Biomedical Engineering Reference
In-Depth Information
Lineal energy, which is a stochastic quantity, has the same dimensions as LET,
which is nonstochastic (being the mean value of the linear rate of energy loss). Lin-
eal energy is the microdosimetric analogue of LET. Unlike specific energy, however,
it is defined only for single events.
A relationship between lineal energy and LET can be seen as follows. Consider
a small volume containing a chord of length
x
traversed by a charged particle with
LET
=
L
. We ignore energy-loss straggling and assume that the energy lost by the
particle in the volume is absorbed there. We assume further that the chord is so
short that the LET is constant over its length. The energy imparted by the single
traversal event is
=
Lx
. For isotropic irradiation of the volume by particles travers-
ing it with
LET
=
L
, the mean value of the imparted energy is
¯
=
Lx
. Under these
conditions, it follows from the definition (12.33) of the lineal energy that its mean
value is the LET:
¯
L
.
For any convex body, having surface area
S
and volume
V
, traversed by isotropic
chords, the mean chord length is given quite generally by the Cauchy relation,
¯
y
=¯
/
x
¯
=
4
R
/3 (Problem 60).
Proposals have been made to use lineal energy instead of LET as a basis for
defining quality factors in radiation-protection work. Whereas the measurement
of LET spectra is a difficult technical problem, distributions of lineal energy and
its frequency- and dose-mean values can be readily measured for many radiation
fields. Disadvantages of using lineal energy include the necessity of specifying a
universal size for the reference volume, usually assumed to be spherical in shape.
There does not appear to be a compelling reason for any particular choice, and the
y
distributions depend upon this specification. In addition, concepts associated with
chords are probably inappropriate for application to the tortuous paths of electrons,
especially at low energies.
4
V
/
S
. For a sphere of radius
R
, it follows that ¯
x
=
x
=
12.11
Suggested Reading
1
Attix, F. H.,
Introduction to Radiolog-
ical Physics and Radiation Dosimetry
,
Wiley, New York (1986). [Clear and
rigorous treatments (and in much
greater depth) of subjects in this chap-
ter. Dosimetry fundamentals and,
especially, instrumentation and mea-
surements are described.]
2
Cember, H.,
Introduction to Health
Physics
, 3rd Ed., McGraw-Hill, New
York (1996).
3
ICRU Report 36,
Microdosimetry
,In-
ternational Commission on Radiation
Units and Measurements, Bethesda,
MD (1983).
4
ICRU Report 60,
Fundamental Quan-
tities and Units for Ionizing Radiation
,
International Commission on Ra-
diation Units and Measurements,
Bethesda, MD (1998). [Provides de-
finitions of fundamental quantities
related to radiometry, interaction co-
efficients, dosimetry, and radioactiv-
ity. Gives standardized symbols and
units.]
5
Martin,J.E.,
Physics for Radiation Pro-
tection: A Handbook
, 2nd Ed., Wiley,
New York (2006).
6
Rossi,H.H.,andM.Zaider,
Micro-
dosimetry and its Applications
,Springer
Verlag, Berlin (1996).
