22.54 Neutron Interactions and Applications (Spring 2004)
Chapter 13 (4/6/04)
Basic Concepts in Theoretical Neutron Dosimetry
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References -Radiation Dosimetry, G. J. Hine and G. B. Brownell, eds. (Academic Press, New York,
1956).
G. S. Hurst and J. E. Turner, Elementary Radiation Physics (Wiley, New York, 1970).
J. A. Coderre et al., "Boron Neutron Capture Therapy: Cellular Targeting of High Linear
Energy Transfer Radiation", Technology in Cancer Research and Treatment 2, 355
(2003).
Monte Carlo Simulation in the Radiological Sciences, R. L. Morin, ed. (CRC Press, boca
Rotan, 1988).
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Besides nuclear reactors, another significant application of neutron interactions is in the
field of nuclear medicine. Medical uses of radiation began shortly after the discovery of
x-ray by Wilhem C. Roentgen in1895 (for which he was awarded the Nobel Prize in
Physics in 1901),. Both the successes, for example, the first recorded tumor treatment in
1899, and failures of these early attempts underscored the importance and the difficulties
of understanding and controlling the quantitative effects of radiation interaction with
humans. The problem of radiation dosimetry involves physical and biological aspects
that cannot be cleanly separated; in neutron dosimetry the challenge is both scientific and
technological - to control the radiation effects and utilize the unique properties of neutron
interactions for maximum human health benefits (or minimized health hazards).
I. Some Basic Notions of Radiation Dosimetry
At the fundamental level the central issue is energy deposition onto the irradiated matter.
How to characterize this process may seem straightforward at first, involving the
specification of the radiation, and a general knowledge of the mechanisms of radiation
interaction with matter. Upon a bit of reflection one realizes the situation is anything but
simple. While there is no difficulty with the processes of radiation interaction, it is not
clear how one can determine a priori the biological response of the medium. In other
words, to correlate the physical characteristics of energy deposition with the subsequent
biological effects, damage or therapy, is a formidable challenge. Admittedly this is not a
subject for which we are prepared to study in 22.54.
In dosimetry what matters is not so much the energy that is deposited (lost by the
radiation) as the energy that is absorbed, either locally or in a distributed manner. While
we speak of physical energy deposition in terms of the amount of energy per unit volume,
we should also realize that biological effects may also depend on the spatial distribution
of the energy released along the track. Instead of being a point-wise process, energy
deposition has an implicit path dependence that makes it difficult to quantify. This aspect
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of a distributed process in radiation dosimetry provides another illustration of what we
had previously discussed concerning neutron interactions, namely, the distinction
between a single reaction event, specified by a certain cross section, and the effects that
involve many collisions, as described by a distribution function.
In correlating the radiation energy absorbed in a medium with the subsequent biological
effects in the system, the local extent of the absorption can play an important role.
Intuitively, one expects some sort of description of energy transport in the biological
system will need to be considered. It does not seem reasonable that a simple quantity
such as the absorbed dose is sufficient to characterize a complex sequence of events,
from ionization of atoms and molecules to clinical observations. Besides the amount of
the energy absorbed, the time rate of absorption (dose rate) also should be important.
Moreover, the manner in which energy is deposited along the radiation track, a property
known as the stopper power, can have an effect on the resultant biological response.
Given that the stopping power is a quantity which we have studied in radiation interaction
with matter (cf. 22.101), this provides an opportunity to put this knowledge to use.
Units of Dose
The notion of energy deposition leads naturally to the definition of physical dose as the
energy absorbed per unit mass of the irradiated matter. A variety of units have been used
to measure this quantity.
The Roentgen (r) = quantity of x-ray producing 1 esu of charge in 1 cm3 of air at STP.
This unit was formalized in 1928; now it is mostly of historical interest.
The Absorbed Dose (rad) = 100 ergs/gm. This was established by the International
Commission on Radiological Units (1953). Note there is no precise definition of what is
a 'dose', only the 'absorbed dose'.
The roentgen-equivalent-man (rem) = rad x RBE (relative biological effectiveness).
Typically RBE for x-ray, gammas and electrons is 1, for fast neutrons and protons up to
10 MeV it is 10, for naturally occurring α -particles it is also 10, and for heavy recoil
nuclei it is 20.
Other units, more recently introduced, are Gray (Gy) = 100 rads, and Sievert (sv) = dose
delivered in 1 hr at 1 cm from point source of 1 mg of Ra enclosed in 0.5 mm Pt
(numerically, ca. 8.4 r or 21.6 C/kg).
Linear Energy Transfer (LET)
Perhaps the most basic concept in radiation dosimetry is the distribution of dose with
energy loss, called the LET distribution. This refers to the amount of energy transferred
to the irradiated matter per unit length along the particle track. LET would be equal to
the stopping power dE/dx, if all of the particle energy were locally absorbed. This would
be the case for a proton. In contrast, dE/dx would be larger than LET for a fast electron
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where part of the particle energy is lost by radiation (Bremsstrahlung) away from the
particle path.
Typical LET values for γ -rays, x-rays, and α -particles in water are a few, a few tens,
and a few hundreds keV/ µ m , respectively. Reason x-rays have higher LET than γ -rays
is that they produce lower-energy secondary electrons which have higher LET. One can
imagine a nonlinear correlation between RBE and LET. In the case of inhibiting cell
division in yeast, RBE values for the above radiations are about 1, 1.2, and 3 respectively
[Hurst and Turner, p. 97].
In the case of neutrons, energy deposition occurs in soft tissue through elastic collisions
with hydrogen. Lower-energy neutrons produce lower-energy recoil protons which have
higher LET. For a range of biological endpoints in mice - intestinal weight loss, thymus
weight loss, 30-lethality, neutron RBE values range from 5 to 3.5 to 1.7 for neutron
energies of 0.1 to 1 to 10 Mev [Hurst and Turner, p. 98].
Variation of RBE with LET does not have to follow a universal behavior. A RBE-LET
correlation can show a peak, indicating a threshold for biological damage, or it can show
a monotonic decrease, which has been observed in small biological objects [Hurst and
Turner, p. 97].
Birdseye View of Theoretical Neutron Dosimetry
Neutron dosimetry is a significant part of radiation dosimetry which is a large field. For
a birdseye view one can look at the topics treated in an early monograph [Hine and
Brownell, 1956], a 900-page collection of contributions by leading workers in the field,
to get an idea of how the field was organized in those days. The book was divided into
three parts, Fundamental Principles of Dosimetry (150 pp), Radiation Detectors and their
Calibration (400 pp), and Radiation Fields and their Dosimetry (350 pp). In the first part
the lead off contribution is Radiation Units and Theory of Ionizing Dosimetry (45 pp),
followed by Interaction of Radiation with Matter (75 pp), and Biological and Medical
Effects of Radiation (25 pp). Thus we see that radiation interaction with matter, the topic
with which we are most familiar in 22.54, constitutes about half of what would be
considered basic knowledge in dosimetry. We expect the contents of the first two
contributions will change with time only in the introduction of new units, and very little
in the fundamental physics. On the other hand, much more is now known about
biological and medical effects than before.
Part two on radiation detection, which is a subject we do not emphasize in 22.54, is
almost half of the book. This shows that dosimetry is primarily an experimental subject,
which is still true. In part three there is a contribution on Neutrons and Mixed Radiations
by Harld H. Rossi (22 pp) in which there is a 4-page section entitled Theoretical Neutron
Dosimetry. The discussion here is quite close in spirit of what we are saying about the
intimate connection between single-event interactions and multiple-event distributions.
In fact, this section has two subheadings - First-Collision Calculations and Calculations
Involving Multiple Collisions.
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Role of Particle Simulations in Theoretical Dosimetry
Since particle simulations are a central part of our syllabus, it is appropriate to mention
that Monte Carlo (MC) simulations have played an significant role in radiological science
investigations. Just as we have done with radiation dosimetry above, we can look to a
monograph on Monte Carlo simulations in the radiological sciences to get a glimpse of
the kinds of applications that have been considered [Morin, 1988]. One finds that there
are two chapters on background, one on Probability and Statistics and another on
Random Number Generation and Testing. There are four chapters on applications,
Photon Transport (50 pp), Diagnostic Radiology (90 pp), Nuclear Medicine (16 pp), and
Radiation Therapy (20 pp). This is only an example, one that is not up to date. We
already know about the widespread interest in MCNP and its many areas of applications,
including dosimetry and radiation therapy. There are a number of other Monte Carlo
codes in the community, one we might mention is TRIM (transport of ions in matter).
In later lectures in this course we will discuss another particle simulation method called
Molecular Dynamics (MD), and we will consider both MD and MC in the discussion of
studying multiple collision events in matter.
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