in the room will be different passing through your body (possibly higher, possibly lower), and different as it passes through the walls, and different as it passes through detectors.

Many Sources of Radiation

Radiation has many natural sources - some natural, some anthropogenic. There is a common misconception that humans create radiation and without humans there would be no radiation. This is not true. All living things spend their entire lives bathed in radiation, and always have. It is good to consider where our exposures to radiation come from.

Natural sources

  • Mineral deposits
  • Cosmic rays
  • The sun
  • Lightning

Anthropogenic sources

  • Wells: water wells bring various buried minerals to the surface including radioactives such as radon.
  • Coal burning power plants: coal contains uranium, thorium and other radioactives. When coal is burned the radioactive particles go up the chimney with the ash.
  • X-rays& medical isotopes
  • Nuclear weapons testing
  • Nuclear power accidents (Chernobyl, Three Mile Island, Fukushima)
  • Non-ionizing sources: transformers, electronic equipment, cell phones, radio towers

From these lists we can see that much of our exposure to radiation comes from hidden non-nuclear sources. A person living down wind of a coal burning power plant, drinking well water, may be absorbing more radiation than a person living near a nuclear plant. However, the types of radiation he absorbs will be different. Thus, its not always clear where to do epidemiological studies on radiation exposure.

Added August 2011

Part 2 was added after I was asked to add more depth to the discussion by people concerned about the radiation leaks at Fukushima.



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